UNIVERSIDAD DE CHILEFACULTAD DE CIENCIAS FISICAS Y MATEMATICASDEPARTAMENTO DE ASTRONOMIA

EMISION ANOMALA EN ONDAS CENTIMETRICAS DE LASNUBES TRANSLUCIDAS ζ OPH Y LDN 1780

TESIS PARA OPTAR AL GRADO DE MAGISTER ENCIENCIAS, MENCION ASTRONOMIA

PROFESOR GUIA:SIMON CASASSUS MONTERO

MIEMBROS DE LA COMISION:LEONARDO BRONFMAN AGUILOGUIDO GARAY BRIGNARDELLO

THOMAS L. WILSON

SANTIAGO DE CHILEMAYO2010

MATÍAS AMBROSIO VIDAL NAVARRO

ResumenLa emision de ondas centimetricas correlacionada con emision en el infrarojo lejano (Kogut

et al. 1996a), la pantalla “anomala” al CMB, se cree es debida a granos de polvo en losubicuos cirrus Galacticos. Aca presentamos datos del Cosmic Background Imager a 31 GHzde dos nubes translucidas, ζ Oph y LDN1780 con la intencion de caracterizar la pantallaanomala al CMB. Las condiciones fısicas en nubes translucidas se aproximan a las de loscirrus. Detectamos un exceso en las distribucion espectral de energıa (SED) en las dos nubesque estudiamos. La SED de ζ Oph en escalas angulares de 1 grado esta dominada por emisionlibre-libre, pero en escalas ∼ 8 arcmin hay un exceso sobre libre-libre cuando la comparamoscon datos a 5 GHz.

En LDN1780 detectamos un exceso en la distribucion espectral que puede ser ajustadousando un modelo de spinning dust. En esta nube encontramos tambien una mejor correlacioncon IRAS 60 µm y IRAC 8 µm que con IRAS 100 µm, lo que sugiere que VSGs son loscausantes de la emision en los datos de 31 GHz.

Las emisividades de radio que encontramos son muy cercanas a las de los cirrus Galacticos.Estudiar la emision anomala en nubes translucidas es entonces util para entender los cirruscomo pantallas al CMB.

Contents

1 Introduction 2

1.1 Galactic foregrounds at GHz frequencies . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Classical emission mechanisms . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Anomalous emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

1.3 Cirrus clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.4 Translucent clouds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.5 Interferometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.6 This work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 The clouds 16

2.1 ζ Ophiuchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 LDN 1780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3 31 GHz data 20

3.1 Cosmic Background Imager . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.2 Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3 Image reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3.1 CLEAN reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3.2 VIR reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.4 CBI flux loss and flux densities . . . . . . . . . . . . . . . . . . . . . . . . . . 25

4 Ancillary data 27

I

4.1 Data description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.2 Point source subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2.1 ζ Oph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.2.2 LDN 1780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.3 Expected radio emission from the Hα image. . . . . . . . . . . . . . . . . . . . 35

5 Spectral energy distributions 37

5.1 ζ Oph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.1.1 Surface brightness spectral comparison . . . . . . . . . . . . . . . . . . 39

5.2 LDN 1780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

6 Morphological analysis 42

6.1 Visibility plane correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.1.1 ζ Oph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

6.1.2 Bi-linear correlations in ζ Oph . . . . . . . . . . . . . . . . . . . . . . . 45

6.1.3 LDN1780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6.2 Sky plane correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

6.2.1 ζ Oph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.2.2 LDN1780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

6.2.3 IRF on LDN 1780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7 Discussion 54

8 Summary & Conclusions 56

Bibliography 58

II

List of Figures

1.1 Spectrum from CMB anisotropies and Galactic foregrounds. . . . . . . . . . . 3

1.2 Correlation between 14.5 GHz and IRAS 100 µm data on cirrus clouds. . . . . 8

1.3 SED from the molecular cloud G159.6-18.5 . . . . . . . . . . . . . . . . . . . . 9

1.4 Schematic diagram of a two element interferometer . . . . . . . . . . . . . . . 12

1.5 Vectors used in de definition of the phase center . . . . . . . . . . . . . . . . . 13

2.1 Color composition of ζ Oph using IRAC images . . . . . . . . . . . . . . . . . 17

2.2 Color composition of LDN1780 . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.1 Front view of CBI and CBI2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.2 (u, v) coverage of the CBI and CBI2 . . . . . . . . . . . . . . . . . . . . . . . . 22

3.3 CLEANed images of ζ Oph and LDN1780 . . . . . . . . . . . . . . . . . . . . 23

3.4 Voronoi image reconstruction applied on LDN 1780 . . . . . . . . . . . . . . . 24

3.5 Voronoi image reconstruction applied on ζ Oph . . . . . . . . . . . . . . . . . 25

4.1 Maps from the ancillary data around the extraction aperture for ζ Oph. . . . . 31

4.2 Maps from the ancillary data around the extraction aperture for LDN 1780 . . 32

4.3 Saturated point spread function of the IRAC camera for the 8µm data. . . . . 33

4.4 Comparison between the IRAC 8µm image of ζ Oph before and after thesubtraction of the point sources. . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.5 SHASSA Hα image of ζ Oph and our processed image . . . . . . . . . . . . . 35

4.6 Comparison between the IRAC 8µm image of LDN 1780 before and after thesubtraction of the point sources. . . . . . . . . . . . . . . . . . . . . . . . . . . 36

III

5.1 SED of ζ Oph . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5.2 4.85 GHz image of ζ Oph from the PMN survey . . . . . . . . . . . . . . . . . 39

5.3 SED of LDN 1780 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

6.1 Comparison of ζ Oph with different templates on the sky plane . . . . . . . . 43

6.2 Comparison of the restored CBI2 image of LDN1780 with IRAS templates. . . 44

6.3 Example of linear correlations in the visibility plane . . . . . . . . . . . . . . . 46

6.4 Examples of simulated data using MockCBI. . . . . . . . . . . . . . . . . . . . 48

6.5 Correlation of CBI data with mock free-free and IRAS 60 µm templates on ζOph. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

6.6 Histograms form the Monte Carlo simulations. . . . . . . . . . . . . . . . . . . 50

6.7 Histograms form the Monte Carlo simulations for LDN 1780 . . . . . . . . . . 51

6.8 Correlation of CBI data with mock IRAS 60 µm and the corrected IRAC 8µmtemplates on LDN 1780. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

7.1 Emission parameters for different clouds observed by the CBI at 31 GHz. . . . 55

1

Chapter 1

Introduction

The study of the Cosmic Microwave Background (CMB) has brought impor-tant advances in modern cosmology. It is one of the observational pillars ofthe Big Bang theory, and the study of its anisotropies during the last decadehas ushered in the field of “precision cosmology”. The next step in CMBstudies is the characterization of the polarization of this radiation. Accuratemeasurements of the CMB polarization place constraints on the effects ofprimordial gravity waves, generated during the inflation epoch.

An important challenge in studies of CMB is the subtraction of Galacticforeground emission. The detailed study of the foregrounds led to the discov-ery of a new radio-continuum mechanism in the diffuse interstellar medium(ISM). The subtraction of this foreground is crucial for the observations ofpolarized anisotropy at 10-70 GHz.

1.1 Galactic foregrounds at GHz frequencies

The cosmological information that we can obtain by studying the CMB iscritically limited by our understanding of Galactic foreground emission. TheGHz spectrum is dominated by Galactic emission except for a small win-dow near 50 GHz, where the CMB anisotropies are more conspicuous. Inthe Wilkinson Microwave Anisotropy Probe (WMAP) data analysis, a linearcombination between different templates of the foregrounds was subtracted tothe temperature maps to produce a template of the CMB anisotropies (Ben-nett et al. 2003). The WMAP team used templates for free-free, synchrotron

2

and sub-mm dust emission. In Figure 1.1 we show the spectrum of CMBanisotropies and the different foregrounds. The CMB anisotropies are moreintense that the foregrounds in the range 30-90 GHz. The ratio between CMBanisotropies and other radiations peaks around 60 GHz where CMB fluctua-tions are a factor of 10 larger than the foregrounds. However, the intensity ofthe B-modes of polarized signal is about 1/100 of the CMB anisotropies, soa very accurate foreground subtraction is crucial for those observations.

Figure 1.1: Spectrum from CMB anisotropies and Galactic foregrounds. Kp0 and Kp2 aretwo different masks of the maps. From Bennett et al. (2003)

1.1.1 Classical emission mechanisms

The radiation from astrophysical objects, is produced principally by chargedparticles undergoing an acceleration or by quantum transitions in atoms ormolecules. Here, I briefly summarize the emission mechanisms that are rele-vant for this study, i.e., those that are at the frequency range of CMB obser-vations. A detailed treatment on radiative processes can be found in Rybicki& Lightman (1986) while radio emission mechanisms are covered by Wilson

3

et al. (2009). I will follow the notation convention that flux density is S ∼ να

and antenna temperature is T ∼ νβ, with β = α − 2.

A charged particle that is being accelerated radiates photons. If the accel-eration of the particle is a and its charge e, the power of the electromagneticradiation emitted into all angles is given, in cgs units by Larmor’s formula:

P =2

3

e2a2

c3(1.1)

where c is the speed of light. The photons are emitted in a dipolar pattern,

dP

dΩ∝ sin2 θ

with θ the angle between the directions of the radiation and acceleration. Themaximum intensity is thus perpendicular to the acceleration vector.

