Spectral Study of Stellar Winds Interacting with
X-rays from Accreting Neutron Stars
Shin Watanabe
Department of Physics
Graduate School of Science
University of Tokyo
December 19, 2003
Abstract
We have observed two archetype high mass X-ray binaries (HMXBs), Vela X-1 and
GX 301−2, with the Chandra grating spectrometer HETGS. By using the instrument
with high energy resolving power E/∆E ∼ 100–1000, we perform precise measurements
of various emission lines and spectral features in their X-ray spectra. In the case of Vela
X-1, emission lines from highly ionized ions driven by photoionization, in addition to
fluorescent lines from ions in various charge states, are clearly detected. The intensities
and the centroid energies of these lines are determined with the highest accuracy ever
achieved for this source. In the case of GX 301−2, fluorescent emission lines are observed
without any signature associated with highly ionized ions. Additionally, the Compton
scattered line profile (Compton shoulder) is discovered in the intense iron Kα line of
GX 301−2, for the first time from a celestial source. In order to deal with such new probes,
we have developed the simulator on the basis of Monte Carlo methods. By adopting this
simulator to Vela X-1, we can find the ionization structure and the matter distribution,
which reproduce the observed line intensities and continuum shapes. Additionally, from
the amount of the Doppler shift due to the stellar wind velocity, we show that the stellar
wind flow is affected by the photoionization by the neutron star radiation. For GX 301−2,
we have demonstrated that Compton shoulders could become a new probe to diagnose
the physical conditions of cold material. In fact, we have found that a cold (< 3 eV) and
dense (NH ∼ 1024 cm−2) cloud is surrounding the neutron star almost spherically from
the profile of observed Compton shoulders. We argue that such a cold dense cloud is the
origin of the differences in the X-ray spectrum when compared with the spectrum of Vela
X-1.
Contents
1 Introduction 1
2 High Mass X-ray Binaries and X-ray Spectroscopy 3
2.1 High Mass X-ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 X-ray Spectroscopic Observations of HMXBs . . . . . . . . . . . . . . . . 4
2.2.1 Iron emission line and absorption edge . . . . . . . . . . . . . . . 4
2.2.2 Emission lines from lighter elements . . . . . . . . . . . . . . . . . 4
2.3 Basic Physical Processes in High Mass X-ray Binaries . . . . . . . . . . . 10
2.3.1 Stellar winds of OB super-giant stars . . . . . . . . . . . . . . . . 10
2.3.2 Capture of the stellar wind by the neutron star . . . . . . . . . . 10
2.3.3 Photoionized plasmas . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3.4 Interactions between X-ray photons and photoionized plasmas . . 13
2.3.5 X-ray emission lines from photoionized plasmas . . . . . . . . . . 18
3 Instrumentation 24
3.1 Chandra Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 High Energy Transmission Grating Spectrometer(HETGS) . . . . . . . . 25
3.2.1 HETGS overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2.2 HETGS performance . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Data Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
4 Observations and Results of Vela X-1 30
4.1 Vela X-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4.2 Observation and Data Reduction . . . . . . . . . . . . . . . . . . . . . . 31
4.3 Continuum Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.4 Emission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.5 Pulse Phase Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4.6 Summary of the Observation and the Implication . . . . . . . . . . . . . 49
5 Observations and Results of GX 301−2 50
5.1 GX 301−2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
5.2 Observation and Data Reduction . . . . . . . . . . . . . . . . . . . . . . 50
5.3 Continuum Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
ii
5.4 Emission Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
5.5 Pulse Phase Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6 Simulation of Photoionized Plasma in HMXB 61
6.1 Modeling of Photoionized Plasmas . . . . . . . . . . . . . . . . . . . . . . 61
6.2 Calculation of the Distribution of Ionization Degree . . . . . . . . . . . . 62
6.3 Monte Carlo Calculation of the X-ray Emission from Photoionization Equi-
librium State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.3.1 Physical processes . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7 Discussion on Vela X-1 70
7.1 Ionization Structure of the Stellar Wind in Vela X-1 System . . . . . . . 70
7.2 The Ionization Structure . . . . . . . . . . . . . . . . . . . . . . . . . . 72
7.3 Estimate of the Mass Loss Rate of the Stellar Wind . . . . . . . . . . . . 75
7.4 Reproduction of the Entire Spectrum . . . . . . . . . . . . . . . . . . . . 77
7.5 Diagnostics by Iron Kα Lines . . . . . . . . . . . . . . . . . . . . . . . . 85
7.6 Doppler Effects of the Stellar Wind . . . . . . . . . . . . . . . . . . . . . 88
7.6.1 Difference between the observation and the simulation . . . . . . 88
7.6.2 Interaction between X-rays and the stellar wind . . . . . . . . . . 89
7.6.3 One dimensional calculation of the velocity structure . . . . . . . 90
8 Discussion on GX 301−2 93
8.1 Compton Shoulder in the PP Phase . . . . . . . . . . . . . . . . . . . . . 93
8.1.1 Time variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
8.1.2 Modeling with Monte Carlo simulation . . . . . . . . . . . . . . . 95
8.1.3 Spectral analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
8.2 Matter Distribution in GX 301−2 . . . . . . . . . . . . . . . . . . . . . . 103
8.3 Unified Picture of HMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . 108
9 Conclusion 111
iii
Chapter 1
Introduction
In high mass X-ray binary (HMXB) systems, the neutron star captures the surrounding
material of the stellar wind from the massive hot star, and converts it into X-ray radi-
ation. This emission interacts with the stellar wind, resulting in various emission lines
and characteristic features in the X-ray spectrum. Because these structures are directly
connected to the physical state of the material, the precise measurement brought by
the high precision X-ray spectroscopy can provide essential information on the physical
conditions and geometry of the matter in the vicinity of the neutron star.
Chandra and XMM-Newton X-ray satellites have opened up a new dimension for X-
ray spectroscopic observations, in the 21st century. The grating instruments on board
Chandra and XMM-Newton have 10–100 times more improved energy resolving powers
than that of past instruments. A number of forested emission lines, which were formerly
seen as one broad line, can be fully-resolved individually. Additionally, hidden structures
can be observed and clearly measured without any ambiguities.
HMXB observations using these grating instruments allow us to study the structure
of stellar winds by the individual emission line from various ions, and, for the first time,
provide a dynamical view of the ionized stellar wind surrounding the neutron star. At the
same time, such observations also provide numerous difficulties that cannot be explained
in the terms of simple models such as a spherically symmetric geometry or uniform
density. Therefore, for capitalizing on the observation results and further understanding
the information contained, new analytical methods and calculations are needed.
In this thesis, we deal with two different archetypes of high mass X-ray binaries, Vela
X-1 and GX 301−2. The former has highly ionized gases while the latter is characterized
by heavy absorption and absence of any features connected with highly ionized ions. We
have observed these two HMXBs with the grating spectrometers on Chandra, and, have
obtained X-ray spectra with high precision. In order to analyze these X-ray spectral
features and investigate the physical nature and geometry of the material, we have newly
constructed a simulator on the basis of Monte Carlo methods.
Chapter 2 gives a description of the current understanding on HMXBs and the basic
physical processes taking place in them. Chapter 3 includes the brief descriptions of the
1
Chandra X-ray Observatory and the grating instrument HETGS used for our observa-
tions. The following two chapters describe observational results. Chapter 4 describes
the results of Vela X-1 observations, and Chapter 5 is for that of GX 301−2 observa-
tions. Chapter 6 describes our newly constructed simulator to calculate physical states
in a HMXB situation and to estimate observed X-ray spectra. The calculation scheme
and our assumptions are given in this chapter. Chapter 7 and Chapter 8 are devoted
to the interpretation and the discussion on the observed spectra by comparison with the
simulation results of Vela X-1 and GX 301−2. For Vela X-1, we attempt to calculate the
photoionized plasma structure and generate the X-ray spectrum within the scheme. For
GX 301−2, by using the first discovered spectral feature of the “Compton shoulder”, we
investigate the physical state of the matter such as the density distribution and electron
temperature, together with the metal abundance. A brief summary is given in Chapter 9.
2
Chapter 2
High Mass X-ray Binaries and X-ray
Spectroscopy
2.1 High Mass X-ray Binaries
A high mass X-ray binary (HMXB) is a system consisting of a neutron star or a black
hole and a massive O- or B-type companion star. OB stars, which are young giant stars,
have powerful stellar winds and are spreading a fraction of their mass continuously. A
neutron star is a compact high-density object with a mass of ∼ 1.4 M¯ and a radius of
∼ 10 km. As it revolves around the companion star, it sweeps up the matter transfered
by the stellar wind. When the matter is accreted on the neutron star, a fraction of its
gravitational potential energy is converted into X-ray radiation. They are among the
brightest X-ray sources in our galaxy and have been observed since the early days of
X-ray astronomy.
X-ray emission from the neutron star in HMXBs have several interesting features;
pulsation sometimes detected with a period of one to several hundred seconds and cy-
clotron absorption structures in the hard X-ray spectra (Mihara, Makishima, & Nagase
1998; Makishima et al. 1999). These features are connected with the accretion and the
strong magnetic field of the neutron star.
The radiation from the neutron star interacts with the stellar wind, which results
in ionization and heating. X-ray photons from the neutron star are reprocessed by the
ionized material, resulting in various emission lines, which carry a wealth of information
about the physical state of the material in HMXBs. The neutron star can, therefore,
be used as a radiation source to probe the structure of the stellar wind and derive the
physical parameters that characterize its nature. Line intensities give us information on
amounts of matter, and, the line energies reflect ionization structures. Energy shifts and
line broadenings due to Doppler effects could become probes of the stellar wind dynamics.
These spectral features can be available only by X-ray observations with high spectral
resolutions.
3
2.2 X-ray Spectroscopic Observations of HMXBs
2.2.1 Iron emission line and absorption edge
Since the early days of X-ray astronomy, emission lines and absorption edges of iron
have played important roles for probing the matter distribution in HMXBs. The gas
scintillation proportional counter (GSPC) on board Tenma satellite demonstrated the
importance of the spectroscopic study of plasmas by using the most abundant material
ions. With Tenma observations of several HMXBs, the emissions lines at 6.4 keV and
the K-edge absorption features of iron ions in a low ionization degree have been shown
in their X-ray spectra (e.g. Vela X-1 Ohashi et al. 1984; Nagase et al. 1986; GX 301−2
Makino 1985; see Figure 2.1).
Figure 2.2 shows the iron line intensity plotted against the absorption-corrected con-
tinuum intensity above the iron K edge energy. The proportional relation between these
two values and the observed energy of the line center indicates that the iron line from
HMXBs is produced through fluorescence of continuum X-rays by cold material.
The matter distribution around X-ray sources were estimated from the relations be-
tween the line equivalent widths and the absorption column densities obtained from the
continuum shape (Koyama 1985; Inoue 1985; Makishima 1986). Figure 2.3 shows the
relation between these two values calculated by Monte Carlo method for some models of
matter distributions, together with observed values for HMXBs and other X-ray sources.
The pictures inferred with Tenma in the 1980s have been confirmed by ASCA in the
1990s. Additionally, the X-ray CCD on board ASCA is capable of investigating energy
shifts and broadenings of the iron Kα line (Endo et al. 2002). However, the energy
resolving power had not reached the level to recognize quantum effects, which is directly
connected to the physical state of the matter.
2.2.2 Emission lines from lighter elements
Emission lines from elements ligher than iron (S, Si, Mg, Ne, O, N, C, etc.) carry
information on the ionization structure of the emission medium. The solid state detector,
X-ray CCD, on board ASCA is the first instrument that is capable of detecting emission
lines from lighter elements and of resolving bright spectral features from H-like and He-
like ions. ASCA observations of several HMXBs have shown that their X-ray spectra
exhibit both soft X-ray emission from highly ionized ions and fluorescent lines from cold,
less ionized material (Vela X-1 Nagase et al. 1994; Cen X-3 Ebisawa et al. 1996; GX 301−2
Saraswat et al. 1996, see Figure 2.4 and Figure 2.5). Although the dominant excitation
mechanism (i.e., collisional or photoionization-driven) that is resposible for producing
the soft X-ray lines cannot be discriminated unambiguously from these observations,
cascades following recombination processes seemed to be the most natural candidate for
the emission mechanism because of the intense X-ray continuum radiation observed at the
4
Figure 2.1: Energy spectrum of Vela X-1 (left) and that of GX 301−2 (right)
obtained with Tenma. ((left) From Nagase et al. 1986, (right) From Leahy et
al. 1989)
Figure 2.2: Correlation between the observed iron-line photon flux and the
observed continuum X-ray flux above the neutral iron K-edge energy (7.1 keV).
(left) Vela X-1 (Ohashi et al. 1984); (right) GX 301−2 (Makino 1985). These
results indicate that the iron line originates in the flourescence of continuum
X-rays. (from Makishima 1986)
5
Figure 2.3: Relation between the matter thickness NH and the iron line equiv-
alent width calculated by Monte Carlo method for the representative Models
I–III illustrated on the left. On the same diagram, the observed equivalent
width and the observed “line of sight” absorption column density are plotted.
(from Makishima 1986)
6
same time from the source. Subsequently, Liedahl & Paerels (1996) and Kawashima &
Kitamoto (1996), for the first time, detected a narrow radiative recombination continuum
(RRC) of S XVI in ASCA spectrum of Cyg X-3, which provided evidence that the plasma
in Cyg X-3 is ionized through photoionization, and the highly ionized gas in the plasma
makes emission lines in the X-ray spectrum.
The spectral resolutions (E/∆E ∼ 100–1000) of diffraction grating spectrometers on
board Chandra and XMM-Newton have a pottential to provide an unambiguous infor-
mation of narrow RRCs in HMXBs. Paerels et al. (2000) resolved narrow RRCs of Si
XIV and S XVI in the spectrum of Cyg X-3 with Chandra HETGS, and measured the
electron temperature, kTe ∼ 50 eV. Schulz et al. (2002) detected a narrow RRC from Ne
X with an electron temperature of ∼ 10 eV in the Chandra HETGS spectrum of Vela
X-1. These observations have revealed that the photoionization-driven plasma indeed
exists in HMXBs.
The first attempt to model the X-ray spectrum as a whole was presented by Sako
et al. (1999) by calculating the ionization structure of the HMXB. They used the X-ray
spectrum of Vela X-1 obtained with ASCA originally published by Nagase et al. (1994).
Sako et al. (1999) characterized the standard wind velocity profile of OB stars proposed
by Castor, Abbott & Klein (1975). Once the velocity profile is characterized and a mass
loss rate of stellar wind is given, the number density of particles is uniquely assigned
everywhere in the wind. And, hence, the ionization structure is determined for a given
X-ray luminosity. By adjusting the mass loss rate, they found a statistically acceptable
fit for the ASCA spectrum (Figure 2.6). However, since the energy resolution of ASCA is
not enough to resolve independent emission lines predicted from the ionization model, the
intensity measurement of each line is very limited. Additionally, the X-ray line shifts and
widths that carry the information of dynamics of the X-ray emitting gas are inaccessible.
7
Figure 2.4: Energy spectra of Vela X-1 obtained with ASCA SIS at (top)
posteclipse, (middle) pre-eclipse, and (bottom) eclipse phases during the or-
bital phase intervals of 0.11 to 0.15, −0.14 to −0.11, and −0.10 to 0.10,
respectively. (From Nagase et al. 1994)
Figure 2.5: Energy spectrum of GX 301−2 obtained with ASCA SIS. (From
Saraswat et al. 1996)
8
Figure 2.6: The energy spectrum of Vela X-1 at the eclipse phase obtained
with ASCA SIS and the model generated by Sako et al. (1999).
Stellar WindStellar Wind
Companion Star(O,B super-giant)
Neutron Star
Scattering
AbsorptionPhoto Ionization
Recombination
X-ray
Figure 2.7: Current understanding picture of HMXBs.
9
2.3 Basic Physical Processes in High Mass X-ray Bi-
naries
2.3.1 Stellar winds of OB super-giant stars
Winds ejected from hot stars such as O-stars and B-supergiants, are characterized by
two global parameters, the terminal velocity v∞ and the mass loss rate M∗. These
winds are initiated and then continuously accelerated by the radiation pressure on ions
with resonance lines in the ultraviolet region. The velocity of the wind reaches to the
maximum, v∞ at very large distances from the star, where the radiative acceleration
approaches zero.
Castor, Abbott & Klein (1975) and Pauldrach, Puls & Kudritzki (1986) showed that
the velocity of the stellar winds obey the approximate formula (CAK-model):
v(r) = v∞
(1− R∗
r
)β
(2.1)
for a given distance r from the center of the star, where R∗ is the stellar radius. Pauldrach,
Puls & Kudritzki (1986) show that the value of β ∼ 0.8 is a better representation of the
wind kinematics for isolated OB stars. From the observational point of view, v∞ and β
can be determined from the analysis of the “P Cygni” profile which appears in the UV
resonance line spectrum, and are actually obtained from many OB-stars. (e.g. Howarth
& Prinja 1989; Prinja et al. 1990; Blomme 1990)
Given the velocity profile, the wind density can be calculated by applying the equation
of mass continuity, assuming spherical symmetry:
n(r) =M∗
4πµmpv(r)r2, (2.2)
where µ is the gas mass per hydrogen atom. (µ = 1.3 for the cosmic chemical abundance.)
2.3.2 Capture of the stellar wind by the neutron star
In the case of high mass X-ray binary systems consisting of a neutron star and an OB
star, mass accretion onto the neutron star takes place through direct capture of the
stellar wind material. Material within a radius Racc will be accreted by the gravitation
of the neutron star, whereas material outside this cylinder will escape (Figure 2.8). This
radius is calculated by a simple assumption that material will be accreted only if it has
a kinetic energy less than the potential energy in the vicinity of the neutron star. When
the neutron star mass is quoted as Mns, it is set by
1
2mv2
rel =GMnsm
Racc
, (2.3)
10
Racc
Neutron Star
D
OB Star
Stellar wind
Mns
Figure 2.8: Geometry of accretion onto a neutron star.
for a particle of mass m. This relation gives
Racc =2GMns
v2rel
, (2.4)
where vrel is the relative velocity of the neutron star and the stellar wind. Therefore, the
mass accreting rate onto the neutron star Macc is given by
Macc =M∗R2
acc
4D2=
(GMns)2 M∗
v4relD
2, (2.5)
where D is the distance of the neutron star from the center of the OB star.
