Radiation Properties of Magnetized Neutron Stars. RBS 1223 V. Suleimanov1,2, A. Potekhin3, V. Hambaryan 4, R. Neuhäuser 4, K. Werner1 1University of Tübingen, Germany 2Kazan State University, Russia 3Ioffe Institute, St. Petersburg, Russia 4University of Jena, Germany

Outline Motivation Local models of highly magnetized neutron star surface Integral spectra and comparison with observations

Motivation Constraining EOS of matter at nuclear densities fundamental problem of NS physics, e.g., necessary for gravitational wave signal computation of merging NSs Need to determine NS masses and radii In principle several methods. One of it involves spectral analysis of thermal radiation from NS surface Best suitable objects for this method: isolated NSs (i.e., not in binaries or SNRs); no magnetospheric emission → we see the thermal emission from their surface Only few such objects known: The “magnificent seven” (M7), or, X-ray dim isolated NSs (XDINSs) Discovered by ROSAT

X-ray emission from isolated neutron stars Blackbody-like spectra, T ~ 0.5 - 1 MK All M7 stars (except one) exhibit one or two broad absorption lines at 0.2 - 0.8 keV with EW ~ 30 - 150 eV Nature of lines is debated; if p-cyclotron lines, then B ~ a few 1013 G (in two cases in agreement with P-dot) RBS 1223 EW = 150 eV E line = 300 eV RX J0720 EW = 40 eV E line = 270 eV XMM-Newton (Haberl et al. 2003, 2004)

Pulsars: Period P vs. P-dot X-ray dim Isolated neutron stars (XDINS) = M7 neutron stars may have evolved from AXPs or SGRs binary

X-ray emission from isolated neutron stars All M7 (except one) show X-ray pulsations. Origin: rotation and non-uniform T-distribution across surface. P= 3-11 s, pulsed fractions 1-19% Origin of non-uniform T-distribution: efficiency of heat transfer through crust depends of B-field distribution (inclination and strength) → two hot spots at magnetic poles XMM lightcurve of RBS1223 (Schwope, Hambaryan, 2005, 2007) Two different peaks  two spots Inferred surface T-distribution (Hambaryan, Suleimanov, et al. in prep.)

Where do bright spots arise from ? 1. Heated by the relativistic particles (like in radio pulsars) But the spot size must be small Р = 10.3 s, В ≈ 5 1013 G → θspot < 1° 2. Inhomogeneous heat transport in NS crust (due to magnetic field) (Geppert et al. 2006)

Problems: What kind of local models of highly magnetized neutron stars can provide observed EW of the absorption features? What distributions of the effective temperature and magnetic field across the neutron star surface we need to explain the observed pulsed fraction and the width of the absorption feature? Limiting case: RBS 1223 - EW ~ 150-200 eV, PF ~ 18 %

Local models of neutron star surface Depending on T and B, surface can be a plasma atmosphere or condensed iron. We investigate properties of - Semi-infinite hydrogen-model atmospheres - Thin H-atmospheres above condensed iron surface Thermal emission spectrum of magnetized condensed iron surface is taken as inner boundary condition for thin atmospheres Approximate Fe-emission spectrum (Suleimanov et al. in prep; after Adelsberg et al. 2005) Ec,i = iron cyclotron energy α = viewing angle Φ = B-field inclination EW ~ 150 eV

Local hydrogen model atmospheres Usual vertical-structure equations for plane-parallel LTE atmospheres: - Hydrostatic & radiative equilibrium - EOS: must account for partial ionisation (although T is high) Main complication arises from polarized radiation transfer in the strongly magnetized plasma with arbitrary field inclination RT formulation in terms of intensity of two normal propagation modes (I1,I2), ordinary and extraordinary mode (O- and X-modes) - In analogy to light propagation in a quartz crystal (bi-refringence) - we can avoid working with Stokes I,Q,U,V, because Faraday rotation is large at τ~1. In this case: - I=I1+I2 Q=I1-I2 U=V=0 Two transfer equations, coupled by e-scattering

Radiation properties of XDINS. Local models. H atmosphere above blackbody H atmosphere above condensed iron surface Approximation of a local spectrum EW ~ 300 – 400 eV

X-ray emission from isolated neutron stars T- and B-distributions across NS-surface can be inferred from X-ray light curve. Information about stellar B-field structure and generation. Proper modeling of total stellar spectrum and light curve requires computation of spectra from many individual surface area elements Each local model is characterized by a particular Teff, B-field strength and inclination (and gravity, of order log g=14). Approximations for the temperature and magnetic field distributions (Perez-Azorin et al. 2006) a = ¼ - corresponds to dipole magnetic field - magnetic colatitude

Radiation properties of XDINS. Integral models. Temperature distributions EW ~ 125 eV Pure dipole field Strong toroidal component (a=60) EW ~ 200 eV EW ~ 65 – 85 eV No strong toroidal component of the magnetic field on the surface !!! We need a thin hydrogen atmosphere on top of a condensed iron surface to explain the observed spectra of M7

a thin hydrogen atmosphere on top of a condensed iron surface Conclusions Strong absorption feature in isolated neutron stars might be explained by a thin hydrogen atmosphere on top of a condensed iron surface There is not a strong toroidal component of the magnetic field on the surface of dim isolated neutron stars (M7) Suleimanov, Potekhin, Hambaryan, Neuhäuser, Werner, A&A, in prep.