1.1.1.1 Bremsstrahlung

Bremsstrahlung or free-free emission is produced by the acceleration of acharged particle (e.g. electron) being deflected by another charged particle(e.g. proton). It is worth mentioning that the net electric dipole in theinteraction must be non-zero to have radiation, so an encounter between twoparticles with the same charge will not produce radiation. The accelerationof the particles during the encounter is not constant, so the emitted photonshave a range of wavelengths. Once the acceleration as a function of time iscomputed, the power radiated can be obtained using Larmor’s formula. Inthe case of optically thin sources, the result is a flat spectrum for flux densityin frequency (in a log-log plot) with an upper cutoff. In an ionized cloudin thermal equilibrium, the particles have a Maxwellian velocity distribution,and the emission per unit volume per frequency interval is given by (Rybicki& Lightman 1986):

dP

dV dν= 6.8 × 10−38 Z2 ne ni T−1/2 e−hν/kT gff , (1.2)

gff(T, ν) is the velocity-averaged a Gaunt factor, which contains the termsby which the quantum mechanics expressions differs from the classical ones.There are many approximations to the gaunt factor, which for the radio rangemay be found in Wilson et al. (2009). An example of exact gaunt factors canbe found in Casassus et al. (2007).

4

Although the radiation from a single interaction is linearly polarized, theemission from a thermalized plasma will not result in a net polarization, as thecollisions do not occur in any particular direction. The free-free spectral indexβff is a slow varying function of frequency and electron temperature (Bennettet al. 1992). A reference value for Te = 8000 K is βff ≈ 2.15 between 31 and53 GHz. The optical Hα line is a good tracer of free-free emission as it alsodepends on electron-ion collisions, although it requires corrections for dustabsorption. Diffuse free-free radiation is important at frequencies between10-100 GHz

1.1.1.2 Synchrotron

Charged particles accelerated by a magnetic field will radiate. The diffuseGalactic synchrotron emission is produced by cosmic rays, relativistic parti-cles (principally electrons) with very high energies spiraling around Galacticmagnetic field lines. These particles are accelerated to relativistic speeds invery energetic environments, like shock-waves from supernovae explosions.

Because of the relativistic speeds, cosmic-ray electrons have very large in-ertia. Hence, their gyration radius around magnetic field lines and gyrationfrequencies have extremely low values. However, relativistic effects result instrong beaming of the dipole field so must be taken into account to calculatethe power measured in the observer’s frame of reference. The power emittedby a single relativistic electron can be computed using Larmor’s formula (1.1)in the frame of the moving electron, and then transforming using Lorentztransformations. Thus,

Psync =2

3

e2a2⊥

c3γ4 (1.3)

where γ is the Lorentz factor and a⊥ is the component of the accelerationthat is perpendicular to the magnetic field B. It can be computed using therelativistic Lorentz force:

d

dt(γmv) = e(v × B) (1.4)

The synchrotron radiation is also highly polarized for ordered B fields. Inthis case, the magnetic field lines provide a privileged direction for the motionof the emitting particles, so the emission is expected to be polarized.

5

As previously stated, synchrotron radiation is heavily beamed along thedirection of motion, i.e. perpendicular to the magnetic field. The emission isconfined to a narrow beam of order 2/γ between the nulls. This beaming has avery important effect on the observed spectrum. The observer can only see theemission when the instantaneous velocity of the electron points toward him,for a time much shorter than the gyration period. Thus, the power receivedas function of time can be described as a series of widely spaced and verysharp pulses. The observed frequency is the Fourier transform of this seriesof pulses: a nearly continuous series of spikes in the frequency domain, whichin practice is effectively continuous (because of different v, B and angles).

The spectrum from an ensemble of electrons depends directly on the energydensity distribution, N(E) of the electrons. It has been found that N(E)is well fitted by a power law spectrum (see for example Meyer 1969). Thisimplies that the volume emissivity of the relativistic electrons is a power law,with index s = (p − 1)/2, being p the index of the distribution of particleenergies.

The synchrotron intensity depends on the electron density (ne) and thestrength of the magnetic field:

S(ν) = ǫsync(ν)

∫

z

neB(1+p)/2⊥ dz (1.5)

where the integral is along the line of sight z and B⊥ =√

B2x + B2

y is the

component of the magnetic field in the sky plane x − y. The emissivitycorrespond to a power law:

ǫsync(ν) = ǫ0ναs (1.6)

with αs = −(p + 3)/2. Therefore, for a given magnetic field,

S(ν) = S(ν0)

(

ν

ν0

)αs

(1.7)

The 408 MHz all sky survey (Haslam et al. 1982) is a very reliable map toestimate the Galactic synchrotron radiation on ∼1 deg scales. Giardino et al.(2002) found a spectral index αs = −2.7 between the Haslam template and the2326 MHz Rhodes/HartRAO survey (Jonas et al. 1998). Finkbeiner (2004)used αs = −3.05 to correct the synchrotron features in WMAP 23 GHz maps.

6

1.1.1.3 Thermal dust radiation

Dust grains are heated by starlight and this energy is re-radiated at longerwavelengths, mainly into the far-infrared. Large dust grains of sizes & 0.01µm are in equilibrium with the interstellar radiation field (IRF) and the equi-librium temperature of the grains is in the range 15 K . T . 20 K.

In a cloud in thermal equilibrium, the emergent intensity from the dustgrains at temperature Td is given by:

Iν = Bν(Td)[1 − e−τd] (1.8)

where, τd(ν) is the optical depth at a certain frequency:

τd(ν) = κ(ν)

∫

ρds (1.9)

and κ(ν) is the dust opacity. Bν(Td) is the Plank function.

Lagache et al. (1999) found, using data from the COBE satellite that inthe Sun’s vicinity, the intensity of the sub-mm wavelengths emission can berepresented by:

Iν = τBν(17.5K). (1.10)

with τ/NHI = 8.7 ± 0.9 × 10−26(λ/250µm)−2cm2. The opacity τ is generallymodeled as a power law of the frequency with a spectral index 1 . α . 3.

The wavelength at which the spectrum peaks (analogy with Wien’s law) is:

λpeak ≈ 2890

(

5

β + 5

)

1

Tbgµm, (1.11)

valid in the wavelength range 100 µm . λ . 1000 µm.

1.2 Anomalous emission

In addition to the invaluable contribution to Cosmology from the discoveryof the CMB anisotropies, the analysis of the Cosmic Background Explorer

(COBE) data brought surprises to the study of the local ISM in our Galaxy.Kogut et al. (1996a,b) statistically detected a correlated far-IR signal with aflat spectral index between 31 and 53 GHz in the Differential Microwave Ra-

diometer maps. Then, observations at high Galactic latitudes by Leitch et al.

7

(1997) showed emission at 14.5 GHz strongly correlated with IRAS 100 µmmaps. Fig. 1.2 shows the comparison between radio and IRAS in differentregions around the north celestial pole. They showed that this cm-wave emis-sion was anomalous in that classical emission mechanisms couldn’t accountfor it. Because of the lack of Hα emission, free-free emission cannot accountfor the excess. Further evidence for anomalous emission has been found indifferent CMB experiments by de Oliveira-Costa et al. (1997, 1999); Lagache(2003); Banday et al. (2003); Fernandez-Cerezo et al. (2006); Mukherjee et al.(2001, 2003); Ami Consortium et al. (2009)

Figure 1.2: Comparison between 14.5 GHz data (solid line) and IRAS 100 µm (dot-dashedline). The dotted line coincident with the x-axis is the free-free contributionexpected from Hα images. Figure taken from (Leitch et al. 1997)

Since its discovery as a CMB foreground, the dust-correlated anomalousemission has been observed in different astrophysical environments, like molec-ular clouds (Watson et al. 2005; Casassus et al. 2008), Hii regions (Dickinsonet al. 2007, 2009) and dark clouds (Casassus et al. 2006; Ami Consortiumet al. 2009).

Different emission mechanism have been proposed, such as spinning dust(Draine & Lazarian 1998a,b), magnetized dust grains (Draine & Lazarian1999), hot (T∼106 K) free-free (Leitch et al. 1997) and flat spectrum syn-chrotron (Bennett et al. 2003). To date, the evidence favors the spinning

8

dust grain model (Finkbeiner et al. 2004; de Oliveira-Costa et al. 2004; Wat-son et al. 2005; Casassus et al. 2006, 2008) in which very small grains (VSG)with a non-zero dipolar moment rotating at GHz frequencies emit cm-waveradiation. The emission has its peak at ∼20 GHz and the models predictthat it is dominated by the smallest grains, Polycyclic Aromatic Hydrocar-bons (PAHs). Ysard et al. (2009) found a correlation across the whole skyusing WMAP data between 23 GHz maps and IRAS 12 µm. Watson et al.(2005), using the COSMOSOMAS experiment, discovered strong emission inthe frequency range 11-17 GHz in the Perseus Molecular Cloud (G159.6-18.5).In this cloud, the spectral energy distribution (SED) Fig. 1.3 is well-fitted bya spinning dust model.