The gravitational energy of the accreting material is converted into X-rays. The X-
ray luminosity resulting from this accretion will simply be the rate at which gravitational
energy is released:
Lx =GMnsMacc
Rns
=(GMns)
3 M∗Rnsv4
relD2
(2.6)
where it is assumed that most of this energy is liberated near the neutron star surface (of
radius Rns). By applying typical parameters (Mns = 1.4M¯, M∗ = 1×10−6M¯ yr−1, Rns =
10 km, vrel = 500 km s−1, D = 50R¯), we obtain a typical X-ray luminosity of HMXB,
Lx ∼ 5× 1036 erg s−1.
A number of models have been proposed to explain the X-ray spectra from the neutron
star of HMXB, including the conventional power-law model with a high-energy exponen-
tial cutoff (White, Swank, & Holt 1983) and those that account for Comptonization in
11
the postshock accretion region (Lamb & Sanford 1979; Sunyaev & Titarchuk 1980; Becker
& Begelman 1986). Kretschmar et al. (1997) applied these models to the spectrum of
Vela X-1 obtained by HEXE on the RXTE satellite and TTM on MirKvant space station.
They concluded that the power-law with an exponential cutoff model generally provides
the best representation to the observed spectra. As the extension of the Comptonization
models, on the other hand, Mihara, Makishima, & Nagase (1998) proposed a new model
with a electron cyclotron resonance absorption feature, and claimed that the model pro-
vides a better representation for the spectra of HMXBs obtained with Ginga. These
analysis of cyclotron resonance absorptions results in the surface magnetic field of the
neutron stars of a few times 1012 G.
2.3.3 Photoionized plasmas
Strong X-ray radiation from the neutron star affect on the ionization and thermal struc-
ture of the surrounding gas. The plasma surrounding the X-ray source is ionized and
heated through photoionization and loses energy mainly through cascades following radia-
tive recombination. Both the equilibrium temperature and the charge state distribution
in this photoionized plasma are determined locally by the X-ray flux, the X-ray spectral
shape and the gas density, and are often characterized by the ionization parameter,
ξ =LX
ner2, (2.7)
where LX is the luminosity of the X-ray source, ne is the electron density of the region,
and r is the distance to the X-ray source (Tarter, Tucker & Salpeter 1969).
Theoretical efforts to determine the response of a gas to X-rays were also investi-
gated. These models are called X-ray nebular models. By Tarter, Tucker & Salpeter
(1969), Halpern & Grindlay (1980), Kallman & McCray (1982) and so on, models of
static gas clouds irradiated by hard X-rays have been developed to address the basic
issues of heating, cooling, ionization, recombination, and the global structure of X-ray
photoionized gases. Such a model begins with a cloud of specified size or column density,
shape, and elemental abundance placed in the vicinity of a point source of continuum X-
rays. Either the particle density or the gas pressure is fixed. Local heating is dominated
by the thermalization of photoelectrons and Auger electrons produced through photoion-
ization by the continuum X-rays. Photoelectrons and Auger electrons are assumed to
deposit their energy at the site of photoionization. Energy flow throughout the gas is in
the form of radiation. The charge state distribution is determined by a balance between
photoionization and recombination. In calculating the charge state distribution, the elec-
tron temperature, which determines the magnitude of the recombination rate coefficients,
must be known. However, since the local heating and cooling rates depend on the charge
state distribution, the energy equation is coupled to the equations of ionization balance.
Among the aims of nebular model calculations is to determine a self-consistent solution.
Several instructive examples are provided by Kallman & McCray (1982) (e.g. Figure 2.9).
12
The principal distinction between collisionally ionized and photoionized plasmas is the
very different electron temperatures that accompany a given charge state distribution.
For collisional ionization, the electron temperature must be comparable to the ionization
potential, whereas for photoionization, the X-ray radiation does most of the work, so
the electron temperature can be much lower. The most useful spectral diagnostic for
observationally distinguishing between the two cases is the radiative recombination con-
tinua. Descriptions of the radiative recombination continua are given in the following
subsections.
2.3.4 Interactions between X-ray photons and photoionized plas-
mas
The physical processes in photoionized plasmas can be summarized.
Photoionization and Radiative Recombination
In the energy region of X-rays, the dominant process by which photons lose energy is
photoionization. This process can be written as
Xi + γ −→ X(∗)i+1 + e−,
where Xi represents an ion in charge state i (i.e. of ion X i+), and an asterisk denotes
an ion in an excited state, while a parenthesized asterisk refers to an ion in either an
excited state or the ground state. If the energy of the incident photon is E, it can eject
electrons, which have binding energies Ebinding ≤ E from atoms, ions and molecules, the
remaining energy (E−Ebinding) being removed as the kinetic energy of the ejected electron.
The energy levels within the atom for which E = Ebinding are called “absorption edges”
because ejection of electrons from these energy levels is impossible if the photons have
lower energy. For photons with higher energies, the cross section for photoionization from
this level decrease roughly as E−3. There is an analytic solution for the photoionization
cross section for photons with energies E À Ebinding and E ¿ mec2 due to the ejection
of electrons from the K-shells of H-like ions,
σK = 2√
2σTα4Z5
(mec
2
E
) 72
(2.8)
In this cross section, α is the fine structure constant and σT is the Thomson cross section.
There is the strong dependence of the cross section on the atomic number Z. Therefore,
although heavy elements are very much less abundant than hydrogen, rare large-Z ele-
ments make important contributions to the photoionization cross section.
Photoionization is balanced by its inverse process, radiative recombination,
Xi + e−1 −→ X(∗)i−1 + γ.
13
Figure 2.9: The charge state distribution and temperature of optically thin
photoionized plasmas. From model 1 of Kallman & McCray (1982). Tem-
perature and relative abundances of the ions of each element are shown as a
function of log ξ for −3 < log ξ < 5.
14
The photons generated in recombination are distributed into a continuum, the radiative
recombination continuum (RRC), which is found above the recombination edge with
a width ∆E ≈ kTe. In photoionized plasmas with a low electron temperature, the
RRC feature is narrow, and appears “line-like”. The emission coefficient for radiative
recombination is given by
ji(E)dE = nevσPIi (v)f(v)dv (2.9)
where ne is the electron density, v is the velocity of the free electron, and f(v) is the
Maxwellian velocity distribution,
f(v) =4√π
(me
2kTe
)3/2
v2 exp
(−mv2
2kTe
). (2.10)
σPIi (v) is the photoionization cross section, and
E =1
2mev
2 + Ei, (2.11)
where Ei is the ionization potential energy of level i of the ion. To date, in X-ray regions,
the only identified RRC features have been associated with recombination to the ground
level of H-like and He-like ions, but more often recombination leaves an ion in an excited
state.
Subsequent to recombination into an excited level, the ion will decay in a series of
spontaneous radiative transitions, until it reaches the ground level.
X∗i −→ Xi + γ
These radiative transitions generate photons whose energies are identified with the source
ions, and form the emission line.
Fluorescence
Fluorescence line emission is also important process in photoionized plasmas, especially
for ions in a low charge state. A photon ionizes an inner-shell electron of an ion in the
ground state and leaves the ion in an excited state. One of the two following processes
can occur at this point. The ion can stabilize itself through either, ejection of one or
more Auger electrons, or emission of a photon. These processes can be described by the
following,
Xi + γ −→ X∗i+1 + e− −→
Xi+1 + e− + e′− (Auger)
Xi+1 + e− + γ′ (fluorescence)
The probability of producing a fluorescent line instead of emitting Auger electrons is
called the fluorescent yield, which increases as the atomic number. Fluorescent yields of
neutral atoms for K and L shells are shown in Figure 2.10. For example, the fluorescent
yield YK of the Kα line of iron at 6.4 keV is 0.30. For the Si Kα line at 1.74 keV, YK is
0.049.
15
Figure 2.10: Fluorescent yields for K and L shells for 5 ≤ Z ≤ 110. (From
X-RAY DATA BOOKLET(http://xdb.lbl.gov/))
Photoexcitation
Photoexcitation occurs when a photon excites a bound state of an ion, and is followed
by a radiative decay resulting in an emission of a photon.
Xi + γ −→ X∗i −→ Xi + γ′
In the X-ray region, photoexcitations due to H-like and He-like ions of C, N, O, Ne, Mg,
Si and so on play important roles on both emission and absorption line formations.
The cross section of photoexcitations from level i to level j (j > i) depends directly
on the oscillator strength of the transition between level i and j (fij), and is given by,
σPEij (E) =
√πe2
mec2
fij
∆νD
H(a, x),
where H(a, x) is a Voigt function,
H(a, x) =a
π
∫ ∞
−∞
e−t2dt
(x− t)2 + a2. (2.12)
In these equations, a = Ar/(4π∆νD), Ar is the radiative decay rate, and x = (ν−νij)/∆νD
is the frequency shift from the line center expressed in units of the Doppler width,
∆νD = νij
√2kT
mzc2. (2.13)
16
Radiative recombination
Photoexcitation
Fluorescence
Photoionization
Figure 2.11: Schematic diagram of physical processes in photoionized plasmas.
17
Compton Scattering
Compton scattering is a fundamental physical process that is responsible for transferring
energy between photons and electrons in a wide variety of astrophysical environments.
Since the Compton scattering opacity relative to that of photoionization is larger for
higher energy photons, it plays an important role in the hard X-ray region. When a pho-
ton propagating through a material undergoes Compton scattering with the constituent
electrons, the energy of photon is modified in a way that depends on the scattering an-
gle, the electron velocity and the electron state, whether it is bound or free. In the limit
where the electrons are free and at rest, a fraction of the photon energy is transferred to
the electron according to the Compton formula,
E1 =E0
1 + (E0/mec2) (1− cos θ), (2.14)
or,
cos θ = 1−mec2
(1
E1
− 1
E0
)(2.15)
where E0 is the energy of the incoming photon, E1 is the energy of the outgoing photon,
θ is the angle between the incoming and outgoing photons, and mec2 is the electron rest-
mass energy (=511 keV). The differential cross section for unpolarized photons is shown
in quantum electrodynamics to be given by the Klein-Nishina formula
dσ
dΩ=
r20
2
E21
E20
(E0
E1
+E1
E0
− sin2 θ
). (2.16)
The total cross section can be shown to be
σ = σT · 3
4
[1 + x
x3
2x (1 + x)
1 + 2x− ln (1 + 2x)
+
1
2xln (1 + 2x)− 1 + 3x
(1 + 2x)2
](2.17)
where x = E0/mec2 and σT is Thomson cross section.
2.3.5 X-ray emission lines from photoionized plasmas
From hydrogen like ions
The most prominent emission lines from H-like ions are the Lyman series transitions:
Lymanα1,2 : 2p 2P3/2,1/2 −→ 1s 2S1/2
Lymanβ1,2 : 3p 2P3/2,1/2 −→ 1s 2S1/2
Lymanγ1,2 : 4p 2P3/2,1/2 −→ 1s 2S1/2
... .
18
Figure 2.12: A model of emission lines from H-like Si.
In photoionized plasmas, Lyman series lines are formed by radiative decays following
either photoexcitation or radiative recombination. The energies of these lines can be
calculated precisely from theory. Therefore, observed profiles of the lines such as widths
and energy shifts enable us to investigate the dynamics of the emission site.
The RRC feature becomes narrow, and appears the line-like profile due to the low
electron temperature of the photoionized plasma. Additionally, the width of the RRC
corresponds to directly electron temperature of the recombination site. A model of X-ray
emission lines from H-like Si is shown in Figure 2.12.
From helium like ions
The most important K-shell He-like transitions are as follows:
w : 1s2p 1P1 −→ 1s2 1S0
x : 1s2p 3P2 −→ 1s2 1S0
y : 1s2p 3P1 −→ 1s2 1S0
z : 1s2s 3S1 −→ 1s2 1S0
19
The line w is an electric dipole transition, also called the resonance transition, and is
sometimes designated with the symbol r. Lines x and y are the so-called intercombination
lines. These are usually blended and are collectively designated with the symbol i. Lastly,
z is the forbidden line, often designated by the symbol f . Emissions from He-like ions
are characterized with the triplet lines of r, i and f .
In photoionization plasmas, as in the H-like case, the excited levels for He-like ions
are fed directly by photoexcitation and radiative recombination. The three He-like lines
ratios can be affected by the electron density and the presence of a significant ultraviolet
radiation field. The density sensitivity comes from the fact that the 3S1 level can be
collisionally excited to the 3P levels. At high-enough electron density, this process suc-
cessfully competes with radiative decay of the forbidden line. In the UV radiation field,3S1 level can be also excited to 3P levels by photoexcitation. These lead to suppression
of the forbidden line and enhancement of the intercombination lines. Additionally, inner-
shell ionization of Li-like ions can lead to the production of the forbidden line in He-like
ions. Despite its use as density, temperature and UV radiation diagnostics, the behavior
of the triplet lines ratios from He-like ions is very complex.
The transition energies of He-like ions can also be determined accurately from the-
oretical calculations. The energy shift of the observed line from the calculated value is
available for study of dynamics. The RRC feature also appears in the same way as that
of H-like ions. A model of emission lines from He-like Si is shown in Figure 2.13.
From ions in a low charge state
Fluorescent line emission from ions in a low charge state is another important line for-
mation process in photoionized plasmas. An intensity of a fluorescent emission is propor-
tional to the fluorescent yield (§ 2.3.4), which increases as the atomic number. Therefore,
an emission line from a fluorescence of a high-Z element like iron becomes appreciable.
The energy of the fluorescent emission is affected by the charge state of the ion, and
behaves intricately. Therefore, in comparison to emission lines from H-like and He-like
ions, it is complex for study of dynamics to utilize fluorescent lines.
Compton shoulder
As described in § 2.3.4, when an X-ray photon propagating through a low-temperature
(< 105 K) medium undergoes Compton scattering with the constituent electrons, a frac-
tion of the photon energy is is transferred to the electron according to the Compton
formula (eq. 2.14, 2.15). The maximum energy shift per scattering due to the electron
recoil is, therefore,
∆Emax =2E2
0
mec2 + 2E0
, (2.18)
for photons that are back-scattered (θ = 180). An X-ray emission line with the en-
ergy of E0 propagating through a medium with substantial Compton optical depth
20
Figure 2.13: A model of emission lines from He-like Si.
21
(τCompton > 0.1) has a non-negligible probability of interacting with an electron, resulting
in down-scattering of photons and, hence, producing a discernible ”Compton shoulder”
between E0 and E0−∆Emax. Alternatively, this Compton energy shift can be written in
wavelength form:
∆λmax =hc
E0 −∆Emax
− hc
E0
=2h
mec= 2λC, (2.19)
where λC = h/mec ∼ 0.024 A is Compton wavelength. Therefore, the maximum wave-
length shift due to Compton scattering is constant independent of the incident energy.
X-ray emission lines at higher energies are ideal for studying the properties of the
Compton shoulders, since the Compton scattering opacity relative to that of photoion-
ization is larger for higher energy photons. The iron Kα fluorescent line complex at
E0 = 6.40 keV, therefore, is particularly promising, and can be produced over an ex-
tremely wide range in column density, which makes it ideal for diagnosing the physical
properties of a cold medium irradiated by X-rays. The energy shift of an iron line photon
due to a single Compton scattering is 156 eV from eq. (2.18).
The 6.4 keV line profile after single Compton scattering by at rest electrons is shown
in Figure 2.14. The shape and flux of the Compton shoulder is sensitive to the electron
column density and electron temperature of the scattering medium, and is also affected
by geometrical conditions. Compton scattering by electrons in bound systems produces
spectral signatures that are distinct from those produced by free electrons (Sunyaev &
Churazov 1996; Vainshtein et al. 1998; Sunyaev, Uskov & Churazov 1999).
22
Figure 2.14: Line profile after single Compton scattering by at rest electrons.
Initial energy is 6.4 keV, comparable to an iron Kα. The differential cross
section is given by the the Klein-Nishina formula (eq. 2.16).
23
Chapter 3
Instrumentation
In this thesis, we utilize observational data obtained with the grating spectrometer on
board the Chandra X-Ray Observatory. In this chapter, we summarize the basic proper-
ties and performance of the satellite and the instruments.
3.1 Chandra Observatory
The Chandra X-Ray Observatory was launched by NASA’s Space Shuttle Columbia on
July 23, 1999. The schematic view of the satellite is shown in Figure 3.1. The Chandra
satellite carries a high resolution X-ray mirror, two imaging detectors, and two sets of
transmission gratings. The important features are: an order of magnitude improvement
in spatial resolution, and the capability for high spectral resolution with the gratings.
The X-ray mirror, High Resolution Mirror Assembly (HRMA), consists of a nested
set of four paraboloid-hyperboloid (Wolter-1) grazing-incidence X-ray mirror pairs. It
achieves an excellent angular resolution of 0.5′′. There are two focal plane instruments.
One is the microchannel plate, High Resolution Camera (HRC). It is used for high an-
gular resolution imaging, fast timing measurements, and for observations requiring a
combination of both. The second instrument, the Advanced CCD Imaging Spectrometer
(ACIS), is an array of charged coupled devices. A two-dimensional array of these small
detectors performs imaging and spectroscopy simultaneously. Pictures of extended ob-
jects can be obtained along with spectral information from each element of the picture.
There are two transmission grating spectrometers, formed by sets of gold gratings placed
just behind the mirrors. One set is optimized for low energies (LETG) and the other
for high energies (HETG). Spectral resolving powers (E/∆E) in the range 100–2000 can
be achieved with good efficiency. These gratings produce spectra dispersed in space at
the focal plane. Either the ACIS array or the HRC can be used to record data. The
thesis utilizes the observation data with the High Energy Transmission Grating Spec-
trometer(HETGS), consisting of HRMA, HETG and ACIS. In the subsequent section,
the properties of HETGS are briefly summarized.
24
Figure 3.1: A schematic view of Chandra satellite. The satellite is more than
10 m long and weights about 5 tons. The satellite is thrown into an elliptical
high-Earth orbit with the perigee altitude of 10,000 km, the apogee altitude
of 140,000 km, with the orbital period of about 64 hours.
