On the theory of cyclotron lines in the spectra of magnetic white dwarfs

The radiation transfer at the gyrofrequency in the coronae of magnetic white dwarfs is considered. The electron distribution over Landau levels, taking both radiative and collisional transitions into account, is obtained. The emissivity and absorption coefficients of extraordinary radiation at the gyrofrequency are calculated. The ranges of parameters where cyclotron lines are observed in emission or absorption are found. The upper limit on coronal plasma density (2×10¹¹ cm^–3) for isolated magnetic white dwarfs with absorption lines in the spectrum is specified.     

Cyclotron lines in the spectra of solar flares and solar active regions

It was shown by Zheleznyakov and Zlotnik (1980a, b) that in complex configurations of solar magnetic fields (in hot loops above the active centres, in neutral current sheets in the preflare phase, in hot X-ray kernels in the initial flare phase) a system of cyclotron lines in the spectrum of microwave radiation is likely to be formed. Such a line was obtained by Willson (1985) in the VLA observations at harmonics of the electron gyrofrequency. This communication interprets these observations on the basis of an active region model in which thermal cyclotron radiation is produced by hot plasma filling the magnetic tube in the corona above a group of spots. In this model the frequency of the recorded 1658 MHz line corresponds to the third harmonic of electron gyrofrequency, which yields the magnetic field (196 ± 4) G along the magnetic tube axis. The linewidth f/f 0.1 is determined by the 10% inhomogeneity of the magnetic field over the cross-section of the tube; the line profile indicates the kinetic temperature distribution of electrons over the tube cross-section with the maximum value 4 × 10⁶ K. Analysis shows that study of cyclotron lines can serve as an efficient tool for diagnostics of magnetic fields and plasma in the solar active regions and flares.     

On the theory of X-ray pulsar radiation

The origin of hard X-ray spectrum (continuum and cyclotron lines) of pulsars in binary systems is discussed. A model of the polar region of a neutron star consisting of a hot spot in a dense plasma atmosphere with a quasi-homogeneous magnetic field and an extended accreting column in an inhomogeneous dipolar field is investigated. In the hot spot bremsstrahlung and Thomson scattering form continuum radiation, while bremsstrahlung and cyclotron scattering produce the absorption cyclotron lines. By the observed continuum intensity one can estimate the maximum distances to pulsars. Cyclotron scattering in gyro-resonant layers localized in the accreting column leads to a general attenuation of the radiation of a hot spot, but is unable to ensure the formation of cyclotron lines. For strong accretion the hot spot radiation becomes insignificant, the lines disappear and the pulsating component of an X-ray pulsar is produced by the accreting column bremsstrahlung transformed by Thomson scattering.     

The polarization of optical radiation from the magnetic white dwarfs

It is pointed out that, because of the large Faraday rotation an outlet of linear polarization from the photosphere of a white dwarf is hampered. In accordance with this fact it is proposed to distinguish two types of magnetic white dwarfs. The first type (its representative is Grw 70°8247) has a linear polarization which is comparable in magnitude with the circular one. Polarization of radiation from the white dwarfs of the first type cannot arise in the photosphere. It arises in the corona of the star either as a result of cyclotron emission of hot electrons (T～10⁶ K) or as a result of scattering of slightly polarized emission from the photosphere in the corona. For the first type dwarfs such magnetic fields are required thatω _B ω_opt, i.e.B(1?3)×10⁸G. The white dwarfs of the second type (its representative is G 99-37) have their linear polarization much smaller than the circular one. Polarization of these white dwarfs can arise as a result of the transfer of radiation in the nonisothermal photosphere. Magnetic fields required for the second type can be much smaller:B cos γ=(1?10)×10⁶ G. It is shown that the photospheric model allows to obtain the quantitative accordance of the theory with all the observational data for G 99-37 and is not in accordance with the data for Grw 70°8247, at the same time the model with cyclotron emission from the corona explains the magnitude of both linear and circular polarization and their wavelength dependence for Grw 70°8247.     

