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The Case of RX J1856.5-3754

RX J1856.5-3754: a Bare Quark Star or a Naked Neutron Star?. The Case of RX J1856.5-3754. S. Zane MSSL, UK R. Turolla University of Padova, Italy J.J. Drake Smithsonian Obs., USA 2002, ApJ Submitted. HST image of the bow-shock nebula around RX J1856.5-3754 (van Kerkwick & Kulkarni 2001).

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The Case of RX J1856.5-3754

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  1. RX J1856.5-3754: a Bare Quark Star or a Naked Neutron Star? The Case of RX J1856.5-3754 S. Zane MSSL, UK R. Turolla University of Padova, Italy J.J. Drake Smithsonian Obs., USA 2002, ApJ Submitted HST image of the bow-shock nebula around RX J1856.5-3754 (van Kerkwick & Kulkarni 2001) Similar results presented by J. Trumper at the 34th Cospar meeting; Burwitz et al., 2002

  2. 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) Thermal emission detected in more than 20 NSs (SGRs, AXPs, PSRs, Radio-quiet NSs) RINSs are the largest class of thermally emitting Neutron Stars (Treves et al, 2000)

  3. 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)

  4. 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

  5. (Drake et al, 2002; Xu, 2002)  Bare quark stars not covered by an atmosphere would presumablyemit a pure blackbody spectrum  (2th component for the optical emission) • Is RX J1856.5-3754 the first quark/strange star discovered ? • 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 ??

  6.  Can rotation smear out spectral features? HRC-S limits preclude sensitivity searches below ~10 ms • Braje and Romani, 2002 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

  7.  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 • Braje and Romani, 2002 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 of1%

  8. An alternative explanation: BARE NSs • 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) If B >> mee3c/h32.35 x109 G atoms and condensed matter change: 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 Tcrit for phase separation between condensed H and vapor: Situation more uncertain for heavy elements (as Fe)

  9. 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. 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 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?

  10. Brinkmann 1980  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) 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|2ij +(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

  11. Once nm, m=1,2 are known:  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 Reflectivity :  Absorption coefficient:  = (1 - ) Total Flux :

  12. 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).

  13. 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

  14. B =3x1013G Teff = 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.

  15. 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

  16. 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% • Well within the ~10% accuracy limit for spectral fit to Chandra data / calibration uncertainties of the LETGS (Braje & Romani, 2002; Drake et al, 2002) Compatible with the constraints from the bow-shock nebula: B12 6~ 3(star age ~ 105 yrs)

  17. Correcting the Angular Size R /(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(). If d ~ 130 pc + emission from the entire star surface + 1 < p /  p, 0 < 2.5: 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 THE MERIDIONAL T DISTRIBUTION CAN PROVIDE R  ~10-12 km COMPATIBLE WITH (SOFT) EOS of NSs (Lattimer & Prakash, 2001)

  18. 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: Is 200 times larger than

  19. Is the situation stable ? The gas may cool down rapidly ENERGY RADIATED BY THE LAYER PER UNIT TIME (Opt. thin bremsstrahlung losses are negligible) THERMAL CONTENT tcoolingU/L7 x10-6 s UNLESS …. H is kept at T Tstar (106 K) by e- - conduction from the crust.

  20. Energy Balance Coupling between thermal conduction and radiative transfer kT=kf+kes kf, kp, kj = flux, planck and absorption mean opacities kes = 0.2(1+X) = scattering opacity X = hydrogen fraction Thermal conductivity Boundary conditions: Energy-averaged and angle-averaged depression factor for the surface emissivity (computed numerically as before)

  21. 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

  22. 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)

  23. B = 3x10 13 G Teff = 75 eV Left : T=cost Right : 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

  24. Iron, 1=2x10-3 g/cm3NO 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

  25. Observed optical excess is 6-7 (Walter & Lattimer, 2002) • Depression factor in the X-ray  0.15 • Optical excess  6.67 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.

  26. z’ z  y x’ = observer x i y’   z y x’  Larger ratios: slightly larger Tgas, external heating, wave dissipation .. OR DIFFERENT VIEWING ANGLES! EQUATOR-ON CASE x Energy-dependent and ANGLE dependent depression factor for the surface emissivity (computed numerically)

  27. Log F Log E (keV) EQUATOR-ON CASE B=3x1013 G 1=10-3 g/cm3

  28. 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 • …..

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