3.2 High Energy Transmission Grating Spectrome-
ter(HETGS)
3.2.1 HETGS overview
The HETGS provides high resolution spectra (with E/∆E up to 1000) between 0.4 keV
and 10.0 keV for point and slightly extended (few arc seconds) sources. The HETGS
consists of two sets of gratings, each with different period. One set, the Medium Energy
Grating (MEG), is optimized for medium energies. The second set, the High Energy
Grating (HEG), is optimized for high energies. The HETG is designed for use with the
spectroscopic array of the Chandra CCD Advanced Imaging Spectrometer (ACIS-S).
A schematic layout of the HRMA-HETG-detector system is shown in Figure 3.2. X-
rays from the HRMA strike the transmission gratings and are diffracted by an angle β
given according to the grating equation,
sin β = mλ/p, (3.1)
where m is the integer order number, λ is the photon wavelength, p is the spatial period
of the grating lines, and β is the dispersion angle. An undispersed image is formed by
the zeroth-order events, m = 0, and dispersed images are formed by the higher orders,
25
Figure 3.2: A schematic layout of the High Energy Transmission Grating
Spectrometer. (from The Chandra Proposers’ Observatory Guide)
Figure 3.3: A HETGS raw image.
primarily the first-order, |m| = 1. MEG has a period of 4001.41 A and HEG has a
period of 2000.81 A. The two sets of gratings are mounted with their rulings at different
angles so that the dispersed images from the HEG and MEG form a shallow “X” like
image centered on the undispersed (zeroth order) position: one leg of the “X” is from
the HEG, and the other from the MEG (Figure 3.3).
3.2.2 HETGS performance
The effective area of HETGS depends on the HETG efficiency coupled with the HRMA
effective area and the ACIS efficiency. Additional effects that could reduce the effective
area comes from the process of selecting events and the effect of gaps between chips.
Combining the HETG diffraction efficiencies with the HRMA effective area and the ACIS-
S detection efficiency produces the total effective area of the system as a function of
26
Figure 3.4: The HETGS effective area, integrated over the Point Spread Func-
tion (PSF), is shown with energy and wavelength scales. The two panels in
the left side show HEG effective areas, and the two panels in the right side
show MEG effective areas. The m = +1, +2, +3 orders are displayed in the
top panels and m = −1,−2,−3 orders are in the bottom panels. The thick
solid lines are first order, the thin solid lines are third order, and the dotted
lines are second order. (from The Chandra Proposers’ Observatory Guide)
energy, described as an “ancillary response file” or ARF. Effective area of HEG and
MEG extracted from nominal HETGS ARF ’s are shown in Figure 3.4. Based on the
results from the HETGS calibration observations, the systematic uncertainties of HETGS
spectral fluxes are estimated as follows,
• 10 % for 1.5 < E < 6 keV (both MEG and HEG)
• 20 % for 6 < E < 8 keV (HEG only)
• 20 % in the Si-K edge region (1.83–1.84 keV) (both MEG and HEG)
• 20 % for 0.8 < E < 1.5 keV (both MEG and HEG)
• 30 % for 0.5 < E < 0.8 keV (MEG only).
The HETGS covers an energy range between 0.5 keV and 10.0 keV. The short wave-
length is limited by the declining reflectivity of the mirrors and the efficiency of the
gratings at approximately 1.2 A (10 keV). The long wavelength end is determined by the
declining efficiency of the gratings (which are mounted on a thin plastic sheet for extra
support), and ultimately, the finite linear extent of the detectors. The MEG spectrum
goes out to ∼ 24 A (500 eV).
27
Figure 3.5: HEG and MEG Resolving Power (E/∆E = λ/∆λ) as a function of
energy for the nominal HETGS configuration. The ”optimistic” dashed curve
is calculated from pre-flight models and parameter values. The ”conservative”
dotted curve is the same except for using plausibly degraded values of aspect,
focus, and grating period uniformity. The cut-off at low-energy is determined
by the length of the ACIS-S array. Measurements from the HEG and MEG
m = −1 spectra, are typical of flight performance and are shown here by
the diamond symbols. The values plotted are the as-measured values and
therefore include any natural line width in the lines; for example, the ”line”
around 12.2 A is a blend of Fe and Ne lines. (from The Chandra Proposers’
Observatory Guide)
The wavelength resolution ∆λ is written as
∆λ =p
mcos β∆β, (3.2)
according to eq.(3.1). For small β, the resolution is independent of λ for a fixed telescope
angular resolution ∆β. The resolving power, E/∆E = λ/∆λ, of HETGS are shown with
respect to the energy of incident photons in Figure 3.5. The ∆λs (FWHM) are 0.012 A
and 0.024 A for HEG and MEG, respectively. Therefore, the energy resolutions of HEG
are 4 eV at 2 keV and 40 eV at 6.4 keV.
The absolute energy scale is measured to be less than 100 km/s in doppler velocities.
It is limited by the knowledge of the ACIS-S chip locations, which is of order 0.5 pixels:
0.0028 A for the HEG and 0.0055 A for the MEG in the wavelength. In addition, the
location of the zeroth order image can be in error by ∼ 0.5 pixels, which translates to
slight and opposite sign-shifts of the wavelengths derived from the plus and minus orders.
28
Figure 3.6: A HEG event distribution in dispersion angle/energy obtained
from CCD pulse height space. Each order events can be seen.
3.3 Data Process
When we observe an X-ray source with HETGS, we obtain a dispersed image such as
raw data (Figure 3.3). By using the image, we can select dispersed events of MEG and
HEG on the basis of spatial positions. And then, we use an order sorting mask by using
the energy information obtained with ACIS. Figure 3.6 shows a distribution of events
in the dispersion angle/CCD pulse height space. Dispersion angles are converted from
the distance from the center point of the zeroth order image. As shown in Figure 3.6,
events of each order are clearly separated. In the data analysis, we first select events of
the intended order, and then, extract a spectrum by projecting the events on dispersion
angle axis. Finally, by converting the dispersion angle into wavelength or energy on the
basis of eq.(3.1), we obtain a wavelength spectrum or an energy spectrum.
Thanks to the order sorting mask, background events of HETGS can be removed
and can be kept to a low level. The background events are usually estimated from the
adjacent region to the dispersed events region.
29
Chapter 4
Observations and Results of
Vela X-1
4.1 Vela X-1
Vela X-1 is an eclipsing high mass X-ray binary pulsar with a pulse period of 283 s
(McClintock et al. 1976) and an orbital period of 8.964 days (Forman et al. 1973). The
optical companion star, HD 77581, is a B05 Ib supergiant (Brucato & Kristian 1972;
Hiltner, Werner & Osmer 1972), which drives a stellar wind with a mass-loss rate of (1–
7) × 10−6M¯ yr−1 (Hutchings 1976; Dupree et al. 1980; Kallman & White 1982; Sadakane
et al. 1985; Sato et al. 1986a). The 1100 km s−1 terminal velocity of the stellar wind was
measured by Prinja et al. (1990) from the P-Cygni profile of the UV resonance line. Its
intrinsic X-ray luminosity is ∼ 1036 erg s−1, consistent with accretion of a stellar wind
captured by the neutron star gravitation for the mass-loss rate and the velocity structure
(see Chapter 2).
Neutron Star
EarthEclipse
Phase 0.25
Phase 0.50
HD 77581
Figure 4.1: The location between the neutron star and the companion star in
Vela X-1. The bold lines show the observed orbital phases.
30
streak
Zeroth order
HEG
MEG
Figure 4.2: The grating image of Vela X-1 in the phase 0.50.
4.2 Observation and Data Reduction
Chandra observed Vela X-1 three times. In order to observe from different places and
to compare the results, we have planned to observe Vela X-1 at different orbital phases
in the same orbit. The actually observed orbital phases are (1) φ = 0.237–0.278, (2)
φ = 0.481–0.522, and (3) φ = 0.980–0.093, hereafter referred to as phase 0.25, phase 0.50,
and eclipse, respectively. The observation dates and exposure times are summarized in
Table 4.1.
All of the data are processed using CIAO v2.3, and spectral analyses are performed
using XSPEC 1. Since the zeroth order image was severely piled-up (Figure 4.2) during
phase 0.25 and phase 0.50, the locations of the zeroth order image were determined by
finding the intersection of the streak events and the dispersed events. We apply spatial
filters for both the MEG and the HEG, and then use an order sorting mask by using the
energy information obtained with ACIS. In our analysis, only the first order events are
used to extract spectra. The background events are estimated from the adjacent region
to the dispersed event region. According to this estimation, the background levels are at
most 5% for the eclipse data and 3% for phase 0.25 and phase 0.50 data.
The light curves in the three orbital phases extracted from the HEG in the energy
interval between 1 and 10 keV (Figure 4.3). Pulsations with periods of 283.2 s and
283.5 s are found from the light curves of phase 0.25 and phase 0.50, respectively, by the
epoch holding method. The HEG integrated spectra for each orbital phase are shown in
Figure 4.4.
1http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/
31
Table 4.1. Summary of Vela X-1 Observations
Label OBSID Start Date Orbital Phase Exposure (sec)
0.25 1928 2001-02-05 05:29:55 0.237 – 0.278 29570
0.50 1927 2001-02-07 09:57:17 0.481 – 0.522 29430
eclipse 1926 2001-02-11 21:20:17 0.980 – 0.093 83150
Figure 4.3: The light curves of Vela X-1 in phase 0.25 (top), phase 0.50
(middle) and the eclipse (bottom). The bin sizes are 10 sec for phase 0.25 and
phase 0.50, and 500 sec for the eclipse.
32
Table 4.2. Properties of continuum spectra derived from spectral fits.
Orbital NHa Photon Index Observed Flux Luminosityb χ2/ d.o.f.
Phase (1022 cm−2) (erg cm−2 s−1) (erg s−1)
0.25 1.45 ± 0.03 1.01 ± 0.01 3.0 × 10−9 1.6 × 1036 2872./ 3318
0.50 18.5 ± 0.3 1.01 (fixed) 1.5 × 10−9 1.6 × 1036 1000./ 1051
Note. — Fitting regions are 1.0–10.0 keV and 3.0–10.0 keV from HEG for 0.25 and
0.50 orbital phases, respectively. The iron K-line region (6.3–6.5 keV) is excluded.
Errors correspond to 90 % confidence levels.
aThe metal abundance is assumed to be 0.75 cosmic.
b0.5–10.0 keV luminosity corrected for absorption.
4.3 Continuum Emission
X-rays emitted from the neutron star are clearly observed from the spectra taken in
phase 0.25 and phase 0.50, as featureless continuum spectra. As expected from the
geometry, the spectrum taken in the eclipse phase is dominated by line emission and
scattered components. In order to parameterize the properties of the continuum part of
the spectra, we fit it with a photo-absorbed power-law function. Since the spectrum of
phase 0.25 is less affected by absorption, we leave both the hydrogen column density and
the photon index as free parameters in the fit. On the other hand, for phase 0.5, we fix
the photon index to the value obtained from phase 0.25 and calculate the absorption. As
for a metal abundance of the photo-absorption material, we use 0.75 times the cosmic
chemical abundance (Feldman 1992), which is known to be representative for typical
OB-stars (Bord et al. 1976). The derived parameters from the spectral fits are listed
in Table 4.2. The best-fit models are superimposed on the spectra in Figure 4.4. The
absorption-corrected luminosity is determined to be identical for observations in phase
0.25 and in phase 0.50 and corresponds to 1.6 × 1036 erg s−1 in the 0.5–10 keV range,
assuming a distance of 1.9 kpc (Sadakane et al. 1985).
4.4 Emission Lines
A number of emission lines are clearly seen in the spectra of phase 0.50 and eclipse. The
observed spectra in the entire energy range are shown in Figure 4.5 and Figure 4.6. It is
apparent that the data obtained with an extremely high energy resolution leads to the
33
Figure 4.4: The spectrum of Vela X-1 obtained with HEG. The green, the blue
and the red show the spectra of the phase 0.25, the phase 0.50 and the eclipse,
respectively. The black lines are spectral fits results listed in Table 4.2.
34
detection and the identification of K-shell Si fluorescent lines from a wide range of charge
state, for the first time from Vela X-1. The emission lines from highly ionized S, Si, Mg
and Ne can be seen, in addition to fluorescent lines from Fe, Ca, S, and Si ions in lower
charge states. Additionally, in the both spectra of phase 0.50 and eclipse, emission lines
from the same ions are detected.
Blown-up spectra of the Si K lines region are shown in Figure 4.7. Intense Lyα line
from H-like ions and fully-resolved He-like triplet lines are clearly seen in phase 0.50 and
eclipse. At the lower energy end below 1.74 keV, fluorescent lines from near-neutral Si is
also detected in both phases. Additionally, between the He-like lines and nearly neutral
line, Si VII–Si XI Kα lines can be resolved. The forest of Si K lines is a clear evidence
that plasma in various ionization states exist in the Vela X-1 system.
The centroid of energies, the widths and the intensities of each line are determined by
fitting the data with a single gaussian model. In the spectral fittings, we use the Poisson
likelihood statistics, in stead of the χ2 statisitics, because numbers of photons in some
of the bins in the spectra are very small. As an example of the fittings, the Lyα line
profiles from H-like ions of Si are shown in Figure 4.8, together with the best-fit models.
The derived parameters for phase 0.50 and eclipse are listed in Table 4.3 and Table 4.4,
respectively. The line intensity ratios of phase 0.50 to eclipse are listed on Table 4.5 for
lines from H- and He-like ions which were detected with statistical significance of more
than 5 σ. These ratios are 8–10 for the H-like lines and are 4–7 for the He-like lines.
One of the striking results seen from Figure 4.8 is the Doppler shift of lines. Thanks
to the resolving power of the HEG, Doppler shifts can be measured with an accuracy of
∼ 100 km s−1. Figure 4.9 compares the line profiles of Si Lyα and Mg Lyα between the
phase 0.50 and the eclipse data. The differences in the line center energies are clearly
seen in each line.
In Figure 4.10, the velocity shifts are plotted for both of the phases for all emission
lines from H- and He-like ions. Though some fluctuations are seen, there is a trend that
blue shifts are detected in phase 0.50 and red shifts are observed in eclipse. The shifts
between phase 0.50 and eclipse (∆v) range in ∼ 300–600 km s−1 (Table 4.5). Additionally,
the emission lines from highly ionized ions have widths of σ . 300 km s−1.
The radiative recombination continuum (RRC) is detected clearly from H-like Ne.
The blow-up spectra of phase 0.50 and that of eclipse are shown in Figure 4.11. We
fitted the RRC spectra using the “redge” model in XSPEC. The electron temperatures
are derived to be kTe = 7.4+1.6−1.3 eV and kTe = 6.6+2.5
−1.8 eV during phase 0.50 and eclipse,
respectively.
Iron Kα fluorescent lines are detected in all three orbital phases. The profiles of these
lines are shown in Figure 4.12. The parameters derived from the spectral fittings with a
single gaussian model are listed in Table 4.4. The equivalent width of the iron Kα line is
measured to be 116 eV and 51 eV for phase 0.50 and for phase 0.25, respectively. At the
eclipse phase, a high equivalent width of 844 eV is observed. As shown in Figure 4.12,
35
there is a sign of a Compton shoulder in the iron Kα spectrum of phase 0.50.
36
Figure 4.5: The spectrum of Vela X-1 in the orbital phase of 0.50. The red
shows MEG data and the blue shows HEG data. The green lines mark the
energies of the emission lines listed in Table 4.3.
37
Figure 4.6: The spectrum of Vela X-1 in the eclipse phase. The red shows
MEG data and the blue shows HEG data. The green lines mark the emission
lines listed in Table 4.4.
38
Si XIV Lyα
Si XIII
rf
i
Si II-VI
Si X
IS
i XS
i IX
Si V
III
Si V
II
phase 0.25
phase 0.50
eclipse
due to the detector
response (Si-Kedge)
Figure 4.7: The spectrum of the Si K lines regions in each orbital phase.
39
Figure 4.8: The Lyα lines from H-like Si in phase 0.50 (left) and in eclipse
(right). The bold lines show the best-fit models. Fitting model is the single
gaussian.
40
Table 4.3. Derived Parameters of emission lines in the 0.5 orbital phase spectrum
Center Energy Sigma Intensitya Candidate Line Shift
(keV) (eV) (photon cm−2 s−1) (energy keV) (km s−1)
3.69053 0.35 8.82e−5 Ca Kα
(3.68963–3.69273) (0.00–3.84) (5.73–11.87)
2.62213 4.04 1.77e−4 S XVI Lyα
(2.62094–2.62327) (2.81–5.53) (1.44–2.09)
2.46197 0.64 6.84e−5 S XV r
(2.46110–2.46273) (0.00–1.71) (5.18–8.66)
2.31112 0.20 1.03e−4 S Kα
(2.31070–2.31184) (0.00–2.12) (8.32–12.5)
2.00634 1.16 2.38e−4 Si XIV Lyα +127
(2.00618–2.00650) (0.89–1.42) (2.23–2.52) (2.00549) (+103–+151)
1.86614 1.38 1.36e−4 Si XIII r +183
(1.86592–1.86636) (1.09–1.67) (1.25–1.48) (1.86500) (+148–+219)
1.85537 0.82 3.05e−5 Si XIII i +257
(1.85483–1.85592) (0.00–1.77) (2.39–3.77) (1.85378) (+170–+346)
1.84136 2.15 1.41e−4 Si XIII f +311
(1.84109–1.84162) (1.86–2.47) (1.29–1.53) (1.83945) (+267–+353)
1.74447 2.35 1.46e−4 Si Kα
(1.74421–1.74473) (2.07–2.67) (1.36–1.58)
1.72998 0.44 3.36e−5 Al XIII Lyα?
(1.72962–1.73033) (0.00–1.10) (2.78–3.99)
1.59900 0.66 1.31e−5 Al XII r ?
(1.59832–1.59967) (0.00–1.68) (0.86–1.87)
1.57976 2.01 3.90e−5 Mg XI
(1.57920–1.58032) (1.38–2.64) (3.18–4.64)
1.55231 0.58 1.78e−5 Fe XXIV ?