Ionization structure in accretion shocks with a composite cooling function

We have investigated the ionization structure of the post-shock regions of magnetic cataclysmic variables, using an analytic density and temperature structure model in which effects caused by bremsstrahlung and cyclotron cooling are considered. We find that in the majority of the shock-heated region where H- and He-like lines of the heavy elements are emitted, the collisional-ionization and corona-condition approximations are justified. We have calculated the line emissivity and ionization profiles for iron as a function of height within the post-shock flow. For low-mass white dwarfs, line emission takes place near the shock. For high-mass white dwarfs, most of the line emission takes place in regions well below the shock and hence it is less sensitive to the shock temperature. Thus, the line ratios are useful to determine the white dwarf masses for the low-mass white dwarfs, but the method is less reliable when the white dwarfs are massive. Line spectra can, however, be used to map the hydrodynamic structure of the post-shock accretion flow.     

White dwarf masses in magnetic cataclysmic variables: multi-temperature fits to Ginga data

One method of obtaining the mass of the white dwarf in magnetic cataclysmic variables (mCVs) is through their hard X-ray spectra. However, previous mass estimates using this method give lower limits because the temperature of the plasma in the post-shock region (where the hard X-rays are emitted) is lower than the temperature of the shock itself. In AM Her systems, the additional cooling of the post-shock plasma by cyclotron emission will further lower the derived mass. Here we present estimates of the masses of the white dwarf in 13 mCVs derived using Ginga data and a model in which X-rays are emitted from a multi-temperature emission region with the appropriate temperature and density profile. We include in the model reflection from the surface of the white dwarf and a partially ionized absorber. We are able to achieve good fits to the data. We compare the derived masses with previous estimates and the masses for larger samples of isolated white dwarfs and those in CVs.     

Propagation and absorption of electron-cyclotron maser radiation during solar flares

The electron-cyclotron maser is believed to be the source of microwave spike bursts often observed during solar and stellar flares. Partial absorption of this radiation as it propagates through the corona can produce plasma heating and soft X-ray emission over an extended region. In this paper, the propagation and absorption of the maser radiation during solar flares are examined through linear theory and electro-magnetic particle simulations. It is shown using linear theory that strong absorption of the radiation should occur as it propagates towards the second harmonic layer where the magnetic field is half as strong as in the emission region. Only radiation propagating nearly parallel to the magnetic field in a low-temperature plasma may be able to escape under certain, limited conditions. Finite temperature effects can cause radiation propagating nearly perpendicular to the magnetic field to refract, causing enhanced absorption. Particle simulations are then used to evaluate the nonlinear response of the plasma as the maser radiation propagates through the absorption layer. It is shown that some of the maser radiation is able to escape through a process of absorption below the second harmonic of the local gyrofrequency and re-emission above it. The fraction able to escape is much higher than that predicted by linear theory, although the amount of escaping energy is only a small fraction of the incident energy. The bulk of incident energy goes into the perpendicular heating of the ambient electrons, with the rate of energy absorption showing no signs of leveling off during the simulations. This indicates that the absorption layer does not become optically thin after continuous heating by the maser radiation. A few electrons are accelerated to several tens of keVs as a result of the heating.     

Instability of Electrons Trapped by the Coronal Magnetic Field and Its Evidence in the Fine Structure (Zebra Pattern) of Solar Radio Spectra

