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Atmospheres of neutron stars with strong magnetic fields: progress and vistas
Alexander Y. Potekhin1,2 in collaboration with: Gilles Chabrier2 Wynn Ho3,4 Dong Lai3 Zach Medin3,5 Valery Suleimanov6,7 Matthew van Adelsberg3,8 Klaus Werner6
1 2 3 4 5 6 7 8

Ioffe Physical-Technical Institute, St.Petersburg (Russia) CRAL, Ecole Normale SupÈrieure de Lyon (France) Cornell U. (USA) U. Southampton (UK) McGill U. (Canada) U. TÝbingen (Germany) Kazan Federal U. (Russia) KITP ­ UCSB (USA)


Multiwavelength spectrum of a neutron star

Multiwavelength spectrum of the Vela pulsar
G.G.Pavlov, V.E.Zavlin, & D.Sanwal (2002) in Neutron Stars, Pulsars, and Supernova Remnants, ed. W.Becker, H.Lesch, & J.TrÝmper, MPE Report 278, 273


Absorption lines in spectra of isolated neutron stars
CCO 1E 1207.4­5209

D.Sanwal et al. (2002); S.Mereghetti et al. (2002); G.Bignami et al. (2003): 2 (3? 4?) lines in 1E1207.4­5209.
[Figure from Bignami et al. (2004) Mem.S.A.It. 75, 448]


Absorption lines in spectra of isolated neutron stars
Examples for XDINSs

F.Haberl et al. (2003, Astron. Astrophys. 403, L19): spectrum of RBS 1223 (RX J1308.6+2127) with an absorption line near 300 eV.


Absorption lines in spectra of isolated neutron stars
Examples for XDINSs

F.Haberl et al. (2004) A&A 419, 1077: absorption line in RX J0720.4­3125

M. van Kerkwijk et al. (2004) ApJ 608, 432: absorption line in RX J1605.3+3249


Neutron star atmospheres without magnetic field
Standard methods ­ D.Mihalas (1978) Stellar Atmospheres General algorithm - solution of coupled equations: · Hydrostatic equilibrium · Energy balance · Radiative transfer Basic ingredients: · Equation of state · Radiative opacities This generally requires: · Atomic and molecular data (binding energies, cross sections) · Ionization and dissociation equilibrium · Thermodynamic quantities · Treatment of plasma effects (line broadening, pressure ionization, etc.)


Neutron star atmospheres without magnetic field (an example)

Iron: comparison of LTE [B.T.GÄnsicke, T.M.Braje, R.W.Romani (2002) A&A 386, 1001] and NLTE [K.Werner & J.L.Deetjen (2000) in Pulsar Astronomy ­ 2000 and beyond, IAU Coll. 177]


Characteristic values of the magnetic field
· Strong magnetic field B : c = eB/mec > 1 a.u. B > me2ce3/ 3 = 2.35 x 109 G · Superstrong field : c > mec
2

B > me2c3/ e = 4.4 x 1013 G · Strongly quantizing magnetic field : < B = mionnB / 7 x 103 B12 T << TB = c / kB 1.3 x 108 B12 K
3/2

(/) g cm-3


Fully ionized neutron star atmospheres with strong magnetic fields

W.C.G.Ho & D.Lai (2001) MNRAS 327, 1081

Bottom of the atmosphere for X- and O-modes of polarization in strong magnetic fields


Fully ionized neutron star atmospheres with strong magnetic fields

W.C.G.Ho & D.Lai (2001) MNRAS 327, 1081

Comparison of spectra for non-magnetic and magnetic H atmospheres


The effect of vacuum polarization

M.van Adelsberg & D.Lai (2007) MRNAS 373, 495


Bound species in a strong magnetic field

The effects of a strong magnetic field on the atoms and molecules. a­c: H atom in the ground state (a: B<<109 G, b: B~1010 G, c: B~1012 G). d: The field stabilizes the molecular chains (H3 is shown). e: H atom moving across the field becomes decentered.


Bound species in a strong magnetic field

Main transition energies of the hydrogen atom in a magnetic field
[Potekhin & Chabrier (2004) ApJ, 600, 317]

Binding energies of the hydrogen atom in the magnetic field B=2.35x1012 G as functions of its state of motion across the field
[Potekhin (1994) J.Phys.B: At. Mol. Opt. Phys. 27, 1073]


Ionization equilibrium and the equation of state of hydrogen in strong magnetic fields: the effects of nonideality and partial ionization

EOS of ideal (dotted lines) and nonideal (solid lines) H plasmas at various field strengths
[Potekhin & Chabrier (2004) Astrophys.J. 600, 317]


Radiative transitions of hydrogen in strong magnetic fields

Oscillator strengths for transitions between 2 levels of the hydrogen atom at B=2.35x1012 G, as functions of pseudomomentum
[Potekhin (1994) J.Phys.B: At. Mol. Opt. Phys. 27, 1073]


Radiative transitions of hydrogen in strong magnetic fields

Photoionization cross sections for the ground-state H atom at B=2.35x1012 G
[Potekhin & Pavlov (1997) Astrophys. J. 483, 414]