(1.55175–1.55284) (0.00–1.42) (1.27–2.35)
1.47282 1.18 2.35e−4 Mg XII Lyα +102
(1.47268–1.47296) (1.02–1.35) (2.17–2.53) (1.47232) (+73–+130)
1.35279 1.00 1.47e−4 Mg XI r +120
(1.35263–1.35296) (0.81–1.20) (1.32–1.62) (1.35225) (+84–+157)
1.34346 0.69 7.34e−5 Mg XI i +80
(1.34324–1.34367) (0.36–1.02) (6.25–8.53) (1.34310) (+31–+127)
41
Table 4.3—Continued
Center Energy Sigma Intensitya Candidate Line Shift
(keV) (eV) (photon cm−2 s−1) (energy keV) (km s−1)
1.33213 0.95 9.13e−5 Mg XI f +230
(1.33190–1.33236) (0.65–1.25) (7.89–10.5) (1.33111) (+178–281)
1.30808 1.06 4.99e−5 Fe XXI ?
(1.30766–1.30843) (0.61–1.49) (3.96–6.12)
1.27783 1.10 8.44e−5 Ne X Lyγ
(1.27756–1.27811) (0.78–1.38) (7.18–9.84)
1.21160 0.94 1.33e−4 Ne X Lyβ
(1.21139–1.21181) (0.72–1.17) (1.15–1.52)
1.12732 1.54 7.41e−5 Ne IX
(1.12683–1.12780) (1.13–2.03) (5.71–9.27)
1.07432 0.12 5.76e−5 Ne IX
(1.07397–1.07450) (0.00–0.73) (4.07–7.74)
1.02242 0.64 4.42e−4 Ne X Lyα +182
(1.02230–1.02253) (0.52–0.76) (3.91–4.97) (1.02180) (+147–+214)
0.922458 0.80 2.89e−4 Ne IX r +149
(0.922186–0.922725) (0.52–1.11) (2.24–3.64) (0.922001) (+60–+235)
0.916254 1.44 4.91e−4 Ne IX i +475
(0.915937–0.916584) (1.21–1.73) (4.03–5.89) (0.914803) (+371–+583)
0.905561 1.78 3.71e−4 Ne IX f +165
(0.905013–0.906071) (1.38–2.27) (2.88–4.65) (0.905062) (−16–+334)
aInter stellar gas absorption is corrected. The hydrogen column density of
6 × 1021 cm−2 is assumed, corresponding to the density of 1 H cm−3 and the distance
of 1.9 kpc.
Note. — Errors correspond to 90 % confidence level.
42
Table 4.4. Derived Parameters of emission lines in the 0.0 orbital phase spectrum
Center Energy Sigma Intensitya Candidate Line Shift
(keV) (eV) (photon cm−2 s−1) (energy keV) (km s−1)
3.69431 8.59 9.27e−6 Ca Kα
(3.69006–3.69836) (5.35–12.9) (6.57–12.3)
2.95657 0.00 4.92e−6 Ar Kα
(2.95507–2.95849) (0.00–3.35) (2.97–7.27)
2.61857 0.57 1.38e−5 S XVI Lyα
(2.61781–2.61947) (0.04–2.62) (1.08–1.73)
2.31035 2.19 1.76e−5 S Kα
(2.30935–2.31138) (0.87–3.50) (1.35–2.23)
2.00339 1.70 2.32e−5 Si XIV Lyα −314
(2.00305–2.00373) (1.28–2.14) (2.07–2.59) (2.00549) (−365–−263)
1.86299 1.58 2.34e−5 Si XIII r −323
(1.86267–1.86330) (1.25–1.94) (2.08–2.62) (1.86500) (−375–−273)
1.85271 0.00 2.76e−6 Si XIII i −173
(1.85254–1.85357) (0.00–1.12) (1.67–4.05) (1.85378) (−201–−34)
1.83924 2.92 2.11e−5 Si XIII f −34
(1.83878–1.83969) (2.48–3.43) (1.88–2.36) (1.83945) (−109–+39)
1.74247 1.67 1.96e−5 Si Kα
(1.74217–1.74276) (1.39–1.99) (1.74–2.20)
1.65752 0.12 2.84e−6 Mg XI or
(1.65697–1.65855) (0.00–1.53) (1.86–4.00) Fe XXIII
1.57719 1.34 6.02e−6 Mg XI
(1.57659–1.57776) (0.68–2.05) (4.59–7.64)
1.47068 1.23 2.63e−5 Mg XII Lyα −334
(1.47044–1.47093) (0.99–1.50) (2.29–2.99) (1.47232) (−383–−283)
1.35057 1.54 2.58e−5 Mg XI r −373
(1.35026–1.35088) (1.21–1.90) (2.23–2.97) (1.35225) (−442–−304)
1.34238 1.18 6.33e−6 Mg XI i −161
(1.34170–1.34307) (0.39–2.04) (4.33–8.65) (1.34310) (−313–−7)
1.33122 2.27 2.03e−5 Mg XI f +25
(1.33072–1.33171) (1.87–2.77) (1.70–2.40) (1.33111) (−89–+135)
1.30640 1.26 6.61e−6 Fe XXI ?
(1.30574–1.30701) (0.71–1.97) (4.56–9.05)
43
Table 4.4—Continued
Center Energy Sigma Intensitya Candidate Line Shift
(keV) (eV) (photon cm−2 s−1) (energy keV) (km s−1)
1.27592 0.89 8.70e−6 Ne X Lyγ
(1.27547–1.27636) (0.00–1.44) (5.62–11.4)
1.23618 1.57 5.94e−6 Fe XX ?
(1.23507–1.23727) (0.71–2.79) (3.13–8.95)
1.20980 1.34 1.43e−5 Ne X Lyβ
(1.20930–1.21033) (0.96–1.82) (1.07–1.84)
1.07241 0.78 1.91e−5 Ne IX
(1.07205–1.07276) (0.44–1.19) (1.38–2.54)
1.02075 0.99 8.54e−5 Ne X Lyα −308
(1.02056–1.02095) (0.81–1.18) (7.25–9.98) (1.02180) (−364–−249)
0.920773 0.92 5.48e−5 Ne IX r −400
(0.920390–0.921159) (0.60–1.30) (3.86–7.43) (0.922001) (−524–−274)
0.914926 1.05 4.68e−5 Ne IX i +40
(0.914407–0.915448) (0.75–1.53) (3.03–6.70) (0.914803) (−130–+211)
0.904058 0.75 8.98e−5 Ne IX f −333
(0.903784–0.904342) (0.48–1.10) (6.75–11.6) (0.905062) (−424–−239)
aInter stellar gas absorption is corrected. The hydrogen column density of
6 × 1021 cm−2 is assumed, corresponding to the density of 1 H cm−3 and the distance
of 1.9 kpc.
Note. — Errors correspond to 90 % confidence level.
4.5 Pulse Phase Dependence
Figure 4.13 shows the pulse profiles at the orbital phase 0.25 and phase 0.50 obtained by
folding the light curve of the 1–10 keV events from HEG ± 1 order. The pulse periods
are 283.2 s and 283.5 s for phase 0.25 and phase 0.50, respectively. The pulse phase of
0.0 employed the barycentric start time of each observation. The observed pulse profiles
are consistent with those reported in past observations; e.g. McClintock et al. (1976);
Sato et al. (1986a); Kreykenbohm et al. (1999).
In order to examine the pulse phase dependence of the X-ray spectra, we extract two
spectra by dividing each dataset into two pulse phases (“peak” and “bottom”). These two
pulse phases are defined in Figure 4.13. Figure 4.14 shows the spectra of peak and bottom
44
Figure 4.9: The line profiles of Si H-like Lyα (left) and Mg H-like Lyα. The
blue lines show the observed data in phase 0.5, and the red lines show the
data in eclipse. The HEG data is used for the Si Lyα lines, and the MEG
data is used for the Mg Lyα lines.
Figure 4.10: The plot of velocity shift for emission lines from highly ionized
ions. Closed circles show the data from phase 0.50, and open circles show the
data from eclipse.
45
Table 4.5. Comparison between lines of the phase 0.50 and of the eclipse.
line Intensity(0.50)/Intensity(eclipse) ∆v (km s−1)
Si XIV Lyα 10.3 ± 1.3 441 ± 56
Si XIII resonance 5.81 ± 0.83 506 ± 62
Si XIII forbidden 6.68 ± 0.95 345 ± 86
Mg XII Lyα 8.94 ± 1.37 436 ± 58
Mg XI resonance 5.70 ± 1.00 493 ± 78
Mg XI forbidden 4.50 ± 1.01 205 ± 123
Ne X Lyα 5.18 ± 1.04 490 ± 60
Ne IX resonance 5.27 ± 2.14 549 ± 153
Ne IX forbidden 4.13 ± 1.49 498 ± 198
Figure 4.11: The spectra of radiative recombination continua from H-like Ne
in phase 0.50 (left) and in eclipse (right). The best-fit models based on the
“redge” model in XSPEC are shown in lines. The electron temperature is
derived to be 7.4 eV and 6.6 eV, respectively.
46
Table 4.6. Derived Parameters of the Fe Kα line.
Orbital Phase Center Energy Sigma Intensity EW
(keV) (eV) (photon cm−2 s−1) (eV)
0.00 6.3958 (6.3936–6.3980) 7.2 (1.9–11.1) 1.70e−4 (1.50–1.90) 844
0.25 6.3992 (6.3987–6.4010) 0.0 (0.0–7.4) 1.92e−3 (1.78–2.07) 51
0.50 6.3965 (6.3953–6.3976) 11.0 (9.1–12.8) 3.40e−3 (3.21–3.58) 116
Note. — Only HEG data is used. The fitting model is single gaussian.
Note. — Errors correspond to 90 % confidence level.
Figure 4.12: The blow-up spectra of the iron Kα lines in eclipse (left), in phase
0.25 (middle), and in phase 0.50 (right).
47
Figure 4.13: Pulse profiles of Vela X-1 at orbital phase 0.25 (top panel) and
0.50 (bottom panel), obtained by folding the light curves at the barycentric
periods of 283.2 s and 283.5 s, respectively. Two phase cycles are shown for
clarity. The HEG ± 1 order events are used, and the energy band is 1–10 keV.
The pulse phase of 0.0 corresponds to the start time of each observation.
for each orbital phase, and Table 4.7 lists the observed fluxes and the corresponding iron
Kα intensities.
Although the observed overall flux changes between the peak and the bottom by a
factor of 1.3, the iron Kα line flux does not change within statistical uncertainty. Addi-
tionally, the 1.0–2.1 keV count rate in orbital phase 0.50, dominated by Ne, Mg and Si
emission lines, is constant between the peak and the bottom; specifically, 0.15 ± 0.01 c s−1
and 0.14 ± 0.01 c s−1 for the peak and the bottom, respectively.
Table 4.7. Total and iron Kα fluxes of the pulse phase divided spectra
orbital Flux (1.0–10.0 keV)(erg s−1) Fe Kα flux (photon cm−2 s−1)
phase peak bottom peak bottom
phase 0.25 (3.3 ± 0.1) × 10−9 (2.5 ± 0.1) × 10−9 (1.8 ± 0.2) × 10−3 (2.1 ± 0.2) × 10−3
phase 0.50 (2.0 ± 0.1) × 10−9 (1.5 ± 0.1) × 10−9 (3.3 ± 0.3) × 10−3 (3.5 ± 0.4) × 10−3
48
Figure 4.14: X-ray spectra divided by the pulse phase. The left panel shows
spectra at orbital phase 0.25, and the right panel at orbital phase 0.50. Ma-
genta and cyan spectra refer to the pulse peak and pulse bottom, respectively,
as defined in Figure 4.13.
4.6 Summary of the Observation and the Implication
From the continuum spectral shapes, the direct radiation from the neutron star are the
same between phase 0.50 and phase 0.25 after correction for absorption. Considering the
geometric relationship, this absorber is located behind the neutron star as viewed from
the companion star. Due to this absorption, the emission lines in the low energy range
can be observed in phase 0.50.
The intensity ratios of emission lines in phase 0.50 to that in eclipse are 8–10 for lines
from H-like ions and 4–7 for lines from He-like ions. These ratios indicate that the region
emitting these line X-rays is mostly located between the neutron star and the companion
star, which is occulted during eclipse.
The information of the Doppler effects also confine the line emission region. The
energy shifted emission lines are detected and the shift direction in the eclipse is opposite
to that in phase 0.5. The Doppler broadenings of emission lines from highly ionized ions
are less than 300 km s−1. These observational results shows that the emission site of
lines from highly ionized ions is distributed on a plane between the neutron star and the
companion star.
Narrow radiative recombination continua from H-like ions of Ne are detected in phase
0.5 and in eclipse. Electron temperatures of 6–8 eV are derived from the spectral fits. It
is a direct evidence that the emission lines from highly ionized gas in Vela X-1 are driven
through photoionization, not collisional origin.
49
Chapter 5
Observations and Results of
GX 301−2
5.1 GX 301−2
GX 301−2 is a high mass X-ray binary consisting of a neutron star and a B2 Iae Com-
panion star, WRA 977. The neutron star moves in a highly eccentric orbit (e = 0.46;
Sato et al. 1986b; Koh et al. 1997) with an orbital period of ∼ 41 days. The X-ray light
curve is known to lack a signature of eclipse. X-ray pulsations with a period of ∼ 700 s
were discovered by White et al. (1976).
The mass loss rate of WRA 977 is estimated to be in the range (3–10) × 10−6 M¯ yr−1
from optical spectroscopic observations (Parkes et al. 1980). The stellar wind velocity
of WRA 977 measured by Parkes et al. (1980) is ∼ 300 km s−1 at a distance of 3 Rc,
where Rc is the radius of the companion star. This result suggests a terminal velocity
400 km s−1.
The X-ray luminosity varies in the range (2–200) × 1035 erg s−1. It is known that an
X-ray flare always appears at an orbital phase ∼ 1.4 days before the periastron passage
of the neutron star (Sato et al. 1986b). In the flare, the X-ray luminosity, absorbing
column density, and the iron line equivalent width reach the highest level among in the
entire orbit (Endo et al. 2002). In addition, BATSE observations reported the presence
of secondary X-ray flares near the apastron passage (Pravdo et al. 1995; Koh et al. 1997).
5.2 Observation and Data Reduction
Chandra observed GX 301−2 at three different orbital phases: (1) φ = 0.167–0.179, (2)
φ = 0.480–0.497, and (3) φ = 0.970–0.982, hereafter referred to as intermediate (IM), near-
apastron (NA), and pre-periastron (PP) phases, respectively. NA and PP correspond to
the X-ray flare phases mentioned previously. The observation dates and exposure times
are summarized in Table 5.1.
50
IM
NA
PP
Neutron Star
WRA 977
Figure 5.1: The location between the neutron star and the companion star in
GX 301−2. The bold lines show the observed orbital phases.
Table 5.1. Summary of GX 301−2 Observations
Label OBSID Start Date Orbital Phase Exposure (sec)
IM 103 2000-06-19 13:57:26 0.167 – 0.179 39516
NA 3433 2002-02-03 12:34:10 0.480 – 0.497 59033
PP 2733 2002-01-13 09:00:24 0.970 – 0.982 39233
All of the data are processed using CIAO v2.2.1, and spectral fittings were performed
using XSPEC. As in the case of Vela X-1, the zeroth order images are severely piled-up,
especially during the NA and PP. Therefore, the locations of the zeroth order image are
determined by finding the intersection of the streak events and the dispersed events. We
apply a spatial filter for both the MEG and the HEG, and then use an order sorting mask
by using the photon energy information obtained with ACIS. In our analysis, only the
first order events are used for extracting spectra. The background events are estimated
from the adjacent region events to the dispersed event region. The background level is
less than 5% for all three phase observations.
The light curves in the three orbital phases extracted from the HEG 1–10 keV events
are shown in Figure 5.2. By applying the epoch holding method, we confirmed the
presence of pulsations with periods of 683.2 s, 680.8 s and 681.2 s in the light curves of
IM, NA and PP phase, respectively.
51
Figure 5.2: The light curves of GX 301−2 in IM (top), in NA (middle) and
in PP (bottom). Pulsations are found with the epoch holding method. The
periods are determined to be 683.2 s, 680.8 s and 681.2 s for IM, NA and PP,
respectively.
52
Figure 5.3: The spectra of GX 301−2 obtained with HEG. The red, the blue
and the green plots show the spectra in PP phase, NA phase and IM phase,
respectively.
5.3 Continuum Emission
In order to constrain the continuum emission, we extract energy spectra from 4 keV to
10 keV for three orbital phases. The HEG spectra above 4 keV are shown in Figure 5.3.
We fit the spectra by a photo-absorbed power-law model, in which the metal abundance
of the absorption material is assumed to be 0.75 times the cosmic chemical abundance
(Feldman 1992), as we do in the case of Vela X-1. The energy region, 6.3–6.5 keV,
is excluded in the fit because of the strong iron Kα emission. First, we fit the NA
spectrum. In this fit, both the hydrogen column density and the photon index are left
as free parameters. From this analysis, we obtain the photon index of 0.98–1.12 for
the NA spectrum. In the following analysis, the photon index is fixed to 1.0 assuming
that there is no change in it. By fitting all three spectra with the fixed photo index
of 1.0, the hydrogen column densities are derived. The derived parameters are listed
on Table 5.2, and the best-fit models for each phase data are also shown in Figure 5.3.
Heavy absorptions (2–10 × 1023 cm−2) are observed in all three phases. Assuming a
distance of 1.8 kpc (Parkes et al. 1980), the absorption-corrected X-ray luminosities in
the 0.5–10 keV band are 3.8 × 1035 erg s−1, 1.4 × 1036 erg s−1 and 2.7 × 1036 erg s−1 for
the IM, NA and PP phases, respectively.
53
Table 5.2. Derived Parameters from spectral fits of the GX 301−2 continuum
Orbital NHa Photon Index Observed Flux Luminosityb χ2/ d.o.f.
Phase (1023 cm−2) (erg cm−2 s−1) (erg s−1)
NA 3.05 ± 0.11 1.05 ± 0.07 1.1 × 10−9 1.3 × 1036 655./ 743
IM 6.51 ± 0.24 1.0 (fixed) 2.4 × 10−10 3.8 × 1035 220./ 302
NA 2.97 ± 0.05 1.0 (fixed) 1.2 × 10−9 1.4 × 1036 657./ 744
PP 10.3 ± 0.2 1.0 (fixed) 1.0 × 10−9 2.7 × 1036 903./ 515
Note. — Fitting regions are 4.0–10.0 keV. Only HEG data is used. The iron
K-line region (6.3–6.5 keV) is excluded. Errors are corresponding 90 % confidence
levels.aThe metal abundance is 0.75 cosmic.
b0.5–10.0 keV luminosity. The absorption is corrected.