Solar radio emission is a significant source of information regarding coronal plasma parameters and the processes occurring in the solar atmosphere. High resolution frequency, space, and time observations together with the developed theory make it possible to retrieve physical conditions in the radiation source and recognize the radiation mechanisms responsible for various kinds of solar radio emission. In particular, the high brightness temperature of many bursts testifies to coherent radiation mechanisms, that is, to plasma instabilities in the corona. As an example, the fine structure of solar radio spectra looking like a set of quasi-harmonic stripes of enhanced and lowered radiation, which is observed against the type IV continuum at the post-flare phase of activity, is considered. It is shown that such emission arises from a trap-like source filled with a weakly anisotropic equilibrium plasma and a small addition of electrons which have a shortage of small velocities perpendicular to the magnetic field. For many recorded events with the mentioned fine spectral structure the instability processes responsible for the observed features are recognized. Namely, the background type IV continuum is due to the loss-cone instability of hot non-equilibrium electrons, and the enhanced striped radiation results from the double-plasma-resonance effect in the regions where the plasma frequency f _p coincides with the harmonics of electron gyrofrequency f _B ; f _p=sf _B . Estimations of the electron number density and magnetic field in the coronal magnetic traps, as well as the electron number density and velocities of hot electrons necessary to excite the radiation with the observed fine structure, are given. It is also shown that in some cases several ensembles of non-equilibrium electrons can coexist in magnetic traps during solar flares and that its radio signature sensitively depends on the parameters of the distribution functions of the various ensembles.     

Polarization line radiative transfer in the atmospheres of magnetic white dwarfs

Some physical mechanisms which can affect the Zeeman line profiles of magnetic white dwarfs are studied. The pure absorption polarization transfer equation is solved including these mechanisms. The broadening of lines in magnetic white dwarfs is briefly discussed.     

An upper limit to coronal X-rays from single,magnetic white dwarfs

Pointed ROSAT PSPC exposures of 9277 and 6992 sec, directed toward the nearby, single, cool, magnetic white dwarfs GR 290 and EG 250 yielded no counts significantly above the expected background rate. The corresponding flux limits (for an assumed source temperature of l keV) are 1.0 and 1.7 × 10⁻¹⁴erg cm⁻² s⁻¹, within the 0.1–2.5 keV bandpass of the instrument (99% confidence limits). This is more than an order of magnitude below the tentative detection level (for GR 290) and limits (for four other similar stars) obtained from archival Einstein data in 1991. The corresponding limits on coronal electron density are comparable with those implied if cyclotron emission is not responsible for any of the features observed in the optical spectra of magnetic white dwarfs. X-ray data currently provide no evidence for the existence of coronae around these stars. A final long observation (25,000 sec of GD 356) is scheduled for later this year on ROSAT, along with coordinated EUVE observations.     

Interaction of particles with ion cyclotron waves and magnetosonic waves. Observations from GEOS 1 and GEOS 2

Coordinated observations involving ion composition, thermal plasma, energetic particle, and ULF magnetic field data from GEOS 1 and 2 often reveal the presence of electromagnetic ion cyclotron and magnetosonic waves, which are distinguished by their respective polarization characteristics and frequency spectra. The ion cyclotron waves are identified by a magnetic field perturbation that lies in a plane perpendicular to the Earth's magnetic field B₀ and propagate along B₀. They are associated with the abundance of cold He⁺ in the presence of anisotropic pitch angle distributions of ions having energies E > 20 keV, and were observed at frequencies near the He⁺ gyrofrequency. The magnetosonic waves are characterized by a magnetic field perturbation parallel to B₀ and thus seem to be propagating perpendicular to the Earth's magnetic field. They often occur at harmonics (not always including the fundamental) at the proton gyrofrequency and are associated with phase-space-density distributions that peak at energies E ～ 5–30 keV and at a pitch angle of 90°. Such a ring-like distribution is shown to excite instability in the magnetosonic mode near harmonics of the proton gyrofrequency. Magnetosonic waves are associated in other cases with sharp spatial gradients in energetic ion intensity. Such gradients are encountered in the early afternoon sector (as a consequence of the drift shell distortion caused by the convection electric field) and could likewise constitute a source of free energy for plasma instabilities.     