Figure 1.3: SED from the molecular cloud G159.6-18.5. A spinning dust spectrum fromDraine & Lazarian models account very well for the excess. (Watson et al. 2005)

1.3 Cirrus clouds

The large-scale filamentary emission from diffuse interstellar dust detected byIRAS at high Galactic latitude was named “cirrus” by Low et al. (1984) be-

9

cause its morphology resembles that of the atmospheric clouds. They are seenpredominantly at 60 and 100 µm and the origin of this radiation is generallyascribed to dust continuum emission, with a contribution from atomic lines,for example Oi (63 µm) (Stark 1990). The radio-IR correlation suggest thatthese high-Galactic-latitude cirrus clouds are responsible for the ubiquitousanomalous emission. On shorter wavelengths (eg. 12 and 25 µm), the emis-sion is from VSG subject to thermal fluctuations. Cirrus clouds span a widerange of physical parameters. Most are mainly atomic and some are partlymolecular (e.g. Miville-Deschenes et al. 2002; Snow & McCall 2006). Starket al. (1994), using a combination of absorption and emission line measure-ments, found Hi gas temperatures in the range between 20 and > 350 K. Thelow temperatures correspond to the coldest clumps in the clouds that repre-sent the cores of the much more widely distributed and hotter Hi gas. Cirrusclouds are pervaded by the interstellar radiation field (IRF), to which they aretransparent. They present neutral hydrogen column densities of the order ofN(Hi)≈ 1−10×1020 cm−2, which corresponds to visual extinctions of AV . 1mag assuming a normal dust-to-gas ratio. It is commonly found that theseclouds are not gravitationally bound, but their are in pressure equilibrium,and their kinematics are dominated by turbulence (Magnani et al. 1985).

1.4 Translucent clouds

Translucent clouds are interstellar clouds with some protection from interstel-lar radiation in that their extinction is in the range AV ∼ 1−2 mag. They canbe understood as photo-dissociation-regions (PDR) (Snow & McCall 2006).Across translucent clouds carbon undergoes a transition from singly-ionizedinto neutral atomic or molecular (CO) form. The cm-wave emission in thesetype of clouds is the least well understood of all the cloud regimes. The lackof observational data is due to their small column densities (∼ 1021 cm−2).Translucent clouds are better suited to understand the anomalous foregroundthan the denser clouds. In translucent clouds physical properties, such asdensity and temperature, and environmental conditions, such as exposure tothe IRF, approach those of the cirrus clouds. By bridging the gap in phys-ical conditions, translucent clouds are test beds for the extrapolation of theradio/IR relative emissivities seen in dense clouds.

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1.5 Interferometry

The necessity for higher angular resolution and sensitivity has lead to theconstruction of very large (∼ 100 m) radio telescopes. However, there arepractical limits to the size of these devices given by the technical feasibilityand the financial budget. The angular resolution θ of a single dish telescopeof diameter D is restricted by the diffraction limit, so θ & λ/D.

By combining the outputs of two or more antennas, it is possible to achievelarger angular resolution and sensitivity. This is the idea of interferometry. Iwill resume the principles of this technique and define the terminology usedduring this thesis. A detailed description of interferometry is found in theseries of lectures Taylor et al. (1999). See the textbook by Wilson et al. (2009)for a description of Radio Astronomy techniques, including interferometry.

In interferometry, the signals from an assembly of antennas are correlatedby pairs. I will now describe the properties of a two element interferometer.Assume there are two antennas pointing toward a distant radio source inthe direction of the unit vector s. The antennas are separated by a baselineb. Figure 1.4 shows a diagram of such configuration. The plane-parallelwavefront coming from the sky reaches the different antennas at differenttimes, given by a geometric delay, τg = b · s/c, where c is the speed of light.

A plane monochromatic wave of frequency ν will induces a voltage V1 inone antenna:

V1 ∝ E eiωt (1.12)

and a voltage V2 in the second antenna:

V2 ∝ E eiω(t−τg), (1.13)

with ω = 2πν

The most important quantity in interferometry is the spatial coherence func-

tion R(τg) of the wavefront at the positions of the antennas r1, r2. This cor-relation is defined as the expectation of a product between the two voltagesmeasured by the antennas

R(τg) ∝E2

T

∫ T

0

eiωte−iω(t−τg)dt (1.14)

if the integration is made in a period much longer than the period of the waveoscillation, i.e. T ≫ ν−1, the high frequency terms in the product will be

11

Figure 1.4: Schematic diagram of a two element interferometer. Figure from Taylor et al.(1999)

removed from the average, and the output of the correlator will be:

R(τg) ∝1

2E2 eiωτg (1.15)

Now, if the brightness distribution of the radio source is given by Iν(s), thepower per frequency unit dν per solid angle dΩ is

dP = A(s) Iν(s) dν dΩ (1.16)

with A(s) the effective collecting area of the interferometer elements (we willassume that the antennas are similar). As before, the geometric time delayis τg = b · s/c. Then, the output of the correlator will be

R12(τg) =

∫∫

A(s) Iν(s) eiωb·s/c dν ds (1.17)

To solve this equation for Iν(s), a coordinate change can be done. The positionin which the synthesized field of view is centered, the phase tracking center orphase reference position by the vector s0 as shown in Fig. 1.5, then, we canwrite s = s0 + σ with |σ| = 1. Now, we can rewrite Equation 1.17

12

Figure 1.5: Vectors used in de definition of the phase center. From Taylor et al. (1999)

R12(b) = exp

[

iω

(

1

cb · s0

)]∫∫

A(σ) Iν(σ) eiωb·σ/c dν dΩ (1.18)

The integral term is called the visibility function of the intensity distributionIν(σ). We can now choose the a coordinate system that

ω

2πcb =

1

λb ≡ (u, v, w). (1.19)

Note that b is the baseline. Here, u, v, w are measured in units of the wave-length λ and they point to East, North and to the position of interest (i.e.parallel to s0) respectively. σ = (x, y, z) is defined such that x, y are thedirection cosines with respect to the u, v axes. Using these transformations,the visibility function from Equation 1.18 becomes

V (u, v, w) =

∞∫

−∞

∞∫

−∞

A(x, y) Iν(x, y) e2iπ(ux+vy+w√

1−x2−y2) dxdy√

1 − x2 − y2

(1.20)where we can set the limits to ±∞ because A(x, y) = 0 outside the primarybeam of the telescopes. Equation 1.20 is an exact Fourier transform unlessthe term w

√

1 − x2 − y2. However, if the interferometer is mapping a smallregion of the sky,

√

1 − x2 − y2 ∼= 1 and it can be extracted from the integral.Then 1.20 is now

V (u, v, w) e−2iπω =

∞∫

−∞

∞∫

−∞

A(x, y) Iν(x, y) e2iπ(ux+vy) dxdy (1.21)

13

Now, the measured visibilities in the uv plane are:

V (u, v, w) e−2iπω ∼= V (u, v, 0). (1.22)

The last equation is equal to the Fourier transform of the intensity modifiedby the primary beam shape:

A(x, y) Iν(x, y) =

∞∫

−∞

∞∫

−∞

V (u, v) e−2iπ(ux+vy) dudv (1.23)

So if we measure the visibility function for the entire uv plane and we knowthe primary beam shape of the antennas, we can recover the intensity of thesky emission. However, in practice V (u, v) can only be sampled in discretepoints, and the data is usually grided on a rectangular coordinate system.Thus, Eq. 1.23 is written in the discrete form

ID(x, y) =∑

k

g(uk, vk)V (uk, vk) e−2iπ(ukx+vky) (1.24)

ID is called the dirty map and g(u, v) is the weighted sampling function. g(u, v)is used to weight the visibility data to account for the reliability of data, tochange the effective beam shape and to compensate for clustering of data inthe (u, v)plane. Commonly used weightings functions are Natural Weighting

which uses g(u, v) = 1 and Uniform Weighting where g(u, v) = 1/Ns(k), Ns(k)is the number of data points that are in a certain region of characteristic widths centered in the point k of the (u, v)plane. Natural weighting provides highersignal-to-noise ratio, useful to detect weak features. However, usually most ofthe data points in the (u, v)plane are close to the origin, the short baselinesare favored and the angular resolution is lowered. In the other hand, uniformweighting gives better angular resolution at the cost of lower sensitivity.

From Eq. 1.24, an image can be obtained using a direct Fourier transform(DFT).

1.6 This work

Our study is based in interferometric observations with the Cosmic Back-ground Imager (CBI) at 31 GHz of two translucent clouds: ζ Oph and

14

LDN 1780. The motivation for this study is the characterization of the anoma-lous CMB foreground. ζ Oph and LDN 1780 resemble cirrus clouds in theirshallow column densities and exposure to the IRF. The aim is to bridge, forthe first time, the gap between the very diffuse cirrus clouds and the denseand dark clouds already studied.

The focus of this study is a morphological analysis of the 31 GHz emission.We compared the radio data with different IR (dust) templates in order todeterminate which tye of grains are more suitable to be the source of theanomalous emission.

The spectral energy distribution (SED) of the clouds in the cm-wave rangeis useful to discriminate among the candidates for the anomalous emission.We made SEDs for the two clouds including a spinning dust model to fit thecentimetric data.

This thesis is organized as follows. A description of the clouds studied is inChapter 2. The observations with the CBI interferometer and the ancillarydata used are in Chaps. 3 and 4. Using the auxiliary data we constructedSEDs for the clouds in Chap. 5. 6 Describes the morphological comparisonsbetween CBI data and different templates both in the sky plane as in thevisibilities plane. A discussion of the relevant points, results and scopes ofthis study is in Chap. 7. Chap. 8 concludes.

15

Chapter 2

The clouds

2.1 ζ Ophiuchi

The cloud coincident with ζ Oph is a prototypical and well-studied translucentcloud. ζ Oph itself is a O9Vb star at a distance of 140±16 pc (Perryman et al.1997). In this line of sight, the total H-nucleus column density is fairly welldetermined, N(H)∼1.4 × 1021 cm−2, with 56% of the nuclei in molecular form(Morton 1975). Although this line of sight consists of several interstellar com-ponents at different heliocentric velocities, one component at v⊙ = −14.4 kms−1 contains most of the material and is referred to as the ζ Oph cloud. Therehave been numerous efforts (Black & Dalgarno 1977; van Dishoeck & Black1986; Viala et al. 1988) to build chemical models of this cloud. In the pioneer-ing work of Black & Dalgarno (1977), a two shell model is proposed to fit theobservational data: a cold and denser core surrounded by a diffuse envelope.The density and temperature in these models are in the range n = 250−2500cm−3, T = 20− 100 K for the core and n = 200− 500 cm−3, T = 100− 200 Kfor the envelope. These conditions approach those of the cirrus clouds coreswhose densities (Turner 1994) fall into the same range. Translucent clouds,as well as cirrus, are exposed to the Interstellar Radiation field (IRF), whichhas an extreme in the vicinity of ζ Oph.