5.4 Emission Lines
Figure 5.4 shows the low energy regions of the spectra of the three orbital phases. Flu-
orescence emission lines from Si, S, Ar, Ca ions in low charge states are detected in all
orbital phases. As shown in Figure 5.3, intense iron Kα and Kβ lines are observed in
each spectrum. In the PP phase data, fluorescent lines from Cr and Ni are also seen. We
fit these lines with a single gaussian model. For lines from Si, S, Ar, Ca and Cr, both
the HEG and the MEG data are used. For other lines above 6.0 keV, only HEG data
are applied to spectral fits because MEG does not have sufficient efficiency. The derived
parameters are listed in Table 5.3. In contrast to the detection of these fluorescent lines,
emission lines from highly ionized ions are entirely absent in the spectra of the three
phases.
The blown-up spectra of the iron Kα region in the three orbital phases are shown
in Figure 5.5. A “shoulder” component in low energy side of the iron Kα line is clearly
detected and fully resolved. The shoulder extends down to ∼ 6.24 keV and its width
is ∼ 160 eV. This value precisely matches what is predicted in § 2.3.5, which strongly
indicates that the feature is formed primarily through single Compton scattering of the
iron Kα photons.
54
Figure 5.4: The low energy part of spectra in NA (top), in IM (middle) and
in PP (bottom). The red lines show MEG data and the blue lines show HEG
data. The fluorescence lines from Si, S, Ar and Ca are observed.
55
Table 5.3. Derived Parameters of emission lines in the GX 301−2 spectra of the three
phases.
Orbital phase line Energy Sigma Intensityb
(keV) (eV) (photon cm−2 s−1)
IM Si Kα 1.74136 0.01 5.74e−6
(1.74104–1.74197) (0.00–1.05) (4.18–7.62)
IM S Kα 2.30917 3.14 2.03e−5
(2.30773–2.31057) (0.64–4.90) (1.47–2.71)
IM Ar Kα 2.95837 4.56 8.75e−6
(2.95438–2.96157) (4.56–8.88) (5.02–13.1)
IM Ca Kα 3.69217 0.00 1.58e−5
(3.69012–3.69239) (0.00–4.62) (1.10–2.13)
IM Fe Kαa 6.39483 11.8 8.91e−4
(6.39325–6.39641) (9.39–14.2) (8.33–9.52)
IM Fe Kβ 7.05415 28.2 2.68e−4
(7.02218–7.06881) (12.7–69.2) (1.53–3.72)
NA Si Kα 1.74242 1.35 1.34e−5
(1.74207–1.74277) (0.95–1.76) (1.13–1.56)
NA S Kα 2.31014 4.49 3.33e−5
(2.30873–2.31158) (3.12–6.11) (2.64–4.10)
NA Ar Kα 2.95907 6.01 3.39e−5
(2.95582–2.96223) (3.42–10.2) (2.38–4.53)
NA Ca Kα 3.69164 1.86 3.88e−5
(3.68809–3.69434) (0.00–7.57) (2.52–5.34)
NA Fe Kαa 6.39574 13.2 3.43e−3
(6.39500–6.39649) (12.2–14.2) (3.33–3.54)
NA Fe Kβ 7.06731 15.9 4.77e−4
(7.06032–7.07438) (6.04–24.9) (3.63–6.01)
PP Si Kα 1.74350 0.42 6.64e−6
(1.74298–1.74396) (0.00–1.31) (4.96–8.65)
PP S Kα 2.31211 2.59 2.77e−5
(2.31106–2.31315) (1.68–3.77) (2.11–3.56)
PP Ar Kα 2.95942 4.60 2.49e−5
(2.95765–2.96115) (2.83–6.48) (1.95–3.11)
PP Ca Kα 3.69166 2.93 5.92e−5
(3.69051–3.69283) (1.67–4.94) (5.06–6.87)
56
Table 5.3—Continued
Orbital phase line Energy Sigma Intensityb
(keV) (eV) (photon cm−2 s−1)
PP Cr Kα 5.41140 0.00 7.53e−5
(5.40826–5.41166) (0.00–5.98) (4.99–10.2)
PP Fe Kαa 6.39469 13.2 8.12e−3
(6.39421–6.39516) (12.5–13.9) (7.94–8.31)
PP Fe Kβ 7.05755 13.8 1.54e−3
(7.05476–7.06035) (9.85–17.5) (1.37–1.69)
PP Ni Kα 7.45984 0.00 5.07e−4
(7.45682–7.46916) (0.00–15.5) (3.73–6.40)
aThe Compton shoulder region (6.24–6.34 keV) is excluded.
bInter stellar gas absorption is corrected. The hydrogen column density of
6 × 1021 cm−2 is assumed, corresponding to the density of 1 H cm−3 and a
distance of 1.8 kpc.
Note. — Errors correspond to 90 % confidence levels.
5.5 Pulse Phase Dependence
Figure 5.6 shows the pulse profiles obtained by folding the light curve of the 1–10 keV
events from HEG ± 1 order. The barycentric pulse periods are 683.2 s, 680.8 s and 681.2 s
for IM, NA and PP, respectively, which are obtained from the epoch holding method.
The pulse phase of 0.0 corresponds to the start time of each orbital phase observation.
As seen from Figure 5.6, the pulse profiles of GX 301−2 have a double-peak structure,
as has already been reported previously (e.g. Orlandini et al. 2000; Endo et al. 2002).
In order to examine the pulse phase dependence, we extract two spectra by dividing
into two pulse phases. One is the pulse phase with the larger peak (“peak(1)”), and the
other is the pulse phase with the smaller peak (“peak(2)”). The peak(1) and the peak(2)
of each orbital phase are defined in Figure 5.6. Figure 5.7 shows the spectra of peak(1)
and peak(2) for each orbital phase, and Table 5.4 lists the observed fluxes and the iron
Kα intensities. Although the observed flux changes between peak(1) and peak(2), there
is no significant change of the intensity of the iron Kα line within statistical uncertainty.
57
Figure 5.5: The blown-up spectra of the iron Kα lines in the PP (bottom),
the IM (middle) and the NA (top). A shoulder component extending toward
the low-energy side of the line is clearly seen and fully resolved. The width of
the shoulder (∆E ∼ 160 eV: 6.24–6.40 keV) matches the energy distribution
of iron Kα photons that suffer single Compton scattering. The line shows the
best-fit model in the spectral fits of the continuum.
58
Figure 5.6: Pulse profiles of GX 301−2 in IM (top panel), NA (middle) and
PP (bottom) by folding the light curves at the periods of 683.2 s, 680.8 s and
681.2 s, respectively. Two phase cycles are shown for clarity. The HEG ± 1
order events are used, and the energy band is 1–10 keV. The pulse phase of
0.0 corresponds to the start time of each observation.
Table 5.4. Total and iron Kα fluxes of pulse phase divided spectra
orbital Flux (2.0–10.0 keV)(erg s−1) Fe Kα flux (photon cm−2 s−1)
phase peak(1) peak(2) peak(1) peak(2)
IM (2.5 ± 0.1) × 10−10 (1.8 ± 0.1) × 10−10 (8.8 ± 1.1) × 10−4 (6.9 ± 0.8) × 10−4
NA (1.5 ± 0.2) × 10−9 (1.1 ± 0.1) × 10−9 (3.3 ± 0.2) × 10−3 (3.2 ± 0.2) × 10−3
PP (1.2 ± 0.1) × 10−9 (8.9 ± 0.2) × 10−10 (7.8 ± 0.4) × 10−3 (7.7 ± 0.4) × 10−3
59
Figure 5.7: X-ray spectra divided by pulse phase. The magenta spectra are
obtained from the events in peak(1), whose count rates are relatively high (see
Figure 5.6). The cyan spectra are extracted from the events in peak(2).
60
Chapter 6
Simulation of Photoionized Plasma
in HMXB
6.1 Modeling of Photoionized Plasmas
The unprecedented spectral resolution of the grating system onboard the Chandra satel-
lite gives us a wealth of information about X-ray emission lines from HMXBs, Vela X-1
and GX 301−2. As already shown in previous chapters, we have succeeded in detecting
lines from highly ionized ions, such as H-like and He-like Si, S, Mg, from photoionized
plasma, together with clear signals from radiative recombination continua in Vela X-1.
As expected from the dynamical motion of the gas in the stellar wind, opposite shifts of
the central energy appear to exist in phase 0.50 and eclipse for Vela X-1. On the other
hand, GX 301−2 shows only fluorescent lines from low charge states. From the detail
analysis of the line profiles of the iron fluorescence line, we discovered a shoulder-like
structure which could be accounted by the effect of Compton scattering.
The emission lines we detected from Vela X-1 and GX 301−2 can be interpreted
as due to emission from a gas photoionized by the X-ray radiation from the neutron
star. In this case, the spectrum emerged from the binary system is the result of the
propagation of X-rays through the gas. Line emission, presumably due to processes,
such as photoionization, recombination and fluorescence, are controlled by the ionization
structure and the density distribution of the gas in the stellar wind. Therefore, by
investigating characteristics of lines, we will be able to obtain an important clue to
addressing the questions about how the photoionized plasma is distributed spatially in
the stellar wind and how the distributions can affect the nature of the X-ray emission
observed in HMXBs.
In previous studies of photoionization plasmas, modeling were performed based on
very simple assumptions. Kallman & McCray (1982) presented theoretical models to
calculate the ion abundances and the temperature for the given X-ray spectrum and the
wind density. Since the introduction of their model as a computer code (called XSTAR
61
1), it has been frequently used to characterize X-ray spectra from HMXBs. However,
most of the analysis are based on very simple assumptions such as symmetric geometry
and constant density distribution in the volume.
In order to find the ionization structure from the HETGS results, it is necessary to
model the emission from more realistic environments in the stellar wind. Therefore, we
have developed a new code to simulate X-ray interactions in the stellar wind. Most
important ingredients in the code is that fully three dimensional treatment is adopted for
both the ionization structure and the photon transportation in the plasma. For the case
that the optically thin approximations are allowed, the condition of photoionized plasma
can be characterized only by the ionization parameter ξ. However, the Chandra results
indeed imply that the emission lines with high ionization degree actually come from a
dense region (particle density n > 109 cm−3). In this situation, we have to consider not
only the ξs, but also the effect of absorption by the matter between the neutron star and
the emission site, because, the incident flux is absorbed by the material and changes the
shape and the flux.
Another important issue to be stressed is that we now see the effect of the Doppler
shift due to the emission from the material moving with fast velocity. The information
on the Doppler shift could also constrain the velocity field of the X-ray emitting region
in the stellar wind. The model to be used for the re-construction of physical environment
in the stellar wind has to deal with these kinematical effects.
Our simulation code consists of two parts:
(1) Calculation of the ionization structure,
(2) Monte Carlo simulation for tracking X-ray photon transportation.
In part (1), we construct the map of the ion abundance in the stellar wind. In part (2), we
have implemented the physical process which are related to highly ionized gas, together
with the Lorentz transformation for the calculation of Doppler effects. The simulation is
held in three dimensional space divided into grids such that we can handle more complex
geometries. Our procedure of each of these parts is described in the following sections.
6.2 Calculation of the Distribution of Ionization De-
gree
An ionization balance and an electron temperature are dictated by the flux and spectral
shape of injected X-rays and the density of the region. Figure 6.1 shows a schematic of
the calculation of the ionization structure. The intrinsic luminosity and spectrum shape
of the X-ray source are deduced from the observation. The density structure around the
1http://heasarc.gsfc.nasa.gov/docs/software/xstar/xstar.html
62
Region1 Region2 Region3 RegionN
Neutron Star
abund[0]1
abund[1]1
:
abund[139]1
abund[0]2
abund[1]2
:
abund[139]2
abund[0]3
abund[1]3
:
abund[139]3
abund[0]N
abund[1]N
:
abund[139]N
ni : particle density of region i
abund[0]-abund[139] : ion abundance of
H I, He I-II, C I-VI, N I-VII, O I-VIII,
Ne I-X, Mg I-XII, Si I-XIV, S I-XVI,
Ar I-XVIII, Ca I-XX, Fe I-XXVI
n1 n2 n3 nN
Calculation Sequence
X-ray spectrum
E
Ph
oto
n
E
Ph
oto
n
E
Ph
oto
n
E
Ph
oto
n
Figure 6.1: The schematic of the software for calculations of ionization structures
companion star is given from the velocity profile determined from the UV obserservation
as mentioned in § 2.3.1. Since an X-ray flux and spectrum shape injected into the
region are derived from the distance and the ions’ column densities in between the X-ray
source, the central neutron star, and the region, we can obtain the ionization structure
by calculating the ionization balance starting from the grid closest to the neutron star to
the most distant grid, sequentially. In order to calculate the ionization abundance and
the electron temperatures for the given X-ray spectrum (and the flux) and the density
as inputs, we use the XSTAR program.
6.3 Monte Carlo Calculation of the X-ray Emission
from Photoionization Equilibrium State
The map of the ionization abundance (ionization structure) calculated by following the
prescription given in the previous section assures equilibrium between photoionization
63
Geometrydivided into small cubes
Parameters:
Density
Wind Velocity and Direction
Metal Abundance (Z>2)
Electron Temperature
Ion Abundance
(H,He,C,N,O,Ne,Mg,Si,S,Ar,Ca,Fe)
Physical ProcessesPhotoionization(nelectron > 2) -> Fluorescence
Photoionization(H-,He-like) -> Recombination
Photoexcitation(H-,He-like) -> Radiative Transition
Compton Scattering
(with Doppler effect due to Stellar Wind)
Data Pick-up and Savefor escaped photons
energy, momentum direction,
generating postion, incident energy
Incident Generatorenergy distribution
(e.g. power-law)
Monte Carlo
Managers
Monte Carlo Simulator
Simulated Spectrum
calculation ofstellar windconditions
assumption ofphotoionizationequilibrium
observationresults
data
data
data
data
Figure 6.2: The schematic of our Monte Carlo simulation.
and recombination. Therefore, an X-ray spectrum emitted from the given ionization
structure can be obtained through the transportation of X-ray photons by Monte Carlo
methods.
We start the Monte Carlo simulation with a photon at the position of the central neu-
tron star (X-ray source). The incident photons to the region are generated in accordance
with the energy distribution like a power-law, which is provided from the observation
results. The X-ray photon interacts with the stellar wind that includes highly ionized gas
and generates secondary photons through radiative recombination, radiative transitions,
fluorescent emission, and so on. In the simulation code, the incident and all other photons
produced by interactions are tracked until they either completely escape the simulation
space or are destroyed by some physical processes. The emergent photons are then se-
lected under some conditions which depend on the analysis, and the energy distribution
of the selected photons are histogrammed to produce a spectrum.
64
6.3.1 Physical processes
As for physical processes for X-ray photons, we account for photoionization, photoexcita-
tion and Compton scattering. In the newly developed code, we have implemented these
processes. We only deal with photons in the code. Although processes mentioned above
generate electrons with some amount of energies, we do not trace these secondary elec-
trons, because we are interested in only X-ray photons, and the probability of secondary
electrons further emitting X-ray photons by bremsstrahlung is small.
As mentioned earlier, our code to deal with physical processes are constructed on
the premise that photoionization equilibrium is established locally everywhere in the
plasma. Therefore, if photoionization takes place in the Monte Carlo simulation, radiative
recombination and radiative transitions to the ground level always follow, or, fluorescent
emissions are induced at the same place, and then, X-ray photons with appropriate
energies are generated. In this way, the recombination rate equals the photoionization
rate locally. In the case of photoexcitation, the ion in an excited state produces an X-
ray photon by one or more transitions that eventually lead to the ground level. Various
emission lines arise as results of such photoionization and photoexcitation.
For the physical processes related to H-like and He-like ions, photoionization followed
by radiative recombination and radiative transitions, and photoexcitation are taken into
account. The cross sections of photoionization and emission line probabilities from recom-
bination cascades are needed for photoionization codes. Additionally, transition energies,
oscillator strength, radiative decay rate and line emission probabilities for each excited
level to the ground level are required for the Monte Carlo codes of photoexcitation. We
look up a table generated with the Flexible Atomic Code (FAC) 2. The table is used
in our code to handle physical proceses. Collisional transfers and UV photoexcitations
in the He-like ions are not included in the current version of the code. Results from
simple Monte Carlo simulations for H-like and He-like Si ions are shown in Figure 6.3
and Figure 6.4.
In our Monte Carlo codes, photoionization by ions with three or more electrons de-
excites by fluorescent emission or ejection of Auger electrons. The K-shell cross sections
of this type photoionization are applied to the fitting formulae provided by Band et al.
(1990), which include changes of K-edge energy and cross section for ions in each charge
state. Subsequent K fluorescent emissions are induced according to the K fluorescent
yields. However, in K fluorescent emission processes, the effects of ion charge states are
not included, and, X-ray energies (Larkins 1977) and fluorescent yields (Salem, Panossian
& Krause 1974; Krause 1979) for neutral atoms are applied to ions in all charge state.
Therefore, we do not take into account K-shell ionization of Li-like ions, which can lead
to the production of the forbidden line in He-like ions. For the L-shell cross sections,
we utilized EPDL97 3, which is also for neutral atoms. The L1, L2 and L3-shell cross
2http://kipac-tree.stanford.edu/fac/3http://www.llnl.gov/cullen1/photon.htm, and distributed with Geant4 low energy electromagnetic
65
Figure 6.3: A result of a Monte Carlo simulation. Emission lines from a cloud
made of only H-like ions of Si are shown. The column density of H-like Si
is 1016 cm−2. The electron temperatures are 2 eV, 5 eV, 10 eV and 20 eV
from the top to the bottom. The widths of RRCs change as a function of the
electron temperatures.
66
Figure 6.4: A result of a Monte Carlo simulation. Emission lines from a cloud
made of only He-like ions of Si are shown. The electron temperature is 5 eV.
The column densities of He-like Si are 1014 cm−2, 1015 cm−2, 1016 cm−2 and
1017 cm−2 from the top to the bottom. The amount of emission is increased
as a function of the column densities. The ratios of He-like triplet lines also
change with to the column density.
67
sections are taken into account for the ions with three, five, and six electrons, respectively.
