A. D. Kaminker

Radiation from a strongly-magnetized plasma: The case of predominant scattering

On the basis of diffusion approach for normal modes, solutions of the radiative transfer problem are obtained and analysed for an optically thick tenuous plasma with a strong magnetic field. The case is considered when the scattering processes without change of photon frequency ω are dominant. The radiative transfer coefficients as well as spectra, angular dependences and polarization of the outgoing radiation are investigated in detail for a ‘cold’ plasma,kTe≩mc2, |ω−sωB|≫ωkTe/mc2 )1/2|cosϑ|, whereTe is the electron plasma temperature,ωB=eB/mc the electron cyclotron frequency,s=1,2,... the number of cyclotron harmonic and ϑ the angle between the magnetic field and wave vector. The effects of electronpositron vacuum polarization are taken into account and shown to be very significant. Simple analytic solutions are obtained for various limiting cases (small and large vacuum polarization; high, low and close to the cyclotron resonance radiation frequencies; different orientations of the magnetic field, etc). The results obtained are necessary for analysing X-ray and gamma-ray radiation from strongly magnetized neutron stars.

Spectra of radiation from a strongly magnetized plasma

AbstractRadiation from an optically thick, tenuous, isothermal and magnetized plasma is considered under conditions typical for X-ray pulsars, in the approximation of coupled diffusion of normal modes. The spectra are calculated of the fluxes and specific intensities of outgoing radiation, their dependences on the plasma densityN, temperatureT and magnetic fieldB are analysed with due regard to the vacuum polarization by a strong magnetic field. Simple analytical expressions are obtained in the limiting cases for the fluxes and intensities. It is shown that atEB »Ea (EB=11.6B12 keV,Ea≃0.1N221/2T1−3/4 keV,B12=B/1012 G,N22=N/1022 cm−3,T1=T/10 keV) the magnetic field strongly intensifies the flux and changes its spectrum in the regionEa ≲E ≲EB. AtE ≲T the spectrum of the energy flux is almost flat in the region

Astron observations of the Rapid Burster MXB 1730-335 and constraints on burster parameters from spectra of trailing bursts

\sqrt {E_a E_B } \lesssim E \lesssim E_B

Annihilation radiation from thermal electron-positron plasma on the ground Landau level: The case of low magnetic fields

. For homogeneous plasma without Comptonization the cyclotron line atE≃=EB appears in emission, though in many other cases it may appear in absorption. The vacuum polarization may produce the ‘vacuum feature’ atE≃EW≃13N221/2B12−1 keV, which, as a rule, appears in absorption. The intensity spectra vary noticeably with the direction of radiation, in particular, at some directions nearB, the spectra become harder than in other directions. Quantization of the magnetic field (EB>T) strongly increases the plasma luminosity (∝EB/T for homogeneous plasma). The results obtained explain a number of basic features in the observed X-ray pulsar spectra.

Spectral evolution of an X-ray burst from MXB 1728-34 and constraints on burster parameters

Spectra, angular distributions, and polarization of two-photon annihilation radiation in a magnetic field are studied in detail in the case of small longitudinal velocities of annihilating electrons and positrons which occupy the ground Landau level. Magnetic field essentially affects the annihilation if its magnitudeB is not very low in comparison withBcr=4.4×1013G, which may take place near the surface of a neutron star. The magnetic field broadens the spectra (the width depends on an angle ϑ betweenB and a wave vector) and leads to their asymmetry. The angular distribution may be highly anisotropic, being fan-like or pencillike for different photon energies ω. The total annihilation rate is suppressed by the magnetic field (∝B−3 forB≫Bcr).The radiation is linearly polarized; the degree and orientation of the polarization depend onB, ϑ and ω. The polarization may reach several tens percent even for comparatively small fieldsB ∼ 0.1Bcrtypical for neutron stars. This means that the polarization may be detected, e.g., in the annihilation radiation from the gamma-ray bursts.