Fig. 2.1 shows a beautiful color composition using near-IR images from theSpitzer telescope. Shown in red is 8µm, tracing PAHs emission, in green is4.5µm which is sensitive to H2 rotational lines and in blue is 3.6µm, showingmainly the stellar contribution(Jørgensen et al. 2006). The cloud resemblesa feather and we can note that the maximum of the near-IR emission is not

16

coincident with the ζ Oph star, in the center of the image.

30.0 38:00.0 30.0 16:37:00.0 30.0 36:00.0

10:00.0

15:00.0

20:00.0

25:00.0

-10:30:00.0

35:00.0

40:00.0

45:00.0

50:00.0

55:00.0

R.A.

DE

C.

Figure 2.1: Color composition of ζ Oph using IRAC images: 8µm in red, 4.5µm in green and3.6µm in blue. The brightest star in the center of the image is ζ Oph.

2.2 LDN 1780

The Lynds Dark Nebula (LDN) 1780 is a high galactic latitude (l = 359.0, b

= 36.7) translucent region at a distance of 110 ± 10 pc (Franco 1989). Rid-derstad et al. (2006) found that the spatial distribution of the mid-IR emissiondiffers significantly from the emission in the far-IR. Also, they show that theIR color ratios indicate an overabundance of PAHs and VSGs with respectto the solar neighbourhood. Using an optical-depth map constructed from

17

ISO 200 µm emission, they found a mass of ∼ 18 M⊙ and reported no youngstellar objects from the absence of color excess in point sources. Because ofthe morphological differences in the IR, this cloud is a very interesting targetto make a morphological comparison with the radio data from the CBI in or-der to determine the origin of the anomalous emission. In Fig. 2.2 is a colorcomposition of the cloud. In red is IRAS 100µm tracing the column density,in green IRAC 8µm tracing VSGs and PAHs and in blue an optical imagefrom the 2nd Digitized Sky Survey (DSS2) that helps to distinguish the moretranslucent parts of the cloud from the optically thick parts. We can see themorphological differences in the emission from the different bands. In thiscloud, the incident radiation field is rather non-isotropic: the Galactic planeis to the bottom left on the image while the bright Sco-Cen OB associationis to the bottom right.

18

42:00.0 41:00.0 15:40:00.0 39:00.0 38:00.0

-6:40:00.0

50:00.0

-7:00:00.0

10:00.0

20:00.0

30:00.0

40:00.0

50:00.0

R.A.

DE

C.

Figure 2.2: LDN1780 in a color composition with IRAS 100µm in red, IRAC 8 µm in greenand an optical DSS2 image in blue.

19

Chapter 3

31 GHz data

3.1 Cosmic Background Imager

The observations at 31GHz were carried out with the Cosmic BackgroundImager (CBI), a 13 element interferometer located at the high altitude Llanode Chajnantor site in Chile (see Padin et al. 2002). This instrument wasdesigned to measure the power spectrum of the CMB on angular scales in therange ∼ 5′ to 0.5.

The receivers operate in ten frequency channels from 26 to 36 GHz. Thisfrequency range was chosen to minimize the contribution from foregroundsources at lower frequencies and atmospheric noise at higher frequencies. Eachreceiver measures either left (L) or right (R) circular polarization. Each an-tenna is 0.9 m in diameter. The primary beam (hereafter PB) corresponds to45.2 arcmin full-width half maximum at 31 GHz.

The antennas are mounted in a alt-azimuthal planar rigid platform whichcan be rotated about the optical axis. This platform allows an easy detectionand remotion of false signals produced by the instrument, because the spu-rious signals rotates with the array while the sky signal does not. Moreover,the additional rotation axis can be used to increase the (u, v)coverage. Thebaselines ranges from 1 to 5.5 m. The pointing model is calculated from ob-servations of stars using a 15 cm refractor telescope in the antenna platform.The rms pointing accuracy of CBI is ∼ 0.5 arcmin.

The interferometer was upgraded in 2006 with 1.4 m dishes (CBI2) to in-crease temperature sensitivity. The PB of CBI2 is 28.2 arcmin FWHM at 30

20

(a) (b)

Figure 3.1: Front view of CBI (a) and CBI2 (b).

GHz. In Fig. 3.1 is CBI and CBI2.

3.2 Observations

The observations of ζ Oph were done with CBI whereas LDN1780 was ob-served with CBI2. The observations of both clouds were made in total inten-sity mode (all receivers measuring L only).1

We acquired 31 GHz visibilities during the night of 2004 July 8 in a singlepointing on the ζ Oph region (R.A.= 16h37m9s.5, decl. = −1034′01′′; J2000)with an integration time of ∼ 8000 s on-source. LDN1780 was observed intwo different pointings: LDN1780E (R.A. = 15h40m30s, decl. = −0714′18′′;J2000) and LDN1780W (R.A. = 15h39m40s, decl. = −0711′40′′; J2000).LDN1780E was observed with CBI2 during the nights of 2007 April 13 and 28with a total integration time of ∼ 12000 s. LDN1780W was observed duringthe nights of 2007 April 17 and 18. Here the integration time was ∼ 8000 s.The configurations of the CBI1 and CBI2 interferometers result in the (u, v)coverage shown in Fig. 3.2.

We reduced the data using similar routines to those used for CMB data(Pearson et al. 2003; Readhead et al. 2004a,b). Integrations of 8-min on source

1The measured quantity is (Hamaker et al. 1996) 〈LL∗〉 = I − V , with I, V the Stokes parameters forintensity and circular polarization respectively. Under the assumption that the signal is not circular polarized,〈LL∗〉 = I. Finite V has only been seen in stellar sight-lines, mainly through dichroic extinction in the visible.

21

Figure 3.2: (u, v) coverage of the CBI and CBI2 in the configurations used for the observationsof ζ Oph on the left and LDN1780 on the right.

were accompanied by a comparison field, with an offset of 8 arcmin in R.A.,observed at the same hour angle for the subtraction of ground emission. Fluxdensity calibration is based on a Jupiter temperature of TJ = (147.3± 1.5) K(Readhead et al. 2004a).

3.3 Image reconstruction

We restored the calibrated visibilities using the traditional CLEAN algorithm(Hogbom 1974) and also using a new technique based on a Voronoi tessellationand MEM reconstruction.

3.3.1 CLEAN reconstruction

The reduced visibilities were imaged using the CLEAN algorithm from theDIFMAP package (Shepherd 1997). We chose natural weights in order toobtain a deeper restored image. The theoretical noise level (using naturalweights, as expected from the visibility weights evaluated from the scatterof individual frames) is 4.9 mJy beam−1 for ζ Oph. Fig. 3.3a shows therestored image of ζ Oph. Two regions of negative emission, peaking at -0.01 Jy beam−1, are within the theoretical noise (at ∼ 2σ) but may also reflectthe limited accuracy of the visibility calibration (these negatives persisted

22

despite repeated experiments with a variety of reconstructions techniques).The synthesized beam of this image is ≈ 7 arcmin FWHM. The restoredimage was then corrected by the PB of CBI1 at 31GHz (45 arcmin FWHM).For LDN1780, we obtained “clean” images of the two fields. The estimated

Figure 3.3: CLEANed images of ζ Oph (a, left) and LDN1780 (b, right). Contours are 10,30, 50, 70, 90% of the peak brightness, which is 9× 10−3 MJy sr−1 in ζ Oph and0.016 MJy sr−1 in LDN1780. The primary beams of CBI and CBI2 are shown asa dashed line. These images have not been primary-beam-corrected. The pointsource NVSS 153909-065843 is visible in the north edge of LDN1780W. The sizesof the synthesized beams are ≈ 7 for ζ Oph and ≈ 4.8 for LDN 1780

noise level is 4.26 mJy beam−1 for LDN1780E and 3.03 mJy beam−1 forLDN1780W. In LDN1780W there is a compact source, NVSS 153909-065843(Condon et al. 1998). It is visible just in the north edge of the PB in Fig. 3.3.The position of this source allow us to fix the astrometry of the CBI data.We corrected by an offset of 30 and 56 arcsec in R.A. and Dec. These offsetsare within the rms pointing accuracy of ∼ 0.5 arcmin.

With the restored fields, we made a linear mosaic adding both restoredimages. This mosaic IM was done first, phase-shifting one template in orderto have the same phase center x in both images. Then, correcting the pixelsby the primary beam of the array. We added these corrected images, eachmultiplied by a statistical weight w (inverse of rms noise squared). The sizeof the averaged synthetic beam is ≈ 4.8. Finally, we divided by the PB

23

multiplied by the statistical weight.

IM(x) =

∑

p wp(x)Ip(x)/Ap(x)∑

p wp(x), (3.1)

where wp(x) = A2p/σ

2p. p is the label for the pth. This mosaic is shown in Fig.

3.3b.

3.3.2 VIR reconstruction

We also used an alternative method to restore the visibilities. We applied theVoronoi image reconstruction (VIR) from Cabrera et al. (2008). This noveltechnique uses a Voronoi tessellation instead of the usual grid , and has theadvantage that it is possible to use a smaller number of free parameters duringthe reconstruction.