Additionally, we do not include L fluorescent emissions for any ions.
For Compton scattering, we considered only scattering by unbound electrons. The
differential cross section given by the the Klein-Nishina formula (eq. 2.16) and the total
cross section shown in eq. 2.17 are taken into account. The Compton Doppler effects due
to an electron velocity according to Maxwellian energy distribution with a temperature
are calculated in our code.
We took Doppler shifts due to stellar winds into account for all of the physical pro-
cesses. When a photon comes into a region, we calculate cross sections of all physical
processes from the photon energy in the co-moving frame with the stellar wind. Then,
if a physical process is selected and any secondary photons are generated, energies and
directions of the photons are converted to the rest frame. An example result of a simple
Monte Carlo simulation for the Doppler shift is shown in Figure 6.5.
package
68
500 km/s
Si Cloud(H-like 50%,
He-like 50% )
(1)
(2)
(3)
Figure 6.5: A example result of a Monte Carlo simulation for the Doppler
shift. Emission lines from a moving Si cloud consisting of 50% H-like ions and
50% He-like ions are shown. The velocity of the cloud is 500 km s−1. The
shift of line energy change as a faction of the direction to the line of sight.
69
Chapter 7
Discussion on Vela X-1
7.1 Ionization Structure of the Stellar Wind in Vela
X-1 System
One of most important features of the Vela X-1 observations with Chandra is the precise
measurement of line intensities with a high resolution instrument, HETGS. The intensities
of strong lines such as the H-like Lyαs and the He-like triplets from three different location
in the orbit provide us an important clue to study the physical condition and the spatial
structure of the stellar wind near the neutron star, because the intensities of the observed
lines are actually determined from the ionization structure, e.g. the distribution of ion
abundance and the ion density in the wind. First, we try to find the distributions that
could account for the observed line emissions, both the absolute intensities and the ratios
of the intensities at different phase.
As already discussed in Chapter 2, the wind density can be expressed as
n(r) =M∗
4πµmpv(r)r2, (7.1)
where µ is the gas mass per hydrogen atom, and µ = 1.3 for cosmic chemical abundances.
Once the mass loss rate and the velocity profile are provided, the map of the wind density
can be calculated. For the calculated density distribution and the X-ray luminosity from
the neutron star, we obtain the map of the ionization structure, which controls the line
emission. Here, we adopt a forward method to find the structure. Namely, we simulate the
HMXBs based on a set of parameters that describes the Vela X-1 system with different
mass loss rates. The simulation gives us line spectra from Vela X-1 corresponding to
the phase of the observation. By changing the mass loss rate, we try to find the most
appropriate number that reproduces the observational results.
The parameters used in the Vela X-1 calculations and Monte Carlo simulations are
listed in Table 7.1. The X-ray radiation from the neutron star is modeled based on the
parameter determined from the fits to the observed spectra in the phase 0.25 and in
the phase 0.5. Since no change in the average intrinsic luminosity is observed between
70
Table 7.1. Adopted parameters for the Vela X-1 simulation
Parameter Value Reference
Geometry · · ·Binary Separation D 53.4 R¯ van Kerkwijk et al. (1995)
Companion Star Radius R∗ 30.0 R¯ van Kerkwijk et al. (1995)
Stellar Wind · · ·Velocity Structure v(r) v∞(1−R∗/r)β Castor, Abbott & Klein (1975)
Terminal Velocity v∞ 1100 km s−1 Prinja et al. (1990)
β 0.80 Pauldrach, Puls & Kudritzki (1986)
Mass Loss Rate M [M¯ yr−1] (0.5, 1.0, 1.5, 2.0) × 10−6 (a variable parameter)
Metal Abundance (Z > 2) 0.75 comic for typical OB-stars
(Bord et al. 1976)
X-ray Radiation · · ·Luminosity(0.5–20 keV) 3.5 × 1036 erg s−1 This observation
(1.6 × 1036 erg s−1 (0.5–10 keV))
Spectrum Shape Power-Law (Γ = 1.0) This observation
Energy Range 13.6 eV – 20.0 keV
the phase 0.25 and the phase 0.5 observations, we assumed that the luminosity stays
unchanged in the three orbital phases. The power-law spectrum with a photon index
Γ = 1 is assumed to be extended up to 20 keV, which is the cut-off energy detected
by past hard X-ray observations such as Ginga (Makishima et al. 1999) and RXTE
(Kreykenbohm et al. 1999). The 0.5–20 keV X-ray luminosity of 3.5 × 1036 erg s−1 in
simulations is derived from the observed 0.5–10 keV luminosity of 1.6 × 1036 erg s−1.
We assume that the velocity structure of the stellar wind is followed by the formulation
of the CAK-model (eq.(2.1)). We use the 1100 km s−1 terminal velocity of the stellar
wind is given from the results of Prinja et al. (1990) and the fixed β of 0.80 as expected
from the assumption by Pauldrach, Puls & Kudritzki (1986). In the following simulation,
we simulate the cases for four mass loss rates; 5.0 × 10−7, 1.0 × 10−6, 1.5 × 10−6 and
2.0 × 10−6 M¯ yr−1.
In order to handle the three dimensional distributions of physical parameters in the
vicinity of the neutron star and the companion star, the calculations and the simulations
are performed under the geometry divided into the grid. The grids used in the calculation
of the ionization structure and in the Monte Carlo simulation are shown in Figure 7.1.
A smaller grid is used for regions closer to the neutron star so that we can minimize
the possible error caused by the rapid change of parameters. In the calculation of the
71
ionization structure, all elements in the region hatched by a shadow in the figure are
assumed to be neutral, because the X-rays from the neutron star are blocked by the
companion star.
7.2 The Ionization Structure
Based on the parameter listed in Table 7.1 and the code described in § 6.2, we calculate
how the photoionization by the neutron star radiation is related to the amount of the
material, which surrounds the neutron star. From the calculations, an electron temper-
ature map and relative ionic abundance maps for 140 ions (H, He, C, N, O, Ne, Mg, Si,
S, Ar, Ca, and Fe) are obtained for each mass loss rate. Figure 7.2–7.4 show parts of our
results for H-like Si.
In order to predict the intensities of the emission lines from the ionized ions, we
need to calculate the wind density and the ionization abundance at each grid point.
Figure 7.2 shows maps of relative abundances of H-like Si ion at different mass loss rates.
As clearly visualized in the figure, when the mass loss rate becomes higher the H-like
Si is more pronounced in the region closer to the neutron star. This can be explained
by the fact that the recombination rate is higher and the X-rays are more absorbed
when the density becomes higher. Figure 7.3 shows the distribution of the number
density of H-like Si (nSiH−like), which are given by multiplying the relative abundance of
H-like Si to the number density of Si ions in the region. Maps of nSiH−like/r2ns, where
rns is the distance from the neutron star, are shown in Figure 7.4. Since the cross
section of the photoionization of H-like Si is proportional to nSiH−like and the X-ray flux
injected into the grid is approximately proportional to 1/r2ns, nSiH−like/r
2ns corresponds
to the photoionization rate. Under the condition of the photoionization equilibrium, the
photoionization rate is balanced with the recombination rate. Since the rate is equal to
the emissivity of X-ray photons that produce emission lines, maps given in Figure 7.4
show the emission site of X-ray lines related to H-like Si.
According to the above calculations and calculations for other ions that are located
at different ionization degree, a large fraction of emission lines from highly ionized ions
such as H-like Si are produced in the region between the companion star and the neutron
star. This tendency is much more clear for the case of higher mass loss rate. Importantly,
this is the region where the companion star obscures during the eclipse phase. Therefore,
the mass loss rate is very sensitive to the ratio of line fluxes between phase 0.5 and the
eclipse, because the area of the region becomes larger when we increase the mass loss
rate.
If a different terminal velocity is used for the velocity profile, another mass loss rate
would come out for the same ionization structure. Since the density structure is propor-
tional to M∗/v∞, if we increase both the mass loss rate and the terminal velocity by a
factor of two, the ionization structure is identical to the original one.
72
Companion StarNeutron Star
Shadow Region 4 x 1011 cm
2.44 x 1013 cm
12.4
x 1
01
3 c
m
Companion Star Neutron Star
2.1 x 1013 cm
Figure 7.1: Vela X-1 geometries in the calculation of the ionization structure
(top) and in the Monte Carlo simulation (bottom).
73
-2 0 2 4 6 8 10
0
2
4
6
8
10
12
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
-2 0 2 4 6 8 10
0
2
4
6
8
10
12
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
-2 0 2 4 6 8 10
0
2
4
6
8
10
12
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Abundance for
all
Si
x [1012 cm] x [1012 cm] x [1012 cm]
y[1
01
2 c
m]
Companion
Star
Shadow
Neutron
Star
Figure 7.2: The map of Si H-like ion abundance for all charge state Si.
-2 0 2 4 6 8 10
0
2
4
6
8
10
12
0
1
2
3
4
5
6
7
8
9
10
-2 0 2 4 6 8 10
0
2
4
6
8
10
12
0
1
2
3
4
5
6
7
8
9
10
-2 0 2 4 6 8 10
0
2
4
6
8
10
12
0
1
2
3
4
5
6
7
8
9
10
x [1012 cm] x [1012 cm] x [1012 cm]
y[1
012 c
m]
Companion
Star
Shadow
Neutron
Star
Density [10
4 c
m-3
]Figure 7.3: The density map of Si H-like ion.
-2 0 2 4 6 8 10
0
2
4
6
8
10
12
0
1
2
3
4
5
-2 0 2 4 6 8 10
0
2
4
6
8
10
12
0
1
2
3
4
5
-2 0 2 4 6 8 10
0
2
4
6
8
10
12
0
1
2
3
4
5
x [1012 cm] x [1012 cm] x [1012 cm]
y[1
01
2 c
m]
Companion
Star
Shadow
Neutron
Star
De
nsity/r
ns2 [
10
-20 c
m-5
]
Figure 7.4: The map of nSiH−like/r2ns, where nSiH−like is the density of H-like
Si, and rns is the distance from the neutron star. This value corresponds to
the ionization rate and the recombination rate.
74
Table 7.2. Summary of Si Lyα line in the Vela X-1 spectra.
Intensity in the phase 0.50 Intensity in the eclipse Intensity ratio
(photon cm−2 s−1) (photon cm−2 s−1) (the phase 0.50/eclipse)
2.38 × 10−4 2.32 × 10−5 10.3 ± 1.3
(2.23–2.52) × 10−4 (2.07–2.59) × 10−5
7.3 Estimate of the Mass Loss Rate of the Stellar
Wind
In order to find an ionization structure of the stellar wind that can consistently explain
the spectrum of Vela X-1 taken at three different phases, we try to estimate the mass
loss rate by a forward method. In this method, photons from the central neutron star are
transported one by one in the space defined by the map of ionization structure describe
in the previous section. Then we compare results related to line emissions which are
collected from the simulated events with the results obtained from the actual observation.
In order to allow a comparison with high accuracy, we focus on the the Lyα lines from
H-like Si in phase 0.50 and eclipse. Both the absolute intensity at each phase and the
ratio between the two phases are used for the comparison. Observed Si Lyα parameters
derived in Chapter 4 are summarized in Table 7.2.
Monte Carlo simulations are performed for each mass loss rate. The ionization struc-
ture and the distribution of electron temperature are calculated by following the prescript
described in § 7.2. In order to select photons that come out from the region of stellar
wind and reach to the earth, we use the angle (θ) of the momentum vector of photons
with respect to the line defined by the center of companion star and the neutron star
(see Figure 7.5). If θ < 10, the photons are classified into the phase 0.50 photons, and
if 170 < θ < 180, then, the photons are categorized as the photons in the eclipse. In
this calculation, photons directly coming from the neutron star are neglected since only
the emission lines are of interest.
Figure 7.6 shows spectra obtained from the simulations in the energy range from 1.0
keV to 2.28 keV for a mass loss rate of 1.0 × 10−6 M¯ yr−1 at phase 0.5 and the eclipse.
All emission lines from highly ionized ions of Si, Mg, Ne and so on are clearly seen in the
spectra simulated for two phases.
Although many emission lines are resolved in the Chandra observations, we only use
the Lyα line from H-like Si for the estimation of the mass loss rate because the energy
of these line is sufficiently high and the possible errors caused by systematics of the
absorptions can be minimized in comparison with other low energy lines. If there exists a
75
θ
Companion Star
Neutron Star
Escaped Photon
Momentum Vector
Figure 7.5: The definition of θ.
Figure 7.6: Spectra obtained from the Monte Carlo simulations for the phase
0.50 (left) and the eclipse (right). The mass loss rate of the stellar wind is
1.0 × 10−6 M¯ yr−1. The number of Si Lymanα photons (2.005 keV) are 99
and 25 in the phase 0.50 and in the eclipse, respectively.
76
fluctuation of 1 × 1021 cm−2 in localized absorptions, the change of the Si Lyα intensity is
estimated to be smaller than 5%. Additionally, in our Monte Carlo simulation, emission
lines from He-like ions have uncertainties because we do not include the behaviors of
emission lines from He-like ions such as collisional transfers, UV photoexcitations in He-
like ions, and forbidden line productions by Li-like ions.
The intensity ratio of Si Lyα between phase 0.5 and eclipse is shown in Figure 7.7.
The points with errors are results of the simulation, and the horizontal lines show the
range of observed value. As expected from the discussion in § 7.2, the ratio becomes
larger as the mass loss rate is increased. The intensities of the Si Lyα in the phase 0.5
and in the eclipse are shown in Figure 7.8. The number of photons obtained with the
simulation is multiplied by a factor of:
LX
4πd2
/ (Esim
Ω
4π
)(7.2)
where LX is the luminosity derived from the observation, d is the distance to Vela X-1,
Esim is the total energy of incident photons in the Monte Carlo simulation and Ω is the
solid angle of objective momentum directions for escaped photons (= (2π (1− cos 10))),and then, is converted into an intensity. From these three plots in Figure 7.7 and Fig-
ure 7.8, the mass loss rate is estimated to be (1.5–2.0) ×10−6M¯yr−1.
The estimated mass loss rate of the stellar wind is consistent with the observed X-
ray continuum luminosity. If Mns = 1.7M¯ (van Paradijs et al. 1977; Barziv et al.
2001), Rns = 10 km, vrel = 640 km s−1 (vwind = 570 km s−1, vorbit = 300 km s−1),
D = 53.4R¯ and M∗ = 1.5 × 10−6M¯yr−1 are applied to eq.(2.6), an X-ray luminosity
of LX = 4.7 × 1036 erg s−1 is obtained, which agrees with the observed luminosity of
3.5 × 1036 erg s−1 within a factor of 2.
7.4 Reproduction of the Entire Spectrum
By using the estimated mass loss rate of 1.5 × 10−6 M¯ yr−1, we further perform Monte
Carlo simulations to generate a spectrum spanning the whole energy band covered by
HETGS for the three orbital phases. The criteria to make model spectra in three phases
from Monte Carlo events are as follows. Photons with the θ of 0–10, 85–95and 170–180, are selected and are classified into the photons of phase 0.50, phase 0.25 and eclipse,
respectively. Then, the energy distribution of photons in each phase is accumulated
to a histogram to produce the model spectrum. However, since the absorption of the
continuum component is observed in phase 0.50, we multiply the absorption factor for
photons directly coming from the neutron star in the case of phase 0.50. An NH of
1.7 × 1023 cm−2 is applied, which is subtracted the absorption of the stellar wind from
the observed NH (1.85× 1023 cm−2). Additionally, for the phase 0.25, the model spectrum
is scaled by a factor ((1− cos 10)/2 cos 85) in order to correct for the solid angle.
77
Figure 7.7: Intensity ratio of Si Lyα between the phase 0.5 and the eclipse. The
data is derived from the Monte Carlo simulations, and the error corresponds
to a 1σ Poisson error due to a limited number of trials. The horizontal lines
show the range of the observed value.
Figure 7.8: Simulation results of the Si Lyα intensity for the eclipse (left)
and for the phase 0.50 (right). The horizontal lines show the ranges of the
observational results.
78
Figure 7.9: Monte Carlo simulation spectrum for the mass loss rate of
1.5 × 10−6 M¯ yr−1. The three panels show the spectra in the phase 0.25, in
the phase 0.5 and in the eclipse, in order from the top.
Figure 7.9 shows the Monte Carlo simulation spectra in the three orbital phases. These
spectra are multiplied by the effects of inter-stellar absorption (NH = 6 × 1021 cm−2),
and are convolved with the response of the HETGS for comparison with the observed
spectra.
Figure 7.10 shows both the observed spectra and the simulated model spectra above
2 keV. The normalization of the simulation models are fixed between the three phases
assuming that the X-ray luminosity does not change. Since we assumed a continuum
spectral shape derived from the observation data, the line free of the spectra in the phase
0.25 and the phase 0.50 are well-fitted to the data. Not only in the direct component
observed in the non-eclipse phase well-fit, but the scattered-dominant spectrum in eclipse
is also well reprocessed.
The observed spectra of the emission line region are shown parallel with the simulation
spectra in Figure 7.11 and Figure 7.12 for phase 0.50 and eclipse, respectively. The
79
Figure 7.10: Comparison of the simulation spectra with observed data above
2 keV. The normalization of the simulation models are fixed among the three
phases models, assuming that the X-ray luminosity does not change. The
simulated models shown in Figure 7.9 are multiplied by the absorption effects
due to inter stellar gas (NH = 6 × 1021 cm−2), and then, convolved with the
response of the instruments.
80
simulation spectra match well the emission lines from H-like, He-like and neutral ions,
as well as the radiative recombination continuum emission. It is noted that the emission
lines from Li-like or lower charge state ions, which are seen in observed spectra, are not
reproduced in the simulation spectra, because such ions are not included in the simulation.
The ratios of simulated line intensities to observations are plotted for the 5 σ detected
lines from the highly ionized ions in Figure 7.13. All line intensities obtained with the
simulation are consistent with those of the observations to within a factor of 3.
81
Figure 7.11: The spectra in the phase 0.50. Upper two panels show observation
data obtained with MEG and the Monte Carlo data with the MEG response.
Lower two panels are for those for the HEG.
82
Figure 7.12: Comparison of spectra between the Monte Carlo simulation and
the observation in eclipse.
