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

The "Magnificent Seven" RX J (Walter et al. 1996) RX J (Haberl et al. 1996) RX J (Haberl et al. 1998) RX J (RBS 1556, Schwope et al. 1999) RX J (RBS 1223, Schwope et al. 1999) RX J (Haberl et al. 1999) 1RXS J (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 J ks DDT Chandra exposure (i) RX J 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 J 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 ~ pc (Kaplan et al, 2001; Walter & Lattimer, 2002)  radiation radius of only 5-6 km! (Drake et al, 200

Is RX J 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   (2 th 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/10 8 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 x10 32 erg/s Magneto-dipolar breaking (PdP/dt  B 12 2 ) dE/dt ~ (B 12  6 ) -2 erg/s  B 12  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 < T crit (B) An alternative explanation: BARE NSs If B >> m e e 3 c/h 3  2.35 x10 9 G atoms and condensed matter change: T crit for phase separation between condensed H and vapor: Situation more uncertain for heavy elements (as Fe) 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

The coolest thermally emitting NSs with available B + RX J [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, Most Isolated Neutron Stars have T well in excess of T H crit :   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 J 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 J

  dA = R 2 sin  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| 2  ij +(  2 /c 2 )  ij = Maxwell tensor  | ij | = 0 = dispersion relation  refractive index n m, m=1,2  g  390 A 5/2 T 5/2 exp(-Q S /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 (n m )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 n m, 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=10 12 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, The monochromatic absorption coefficient integrated over the star surface for B=10 12 G, B=5x10 12 G, B=10 13 G and B=5x10 13 G Turolla, Zane & Drake, Apj submitted

B =3x10 13 G T eff = 75 eV Left : T=cost Right : T(  ) as given by Greenstein & Hartke 1983 Dashed line: bb at T eff Dashed-dotted line: best fitting bb in the keV range Solid lines: spectra. Upper curve:  p Lower curve: 2.5  p B =5x10 13 G Turolla, Zane & Drake, Apj subm.

A Few Numbers For B  5 x G: No features whatsoever in the keV band The spectrum is within  4% from the best-fitting bb The total power radiated by the surface in the 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 J For the surface layers of RX J to be in form of condensed iron  B  3-5 x10 13 G, high but well below the magnetar range For such B’s: featureless keV spectrum. Deviations from a bb distribution less than 4% Compatible with the constraints from the bow- shock nebula: B 12  6 ~ 3 (star age ~ 10 5 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 Size R  /(d/100 pc) = 4.12  0.68 km (Drake et al, 2002) Ratio of the emitted to the bb power in the keV range for different values of the plasma frequency and B =3 x10 13 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  <  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) g of H in 10 5 yr  deposition rate 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

Is the situation stable ? The gas may cool down rapidly H is kept at T  T star (10 6 K) by e - - conduction from the crust. t cooling  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 k T =k f +k es k f, k p, k j = flux, planck and absorption mean opacities k es = 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)

Solid lines :  1 = 10 –3 g cm 3 and 3 different crust emissivities in input Dashed line :  1 = 3x10 –3 g cm 3 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 G T eff = 75 eV Left : T=cost Right : T(  ) Spectrum of a bare NS after crossing a pure H layer with  in =2x10 -3 g/cm 3 X-rays will cross the layer unhindered, but the low-energy photons get reprocessed and re-emitted as a blackbody at T gas 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/cm 3 NO Iron,  1 =6x10 -4 g/cm 3 NO 70% H, 30% He (mass fraction)  1 =2x10 -3 g/cm 3 OK 70% H, 30% He (mass fraction)  1 =6x10 -4 g/cm 3 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, Depression factor in the X-ray  0.15 Optical excess  6.67

Larger ratios: slightly larger T gas, external heating, wave dissipation.. z y’ x’ z’ y x   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=3x10 13 G  1 =10 -3 g/cm 3 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 …..