Emission of solar radio spikes by beam-driven cyclotron resonance

The generation of bright solar radio spikes by the beam-driven cyclotron resonance maser mechanism (the resonant interaction of an electron beam with a circularly polarized wave in a background plasma under the action of a guide magnetic field) is studied. Nonlinear effects such as radiation damping and gyrophase bunching on electron energy and momentum are responsible for the enhanced direct energy conversion between the beam and the coherent wave. Factors such as beam energy spread and pitch angle distribution are analyzed. The intense maser radiation is carried at the source by the circularly polarized wave propagating along the magnetic field. Due to the magnetic field curvature, the outgoing maser radiation converts into extraordinary and ordinary modes. The extraordinary mode suffers from plasma absorption at the second harmonic layer, whereas the ordinary mode is likely to get through.     

Estimation of plasma parameters in an accretion column near the surface of accreting white dwarfs from their flux variability

We consider the behavior of matter in the accretion column that emerges under accretion in binary systems near the surface of a white dwarf. The plasma heated in a standing shock wave near the white dwarf surface efficiently radiates in the X-ray energy band. We suggest a method for estimating post-shock plasma parameters, such as the density, temperature, and height of the hot zone, from the power spectrum of its X-ray luminosity variability. The method is based on the fact that the flux variability amplitude for the hot region at various Fourier frequencies depends significantly on its cooling time, which is determined by the parameters of the hot zone in the accretion column. This allows the density and temperature of the hot matter to be estimated. We show that the characteristic cooling time can be efficiently determined from the break frequency in the power spectrum of the X-ray flux variability for accreting white dwarfs. The currently available X-ray instruments do not allow such measurements to be made because of an insufficient collecting area, but this will most likely become possible with new-generation large-area X-ray spectrometers.     

The thermomagnetic instability in degenerate cores of white dwarfs

The degenerate cores of sufficiently hot white dwarfs are shown to suffer the thermomagnetic instability which generates magnetic field and excites hydrodynamical motions. The necessary conditions for the instability to occur and the parameters of an unstable zone are determined. It is shown that, in hot white dwarfs, this zone can be very extended. The characteristic time scale of the instability is evaluated and some effects due to this instability are discussed.     

Constraints on accretion column parameters for the intermediate polar LS Pegasi from the power spectrum of its optical light curve

The properties of the hot zone in the accretion flow near the surface of a magnetized white dwarf have been studied. For this purpose, the aperiodic optical variability of LS Peg, one of the brightest intermediate polars in the northern sky, has been investigated. The main radiation of the hot zone, which is then reemitted in the optical band, results from the radiation of an optically thin plasma heated during the passage of the accretion flow of a standing shock. Recently, Semena and Revnivtsev (2012) have shown that the aperiodic variability (flickering) of accreting magnetized white dwarfs should have a characteristic feature in the range of Fourier frequencies corresponding to the plasma cooling time in this hot region. The photometric brightness measurements for LS Peg made with the RTT-150 telescope using a high-speed ANDOR iXon CCD array have allowed the break frequency in the power spectrum of the source’s variability to be constrained. Constraints on the geometry of the accretion column for the white dwarf in LS Peg and on the plasma parameters in it have been obtained.     

Emission of cyclotron radiation by interstellar planets

In the solar system all planets that have significant magnetic fields also emit electron cyclotron radiation, usually near the auroral regions around the magnetic poles. In this study we use scaling laws based on solar system data to estimate the power and frequency of the auroral cyclotron emissions from interstellar planets (or sub-brown dwarfs). The emission can be powered either by motion of the planet through the interstellar plasma or by unipolar induction due to a moon. According to our results, in interstellar space the unipolar induction mechanism is potentially more effective than the motional emission mechanism. Typical emission power is around 10¹⁰-10¹² W, but significantly stronger emissions are obtained in the most optimistic estimates. We have to conclude that detection of a rogue Jupiter would be very difficult, if not impossible with the radio telescopes available now or in the near future, but in very favorable conditions a much more massive and rapidly rotating (or otherwise strongly magnetized) gas giant with a large nearby moon could be detected up to ∼57 pc distance with the square kilometer array. There may be a few thousand large enough interstellar planets this close to the solar system. For reference, we point out that according to previous studies some known hot Jupiters are expected to emit up to 10¹⁴-10¹⁶ W of cyclotron radiation, orders of magnitude more than the typical interstellar planets discussed here. However, these emissions have not yet been detected.     

