1. 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

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

3. 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

4. X-ray emission from isolated neutron stars
Blackbody-like spectra, T ~ MK
All M7 stars (except one) exhibit one or two broad absorption lines at keV with EW ~ 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)

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

6. 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.)

7. 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 ≈ G → θspot < 1°
2. Inhomogeneous heat transport in NS crust (due to magnetic field)
(Geppert et al. 2006)

8. 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 EW ~ eV, PF ~ 18 %

9. 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

10. 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+I Q=I1-I U=V=0
Two transfer equations, coupled by e-scattering

11. 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

12. 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

13. 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

14. 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.