Radiative transitions of hydrogen in strong magnetic fields

Photoionization cross sections for the ground-state H atom at B=2.35x1012 G
[Potekhin & Pavlov (1997) Astrophys. J. 483, 414]


Radiative transitions of hydrogen in strong magnetic fields

Photoionization cross sections for the ground-state H atom at B=2.35x1012 G
[Potekhin & Pavlov (1997) Astrophys. J. 483, 414]


Radiative transitions of hydrogen in strong magnetic fields

Photoionization cross sections for the ground-state H atom at B=2.35x1012 G
[Potekhin & Pavlov (1997) Astrophys. J. 483, 414]


Radiative transitions of hydrogen in strong magnetic fields

Photoionization cross sections for the ground-state H atom at B=2.35x1012 G
[Potekhin & Pavlov (1997) Astrophys. J. 483, 414]


Radiative transitions of hydrogen in strong magnetic fields

Photoionization cross sections for the ground-state H atom at B=2.35x1012 G
[Potekhin & Pavlov (1997) Astrophys. J. 483, 414]


Plasma absorption and polarizabilities in strong magnetic fields: The effects of nonideality and partial ionization

Spectral opacities for 3 basic polarizations. Solid lines ­ taking into account bound states, dot-dashes ­full ionization
[Potekhin & Chabrier (2003) ApJ 585, 955]

To the right: top panel ­ basic components of the absorption coefficients; middle and bottom ­ components of the polarizability tensor
[Potekhin, Lai, Chabrier, & Ho (2004) ApJ 612, 1034]


Opacities for normal modes in a strongly magnetized plasma: The effects of nonideality and partial ionization

Opacities for two normal modes of electromagnetic radiation in models of an ideal fully ionized (dash-dot) and nonideal partially ionized (solid lines) plasma
at the magnetic field strength B=3x1013 G, density 1 g/cc, and temperature 3.16x105 K. The 2 panels correspond to 2 different angles of propagation with respect to the magnetic field lines. An upper/lower curve of each type is for the extraordinary/ordinary polarization mode, respectively
[Potekhin, Lai, Chabrier, & Ho (2004) ApJ 612, 1034]


Result: the spectrum

Potekhin, Lai, Chabrier, Ho, & van Adelsberg (2006) J.Phys.A: Math. Gen 39, 4453

The effect of the atmosphere and its partial ionization on the spectrum of thermal radiation of a neutron star with B=1013 G, T= 106 K
(the field is normal to the surface, the radiation flux is angle-averaged)


Result of modeling: spectra, dipole model

Ho, Potekhin, & Chabrier (2008) ApJS 178, 102

Spectral features are smoothed by surface field distribution. XSPEC: NSMAX ­ http://heasarc.gsfc.nasa.gov/docs/xanadu/xspec/models/nsmax.html


Radiation from condensed surface

van Adelsberg, Lai, & Potekhin (2005) ApJ 628, 902

B=1012 G, B=90o, different angles

Dimensionless emissivity of the iron surface as function of photon energy
(i)

between incident photon direction and normal to the surface


Radiation from condensed surface

van Adelsberg, Lai, & Potekhin (2005) ApJ 628, 902

Monochromatic flux from the condensed surface in various cases
[Matthew van Adelsberg, for Potekhin et al. (2006) J.Phys.A: Math. Gen. 39, 4453]


Thin atmospheres Condensed surface covered by an atmosphere
Idea by Vadim Burwitz; realized by Wynn Ho and by Valery Suleimanov


Thin and layered atmospheres

Emergent spectra (top) and temperature profiles (bottom) for partially ionized H atmospheres: semiinfinite (dashed line) or thin (column density 1.2 g cm­2) atmospheres vs. fully ionized model (dotted)

Emergent spectra of fully ionized atmospheres. Top ­ H (semi-infinite ­ dashes, 100 g cm­2 ­ dot-dash, 1 g cm­2 ­ solid); bottom ­ H/He (25/75 g cm­2). Dottel lines ­ blackbody.

[V.Suleimanov, A.Y.Potekhin, K.Werner, A&A 500, 891 (2009)]


Thin atmospheres: approximate formulae
V.Suleimanov, V.Hambaryan, A.Y.Potekhin, R.NeuhÄuser, K.Werner, A&A 522, A111 (2010)

Emergent spectra (top) and temperature profiles (bottom) of thin partially ionized H atmospheres

Integral spectra for different models, compared with the BB spectra that fit the model at E > 0.5 keV


Atmosphere models for heavier elements

K.Mori, C.Hailey (2006) ApJ 648, 1139

Energies of allowed transitions from the ground state, at B=1012 G Energies and oscillator strengths of allowed transitions from the various tightly bound states


Atmosphere models for heavier elements

K.Mori, W.C.G.Ho (2007) MNRAS 377, 905


Helium ion moving in a strong magnetic field

G.G.Pavlov & V.G.Bezchastnov (2005) ApJ 635, L61

Energies of the ion as functions of N, which characterizes the state of motion across the magnetic field

Transition energies and oscillator strengths as functions of B


Helium atom: photoionization

Z.Medin, D.Lai, A.Y.Potekhin (2008) MNRAS 383, 161

Photoionization cross sections for polarization along B without (solid and dashed lines) and with (dots) account of magnetic broadening.


