The Case of RX J1856.5-3754

HST image of the bow-shock nebula around RX J1856.5-3754 (van Kerkwick & Kulkarni 2001)

S. ZaneMSSL, UK

R. TurollaUniversity of Padova, Italy

J.J. DrakeSmithsonian Obs., USA

2002, ApJ Submitted

RX J1856.5-3754: RX J1856.5-3754: a Bare Quark Star or a Naked Neutron Star?a Bare Quark Star or a Naked Neutron Star?

Similar results presented by J. Trumper at the 34th Cospar meeting; Burwitz et al., 2002

The "Magnificent Seven"

RX J1856.5-3754 (Walter et al. 1996) RX J0720.4-3125 (Haberl et al. 1996) RX J0806.4-4132 (Haberl et al. 1998) RX J1605.3+3249 (RBS 1556, Schwope

et al. 1999) RX J1308.6+2127 (RBS 1223, Schwope

et al. 1999) RX J04020.0-5022 (Haberl et al. 1999) 1RXS J214303.7+065419 (RBS 1774,

Zampieri et al. 2001)

RINSs are the largest class of thermally emitting Neutron Stars (Treves et al, 2000)

Thermal emission detected in more than 20 NSs (SGRs, AXPs,PSRs, Radio-quiet NSs)

The striking case of RX J1856.5-3754

500 ks DDT Chandra exposure

(i) RX J1856.5-3754 has a featureless X-ray continuum(ii) better fit with a simple bb than with more sophisticated atmospheric models (Burwitz et al 2001, Drake et al 2002, Burwitz et al, 2002)

The striking case of RX J1856.5-3754

Optical excess of ~6 over the Rayleigh-Jeans tail of the X-ray best fitting bb (Walter & Lattimer, 2002)

No X-ray pulsations: upper limit on the pulsed fraction 3% (Ramson et al, 2002, Drake et al, 2002) 1% Burwitz et al., 2002; Trumper , Cospar meeting

d ~120-140 pc (Kaplan et al, 2001; Walter & Lattimer, 2002)

radiation radius of only 5-6 km! (Drake et al, 200

Is RX J1856.5-3754 the first quark/strange star discovered ?(Drake et al, 2002; Xu, 2002)

Bare quark stars not covered by an atmosphere would presumably emit a pure blackbody spectrum (2th component for the optical emission)

Other options : NS models based on a two-T surface distribution (Pons et al, 2002; Walter & Lattimer, 2002 )

May account for X-ray to optical emission Give acceptable values for the star radius

But how to produce a featureless spectrum from a NS covered with an optically thick atmosphere ??

How the spectrum of a quark star looks like ??

Braje and Romani, 2002

Can rotation smear out spectral features?

dE/dt from the bow shock standoff gives:

P = 4.6 (B/108 G) ½ ms

So a low field star with a non-magnetic atmosphere should have a ~ms period

HRC-S limits preclude sensitivity searches below ~10 ms

Braje and Romani, 2002

Can rotation smear out spectral features?

Bow shock nebula powered by a relativistic wind of e± generated

by the pulsar spin-down estimate of the spin down power

dE/dt ~ I d/dt ~ 8 x1032 erg/s

Magneto-dipolar breaking (PdP/dt 10-15B122)

dE/dt ~ 1034 (B12 6)-2 erg/s B12 6 ~ 3

Also: no pulsations within 4% gave an allowed fraction of sky 2-4%This fraction is even smaller with the new upper limit on the pulsed fraction of 1%

Lai & Salpeter (1997), Lai (2001): NSs may be left without an atmosphere if they are cool enough. Onset of a phase transition

A gaseous atmosphere turns into a solid when T < Tcrit(B)

An alternative explanation: BARE NSs

If B >> mee3c/h3 2.35 x109 G atoms and condensed matter change:

( ) ( ) eVBBT pBpppBppcritH

⎥⎦

⎤⎢⎣

⎡++−−−−≈ ,

2/12,

2,,

212

37.012 2

1

205.6ln4.41.1941.0 ωωωω h

hh

Tcrit for phase separation between condensed H and vapor:

Situation more uncertain for heavy elements (as Fe)

eVBQT SFe

crit5/2

12271.0 ≈≤eVBZEQ atomS5/2

125/9~05.0≤

Strong magnetic confinement on e-; atoms have cylindrical shape elongated atoms may form molecular chains by covalent bonding along B Interactions between linear chains can then led to the formation of 3-D

condensates

Source Tcol (eV) B (1012 G) Refs RX J1856.5-3754 61.1 ± 0.3 -- 1,2 RX J 0720.4-3125 86.0 ± 0.6 21.3 ± 0.1 3,4 RBS 1223 90.6 ± 1.6 500 ± 150 5 Vela 128.4 ± 7 3.3 6,7 Geminga 48.3 +6.1-9.5 1.5 8,9 PSR 0656+14 69.0 ± 2.5 4.7 10,7 PSR 1055-52 68.1 +10.2 –17.2 1.1 11,7

The coolest thermally emitting NSs with

available B + RX J1856.5-3754

[1] Burwitz et al, 2001; [2] Drake et al, 2002; [3] Paerels et al, 2001; [4]Zane et al, 2002; [5} Hambaryan et al, 2002; [6] Pavlov et al, 2001; [7] Taylor et al, 1993; [8] Halpern & Wang, 1997; [9] Bignami & Caraveo, 1996; [10] Marshall & Schulz 2002; [11] Greivendilger et al, 1996.