In LDN1780, we subtracted the point source from the visibilities before thereconstruction. The restored images are quite similar to that from CLEANand an example is shown in Fig. 3.4.

Figure 3.4: In the left box is the Voronoi model of the visibilities of LDN 1780. This modelhas 55 polygons. The right panel shows the convolution of the model in the leftwith the synthetic beam used to take the data, obtained using natural weights.The synthetic

On ζ Oph the results of this reconstruction is worse than the result with

24

CLEAN. This can be because the data is very noisy and there is a largeamount of extended emission that fills the CBI PB. However the morphologyof the cloud is similar to that obtained with CLEAN. Fig. 3.5 shows the modeland the restored image.

Figure 3.5: The model in the left has 30 polygons. The right panel shows the convolution ofthe model in the left with the synthetic beam of the data, obtained using naturalweights.

3.4 CBI flux loss and flux densities

The integrated flux density in an aperture of 45′ in diameter (the size of theprimary beam of CBI1) is 0.46 ± 0.02 Jy for ζ Oph and 0.260 ± 0.015 Jy forLDN1780. The errors are estimated from the noise in the clean images: weintegrate a rms map corrected for the primary beam in the same extractionaperture (45 arcmin). Because of the incomplete sampling in the uv plane,the missing Fourier components will lower the flux densities on & 45′ scales.For instance, in Casassus et al. (2006) the flux density recovered by the CBIfrom the dark cloud LDN 1622 is less than 50% in a 45 arcmin field of view. Ifwe assume that the emission is distributed in the same way at 31GHz and 100µm, we can estimate the true flux density by integrating in the same aperturea simulated IRAS 100 µm template. The flux recovered in this simulation is18.9 % of the real IRAS flux on ζ Oph and 18.7% for LDN1780. We obtain

25

a flux density corrected by flux loss of 2.43 ± 0.11 Jy for ζ Oph and 1.30 ±0.075 Jy for LDN1780.

26

Chapter 4

Ancillary data

Here we describe the auxiliary data that we used in this investigation and theprocessing we made to it.

4.1 Data description

• Spitzer: we used data 8µm from the Infrared Array Camera (Fazio et al.2004) (IRAC). The angular resolution is ∼ 3′′ in this band. A squaremosaic of 1 deg from LDN 1780 was provided from Adolf Witt. Themosaic of ζ Oph was obtained from the Spitzer database.

• IRAS: we used images of the four IRAS bands: 12, 25, 60 and 100 µ withan angular resolution of 3.8, 3.8, 4.0 and 4.3 arcmin FWHM respectivelyfrom the Improved Reprocessing of the IRAS Survey (IRIS) (Miville-Deschenes & Lagache 2005).

• ISO: 100 & 200 µm templates from the ISO satellite were provided byM. Juvela. These images have an angular resolution ∼ 1 arcmin.

• COBE: the fluxes in the far-IR were obtained from DIRBE instrument.We used the data at 100, 140 & 240 µm.

• WMAP: the WMAP satellite (Hinshaw et al. 2009) provided sensitiveimages of ζ Oph and LDN1780 in 5 bands at 23, 33, 41, 61 and 94 GHzwith approximate Gaussian beam-widths of 0.88, 0.66, 0.51, 0.35, and0.22 deg FWHM respectively. We used these data to make the SED ofthe regions.

27

• SHASSA: The Southern H Alpha Sky Survey Atlas (SHASSA) (Gaustadet al. 2001) covers the southern sky (δ ≤ +15) with an angular resolutionof 0.8 arcmin. We used the continuum-corrected image available on theweb1.

• Additional low-frequency radio data

408 MHz With an angular resolution ∼0.85 deg, the Haslam et al.(1981) covers the whole sky at 408 MHz. We used the map withoutpoint sources available in the web2.

1.4 GHz Reich & Reich (1986) present a radio continuum survey of thenorthern sky at 1.4 GHz. The angular resolution is ∼ 35 arcmin and ithas a sensitivity of ∼ 50 mK in brightness temperature.

2.3 GHz The Rhodes/HartRAO 2.326 GHz radio continuum survey(Jonas et al. 1998) covers about 67 % of the sky with an angular resolu-tion of 20 arcmin. It was made with the HartRAO 26-m radio telescope.And the rms noise fluctuations are less than 30 mK.

2.7 GHz The Stockert 25m telescope was used to carry out a radiocontinuum survey of the galactic plane at 2.72 GHz (Reif et al. 1984).The angular resolution is 20 arcmin and the final rms noise is below20 mK in brightness temperature.

4.8 GHz The 4.85 GHz data comes from the Parkes-MIT-NRAO (PMN)survey (Griffith & Wright 1993). The data has a nominal resolution of ∼5 arcmin and a noise of σ ∼ 10 mJy beam−1. Because the principal ob-jective of this survey was to create a catalog point sources, the reductionof the data produced losses of flux on scales larger than ∼15 arcsec.

In Table 4.1 we present differenced flux densities for ζ Oph and LDN1780.The images were smoothed to a common resolution of 1 deg3.

1http://skyview.gsfc.nasa.gov/2http://lambda.gsfc.nasa.gov/3The data was convolved with a Gaussian with variance σ2 = σ2

f − σ2i , where σ2

f is the variance of a

Gaussian with FWHM = 1 deg and σ2i is the variance of the beam of the data. The variance of a Gaussian

s related with the FWHM by σ = FWMH/2√

2 ln(2).

28

We integrated in a circular aperture 1 deg in diameter around the cen-tral coordinates of the 31GHz data. Background emission was subtractedintegrating in and adjacent region close to the aperture. This backgroundsubtraction is necessary in the case of the low frequency radio data becausethese surveys have large baseline uncertainties (see for example Reich & Reich2009, or the discussion in Davies et al. 1996). Figures 4.1 and 4.2 shows largefields of 3 deg around the extraction aperture for each template. In ζ Oph,the background subtraction was made with the region centered at 16h31m04s,-10d07m17s) at ∼ 1.2 deg from the source. For the mosaic of LDN1780, weintegrated around the centroid of the mosaic, in 15h40m08s, -07h11m34s. Thesubtraction region is at 15h32m47s, -07h39m20s, at ∼1.8 deg of the source.

29

Frequency Telescope/ θ Flux Density Flux Density Flux Density Flux Density(GHz) Survey (arcmin) ζ Oph (Jy) Differenced ζ Oph (Jy) LDN1780 (Jy) Differenced LDN17800.408 Parkes 64m 51 55.4 ± 0.40 13.1 ± 2.62 39.6 ± 0.3 1.2 ± 0.61.4 Stockert 25ma 40 66.9 ± 0.10 13.5 ± 2.7 56.9 ± 0.10 -1.0 ± 0.142.3 HartRAO 26m b 20 19.2 ± 0.10 18.9 ± 1.89 9.5 ± 0.10 -0.09 ± 0.142.7 Stockert 25mc 20.4 23.7 ± 0.06 29.9 ± 2.29 14.9 ± 0.05 0.24 ± 2.2923 WMAP d 52.8 7.62 ± 0.13 7.4 ± 0.36 1.48 ± 0.13 0.62 ± 0.1833 WMAP d 36.6 7.04 ± 0.20 7.1 ± 0.44 0.89 ± 0.20 0.54 ± 0.2741 WMAP d 30.6 7.03 ± 0.22 7.2 ± 0.69 0.58 ± 0.23 0.45 ± 0.3261 WMAP d 21 6.20 ± 0.39 5.9 ± 0.85 < 1.0 (3σ) < 1.5 (3σ)94 WMAP d 13.2 7.23 ± 0.62 6.4 ± 1.30 < 2.1 (3σ) < 2.7 (3σ)2997 (240 µm) DIRBE e 42 5590 ± 202 1411 ± 320 2890 ± 160 1450 ± 1952141 (140 µm) DIRBE e 42 7570 ± 310 2690 ± 456 4150 ± 320 2490 ± 3581249 (100 µm) DIRBE e 42 4940 ± 580 2390 ± 615 1600 ± 92 552 ± 100

Table 4.1: Flux densities for ζ Oph and LDN1780. We extracted flux densities in a 1 deg circular aperture, θ stands for angularresolution. References for each survey are : a :Reich & Reich (1986), b : Jonas et al. (1998), c : Reif et al. (1984),d :Hinshaw et al. (2009), e : Miville-Deschenes & Lagache (2005)

30

Figure 4.1: Maps from the ancillary data around the extraction aperture for ζ Oph, 3 degper side, in J2000 equatorial coordinates. The CBI primary beam FWHM (45’)is shown in dashed line.

31

Figure 4.2: Maps from the ancillary data around the extraction aperture for LDN 1780,3 deg per side, in J2000 equatorial coordinates. The CBI2 primary beam FWHM(22.8’) is shown in dashed line.

32

4.2 Point source subtraction

The IR and optical data (i.e. Spitzer, IRAS 12,25 µm and SHASSA) havea number of point sources. Because we want to compare the 31 GHz withthe emission from the ISM, reprocessing was necessary to get smooth imageswithout point sources.

4.2.1 ζ Oph

IRAC The star ζ Oph is very bright in the IRAC images (see Fig. 2.1),moreover, it is highly saturated. To remove the star, a saturated point spreadfunction (PSF), available in the web4 was used. The PSF (Fig. 4.3) wasscaled and fitted to the stars using a lineal correspondence.

After the subtraction of the saturated stars using the IRAC PSF, a medianfilter was applied to the whole image to eliminate the faint stars that werenot saturated. Fig. 4.4 shows the IRAC 8µm before and after the removal ofthe stars.