Unsolved problem: Energy transport below the plasma frequency may affect the spectrum

The suppression of radiation below the plasma energy Epe is approximately modeled by dashed and dotted lines in the upper panel [Ho et al. (2003) ApJ 599, 1293]

Spectra (upper panel) and photon-decoupling densities for X- and O-modes (lower panel) for a partially ionized H atmosphere.


Energy transport below the plasma frequency can be especially important for superstrong fields

Photon-decoupling densities for X- and O-modes for a partially ionized H amosphere, for magnetic field strengths typical of pulsars (blue lines) and magnetars (red lines).
Dot-dashed lines correspond to the radiative surface, the shadowed region corresponds to E < Epl.


Case of RX J1856.4­3754

Previous attempts to model the spectrum (example)

Pons et al. (2002) ApJ 564, 981: H and Si atmosphere models


Case of RX J1856.4-3754

Previous attempts to model the spectrum (another example)

Burwitz et al. (2003) A&A 399, 1109: combination of two blackbody models


Case of RX J1856.4-3754

W.C.G.Ho et al. (2007) MNRAS, 375, 821 Magnetic hydrogen atmosphere models and the neutron star RX J1856.5-3754


Case of RX J1856.4-3754

W.C.G.Ho et al. (2007) MNRAS, 375, 821 Magnetic hydrogen atmosphere models and the neutron star RX J1856.5-3754

But: M.H.van Kerkwijk & D.L..Kaplan (2008) ApJ 673, L163 B 1.5x1013 G


Absorption lines in spectra of isolated neutron stars
Case of CCO 1E 1207.4-5209 Sanwal et al. (2002); Mereghetti et al. (2002); Bignami et al. (2003, 2004): 2 (3? 4?) lines in 1E1207.4­5209.
[Figure from Bignami et al. (2004) Mem.S.A.It. 75, 448]

G.G.Pavlov & Yu.A.Shibanov (1978); S.Zane, R.Turolla, A.Treves (2001): electron or proton (ion) quantum cyclotron harmonics? K.Mori, J.C.Chonko, C.J.Hailey (2005): only 2 features are real. V.F.Suleimanov, G.G.Pavlov, K.Werner (2010) ApJ 714, 630 Pavlov & Shibanov (1978) + Zane et al. (2001).


Absorption lines in spectra of isolated neutron stars
Case of CCO 1E 1207.4-5209

Atmosphere models for heavier elements
K.Mori, W.C.G.Ho (2007) MNRAS 377, 905


Absorption lines in spectra of isolated neutron stars
Case of CCO 1E 1207.4-5209

Atmosphere models for heavier elements
K.Mori, W.C.G.Ho (2007) MNRAS 377, 905

But: J.P.Halpern & E.V.Gotthelf, 2010, ApJ 709, 436 B < 3.3x1011 G


Cyclotron harmonics in spectra of isolated neutron stars


Cyclotron harmonics in spectra of isolated neutron stars

V.F.Suleimanov, G.G.Pavlov, K.Werner (2010) ApJ 714, 630: approximate treatment of proton recoil
(following G.G.Pavlov & A.N.Panov, 1976, Sov. Phys. JETP 44, 300)


Cyclotron harmonics in spectra of isolated neutron stars


Cyclotron harmonics in spectra of isolated neutron stars

Accurate treatment of the proton-electron-photon system in quantizing magnetic fields
[Potekhin (2010) A&A 518, A24]


Cyclotron harmonics in spectra of isolated neutron stars

Accurate treatment of the proton-electron-photon system in quantizing magnetic fields
[Potekhin (2010) A&A 518, A24]


Absence of ion cyclotron harmonics in spectra of isolated neutron stars


Absence of ion cyclotron harmonics in spectra of isolated neutron stars
A.Y.Potekhin "Cyclotron harmonics in opacities of isolated neutron star atmospheres" Aston. Astrophys. 518, A24 (2010)

- . ­ , , . ­ . ­ .

( ) ( ) , B=5x1013 . ­ , ­ , ­ . , , ( ) .


Conclusions
Partial ionization and strong magnetic fields strongly affect the spectra of outgoing radiation and should be taken into account in atmosphere modeling. Practical models of the EOS and opacities of strongly magnetized plasmas, applicable to neutron stars, are developed in recent years, and applied to modeling the spectra of neutron star thermal radiation. Models of neutron-star thermal spectra with acount of strong magnetic fields, partial ionization, and magnetic condensation are becoming practical for interpretation of observations. Superstrong magnetic fields (1) induce new effects which can reveal themselves in the spectra and (2) lead to theoretical uncertainties which require further study. Even with superstrong fields, ion cyclotron harmonics cannot be observed in neutron-star thermal radiation.

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