Most Isolated Neutron Stars have T well in excess of THcrit :

if surface layers are H-dominated an atmosphere is unavoidable.

But: if some objects have not accreted much gas: we may detect thermal emission directly from the iron surface layers depending on B the outer layers of RX J1856.5-3754 might be in form of condensed matter !

SPECTRUM?

Critical T for H and Fe. Condensation is possible in the shaded region for Fe and in the cross-hatched region for H. Filled circles are the NSs listed in the table. The horizontal line is the color temperature of RX J1856.5-3754

dA = R2sin d d = surface element at magnetic co-latitude = total surface reflectivity for incident unpolarized radiation

= (1 - ) =) = absorption coefficient

j = B (T) = emissivity (Kirchoff’s law)

Brinkmann 1980

Anisotropy of the medium response properties strongly depends on the direction of the refracted ray

• Pure vacuum outside the star (neglect vacuum birefringence)• EM wave incident at the surface with (E,k) is partly reflected (E’,k’) and partly refracted • Birefringence of the medium: the refracted wave is sum on an ordinary (E’’1,k’’1) and an extraordinary (E’’2,k’’2) mode.

ij = k’i k’j - |k|2ij +(2/c2)ij = Maxwell tensor

| ij | = 0 = dispersion relation refractive index nm , m=1,2

g 390 A5/2 T5/2 exp(-QS/T) g cm-3 : ion density of the condensed phase near zero pressure (Lai, 2001) plasma frequency

solve the wave equation for the two refracted modes: ij (nm)E’m,j =0

obtain the ratios E’m,x / E’m,z E’m,y / E’m,z

put these ratios into the BCs at the interface between the two media obtain the E-field of the reflected wave in terms of the E-field of the incident wave

Once nm, m=1,2 are known:

Reflectivity :

Absorption coefficient: = (1 - )

Total Flux :

The Spectrum by a Bare NSs is not necessarily a bb

Strong (angle-dependent) absorption for photons with energy comparable or lower than the plasma frequency.

Strong absorption around the e- and ion cyclotron frequency.

Below the plasma freq, one of the two modes may be non-propagating: a whistler. Whistlers have very large, divergent refractive index (Melrose, 1986).

Appearance of cut-off energies and evanescent modes which can not propagate into the medium.

If the refractive index has large imaginary part : highly damped modes. They can not penetrate much below the surface (Jackson, 1975).

RESULTS: absorption features may or may not appear in the X-ray spectrum, depending on the model parameters (mainly on B).

The monochromatic absorption coefficient as a function of the energy for B=1012 G and different values of the magnetic field angle. From top to bottom: 2/=0.05, 0.2, 0.4, 0.6, 0.8, 0.9, 0.95.

The monochromatic absorption coefficient integrated over the star surface for B=1012 G , B=5x1012 G, B=1013 G and B=5x1013 G

Turolla, Zane & Drake, Apj submitted

B =3x1013GTeff = 75 eV

Left : T=cost

Right : T() as given by Greenstein & Hartke 1983

Dashed line: bb at Teff

Dashed-dotted line: best fitting bb in the 0.1-2 keV range

Solid lines: spectra. Upper curve: p

Lower curve: 2.5 p

B =5x1013G

Turolla, Zane & Drake, Apj subm.

A Few Numbers

For B 5 x 1013 G:

No features whatsoever in the 0.1-2 keV band

The spectrum is within 4% from the best-fitting bb

The total power radiated by the surface in the 0.1-2 keV band is 30-50% of the bb power, slightly larger for the meridional temperature variation models

The constant temperature spectrum shows no hardening, while for T() it is Tcol/Teff = 1.13

The bare NSs Model and The Case of RX J1856.5-3754

For the surface layers of RX J1856.5-3754 to be in form of condensed iron B 3-5 x1013 G, high but well below the magnetar range

For such B’s: featureless 0.1-2 keV spectrum. Deviations from a bb distribution less than 4%

Compatible with the constraints from the bow-

shock nebula: B12 6 ~ 3 (star age ~ 105 yrs)

Well within the ~10% accuracy limit for spectral fit to Chandra data / calibration uncertainties of the LETGS (Braje & Romani, 2002; Drake et al, 2002)

Correcting the Angular SizeR /(d/100 pc) = 4.12 0.68 km (Drake et al, 2002)

Ratio of the emitted to the bb power in the 0.1-2 keV range for different values of the plasma frequency and B =3 x1013 G. Filled circles: T=constant. Open circles: T().

