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Radiation Properties of Magnetized Neutron Stars. RBS 1223
V. Suleimanov1,2, A. Potekhin3, V. Hambaryan 4,R. Neuhäuser 4, K. Werner1
1University of Tübingen, Germany2Kazan State University, Russia
3Ioffe Institute, St. Petersburg, Russia4University 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
• 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)
X-ray emission from isolated neutron stars
RBS 1223EW = 150 eVE line = 300 eV
RX J0720EW = 40 eVE line = 270 eV
XMM-Newton (Haberl et al. 2003, 2004)
Pulsars: Period P vs. P-dot
binary
X-ray dim Isolated neutron stars(XDINS) = M7 neutron stars
may have evolvedfrom AXPs or SGRs
• 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
X-ray emission from isolated neutron stars
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)
2. Inhomogeneous heat transport in NS crust (due to magnetic field)
But the spot size must be small Р = 10.3 s, В ≈ 5 1013 G → θspot < 1°
(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 %
• 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
Local models of neutron star surface
Approximate Fe-emission spectrum(Suleimanov et al. in prep; after Adelsberg et al. 2005)
Ec,i = iron cyclotron energyα = viewing angle Φ = B-field inclination
EW ~ 150 eV
• 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
Local hydrogen model atmospheres
)(),(,)(
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Radiation properties of XDINS. Local models.
H atmosphere above blackbody H atmosphere above condensed iron surface
EW ~ 300 – 400 eV
)10/(635.0,2
)(exp),exp()exp( 14
1,22,1;
22,1;
2,1;02,121 GBkeVEEE
BF LL
L
Approximation of a local spectrum
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).
4min22
244
sincos
cosT
aTT p
2222 sincos aBB p
Approximations for the temperatureand magnetic field distributions
a = ¼ - corresponds to dipole magnetic field
- magnetic colatitude
(Perez-Azorin et al. 2006)
Radiation properties of XDINS. Integral models. Temperature distributions
Pure dipole fieldStrong toroidal component (a=60)
EW ~ 65 – 85 eV
EW ~ 125 eV
EW ~ 200 eV
No strong toroidal component of themagnetic field on the surface !!!
We need a thin hydrogen atmosphere on top of a condensed iron surface to explain the observed spectra of M7
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.