83
Figure 7.13: Plots of intensity ratios of the simulated lines to the observed
lines. Each filled circle shows the data in the phase 0.50, and each open circle
shows that in the eclipse. All data fall within the range of a factor of 3.
84
Figure 7.14: The blown-up spectra of the iron Kα region. The data show the
observation results obtained with the HEG. The lines show the Monte Carlo
models, which include iron fluorescent X-rays only from the stellar wind.
7.5 Diagnostics by Iron Kα Lines
Iron fluorescence Emission lines give information about the distribution of cold matter
around the X-ray source. Figure 7.14 shows the blown-up spectra of the iron Kα lines at
the three orbital phases, together with the models obtained with the simulations described
in the last section. In eclipse, the iron Kα line intensity calculated from the simulation is
consistent with the observed one. Therefore, we can attribute the iron Kα line observed
in the eclipse to the fluorescence by the stellar wind, which is distributed in the Vela X-1
system. On the other hand, the contributions from the stellar wind are not sufficient to
explain the observed intensity of Kα line in the other two phases. The equivalent widths
of the simulations are only 4 eV and 11 eV in phase 0.25 and in phase 0.50, whereas the
observed values are 51 eV and 116 eV, respectively.
As an obvious source of the additional line production, we firstly estimate the con-
tribution from the surface of the companion star by means of a simple Monte Carlo
simulation. By adopting the geometrical parameters listed in Table 7.1, we have ob-
tained iron Kα equivalent widths of 29 eV and 65 eV for phase 0.25 and phase 0.50,
respectively. In this simulation, we assume that the metal abundance of the companion
star is 0.75 cosmic. Thus, the stellar wind and the companion surface add up together to
explain the equivalent widths of 33 eV (phase 0.25) and 76 eV (phase 0.50). The observed
values are still in excess, by 18 eV and 40 eV at phase 0.25 and 0.5, respectively.
At phase 0.50, additional absorption of NH = 1.7 × 1023 cm−2, relative to phase 0.25,
is observed in the continuum spectrum. This suggests that a cold cloud partially covers
85
Solid Angle
Ω
NH = 1.7 x 1023 cm-2
Neutron Star
Cloud
Phase 0.50Phase 0.25
Figure 7.15: Geometry for Monte Carlo simulation to calculate the iron Kα
equivalent width from a local cloud.
the neutron star, and the effects of the cloud is enhanced at phase 0.50. We then expect
that the remaining Fe-K line photons are produced in this cloud, as already pointed out
by Inoue (1985) using the Tenma data.
In order to estimate the contribution of the cloud to the iron line production, we
performed a Monte Carlo simulation for the partially covered cloud. Figure 7.15 shows
the geometry of the simulation. The thickness of the cloud is taken to be NH = 1.7 ×1023 cm−2, and a uniform density is assumed. The cloud is assumed to be neutral, and
its metal abundance is set to 0.75 cosmic. Firstly, the energy of the escaped photons
from the cloud are accumulated to make spectra if the direction of photons satisfy the
condition for one of the three phases. Secondly, the equivalent width of the Fe Kα line
is calculated from the spectra for each phase.
Figure 7.16 shows the relation between the covered solid angle of the cloud and the iron
line equivalent width, calculated according to this method. Thus, the missing equivalent
widths in both orbital phases (18 eV at phase 0.25 and 40 eV at phase 0.50) can be
explained if the cloud covers 25–40 % of the solid angle viewed from the neutron star.
This configuration is consistent with the fact that the spectrum observed at phase 0.25
does not show such a heavy absorption and that we do observe emission lines of highly
ionized ions from the region between the neutron star and the companion star. Sato et
al. (1986a) have shown that the gradual increase of average absorption column density
were seen from NH ' 1 × 1022 cm−2 at orbital phase of 0.2 to NH ' 3 × 1022 cm−2 at
orbital phase of 0.9 in Tenma observations. This may indicate the existence of the cloud
following the orbiting neutron star (”tailing cloud”), which would be consistent with our
86
Figure 7.16: Relation between the covered solid angle and the equivalent width
of the iron Kα line, calculated with a Monte Carlo simulation. The thickness
of the cloud is NH = 1.7 × 1023 cm−2, with a uniform density. Open circles
show the case of phase 0.25, and filled circles phase 0.50.
results.
The enhanced absorption at orbital phase 0.50, and the local cloud responsible for the
iron line production, may be attributed to the “accretion wake”, which is produced when
the stellar wind flow influenced by a variety of competing effects, including gravitational,
rotational, and radiation pressure forces and X-ray heating. Sawada, Matsuda & Hachisu
(1986), Blondin et al. (1990), Blondin, Stevens & Kallman (1991) and Blondin (1994)
carried out numerical simulations of the stellar wind behavior near an accreting neutron
star, and suggested the presence of such density enhancements.
87
Figure 7.17: The line profiles of Si H-like Lyα with HEG (left) and Mg H-like
Lyα with MEG (right). The blue shows in the phase 0.50, and the red appears
in the eclipse. The observed data are shown in the histograms, and the Monte
Carlo simulation models are drawn in the smooth lines. The simulation models
are also convolved with the each HETGS responses.
7.6 Doppler Effects of the Stellar Wind
The energy shifts and broadening of emission lines due to Doppler effects are new in-
formation obtained only with the high energy resolving power by HETGS. The velocity
information derived from the shift of the central energy of lines gives strong constraints
on the location of the line emission, and can be used as a probe to investigate the stellar
wind dynamics.
7.6.1 Difference between the observation and the simulation
We firstly compare the observed line profiles with the spectra obtained from Monte Carlo
simulation of the stellar wind described in § 7.4. Figure 7.17 shows the line profile
obtained from the simulation together with the deta. The simulated line profiles are
convolved with the spectral responses. Despite the fact that the directions of the Doppler
shifts are same for the observations and simulations, the amount of the velocity shift in
the data are smaller than that estimated from the simulation. Figure 7.18 shows the
velocity shift for all emission lines from highly ionized ions in the spectrum. In the
observation, the shifts between the phase 0.50 and the eclipse (∆v) range in ∼ 300–
600 km s−1. However, the ∆v derived from the simulations are ∼ 1000 km s−1, which is
approximately twice as large when compared at the neutron star (∼ 570 km s−1).
88
Figure 7.18: The plot of velocity shift for emission lines from highly ionized
ions. The symbols of circles show the data from the observations, and, the
squares are data derived from the Monte Carlo simulations. Filled symbols
and open symbols show values in the phase 0.50 and in the eclipse, respectively.
7.6.2 Interaction between X-rays and the stellar wind
Since the velocity derived from the Doppler shifts of X-ray lines should reflect the actual
velocity of the material that emit X-rays, we investigate the possible reasons why the
velocity profile used in the simulation does not reproduce the observed Doppler shift.
To this end, we reexamine the acceleration mechanisms of plasmas in stellar winds of
OB-stars. The forces which material in the stellar wind are affected are the gravity, the
gas pressure, and the radiation force by the OB-star. In the CAK-model, the velocity
structure is calculated by taking these forces into account (Castor, Abbott & Klein 1975).
In the stellar wind of OB-stars, the most dominant force is the radiation force due to
the large number of resonance lines in UV range, a large fraction of which is attributed
to lines related to L-electrons in ions of C, N and O, because of their large chemical
abundances.
In HMXB, strong X-ray radiation from the central neutron star are expected to ionize
the material in the stellar wind and, therefore, weaken the acceleration around the neutron
star. If C, N and O are ionized to He-like or higher by photoionization process and lose
their L-electrons, the resonance absorptions producing the acceleration in the stellar
wind become ineffective. As a result, the stellar wind at the site of the X-ray emission
should have lower velocity than that predicted by the CAK-model. The velocity profile
suggested by the UV observation would depend on the environment of the UV emitting
region, while the observed X-ray lines comes from a much deeper region near the neutron
star. This could also explain the discrepancy. The effect of X-ray irradiation on such line-
89
Figure 7.19: The velocity plot of the CAK-model stellar wind (v∞ =
1100 km s−1, β = 0.8) as a function of the distance from the center of the
companion star (left). The right panel shows the relation between the force
for a particle in the stellar wind and the distance. The force is numerically
derived from the CAK-model velocity structure.
driven stellar wind in HMXB systems has been studied only theoretically by MacGregor
& Vitello (1982) and Masai (1984) or on the basis of UV spectral observations (Kaper
et al. 1993).
7.6.3 One dimensional calculation of the velocity structure
In order to study the modification of the stellar wind velocity due to X-ray ionization, we
performed a one dimensional calculation of the velocity structure on the axis connecting
the companion star center and the neutron star. In the calculation, we make two sim-
plifying assumptions. One assumption is that the only force to make the CAK-model
velocity structure is due to the UV resonance absorption. Figure 7.19 shows the velocity
structure of the CAK-model and the relation between the force and the distance, which
is numerically derived from the CAK-model velocity structure. The other assumption is
that the force is proportional to the number of C, N and O ions that have more than
one L-electrons. Therefore, the acceleration of the stellar wind becomes ineffective in the
region where the C, N, O ions exist as He-like, H-like, or fully ionized ions.
If a velocity structure is given, densities for all point is determined, and then, we
can calculate the ionization structure by using our software described in § 6.2. The
obtained ion distribution of C, N and O leads to the radiation force structure, and, on the
basis of the force, another velocity structure is calculated. In other words, the velocity
90
structure determines the ionization structure, and, the ionization structure affects the
velocity structure. Therefore, in order to obtain a self-consistent solution of the velocity
structure, we iterate the calculations as follows:
1. start from the velocity structure (v′1(r) = v0(r) (CAK-model)), and, calculate a
force structure (f1(r)), then, obtain v1(r).
2. start from v′2(r) = v1(r), and, calculate f2(r), then obtain v2(r).
3. start from v′3(r) = (v1(r) + v2(r))/2, and, calculate f3(r), then obtain v3(r).
4. start from v′4(r) = v3(r), and, calculate f4(r), then obtain v4(r).
5. start from v′5(r) = (v3(r) + v4(r))/2, and, calculate f5(r), then obtain v5(r).
6. start from v′6(r) = v5(r), and, calculate f6(r), then obtain v6(r).
The obtained velocity structures (v0(r), v1(r), v2(r), v3(r), v4(r), v5(r) and v6(r)) are
plotted in Figure 7.20. The stellar wind velocity at the point of the neutron star tends to
have a smaller value of∼ 180 km s−1 than the initial velocity∼ 570 km s−1 of CAK-model.
From the reduced velocity, a Doppler shift difference ∆v ∼ 360 km s−1 is expected, which
is almost equal to the observed values.
Further considerations will be needed to conclude the velocity of this mechanism.
For example, 3-dimensional gas flows including gas pressure forces not for only radial
directions but circumferential direction, and time evolution due to the orbital motion of
the neutron star can be important. However, it is evident from our simple calculations
that effects of photoionization by the X-ray radiation can make the stellar wind of the
X-ray line emission region slower by a factor of 2–3.
In addition to the X-ray photoionization effects, the gravitational force and the orbital
motion of the neutron star can be responsible for the small Doppler shifts in comparison
with the CAK-model prediction. This is because the two effects can disperse the flow of
the stellar wind, and make a density enhancement (Blondin et al. 1990; Blondin, Stevens
& Kallman 1991; Blondin 1994). This enhancement would lead to the heavy absorption
seen in the spectrum in phase 0.50. The velocity of the stellar wind in the affected region
should become smaller than that expected from CAK-model as discussed in Blondin et
al. (1990), Blondin, Stevens & Kallman (1991), and Blondin (1994). Therefore, if the
X-ray emission lines are generated in this region, it can explain the discrepancy.
91
Figure 7.20: The results of 1 dimensional calculations of the tellar wind veloc-
ity on the axis between the companion star and the neutron star. The mass
loss rate is assumed to be 1.5 × 10−6M¯yr−1. The flat velocity region in the
plot is corresponds to the highly ionized region.
92
Chapter 8
Discussion on GX 301−2
The X-ray spectra of GX 301−2 is characterized by heavily absorbed continua and fluo-
rescent lines from ions in low charge states. In contrast to the Vela X-1 cases, no emission
line from highly ionized ions is observed. Additionally, thanks to high energy resolving
power of HETGS, we have detected the remarkable Compton shoulder. In this chapter,
we will discuss physical states in the GX 301−2 system by using the observed spectral
features as probes. We will also consider an unified picture of the environment of HMXBs.
8.1 Compton Shoulder in the PP Phase
As shown in Figure 5.5, we have detected a fully-resolved Compton shoulder of the iron
Kα line during the PP phase observation. The Compton shoulder reflects the physical
conditions of the scattering medium. Therefore, we can use this profile as a probe for
diagnosing the matter around the X-ray source. In this section, we will investigate the
properties of the Compton shoulder and discuss what it can provide.
8.1.1 Time variability
We have observed not only the Compton shoulder feature, but also a time variability in
its profiles during the PP phase observation. The X-ray light curve of the PP phase in the
1.0–10.0 keV band extracted from the HEG events is shown in Figure 8.1. An X-ray out-
burst is seen in the first half of the observation. Hence, we chose to divide the data into the
first and second halves as indicated by the vertical dotted line, and extract spectra from
each data segment separately. The observed 2–10 keV flux is 13.2 × 10−10 erg cm−2 s−1
and 9.0 × 10−10 erg cm−2 s−1 during the first and second halves, respectively. The iron
Kα line spectra divided into two periods are shown in Figure 8.2. Changes in the shape
of the Compton shoulder, as well as in the shoulder flux relative to the un-scattered line
flux, is clearly visible. The equivalent widths of the iron Kα lines including the shoulders
are 643 ± 20 eV and 486 ± 18 eV for the first and second halves, respectively.
93
count
s–1
Time [ksec]
Light Curve
Figure 8.1: The light curve of GX 301−2 in the pre-periastron (PP) phase
observed with the Chandra HETGS in the band 1–10 keV (± 1 order of HEG).
Energy[keV] Energy[keV]
cou
nt
s–1 k
eV–1 (a)First
20 ksec
(b)Second
20 ksec
6.24 keV 6.24 keV
Figure 8.2: The spectra of the iron Kα region (6.0–6.6 keV) for the first and
the second halves of the observation as defined by the dotted vertical line
shown in Figure 8.1.
94
8.1.2 Modeling with Monte Carlo simulation
The Compton shoulder can be used to infer various physical parameters that characterize
the scattering medium. The flux ratio of the shoulder to the line is determined by the
metal abundance and the optical thickness of the scattering cloud. Its energy distribution,
on the other hand, is sensitive to the temperature and the geometrical distribution of
the scattering electrons. A discernible change in the profile shown in Figure 8.2 implies
that these physical parameters are variable between the first and second halves of the
observation.
In order to obtain some quantitative information from the spectra, we have con-
structed a Monte Carlo simulator to compute the emergent spectrum from an X-ray
source surrounded by a cloud. We assume a spherical distribution of material and a
constant density cloud. The cloud consists of H, He and astrophysically abundant met-
als (C, N, O, Ne, Na, Mg, Al, Si, S, Cl, Ar, Ca, Cr, Fe and Ni), and all of the metal
abundances (Z > 2) are allowed to vary together relative to the cosmic values of Feldman
(1992). We account for photoionization and subsequent fluorescent emission, as well as
Compton scattering by free electron. The angular-dependence of the Compton scattering
cross section is fully accounted for and the electrons are assumed to have a Maxwellian
energy distribution. The photons may suffer multiple interactions and are traced until
they completely escape from the cloud. The energy distribution of the emergent photons
are then histogrammed to produce a spectrum.
Figure 8.3 shows some of the results from the simulations for the iron line and its
Compton shoulder with varying hydrogen column density (NH) and electron temperature
(kTe). The original iron Kα1 and Kα2 photons are assumed to be distributed according
to the K-shell photoionization rate at each radius from the central continuum source.
This distribution is also calculated using the same simulator, in which a power-law X-ray
source with a photon index of 1.0 is assumed.
In the upper panels of Figure 8.3, one can see an increase in the scattered flux relative
to the narrow line flux as NH is increased. Photons between 6.24 keV and 6.40 keV are
due primarily to single-scattered photons, and the component below 6.24 keV results from
multiple-scattering, which are not negligible even at moderate optical depths. Figure 8.4
shows the intensity ratio of the shoulder to the narrow line as a function of NH. In the
figure, the dependence on the metal abundance is also presented. The intensity ratio of
the shoulder to the line increases as the metal abundance is decreased, because the larger
relative cross section of Compton scattering to absorption is attained at the smaller metal
abundance.
The lower panels of Figure 8.3 show the temperature dependence of the shape of the
Compton shoulder. Larger smearing effects are seen at higher kTe. Therefore, if a square-
shouldered profile is observed, it means that electrons of the scattering region have low
temperatures.
95
0 eV 1 eV 2 eV 5 eV
2x1023cm–2 5x1023cm–2 1x1024cm–2 2x1024cm–2
Figure 8.3: Dependence of the iron Kα line profile on the hydrogen column
density (NH) and the electron temperature (kTe). The upper panels show the
variation of the iron Kα line and its shoulder as a function NH for a fixed kTe
at 0 eV. The lower panels show the variation as a function of kTe between
0 eV and 5 eV for a fixed NH at 1 × 1024 cm−2. In these simulations, the
metal abundances were assumed to be 0.75 times of the cosmic value (Feldman
1992).
96
0.5 cosmic
0.7 cosmic
1.0 cosmic
Figure 8.4: The relations between the flux ratio of the Compton shoulder
to the un-scattered line and the hydrogen column density. As the hydrogen
column density is increased, the Compton shoulder becomes larger relative
to the narrow line component. The colors mean the difference in the metal
abundance. The blue, the green and the red plot show the cases of 0.5, 0.7
and 1.0 times of the cosmic metal abundance (Feldman 1992). As the metal
abundance decreases, the Compton shoulder becomes larger.
97
8.1.3 Spectral analysis
We perform spectral fittings based on the simulation for the iron line and the Compton
shoulder. A file of ”table models” is generated from the result of a set of the simulations
with different parameters, which is then incorporated into XSPEC v11.2. The parameters
of the model are NH, kTe, and the metal abundances. The radial dependence of the
intrinsic Kα line emissivity is fixed to what one expects from a photon index of Γ = 1.0.
We have confirmed that this assumption produces at most a 5 % error in the emergent
line profile for Γ between 0.0 and 2.0.
