J/A+A/572/A69 Opacities of magnetized neutron stars (Potekhin+, 2014)
Opacities and spectra of hydrogen atmospheres of moderately magnetized neutron
stars.
Potekhin A.Y., Chabrier G., Ho W.C.G.
<Astron. Astrophys. 572, A69 (2014)>
=2014A&A...572A..69P 2014A&A...572A..69P
ADC_Keywords: Models, atmosphere ; Magnetic fields
Keywords: magnetic fields - plasmas - stars: atmospheres - stars: neutron
Abstract:
There is observational evidence that central compact objects (CCOs) in
supernova remnants have moderately strong magnetic fields B∼1011G.
Meanwhile, available models of partially ionized hydrogen atmospheres
of neutron stars with strong magnetic fields are restricted to
B≳1012G. Extension of the applicability range of the photosphere
models to lower field strengths is complicated by a stronger asymmetry
of decentered atomic states and by the importance of excited bound
states.
We extend the equation of state and radiative opacities, as presented
in previous papers for 1012G≲B≲1015G, to weaker fields.
We constructed analytical fitting formulae for binding energies,
sizes, and oscillator strengths for different bound states of a
hydrogen atom moving in moderately strong magnetic fields and
calculate an extensive database for photoionization cross sections of
such atoms. Using these atomic data, in the framework of the chemical
picture of plasmas we solved the ionization equilibrium problem and
calculated thermodynamic functions and basic opacities of partially
ionized hydrogen plasmas at these field strengths. Then plasma
polarizabilities were calculated from the Kramers-Kronig relation, and
the radiative transfer equation for the coupled normal polarization
modes was solved to obtain model spectra.
An equation of state and radiative opacities for a partially ionized
hydrogen plasma are obtained at magnetic fields B, temperatures T, and
densities ρ typical for atmospheres of CCOs and other isolated
neutron stars with moderately strong magnetic fields. The first- and
second-order thermodynamic functions, monochromatic radiative
opacities, and Rosseland mean opacities are calculated and tabulated,
considering partial ionization, for 3x1010G<∼B<∼1012^G,
105K≲T≲107K, and a wide range of densities.
Atmosphere models and spectra are calculated to verify the
applicability of the results and to determine the range of magnetic
fields and effective temperatures where the incomplete ionization of
the hydrogen plasma is important.
Description:
Two types of tables are presented: "EOS tables" (14 files named
"eos*.dat") and "opacity tables" (14 files named "op*.dat"),
each table being related to a specific strength of magnetic field B,
which is reflected by the file name (e.g., files eos10_5.dat and
op10_5.dat contain data related to log10(B[G])=10.5).
The EOS tables present values of the first- and second-order
thermodynamic functions, number fractions of atoms, molecules, and
clusters, and Rosseland opacities for photon transport parallel and
perpendicular to the field lines, for 22 values of temperature T from
log10(T[K])=4.9 to log10(T[K])=7.0 with step 0.1, and, for every
T, for 56 values of the parameter R=ρ/T63, where rho is density
in g/cm^3 and T6=T/106K.
The opacity tables contain values of monochromatic (spectral)
opacities for 3 basic polarizations (right [+], left [-], and
longitudinal [0] with respect to the field direction - see the paper
for more detail) and values of plasma polarizability coefficients for
the same 3 polarizations, for every B and T value listed in the
corresponding EOS table and for 301 values of photon energies E from
10eV to 10keV (equidistant in log(E)).
File Summary:
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FileName Lrecl Records Explanations
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ReadMe 80 . This file
eos10_5.dat 109 1232 *EOS table for log10(B[G])=10.5
eos10_6.dat 109 1232 *EOS table for log10(B[G])=10.6
eos10_7.dat 109 1232 *EOS table for log10(B[G])=10.7
eos10a8.dat 109 1232 *EOS table for log10(B[G])=10.845
eos11_0.dat 109 1232 *EOS table for log10(B[G])=11.0
eos11_1.dat 109 1232 *EOS table for log10(B[G])=11.1
eos11_2.dat 109 1232 *EOS table for log10(B[G])=11.2
eos11_3.dat 109 1232 *EOS table for log10(B[G])=11.3
eos11_4.dat 109 1232 *EOS table for log10(B[G])=11.4
eos11_5.dat 109 1232 *EOS table for log10(B[G])=11.5
eos11_6.dat 109 1232 *EOS table for log10(B[G])=11.6
eos11_7.dat 109 1232 *EOS table for log10(B[G])=11.7
eos11a8.dat 109 1232 *EOS table for log10(B[G])=11.845
eos12_0.dat 109 1232 *EOS table for log10(B[G])=12.0
op10_5.dat 61 370832 *opacity table for log10(B[G])=10.5
op10_6.dat 61 370832 *opacity table for log10(B[G])=10.6
op10_7.dat 61 370832 *opacity table for log10(B[G])=10.7
op10a8.dat 61 370832 *opacity table for log10(B[G])=10.845
op11_0.dat 61 370832 *opacity table for log10(B[G])=11.0
op11_1.dat 61 370832 *opacity table for log10(B[G])=11.1
op11_2.dat 61 370832 *opacity table for log10(B[G])=11.2
op11_3.dat 61 370832 *opacity table for log10(B[G])=11.3
op11_4.dat 61 370832 *opacity table for log10(B[G])=11.4
op11_5.dat 61 370832 *opacity table for log10(B[G])=11.5
op11_6.dat 61 370832 *opacity table for log10(B[G])=11.6
op11_7.dat 61 370832 *opacity table for log10(B[G])=11.7
op11a8.dat 61 370832 *opacity table for log10(B[G])=11.845
op12_0.dat 61 370832 *opacity table for log10(B[G])=12.0
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Note on op*: The headlines appear in pairs, the first headline being a text,
and the second contains the values of log10(T[K]), log10(R) (where
R=ρ/T63, as defined above), and log10(B[G]).