Figure 4.3: Saturated point spread function of the IRAC camera for the 8µm data. It wasgenerated joining a core component from observations of reference stars and anextended component fromobservations of a set of bright stars that saturated theIRAC array.

4http://ssc.spitzer.caltech.edu/irac/psf.html

33

Figure 4.4: Comparison between the IRAC 8µm image of ζ Oph before and after the sub-traction of the point sources. The circle shows the primary beam of the CBIobservations.

SHASSA The Hα image was also highly saturated in the region of the ζOph star. The SHASSA team produced the Hα images after the subtractionof a continuous image taken with narrow bands filter just next to the Hαwavelength. Because of this, a PSF subtraction is not possible in this case.Moreover, the pixels in the star region were so saturated that we had to discardan important region to have an usable template. The discarded region wasinterpolated using a spline fit with the adjacent pixels. The remaining brightstars were subtracted using a Gaussian fit, made with the Perl package Vtools(S. Cassassus, priv. comm.). Again, after the interpolation we used a medianfilter to delete the fainter stars that remained in the image. Fig. 4.5 showsthe results of the point source subtraction in this case.

4.2.2 LDN 1780

Here, we also have very saturated stars in the IRAC images. We made thesame PSF subtraction as in 4.2.1. The results are shown in Fig. 4.6.

34

Figure 4.5: In left is the SHASSA Hα image of ζ Oph and in the right our processed image.The circles shows the primary beam of the CBI data.

4.3 Expected radio emission from the Hα image.

The radio free-free emission must be accurately known in order to quantifythe contribution of any dust-related excess emission at GHz frequencies. Oneway to estimate the free-free contribution is with the Hα intensity. The Hα

and free-free emission both trace electron-ion collisions, so for a constant elec-tron temperature, the Hα intensities are proportional to the radio continuumspecific intensities.

We used the continuum-corrected SHASSA image. The image was verysaturated in the position of the star ζ Oph so reprocessing was necessaryto get a smooth image without point sources. We removed the saturatedpixels and interpolated that region using the value of the adjacent pixels.Then a median filter was applied to remove the field stars and to smooth thetemplate. This processed image was corrected for dust absorption using theE(B−V ) template from Schlegel et al. (1998) and the extinction curve givenby Cardelli et al. (1989). The extinction at Hα is A(Hα) = 0.82 A(V) andusing RV = A(V )/E(B − V ) = 3.1 we have that A(Hα) = 2.54 E(B − V ).Using the relationship between Hα intensity and free-free brightness temper-ature presented in Dickinson et al. (2003) and assuming a typical electrontemperature Te = 7000, appropriate for the solar neighborhood, we generated

35

Figure 4.6: Comparison between the IRAC 8µm image of LDN 1780 before and after thesubtraction of the point sources. The circles shows the primary beam of theCBI2 pointings.

a free-free brightness temperature map at 31 GHz.

36

Chapter 5

Spectral energy distributions

The spectral energy distribution (SED) can give us clues about the originof the anomalous emission. Different emission mechanisms have differentspectral indexes so by studying the shape of the spectrum we can discriminatebetween theoretical models.

5.1 ζ Oph

Fig. 5.1 shows a model of the ζ Oph differenced SED, as tabulated in Table4.1. The spectrum is the sum of synchrotron, free-free, thermal dust and spin-ning dust emission. We used a synchrotron spectral-index βS = 2.7 (Davieset al. 2006). We choose a free-free spectral index βff = 2.12. The free-freelaw is fixed to the predicted brightness temperature at 31 GHz obtained fromthe Hα image. The dominant source of error in the determination of thisbrightness temperature is the correction for dust absorption. In Fig. 5.1, thedotted lines denote limits for the free-free law: the lower is the emission ex-pected from the Hα image without dust absorption correction and the upperdotted line is the emission expected with the correction (we assume that allthe absorption occurs as a foreground to the Hα emission).

A modified black body1 with fixed emissivity index β = 1.6 was fitted to theDIRBE 100,140 & 240 µm and to WMAP 94GHz points using the Levenberg-Marquardt algorithm. A temperature of 22 K fits the data points well.

The spinning dust component was fitted using the Draine & Lazarian (1998b)

1νβBν(T )

37

models2. The spinning dust emissivities depend on environment. We usedthe model for cold neutral medium (CNM). The spinning dust emissivitiesare given in terms of the H column density; we used NH = 1.4 × 1021 cm−2

(Morton 1975).

Figure 5.1: SED of ζ Oph. The dotted red lines shows the maximum and minimum free-freecontribution expected given the Hα emission. In green is a compound model forthe spinning dust emission using the models from Draine & Lazarian (1998a).

On 1 deg spatial scales, the synchrotron and free-free emission from the Hii

region dominate the spectrum in the centimeter range. The WMAP data placean upper limit on the spinning dust emission of ∼4 Jy on a 1 deg angular scalebecause of the uncertainty of about 4 Jy of the free-free contribution. Thespinning dust component is consistent with this uncertainty. The angularresolution of the ancillary radio data is lower than that of the CBI, so wecannot make a flux density comparison on the CBI spatial frequencies.

2Available at http://www.astro.princeton.edu/∼draine/dust/dust.mwave.spin.html

38

5.1.1 Surface brightness spectral comparison

The PMN image (Fig. 5.2) has an angular resolution similar to that of theCBI. However this survey is high-pass filtered; extended emission on scaleslarger than 20 arcmin is removed (Griffith & Wright 1993). To avoid thisproblem, we compared surface brightness (MJy/sr) in the CBI and PMNimages at a common resolution given by the CBI beam. Table 5.1 lists thesevalues. The 5/31 GHz spectral index is α = 0.37± 0.06. We can see that α31

5

is 7σ larger than −0.12, the spectral index if the emission at 31 GHz wereproduced by free-free emission at temperatures of Te ∼ 8000K. We can alsocalculate the difference between the 31GHz intensity and the value expectedfrom a free-free power law fixed to the PMN point. The non free-free specificintensity3 is Inff

31 = 3.8 ± 1.0 × 10−3 MJy sr−1, and is significant at ∼ 3.8σ.We can conclude that at the smaller angular scales of CBI we found an excessover optically thin free-free emission.

Figure 5.2: 4.85 GHz image of ζ Oph from Parkes-MIT-NRAO (PMN) survey. Contours asin Fig. 3.3

3Inff31 = I31 − I4.85(4.85/31)−0.12 = 3.8 ± 1.0 × 10−3 MJy sr−1

39

Frequency Telescope Surface brightness(GHz) 10−3 MJy sr−1

4.85 Parkes 64m 5.0 ± 0.431 CBI 10.0 ± 0.9

Table 5.1: Surface brightness values in the peak of the 31 GHz image.

5.2 LDN 1780

In this cloud it is difficult to make an accurate estimate of the free-free emis-sion. There is very little Hα emission in the SHASSA image, and it is probablyscattered light from the radiation field of nearby stars (Mattila et al. 2007).del Burgo & Cambresy (2006) state that the Hα emission is from the clouditself and suggest a very high rate of cosmic rays to explain the H ionisation.Whichever the case, we can set an upper limit to the free-free contributionusing the SHASSA frame.

We built the SED with the differenced fluxes integrated on an aperture of 1deg, similar to the resolution of WMAP K-band (52 arcmin). Here, the fit wasmade using four components: synchrotron, free-free, thermal dust emissionand spinning dust. The spectral indices for free-free and synchrotron are thesame as those we used in the case of ζ Oph.

For the 100, 140 and 240 µm DIRBE and WMAP 94GHz points we fitted amodified black body with fixed emissivity index β = 2 and a temperature of17 K. In this cloud, the spinning dust component was fitted using the warmneutral medium (WNM) model.

We estimated the hydrogen column density using the extinction map fromSchlegel et al. (1998). We used the relation from Bohlin et al. (1978) valid fordiffuse clouds: N(H+H2)/E(B − V )=5.8×1021cm−2mag−1. We found NH =3.5 × 1021cm−2.

Although we have not attempted it, there would be better to use the NICERmulti-band technique (Lombardi & Alves 2001) to estimate the extinction andthe hydrogen column density. To fit the data, we used a correction factor of0.14, so the H column density used in the fit is N(H)= 0.5 × 1021cm−2.

Fig. 5.3 shows the fit. The pair of dotted lines sets limits on the free-

40

Figure 5.3: SED of LDN 1780. as in Fig. 5.1, the red dotted lines shows upper and lowerlimits for the free-free contribution. The symbols with arrows are upper limits(3 σ). In green is a spinning dust model from Draine & Lazarian (1998b).

free contribution from the Hα data. On the figure are also plotted 3 σ upperlimits to the contribution at 61 and 94 GHz from the WMAP V and W bands.This SED shows a excess shows an excess at cm-wavelengths, were no otheremission mechanism are expected to contribute. The spinning dust model tswell the SED extracted from a 1 deg aperture.

41

Chapter 6

Morphological analysis

If dust is responsible for the 31 GHz emission in these clouds, we expect amorphological correspondence with IR emission. A discussion of the infraredemission from dust can be found in Draine & Li (2007) and references therein.The 100 µm emission is due to grains bigger than 0.01 µm that are in equi-librium with the interstellar radiation field at a temperature ∼10-20 K. TheMid-IR emission on the other hand traces hot VSGs grains at ∼100 K, whichare too hot to be in equilibrium with the environment. These grains are heatedstochastically by starlight photons and, given the very small heat capacity ofa VSG a single UV photon increases the particle temperature enough to emitat λ < 60 µm.