T =const: 7.56 1.25 km < R < 9.64 1.59 km T() (larger hardening) : 9.11 1.50 km < R < 11.73 1.94 km

If d ~ 130 pc + emission from the entire star surface + 1 < p / p, 0 < 2.5:

THE MERIDIONAL T DISTRIBUTION CAN PROVIDE R ~10-12 km

COMPATIBLE WITH (SOFT) EOS of NSs (Lattimer & Prakash, 2001)

Explaining the UV-optical Excess Turolla, Zane & Drake in preparation

Can we explain the optical excess with a thin, ionized gasoues layer on the top of the Fe solid?

H deposited by very slow accretion (or fallback). 109g of H in 105 yr deposition rate 10-4 g/s. Orders of magnitude below Bondi.

H is likely not to condensate.

With a typical scale height of 1 cm:

)10( eVopticalff Is 200 times larger than )100(~ eVraysX

ff−

Is the situation stable ? The gas may cool down rapidly

H is kept at T Tstar (106 K) by e- - conduction from the crust.

423

44

3

15TRLL

kT

EL BBBB

thick σ

=<<⎟⎠

⎞⎜⎝

⎛⎟⎠

⎞⎜⎝

⎛≈

( )kTmHRU pAμρπ ρ /4 2≈

4

6

33

104/

10

15

/10

1/

−

−

×≈

≈

≈≈

≈≈

=∫

BB

thick

LL

KT

eVEcmg

cmyH

dzy

tcooling U/L 7 x10-6 s

UNLESS ….

ENERGY RADIATED BY THE LAYER PER UNIT TIME (Opt. thin bremsstrahlung losses are negligible)

THERMAL CONTENT

Energy Balance Coupling between thermal conduction and radiative transfer

kT=kf+kes

kf, kp, kj = flux, planck and absorption mean opacitieskes = 0.2(1+X) = scattering opacityX = hydrogen fraction

Thermal conductivity

Boundary conditions:

Energy-averaged and angle-averaged depression factor for the surface emissivity (computed numerically as before)

Solid lines : 1 = 10–3 g cm3 and 3 different crust emissivities in input

Dashed line : 1 = 3x10–3 g cm3 and crust emissivity as in b

1 = gas density at the interface gas/crust

Energy dependent radiative transfer through the layer

• Finite atmosphere, non illuminated from above

• Bounded on two sides at =0 and =1

Energy-dependent (BUT ANGLE AVERAGED depression factor for the surface emissivity (computed numerically)

B = 3x10 13 GTeff = 75 eV

Left : T=costRight : T()

Spectrum of a bare NS after crossing a pure H layer with in=2x10-3 g/cm3

X-rays will cross the layer unhindered, but the low-energy photons get reprocessed and re-emitted as a blackbody at Tgas

The X-ray emission from the bare star is depressed by a factor ~3-4 with respect to the bb then the optical emission “appears” enhanced

Iron, 1=2x10-3 g/cm3 NO Iron, 1=6x10-4 g/cm3 NO

70% H, 30% He (mass fraction) 1=2x10-3 g/cm3 OK

70% H, 30% He (mass fraction) 1=6x10-4 g/cm3 OK

Observed optical excess is 6-7 (Walter & Lattimer, 2002)

One component model which requires a surface emissivity in the X-ray band which is lower than a black body. Solid and dotted curves represent the absorbed and unabsorbed model spectra, respectively. Burwitz et al, 2002.

• Depression factor in the X-ray 0.15

• Optical excess 6.67

Larger ratios: slightly larger Tgas, external heating, wave dissipation ..

z

y’

x’

z’

yx

OR DIFFERENT VIEWING ANGLES!

EQUATOR-ON CASE

x

z

y

x’ = observer

i

Energy-dependent and ANGLE dependent depression factor for the surface emissivity (computed numerically)

B=3x1013 G 1=10-3 g/cm3

Log E (keV)

Log F

EQUATOR-ON CASE

Greatest Uncertainties and Approximations Current limitations in our understanding of metallic condensates and

lattice structure in strong B and for heavy elements. Sharp transition from vacuum to a smooth metallic surface. Effects

of the macroscopic surface structure neglected. Surface made of pure Fe (effects of mixed composition, impurities..) Quasi-free e- gas inside the star. Lattice structure of the linear chains

neglected. Unpolarized vacuum outside. Neglect vacuum birefringence. Damping effects neglected. e- gas treated as a cold plasma. The reduced emissivity will affect the meridional T variation.

Profiles in the literature are computed assuming a perfect bb emitter at the star surface.

Further effect on the crustal T due to dissipation of rapidly attenuated waves

…..