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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iie

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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.