301 lines following each such header relate to these values of T, R, and B.
Note on eos*.dat: The first and second lines of each file are plain headers;
every subsequent header lists the values of logT (logarithm of temperature
in K) and logB (logarithm of magnetic field strength in G).
Each such header is followed by 56 lines of the table related to these
T and B values.
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See also:
J/A+A/559/A128 : Neutron star properties with unified EoS (Fantina+, 2013)
J/A+A/560/A48 : Neutron-star matter unified EoS FORTRAN codes (Potekhin+ 2013)
J/ApJS/197/20 : Relativistic EOS for core-collapse SN simulations (Shen+ 2011)
Byte-by-byte Description of file(#): eos*.dat
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Bytes Format Units Label Explanations
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1- 6 F6.2 [g/cm3/MK3] lg(R) [-7.4/3.6] log(ρ/T63) (1)
7- 15 F9.4 [10+5Pa] lg(P) [-3.6/17.8] log of pressure (in bar)
16- 23 F8.3 --- P/nkT [0.9/183] Normalized pressure (7)
24- 31 F8.2 --- U/NkT [-23/338] Normalized energy density (7)
32- 38 F7.2 --- S/Nk [3.8/68] Normalized entropy (7)
39- 45 F7.2 --- Cv/Nk [-9.9/158] Normalized specific heat (7)
46- 52 F7.3 --- chiT [-0.7/4.1] χT=dlogP/dlogT (2)
53- 59 F7.3 --- chirho [0.2/6] χρ=dlogP/dlogρ (3)
60- 68 E9.3 --- x(H) [0/1] Number fraction of H atoms (4)
69- 77 E9.3 --- x(H0) [0/1] Number fraction of ground-state
H atoms (4)
78- 86 E9.3 --- x(H2) Twice number fraction of H2
molecules (4) (5)
87- 95 E9.3 --- x(pert) [0/1] Number fraction of protons in
clusters (4) (6)
96-102 F7.3 [cm2/g] lg(op.P) log10(κP), "parallel"
Rosseland opacity
103-109 F7.3 [cm2/g] lg(op.T) log10(κT), "transverse"
Rosseland opacity
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Note (1): R=ρ/T63, where ρ is density in g/cm3 and T6=T/106K.
Values are tabulated with a step of 0.2 (56 values of log10(R))
Note (2): dlogP/dlogT means the partial derivative of logarithm of
pressure with respect to logarithm of temperature.
Note (3): dlogP/dlogρ means the partial derivative of logarithm of
pressure with respect to logarithm of density.
Note (4): Number fractions are counted with respect to the total number of
protons (free and bound) in the plasma.
Note (5): Equivalently, it is number fraction of all the protons that are
comprised in H2 molecules.
Note (6): These are clusters of more than 2 protons with common bound electrons.
In other words, x(pert) is a fraction of strongly perturbed atoms,
according to the criterion adopted in Sect.3 of the paper.
Note (7): normalized to an ideal ion gas
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Byte-by-byte Description of file (#): op*.dat
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Bytes Format Units Label Explanations
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1- 7 F7.3 [eV] lg(E) [1/4] log10 of photon energy (step of 0.01)
8- 15 F8.3 [cm2/g] lg(op+) log10(κ+) of "+"-opacity (2)
16- 23 F8.3 [cm2/g] lg(op-) log10(κ-) of "-"-opacity (2)
24- 31 F8.3 [cm2/g] lg(op0) log10(κ0) of "0"-opacity (2)
32- 41 E10.4 --- chi+ χ+, "+"-polarizability (2)
42- 51 E10.4 --- chi- χ+, "-"-polarizability (2)
52- 61 E10.4 --- chi0 χ+, "0"-polarizability (2)
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Note (2): The labels "+", "-", and "0" mean that a given quantity relates
to the values of the polarization index α=+1, -1, or 0,
respectively, as defined in Sect.4.1 of the paper.
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Acknowledgements:
Alexander Potekhin, palex(at)astro.ioffe.ru
(End) Patricia Vannier [CDS] 08-Oct-2014