Metal Abundance
We first attempt to determine the metal abundances from the total PP-phase spectrum.
In doing this, we note that two independent constraints between the abundance and the
hydrogen column density are available, as described below. The first one arises from the
observed intensity ratio of the shoulder to the narrow line. For a given ratio, an increase
in column density must be accompanied by an increase in abundance (Figure 8.4), and
hence, the two parameters are correlated as shown in Figure 8.5. The other constraint
originates from the observed equivalent width of the line. In this case, the abundance
is anti-correlated with the column density. From these two constraints (see Figure 8.5),
the metal abundance is determined to be 0.65–0.82 times of the cosmic value (Feldman
1992), assuming Γ = 1.0. The slope of the seed power-law emission, however, is not
well-measured due to the limited bandpass of Chandra HETGS and its heavy absorbed
spectrum. If we allow a range in Γ of 1.0–1.5, which has been seen in previous hard
X-ray observations (Pravdo et al. 1995; Orlandini et al. 2000), the metal abundance is
determined to be 0.65–0.90 times of the cosmic value. Note that this is consistent with
that of typical OB-stars (Daflon et al. 2001).
Hydrogen Column Density and Electron Temperature
Adopting the metal abundance of 0.75 cosmic, we find the values for NH by spectral
fittings to the first and the second halves of the PP phase data, separately. The derived
values are listed in Table 8.1, and the models are shown by the lines superimposed on the
data in Figure 8.6. The difference in the observed Compton profile can be described by
a change in the column density, which results in a variation in the number-of-scatterings
distribution even at these moderate optical depths. We have also obtained upper-limits
(90 % confidence levels) to kTe of < 3.4 eV and < 0.6 eV for the first- and second-
half spectra, respectively. In other words, the observed tight and non-smeared Compton
shoulders become direct evidences for the presence of a cold and dense cloud.
The column density as inferred from the Compton profile, in fact, reproduces the
spectrum in the entire HEG bandpass for a power-law photon index of 1.0. Figure 8.7
shows the observed spectra overlaid with the simulated spectra. Reduced chi-squared
98
1.0
0.8
0.6
0.4
Meta
l A
bundance
5 10 20 5 10 20NH [1023 cm-2] NH [1023 cm-2]
First Second
Γ=1.0
Γ=1.0
Γ=1.5
Γ=1.5
Figure 8.5: Confidence contour for NH vs. the metal abundance during the
first half (left) and the second half (right). Each contour represents 68 %,
90 % and 99 % confidence level. The region between each pair of dashed lines
are the values allowed by the observed line equivalent widths of 643 ± 20 eV
(left) and 486 ± 18 eV (right) for two assumed values for the photon index
(Γ = 1.0 and Γ = 1.5). The metal abundance is determined to be 0.65–0.90
(90 % confidence range) times the cosmic value.
99
Figure 8.6: The spectra of the iron Kα region (6.0–6.6 keV) for the first and
the second halves of the observation.
values of 1.30 and 0.95 were obtained for the first and second halves spectra, respectively.
Though some residual flux still remain, the simulations, which are based on parameters
derived from the line and Compton shoulder, provide fairly good descriptions of the
broadband data.
100
Energy [keV]
count
s–1 k
eV–1
count
s–1 k
eV–1
First 20 ksec
Second 20 ksec
χχ
Figure 8.7: The spectra of GX 301−2 from 5 keV to 10 keV for the first and
second halves of the PP-phase observation. The solid lines show the Monte
Carlo models inferred from the data. In addition to the iron Kα emission
line profile, the continuum shape is also successfully reproduced with the pa-
rameters inferred from the Compton shoulder profile. The values for NH are
12.0 × 1023 cm−2 and 8.5 × 1023 cm−2 for the first and second halves, respec-
tively. A photon power-law index of 1.0 is assumed for the seed emission.
101
Table 8.1. Derived Parameters from Spectral fits of the Compton shoulder observed at
the PP phase.
NH (1023 cm−2) τCompton kTe (eV) (upper limit) χ2/ d.o.f.a
First 12.0+3.5−1.3 0.96+0.28
−0.10 0.5 (< 3.4) 65.6 / 71
Second 8.5+2.3−1.4 0.68+0.18
−0.11 0.0 (< 0.6) 82.4 / 71
Note. — Errors and upper limits designate 90 % confidence levels.
aOnly the 6.0 – 6.6 keV region has been used in the spectral fit.
102
8.2 Matter Distribution in GX 301−2
We attempt to consider the distribution of the matter, which creates heavily absorbed
continuum spectra, various fluorescent lines, and Compton shoulders. First, we inves-
tigate how the stellar wind of GX 301−2 contributes the absorption. The mass loss
rate is assumed to be 5 × 10−6 M¯ yr−1, and the velocity structure is followed by the
CAK-model with a terminal velocity of 400 km s−1 and β of 0.8. Figure 8.8 shows the
hydrogen column density (NH) integrated from the position of the neutron star to the
observer. Although the angle we are observing from (θ) is not determined exactly in the
case of GX 301−2, the observed absorptions in all three phases are too high. It cannot
be explained by assuming that the line of sight is passing close to the companion star
surface, because the three observations cover very different orbital phases. If θ = 90 is
assumed, NH of 9.0 × 1022 cm−2, 2.3 × 1022 cm−2 and 4.5 × 1022 cm−2 are derived for PP,
NA and IM, respectively, from the assumed mass loss rate. The amounts are about one
order of magnitude below the observed absorptions of 1.0 × 1024 cm−2, 3.0 × 1023 cm−2
and 6.5 × 1023 cm−2, respectively. In other words, material in addition to the flowing
stellar wind contribute 90% of the total observed absorption.
The leading candidate region where the remaining matters exist is near and around
the neutron star. Since the material is expected in all the three phases, a localized region
in the binary system can be rejected. The Compton shoulder and the whole spectrum
observed during the PP phase also indicates the presence of an almost spherically cloud
surrounding the neutron star. Therefore, we consider a situation where the neutron star
accompanied by a cold dense cloud is moving in the stellar wind of the companion star.
In order to estimate the observed spectra from this situation, we again perform the
Monte Carlo simulation. The GX 301−2 parameters used in the simulation are listed in
Table 8.2, and the grid to describe the stellar wind geometry of GX 301−2 is shown in
Figure 8.9. The concept of such a grid is the same as that in the case of Vela X-1. In
addition to the stellar wind, a cold dense cloud is located at the position of the neutron
star. The hydrogen column density of the cloud in each phase is set to the observed
NH value subtracted the estimated contribution of the stellar wind assuming θ = 90.Concerning the physical processes, photoionization by neutral elements and Compton
scattering by free electrons are taken into account. Since the emission lines from highly
ionized ions are not observed, which is different from the case of Vela X-1, physical
processes of H- and He-like ions and any ionization structures are not included in this
simulation. The simulations of photon transport are started from the neutron star, and
all photons are tracked until they either vanish or escape from the simulation region. We
accumulate the emergent photons with their momentum direction of 60 < θ < 120,and produce spectra to compare with the observed data.
Figure 8.10 shows the results of the Monte Carlo simulations for the three orbital
phases, together with the HEG observation data above 4 keV. The results in the energy
103
Neutron Star
Companion Star
Figure 8.8: The relation between the amount of the hydrogen column density
due to the stellar wind of GX 301−2 and the direction of line of sight. The
mass loss rate of the stellar wind is 5 × 10−6 M¯ yr−1. The velocity structure
is followed by the CAK-model with the terminal velocity of 400 km s−1 and
β of 0.8. The NH at θ = 90 are 9.0 × 1022 cm−2, 2.3 × 1022 cm−2 and
4.5 × 1022 cm−2 for PP, NA and IM, respectively.
104
Table 8.2. Adopted parameters for the GX 301−2 simulation
Parameter Value Reference
Geometry · · ·Binary Separation D ∼ 89 R¯ (PP)
∼ 230 R¯ (NA)
∼ 140 R¯ (IM)
Companion Star Radius R∗ 43.0 R¯ Parkes et al. (1980)
Stellar Wind · · ·Velocity Structure v(r) v∞(1−R∗/r)β Castor, Abbott & Klein (1975)
Terminal Velocity v∞ 400 km s−1 Parkes et al. (1980)
β 0.80 Pauldrach, Puls & Kudritzki (1986)
Mass Loss Rate M 5.0 × 10−6 M¯ yr−1 Parkes et al. (1980)
Metal Abundance (Z > 2) 0.75 comic from Compton shoulder
X-ray Radiation · · ·Spectrum Shape Power-Law (Γ = 1.0)
Energy Range 13.6 eV – 20.0 keV
Neutron Star
(PP)
Neutron Star
(IM)
Neutron Star
(NA)
Companion Star
8.66 x 1013 cm
Figure 8.9: GX 301−2 geometry in the Monte Carlo simulation
105
Figure 8.10: Observed data and results of the Monte Carlo simulation. The
red, the blue, and the green plots show the HEG observation data for the
PP, NA, and IM phases, respectively. The lines overlaid the data appear the
model built by the Monte Carlo simulations.
region of the fluorescent lines from Si, S, Ar and Ca are shown in Figure 8.11 with
the MEG observation data. Although the assumption is very simple, the simulations
reproduce the observed spectral features including the emission lines and continuum
shapes well.
The presence of the dense cloud around the neutron star is consistent with the absence
of emission lines from highly ionized ions in observed spectra. Outside the cloud, the ion-
ized metals cannot exist because the X-ray radiations for photoionization are heavily
absorbed. In the inner side of the cloud, there should be a highly ionized region. How-
ever, the emission lines from this region must be absorbed by the dense cloud material.
Therefore, we can never observe these emission lines.
106
Figure 8.11: Observed data and results of the Monte Carlo simulation. The
IM, NA and PP data are shown in the top, the middle and the bottom panels,
respectively. The red histograms is the MEG observation data, and the black
lines show the model made by the Monte Carlo simulations.
107
8.3 Unified Picture of HMXBs
We have investigated the matter distribution and their physical conditions for Vela X-1
and GX 301−2 using X-ray spectroscopy with high energy resolving power. In Fig-
ure 8.12, we present a conceptual picture of Vela X-1 and GX 301−2 on the basis of the
information obtained from our study. The cold and dense cloud is surrounding the neu-
tron star of GX 301−2, and prevent the stellar wind from photoionization. This situation
makes the heavily absorbed continuum, the fluorescent lines and the Compton shoulder
in their X-ray spectrum. On the other hand, the neutron star of Vela X-1 do not have
such a dense cloud obscuring over all of the directions, and its X-ray radiation ionize the
stellar wind directly. The highly ionized gases in the stellar wind produces the emission
lines by recombination and cascades. Additionally, X-ray photoionization by the neutron
star affects the flow of the stellar wind.
The two types of HMXBs can be distinguished by the presence or absence of the
cold cloud. The one is the “type I HXMB” like Vela X-1, which has highly photoionized
plasmas, and the other is the “type II HXMB” represented by GX 301−2, which has
heavy absorbers and only cold material.
A mechanism to produce such a cloud is possibly related to the efficiency of the X-ray
production. In the case of Vela X-1, the efficiency to capture matter and to convert them
into X-ray radiation is high. The luminosity calculated from eq.(2.6) is given as,
LX =(GMns)
3 M∗Rnsv4
relD2
= 4.7× 1036 erg s−1. (8.1)
Here, we assume a reasonable value for this system; Mns = 1.7M¯, Rns = 10 km,
vrel = 640 km s−1 (vwind = 570 km s−1, vorbit = 300 km s−1), D = 53.4R¯ and M∗ =
1.5 × 10−6M¯yr−1. Assuming that the X-ray spectrum extends up to ∼ 20 keV, the
observed absorption corrected X-ray luminosity is 3.5 × 1036 erg s−1, which is comparable
to the value calculated in eq.(8.1). In other words, almost all of the captured stellar wind
material is accreted onto the neutron star, producing strong X-ray radiation. On the
other hand, the observed luminosity of GX 301−2 does not reach the value calculated
from the stellar wind parameters. We can estimate the luminosity as
LX =(GMns)
3 M∗Rnsv4
relD2
= 8.3× 1036 erg s−1. (8.2)
Here, we assume a value for the IM phase as the most ordinary case; Mns = 1.4M¯,
Rns = 10 km, vrel ∼ 400 km s−1, D ∼ 140R¯ and M∗ = 5.0×10−6M¯yr−1. The observed
absorption corrected luminosity, ∼ 7.9 × 1035 erg s−1 in the energy range of 0.5–20 keV,
is about an order of magnitude lower the value in eq.(8.2).
Such accretions of matters onto a neutron star should be affected by the physical en-
vironment nearby the surface of the neutron star, such as the gravitational field, strength
of the magnetic field, and the spin of the neutron star. These physical states would show
108
their true figures in the hard X-ray spectrum. Therefore, hard X-ray observations with
high precision will become important measurements together with high energy resolution
X-ray observations.
109
Cloud(accretion wake?)
absorption
+fluorescent line
Neutron Star
Emission Region
of lines from highly
ionized ions
Stellar Wind affected
by photoionization of
the X-ray radiation
Companion Star
Stellar Wind
Stellar Wind
(low charge state)
Hard X-ray
(Heavily absorbed)
+ fluorescent X-ray
Neutron Star
+ Cloud
Companion Star
Neutron Star
Ionized gas
Cold Cloud
(fluorescent X-ray,
Compton shoulder)
Vela X-1
GX 301-2
Figure 8.12: Conceptual pictures of Vela X-1 and GX 301−2.
110
Chapter 9
Conclusion
We have observed two high mass X-ray binaries (Vela X-1 and GX 301−2) with the
Chandra HETGS. The observations have been performed at different three orbital phases
for each source. From their X-ray spectra with the high energy resolutions, the following
results have been newly obtained.
• Vela X-1
– A number of emission lines are detected and clearly resolved. The emission
lines from highly ionized S, Si, Mg, and Ne, in addition to fluorescent lines
from Fe, Ca, S, and Si ions in lower charge states are detected in the spectra
of the eclipse phase and the opposite orbital phase (phase 0.50). The narrow
radiative recombination continuum features from H-like ions of Ne are observed
in the both phases, and their widths correspond to the electron temperature of
6.6+2.5−1.8 eV and 7.4+1.6
−1.3 eV for the eclipse and the phase 0.50, respectively. These
results indicate that highly ionized plasmas driven through photoionization
exist in Vela X-1.
– Multiple Si K fluorescent lines from a wide range of charge states are detected
individually for the first time, which is evidence that there exist photoionized
plasmas in various ionization degrees in Vela X-1.
– The similar kinds of emission lines are detected in the both spectra of the
eclipse phase and the phase 0.50. The intensity ratios of emission lines in
phase 0.50 to those in the eclipse are 8–10 for lines from H-like ions and 4–7
for lines from He-like ions.
– From emission lines from highly ionized ions, Doppler shifts are observed.
The lines in the eclipse phase are red-shifted, and those in the phase 0.50 are
blue-shifted. The amount of shifts between these two orbital phases ranged in
∼ 300–600 km s−1.
• GX 301−2
111
– For all three orbital phases, heavily absorbed (NH ∼ (2–10) × 1023 cm−2)
continuum spectra are observed. The emission lines due to fluorescence of Si,
S, Ar, Ca ions in low charge states, in addition to an intense iron Kα line are
also detected in all phases. In contrast, emission lines from highly ionized ions
are entirely absent.
– In the pre-periastron phase observation, the Compton-scattered iron Kα line
profile (“Compton shoulder”) is clearly detected and fully resolved for the first
time from an astrophysical object.
In order to handle such high energy resolution spectra, we have newly constructed the
simulator on the basis of Monte Carlo method. With this simulator, we can deal with
situations, which include asymmetrical geometries and not-optically-thin media. In the
Monte Carlo part for calculations of photo transport, various physical physical processes
are considered, including processes related to highly ionized ions and Doppler effects. By
using this simulator, we have explained the observed spectra as follows.
• Vela X-1
– Assuming that the velocity structure of the stellar wind is followed by CAK-
model, we calculated the ionization structure of the stellar wind and X-ray
spectra of each phase. By using the intensity ratio of Si Lyα between phase
0.50 and eclipse, we found the ionization structure and the matter distribution,
which satisfy line intensities and continuum shapes in both phase 0.50 and
eclipse.
– However, the amount of observed Doppler shifts in the emission lines were
inconsistent with the CAK-model velocity structure, which is assumed in the
ionization structure calculations. As a main cause of this inconsistency, we
showed that photoionization effects by the X-rays slows the stellar wind veloc-
ity and changes the velocity structure. There should be a velocity structure,
which reproduces the observed Doppler shifts leaving the ionization structure
and the matter distribution. Further calculations are needed to search the
solution.
• GX 301−2
– We have demonstrated that Compton shoulders has become a new probe to
investigate the physical conditions of cold material. In fact, we derived from
the observed Compton shoulders that a cold and dense cloud is surrounding
the neutron star almost spherically.
– The geometry consisting of the CAK-model stellar wind and a cold dense cloud
surrounding the neutron star give a good explanation to the observed spectra
of GX 301−2 as the Monte Carlo simulation results.
112
Through the analysis and the consideration, we have established a new method to
investigate the physical state of the HMXBs on the basis of the high precision X-ray
spectrum. And for the different types of HMXBs, Vela X-1 and GX 301−2, we have
specified the physical conditions. GX 301−2 has a cold dense cloud surrounding the
neutron star, while Vela X-1 do not have such a cloud obscuring over all direction. This
difference is probably induced by the accreting mechanism onto the neutron star. In order
to reveal the mechanism, hard X-ray and gamma-ray observations with high precision
are needed together with X-ray spectroscopy.
113
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Acknowledgments
First of all, I would like to thank very much my supervisor Prof. T. Takahashi for his
continuous guidance throughout the five years of my graduate course. It is my pleasure
to thank Dr. M. Sako for his introducing me to HMXB analysis and his precise comment
on atomic physics and photoionized plasma physics. I gratefully thank Prof. F. Nagase
for his advice and comments on this thesis. I thank Prof. M. Ishida and Dr. Y. Ishisaki
for their contributions to discussion on HMXB’s physics. I would also express my thanks
to Prof. S. M. Kahn and Prof. F. Paerels for their suggestions. I thank Dr. K. Nakazawa
for his reading of this thesis.
Finally, I thank my family for their support and understanding.
118