In the SEDs, we could see that in ζ Oph the dominant contribution at31 GHz is free-free emission. However, inspection of the sky-plane imagesin Fig. 6.1, suggests that there is no proportionality between the free-freetemplates (Fig. 6.1 a,b) and the 31 GHz contours. The CBI data seems tomatch better with a combination between free-free and IR emission. We note,however, that although the south-eastern arm of the ζ Oph cloud is slightlyoffset, by ∼ 3 arcmin, from its IR counterpart. This offset is larger than therms pointing accuracy of CBI, of order 0.5 arcmin.

In LDN 1780, there is no significant free-free contribution at 31 GHz. Differ-ences in the IR images are clear in Fig. 6.2. Quantifying these differences wecan find out which kind of dust grains are responsible for the 31GHz emissionin this cloud: if large, classical grains or VSGs.

42

Figure 6.1: Comparison of ζ Oph with different templates on the sky plane. From the upper-left box and in clockwise order we show the free-free template obtained from theHα image, the Stockert 11 cm continuum map, the IRAS 100 µm map (whichtraces large dust grains), and the IRAS 12 µm map (which traces very smallgrains).Shown in contours is the cleaned image of ζ Oph. Contours are as inFig. 3.3. The south-eastern “arm” of the contours has not correspondence withthe free-free templates, although it resembles dust emission.

43

Figure 6.2: Comparison of the restored CBI2 image of LDN1780 with IRAS templates. Theradio point source NVSS 153909-065843 has been subtracted from the CBI2 data.Contours are as in Fig. 3.3. Note the morphological differences among the IRAS

bands. The arrows in the corner are perpendicular to the galactic plane and pointtowards the north Galactic pole.

44

6.1 Visibility plane correlations

In order to make a morphological interpretation of the 31 GHz data, we repeatthe procedure of Casassus et al. (2006) and compare with simulations of theCBI observations on the four IRAS bands, the free-free template obtainedfrom the SHASSA Hα image and the Spitzer 8µm image of LDN1780. Thesesimulations are performed with the MockCBI program (T. J. Pearson, priv.comm.) which calculates the visibilities V (u, v) on the input images Iν(x, y)with the same uv sampling as a reference visibility data set. In what followswe refer to these simulated data as ‘CBI-simulated’ visibilities. The aim ofdoing the comparison in the visibility plane is to avoid spurious features thatcould arise during the deconvolution process. In addition, we want to compareonly the spatial frequencies measured by the interferometer.

We linearly correlated the CBI visibilities (real and imaginary components)with the CBI-simulated visibilities of the different templates: The IRAS im-ages were deconvolved by dividing, in the visibility space, by the FourierTransform of the Gaussian function that accounts for the beam of the IRAS

telescope (inverse taper correction). We made the correlations one templateat a time, eg. V (31 GHz)= aV (IRAS). We fit a by linear regression1.

6.1.1 ζ Oph

Table 6.1 shows the values of the reduced χ2, the linear correlation coefficient2

r and the correlation slope a for the different combinations. The best matchis with the free-free template. Because the data is very noisy, we cannotconclude on which IR template, if any, best approximates the CBI data.Figure 6.3(a) shows an example of one correlation between the radio-emissionand IRAS 12 µm simulated visibilities.

6.1.2 Bi-linear correlations in ζ Oph

For ζ Oph, with the aim of testing what we see on the sky plane (Fig. 6.1),we also made bi-linear correlations using a linear combination of the IRAS

1minimising χ2 =∑

i ‖V (31 GHz)−aV (IRAS)‖2/σ2i

2r ≡ (N∑

xiyi −∑

xi

∑

yi)/([N∑

x2i − (

∑

xi)2]1/2[N

∑

y2i − (

∑

yi)2]1/2), from Bevington & Robinson

(2003)

45

(a) (b)

Figure 6.3: Example of linear correlations in the visibility plane of 31 GHz emission withIRIS 12µm of ζ Oph in the left and 31 GHz data with IRAC 8µm in the right.The data is very noisy and only a small trend appears in these correlations.

Parameter free-free1 12 µm 25 µm 60 µm 100 µmχ2/m 1.075 1.081 1.083 1.081 1.080r 0.122 0.101 0.087 0.096 0.102a 293.9±21.3 1.32± 0.13 0.15± 0.02 0.10± 0.01 0.15± 0.01

Table 6.1: Correlation parameters for ζ Oph. m is the number of degrees of freedom, r isthe linear correlation coefficient and a is the proportionality factor between the31 GHz visibilities and various templates in units of 10−3.

and Hα templates: V (31 GHz) = a1V (IRAS)+a2V (Hα).

Because the free-free template has a large amount of extended emission,we perform these correlations in a sub-sample of the visibilities. We choosea minimum (u, v)radius r2

uv = u2 + v2 in order to discard the data from theshortest baselines (i.e. the more extended emission).

The best match was obtained using the 100 µm template. Here, χ2/m =1.014, and the proportionality coefficients were: a1 = 0.08 and a2 = 488.3,both in units of 10−3. The normalised χ2 in this case is slightly better thatin the single template correlations described before. This indicates that adust component could be present in the 31 GHz data. However, we have notassessed the statistical significance of the improvement in χ2.

46

6.1.3 LDN1780

In the case of LDN1780 we only correlated with the IR templates (i.e. IRAS &IRAC) because we do not expect free-free emission to be important in thiscloud. Moreover, here the Hα photons are probably scattered from the IRF bydust grains so the Hα emission does not account for the free-free contributionon LDN1780. In Fig. 6.2 we see that there is a difference between the fourIRAS channels with respect to the contours of the 31 GHz data, so we expecta quantitative confirmation in the visibilities plane that accounts for this.The peak at 31 GHz is closer to the peak at 12 µm than to 100 µm.

The CBI data is very noisy and from these correlations we cannot differen-tiate between the IR-templates, although IRAS 25 & 60 µm shows the bestcorrelation coefficient. Table 6.2 lists the parameters of the correlations inthe uv plane.

Parameter 8 µm 12 µm 25 µm 60 µm 100 µmχ2/m 2.5 2.5 2.5 2.6 2.6r 0.08 0.103 0.114 0.112 0.08a 22.4 ± 1.2 24.5 ± 1.3 18.5± 0.9 4.6 ± 0.2 0.1± 0.05

Table 6.2: Correlation parameters of LDN1780.

47

6.2 Sky plane correlations

Here we investigate sky-plane cross-correlations. For this, we simulated CBIobservations of the IRAS and free-free templates using MockCBI. We restoredthese simulated visibilities using DIFMAP and then the restored images werecorrected by the primary beam of CBI. Fig. 6.4 shows two examples of thesimulated and reconstructed images of ζ Oph. We correlated all pixels withina square box, 30 arcmin per side, centered at the phase-center of the 31 GHzdata.

m60 µ Free-Free

Free-Freem60 µ

Figure 6.4: Examples of simulated data using MockCBI. The upper images are the referenceimages, IRAS 60 µm and free-fee, which are “observed” by CBI. The images atthe bottom were reconstructed using DIFMAP and were used to perform thecorrelations in the sky-plane. The circle shows the CBI primary beam.

The degeneracy of the reconstruction process in the noisy data that we havecan led to ambiguous conclusions. In order to have more reliable results inthese correlations, we performed a statistical analysis. We added Gaussiannoise to the observed visibilities and reconstructed this set of mock data. Thenoise can produce spurious features in the images, as well as the reconstructionprocess. In this sense, our results are conservative in that the noise can erase

48

characteristics that are real from the data. In the Monte-Carlo simulation,we generated a set of 1000 images reconstructed for each image. Then, wecorrelated the comparison templates with the mock data. The application tothe targets is deferred to the next Sections 6.2.1 and 6.2.2.

6.2.1 ζ Oph

Figure 6.5 shows two examples of the correlation, with the free-free andIRAS 60µm templates. The histogram in Fig. 6.6a shows the distribution ofthe Pearson correlation coefficient of the simulated data. The width of thedistribution gives us a conservative estimate of the errors in the correlationcoefficients and also in the slope of the linear relation between the IR and 31GHz data (the 31 GHz dust emissivity relative to the dust templates). Theusual comparison is Fig. 6.6b. Table 6.3 lists the derived parameters. Theerrors are from the rms dispersion of the Monte Carlo simulations; they areconservative because of the injection of noise to the data.

(a) (b)

Figure 6.5: Pixel-by-pixel correlation of CBI data with mock free-free and IRAS 60 µm tem-plates on ζ Oph. x-axis is the intensity in the pixels of the 31 GHz image andy-axis the intensity in the comparison template.

49

In this case there are no significant differences between the different IRdata and the best correlation is with the free-free template as in the uv-planecorrelations. As we can see in the SED of this cloud (Fig. 5.1), most of theemission can be completely accounted by the free-free contribution, so it isnot a surprise that the best correlation is with the free-free template.

(a) (b)

Figure 6.6: Histograms form the Monte Carlo simulations. Left: histogram of the distribu-tion of the correlation coefficient r for the different templates on ζ Oph. Thecorrelation with the free-fee template is significantly better than the correlationwith any dust template. Right: histogram of dust emissivity at 31 GHz relativeto the 100 µm map. The rms dispersion of these simulations are used as errorbars for our results.

free-free 12 µm 25 µm 60 µm 100 µmr 0.74/0.67±0.05 0.47/0.34±0.05 0.43/0.30±0.05 0.46/0.33±0.05 0.44/0.32±0.06a 457/529±102 2.4/2.6±0.5 2.7/±0.06 0.17/0.19±0.04 0.37/0.42±0.1

Table 6.3: Correlation parameters for ζ Oph. r is the linear correlation coefficient and a isthe proportionality factor between the 31 GHz visibilities and various templatesin units of µK/(MJy/sr)−1. Data given in the form r/rsim ± σsim where r is thevalue for the real data and rsim ± σsim is the value and dispersion given by theMonte Carlo simulations.