Reversal of the polarization of cyclotron radiation in a hot coronal loop

Spectropolarimetric features of thermal cyclotron radiation of solar coronal loops and the possibility of interpretation of the observed reversal of the sense of polarization of centimeter and decimeter waves are discussed. To this end, thermal cyclotron radiation is computed in terms of the simplest model of a three-dimensional hot loop (a half-torus). Such a loop is shown to be capable of changing appreciably the properties of the radiation of a solar active region at centimeter and decimeter wavelengths. A detailed analysis is performed to determine the conditions under which the radiation spectrum of an active region containing a coronal loop may have a complex pattern with several maxima or relatively narrow-band cyclotron lines, and the sense of polarization may change several times in the wavelength interval considered. These conditions are modelled by such parameters as the structure of the magnetic field, electron density, and size of the loop. The results of the computations of two-dimensional brightness temperature distributions at different wavelengths for ordinary and extraordinary waves at fixed points of the loop and the integrated parameters of the flux and polarization of radiation in terms of the model discussed are reported. Cases are considered where the line of sight is crossed by one or two loops. The expected distribution of polarization across the source in the model considered is compared to the results of RATAN-600 observations of the solar active region AR 7962 made on May 12–14, 1996.     

Cosmic gamma-ray burst spectroscopy

A review is given of the gamma-ray burst energy spectrum measurements on Venera 11 and Venera 12 space probes. The gamma burst continuum approximates in shape thermal brems-strahlung emission of a hot plasma. The radiation temperature varies over a broad range, 50–1000 keV, for different events. Spectra of many bursts contain cyclotron absorption and/or redshifted annihilation lines. Strong variability is typically observed in both continuum and line spectra. These spectral data provide convincing evidence for the gamma-ray bursts being generated by neutron stars with superstrong magnetic fields 10¹²–10¹³ G.     

Quantum relativistic theory of the synchrotron/cyclotron radiation in a strongly-magnetized plasma: The case of longitudinal propagation

Full quantum relativistic treatment of the cyclotron/synchrotron emission and absorption in tenuous plasmas with superstrong magnetic field is developed for the case when the radiation wave-vector is parallel to the magnetic field. The emissivities and absorption coefficients for a plasma with arbitrary distribution function of particles are presented in terms of simple sums over the Landau levels. On the basis of these expressions, the negative absorption (maser amplification) is shown to be impossible for the longitudinal propagation in a tenuous plasma. The summation over the Landau levels is performed analytically, and the quantum effects are analysed in detail, for the thermal distribution of plasma particles. A new type of quantum relativistic oscillations is predicted in the emission and absorption spectra for a plasma with anisotropic temperature. The results obtained are useful for an interpretation of the X-ray and gamma-ray observations of the objects associated with strongly magnetized neutron stars (particularly of the gamma-ray bursters).     

Influence of relativistic effects and vacuum polarization on the transfer of gyroresonance radiation and the stability of the atmospheres of compact stars

We consider the transfer of radiation and calculate the force of its pressure in the electron gyroresonance line in the atmospheres of magnetic degenerate stars. We specify the atmospheric parameters for which an outflow of plasma is possible under radiation pressure in the cyclotron line. We show that the permittivity tensor of a mildly relativistic plasma in a strong magnetic field found by applying relativistic corrections to the cyclotron resonance condition and by taking into account the vacuum polarization and recoil effects during photon scattering should be used to obtain proper results. We have determined the real and imaginary parts of the refractive indices and the polarization coefficients for normal electromagnetic waves when scattering dominates over absorption. Relativistic effects, which change greatly the dispersion and resonant absorption of waves propagating almost perpendicular to the magnetic field, and vacuum polarization have been found to change qualitatively the gyroresonance radiation spectrum and pressure for a wide range of parameters of stellar magnetospheres.