Annihilation radiation from a power-law distributed electron-positron plasma on the ground Landau level: the case of low magnetic fields

We report on eight X-ray bursts detected by ASTRON from the Rapid Burster (RB) on 13 and 28 April and 16 August, 1983. Six of them (trailing bursts), with durations of 1.5–2 min, rise times of 5–10 s and intervals of 1–1.5 hours, exhibit spectral softening during the burst decay and may be related to the type I bursts. Two of the bursts (triangle bursts) observed on 28 April at interval of ∼28 min with much longer rise times (30–50 s) and longer durations (≃3 min), do not show distinct spectral softening. Persistent flux from RB on 16 August was estimated asFp≃(2.0–2.4)×10−9 erg cm−2 s−1. Spectral evolution of two trailing bursts was investigated by fitting their spectra in consecutive time intervals with the blackbody (BB), isothermal scattering photosphere (SP) and thermal bremsstrahlung (TB) models. Around the burst maxima the SP model fits the data best whereas in the burst tails the TB model is generally better. The BB model is worse than at least one of the two others. Interpretation of the burst spectra in terms of the BB radiation leads to improbably small neutron star mass and radius (M<0.86M⊙,RNS<5 km) if the peak luminosity does not exceed the Eddington limit. Interpretation of the spectra around the burst maxima (3–15 s from the burst onset) in terms of an isothermal SP yields reasonable constraints onM,RNS, and distanceD. For instance, for the hydrogen photosphere we obtainedM=(1.0–2.1)M⊙RNS=(7.1–16.4) km ifD=11 kpc. If one postulatesM=1.4M⊙, thenD=(8.5–13) kpc for hydrogen photosphere; if, besides,D=11 kpc, thenRNS=(8.1–13.3) km. It follows also from the SP-interpretation that the photosphere radius may increase up to 20–30 km in maxima of the trailing bursts when the luminosity becomes close to the Eddington luminosity.

Annihilation Radiation in Strong Magnetic Fields and Gamma-Ray Burst Spectra

We study thermal relaxation in a neutron star after internal heating events (outbursts) in the crust. We consider thin and thick spherically symmetric heaters, superfluid and non-superfluid crusts, stars with open and forbidden direct Urca processes in their cores. In particular, we analyze long-term thermal relaxation after deep crustal heating produced by nuclear transformations in fully or partly accreted crusts of transiently accreting neutron stars. This long-term relaxation has a typical relaxation time and an overall finite duration time for the crust to thermally equilibrate with the core. Neutron superfluidity in the inner crust greatly affects the relaxation if the heater is located in the inner crust. It shortens and unifies the time of emergence of thermal wave from the heater to the surface. This is important for the interpretation of observed outbursts of magnetars and transiently accreting neutron stars in quasi-persistent low-mass X-ray binaries.

Two-photon annihilation radiation in strong magnetic field

The intensity and polarization of two-photon annihilation in a magnetic fuieldB≪Bcr=4.4×1013 G are studied in detail for a, one-dimensional thermal distribution of annihilating electrons and positrons on the ground Landau level. With the increase of temperatureT the total annihilation rate and energy losses decrease, being higher than for the isotropic thermal distributions at the sameT. The shapes of intensity spectra at sin ϱ=0 (ϱ is the angle betweenB and wave-vector) are close to those in the isotropic case. The widths and blue-shifts of the spectra decrease with increasing sin ϱ and increase with increasingT. Logarthmic singularities arise in the spectra atE»mc2/sin ϱ. Power-like parts are formed in the wings of the spectra forkT≫mc2 and not too small sin ϱ. The direction-integrated spectra reach their (finite) maxima, atE=mc2 for anyT. The radiation concentrates near the plane, perpendicular to the magnetic field forE close tomc2 and is beamed along the magnetic field forE far frommc2. Energy-integrated angular distributions are stretched alongB, the stronger the higherT. The rediation is linearly polarized in the plane formed by the magnetic field and weve-vector. Typical values of the polarization inside the cores of the annihilation spectra are ∼(kT/mc2) sin ϱ and [ln (kT/mc2)]−1 forkT≪mc2 andkT sin ϱ≫mc2, respectively. Annihilation radiation dominates over Bremsstrahlung in thee∓ plasma atkT≲7mc2. The results are useful for interpretation of the annihilation radiation in the gamma-ray bursts. They permit to estimate temperature, gravitational potential, and emission measure of radiating regions and the beaming of the radiation.