50

6.2.2 LDN1780

In this cloud, the correlations between 31 GHz and the IR data shows inter-esting results. Here, all the IR templates correlates better with the CBI datathan in ζ Oph. The best match is with IRAS 60 µm (note that if we go backto Fig. 6.2 this appears to be the most reasonable) and the Monte Carlo sim-ulations confirm this result (Fig. 6.7a). The emission at 60 µm is mainly fromVSGs and a 30-40 % contribution from classical grains (Desert et al. 1990) soour results favours the idea of a VSGs origin for the cm-wave radiation. It isworth to note that in Fig. 6.8 the 60 µm image correlates tighter in the lessintense pixels, while the corrected (see Sec. 6.2.3) 8 µm templates matchesbetter the peak of the CBI image. Table 6.4 list the results.

(a) (b)

Figure 6.7: Histograms form the Monte Carlo simulations for LDN 1780. Left: distributionof the correlation coefficient r for the different IR templates. Right: histogramof dust emissivity at 31 GHz relative to the 100 µm map.

PAH and VSG emission at 8 & 12 µm have similar correlations coefficientsthat the emission at 100 µm. However, we have to remember that the emissionof VSGs depends on the strength of the IRF. The differences in morphologythat appear in this cloud depends both on the distribution of grains withinthe cloud and in the manner that the cloud is illuminated by the IRF. In Sec.6.2.3 we will investigate how the IRF illuminates this cloud.

51

(a) (b)

Figure 6.8: Pixel-by-pixel correlation of CBI data with mock IRAS 60 µm and the correctedIRAC 8µm templates on LDN 1780. IRAS 60 µm correlates better in the morediffuse regions while IRAC 8 µm does better in the peak of the CBI image.

8 µm 12 µm 25 µm 60 µm 100 µmr 0.59/0.59±0.05 0.54/0.52±0.06 0.65/0.64±0.03 0.79/0.76±0.09 0.59/0.58±0.10a 5.32/7.18±1.3 5.20/7.20±1.38 3.69/5.13±0.90 0.88/1.2±0.19 0.22/0.31±0.05

Table 6.4: Correlation parameters for LDN1780. Data given in the form r/rsim±σsim wherer is the value for the real data and rsim ± σsim is the value and dispersion givenby the Monte Carlo simulations. a in units of µK/(MJy/sr)−1

6.2.3 IRF on LDN 1780

The radio emission from spinning VSG is fairly independent of the IRF(Draine & Lazarian 1998b; Ali-Haımoud et al. 2009; Ysard & Verstraete 2009).These grains are heated stochastically by interstellar photons so their near-IRemission is proportional to the amount of VSGs and to the intensity of the ra-diation field. Because of this, a better correlation of the 31 GHz data with thenear-IR templates may not be indicative of a VSG origin of the cm-emission.

The IRF can be expressed (assuming that in this cloud, it has the samespectral distribution as in Mathis et al. 1983) in terms of G0, the averagedintensity of the UV radiation field in units of its value in the solar vicinityand integrated between 6 and 13.6 eV (1.6×10−3 erg/s/cm2, Parravano et al.2003).

52

G0 can be estimated (as in Ysard et al. 2009) from the temperature of thebig grains, TBG, in the cloud using:

G0 =

(

TBG

17.5 K

)β+4

, (6.1)

with β = 2.

We constructed a temperature map using ISO 100 & 200µm. To do this, wesmoothed the 100 µm template to the resolution of the 200 µm image. Then,we fitted a modified black body (as in Chapter 5) to calculate the temperatureof the big grains pixel-by-pixel. Using this temperature map, we calculatedG0 using Eq. 6.1. We divided the near-IR templates (8 & 12µm) by our IRFmap and then repeated the correlations with the 31 GHz data. Again, toestimate error bars, we used the Monte Carlo simulations in these correctedimages.

The correlations with these templates are tighter than with the uncorrectedones. The correlation coefficient in this case is r = 0.69 ± 0.04. This is aninteresting result and favours the VSG origin of the the radio emissivity ofLDN 1780. The templates corrected for the IRF traces better the columndensity of VSGs so are better suited to compare with the cm-wave data.Unfortunately, the improvement in r is only at two σ, but we have to remem-ber that the errors in the correlation coefficient are from the Monte Carlosimulations so they are conservative.

53

Chapter 7

Discussion

One motivation for this work stems from the fact that physical conditionsin translucent clouds approach that in the cirrus clouds. Here, we comparethe radio-emission of different clouds observed by the CBI in terms of theirH-nuclei column density. To avoid differences in beam sizes and frequenciesobserved, we choose to compare only sources observed by the CBI. The cirrusclouds column density was obtained using the extinction map from Schlegelet al. (1998) and the 32 GHz data from Leitch et al. (1997), who used a beamof ∼7 arcmin at a frequency of 32 GHz. This beam and frequency are similarto the synthesised CBI beam and its averaged frequency (31 GHz).

In Table 7.1, we list the radio intensity in the peak of the CBI data, anaveraged value for the column density at the same position and the ratiobetween these two quantities. Fig. 7.1 lists the distributions of the points.

N(H) Peak Intensity 31 GHz Emissivitycm−2 MJy/sr (MJy/sr)/H cm−2

Cirrus1 ∼ 5 × 1020 9 ± 3 × 10−3 1.8 ± 0.7 × 10−23

LDN1780 3.5 × 1021 0.016 ± 0.001 × 10−3 4.5 ± 1.3 × 10−24

ζ Oph 1.4 × 1021 0.009 ± 0.001 × 10−3 5.7 ± 5 × 10−24

LDN16222 1.24 × 1022 30 ± 0.5 × 10−3 2.4 ± 0.2 × 10−24

ρ Oph3 0.4 × 1023 0.20 ± 0.016 1.0 ± 0.2 × 10−23

M784 1.5 × 1023 0.11 ± 0.01 7.3 ± 2.5 × 10−25

Table 7.1: Emission parameters for different clouds, all of them observed by the CBI at31 GHz. References are the following: (1) Leitch et al. (1997), (2) Casassus et al.(2006), (3) Casassus et al. (2008), (4) (Castellanos et al., in preparation.)

The emissivities are fairly constant with column density, although there seems

54

to be a trend in the direction of diminishing emissivity with column density.The large error bar in the ζ Oph point is due to the large contribution fromfree-free to the intensity at 31 GHz. Despite the important variations incolumn density, it is interesting that the emissivities of the clouds lies in asmall range of 1 order of magnitude. However, it is worth noting that if theinverse relation we see is real, it will indicate that the anomalous emissionis not associated with large dust grains, as their number increases becausecondensation in denser clouds. A similar result was obtained by (Lagache2003), who used WMAP data combined with IR templates and gas tracers inthe whole sky on angular scales of 7 deg.

Figure 7.1: Emission parameters for different clouds, all of them observed by the CBI at31 GHz. References are the following: (1) Leitch et al. (1997), (2) Casassus et al.(2006), (3) Casassus et al. (2008), (4) (Castellanos et al., in preparation.)

The anomalous foreground which contaminates the CMB observations comesfrom the cirrus clouds. Here, we see that there is not a large difference be-tween the radio emissivity on cirrus and translucent clouds on 7 arcmin an-gular scales. Because of this similarity, translucent clouds are good places toinvestigate the anomalous CMB foreground.

55

Chapter 8

Summary & Conclusions

We have presented CBI data of two translucent clouds, ζ Oph and LDN 1780with the aim of characterising the radio emissivities. We found an anomalousexcess in both clouds at 31 GHz on angular scales of ∼7 arcmin in ζ Oph and∼ 5 arcmin in LDN1780.

The SED of ζ Oph on large (∼ 1 deg) angular scales is dominated by free-freeemission originated in the Hii region that the ζ Ophiuchi star causes. Becauseof this, it is difficult to quantify any contribution from dust to the 31 GHzdata. However, when comparing with the optically thin free-free extrapolatedfrom the 5 GHz PMN image, we find a 3.8 σ excess at 31 GHz on spatial scalesof 7 arcmin in specific intensity. Because of the low signal-to-noise ratio ofthe 31 GHz data it is difficult to conclude about the morphological propertiesof the emission. The correlations in the visibility plane favor the free-freetemplate and this is confirmed in the sky plane.

In the SED of LDN1780 we can see an anomalous excess on large angularscales (i.e. 1 deg). The free-free contribution in this cloud is expected to bevery low; the Hα emission can even be scattered light from the IRF, so itwould not have a radio counterpart. A spinning dust component can explainthe anomalous excess in the SED. The correlations in the visibility-planebetween the cm-wave data and IR-templates shows a trend favouring IRAS 25& 60 µm. The sky-plane correlations confirm these results. The best matchin this case is with IRAS 60 µm although the peak of the CBI image is bestmatched by IRAC 8 µm. We corrected the IRAC 8 µm and IRAS 12 µm bythe IRF and found a tighter correlation with these corrected templates thanwith IRAS 100 µm. These results support the VSG origin for the anomalous

56

emission on this cloud. Spinning dust models predict that these kind of grainsdominates the emission so our results support this mechanism as the originfor the anomalous emission.

The radio emissivities found in both clouds are similar and have interme-diate values between the cirrus clouds and the dark clouds. The emissivitiesvariations are small with column density, although we find hints of an in-verse relationship, which would support a VSGs origin for the cm-emission.Because of the similarities with the ubiquitous cirrus, translucent clouds areuseful to understand the anomalous foreground.

57

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