Albedo-shift method in the problem of anisotropic light scattering in a plane atmosphere

A standard problem of radiative transfer theory — calculating the diffuse reflection and transmission of radiation by a plane scattering atmosphere — is considered. The recently proposed albedoshift method is used to calculate the X and Y functions (and the H function) for the case of anisotropic scattering with a Henyey-Greenstein indicatrix. The method enables one to “suppress” scattering and obtain iterative solutions of high accuracy in only a few iterations, even when the mean number of photon scatterings in the atmosphere is very large. Translated from Astrofizika, Vol. 41. No. 4, pp. 623–646, October–December, 1998.     

Rayleigh scattering: Volterra equation for the matrix source function

Multiple Rayleigh scattering is examined in a semi-infinite atmosphere with uniformly distributed primary sources of partially polarized radiation. The resulting linear polarization is described by a 2×2 matrix transfer equation. A matrix generalization of Rybicki's two point Q-integral is obtained for this case. It is shown that the Volterra equation for the matrix source function for this problem is a particular case of our Q integral. Applying the Laplace transform to it yields the matrix form of the Ambartsumyan-Chandrasekhar H-equation. The Volterra equation for Sobolev's matrix resolvent function is another simple consequence of this equation. Translated from Astrofizika, Vol. 52, No. 2, pp. 301–310 (May 2009).     

Diffuse reflection of line radiation from a semi-infinite turbulent atmosphere

The diffuse reflection of line radiation from a one dimensional semi-infinite turbulent atmosphere is examined in two limiting regimes of micro-and macroturbulence. Ambartsumyan’s invariance principle is used to solve this problem. In addition to the observed spectral line profile, statistical averages describing the diffusion process in the atmosphere (mean number of scattering events, average time spent by a photon in the medium) are determined. The dependence of these quantities on the average hydrodynamic velocity and scattering coefficient is studied. It is shown that in the microturbulent regime the intensity at the line center depends only slightly on the mean nonthermal velocity. In both regimes, photons in the far wings undergo scattering more frequently than in a static atmosphere, although they spend, on average, less time in the medium. __________ Translated from Astrofizika, Vol. 50, No. 3, pp. 391–403 (August 2007).     

A New Model for the Separation of Meteoroid Fragments in the Atmosphere

This work is devoted to modeling of the transverse scattering of meteoroid fragments in the atmosphere by adopting supersonic gas dynamics around a system of bodies. Artem’eva and Shuvalov (1996, Shock Waves, 367) and Zhdan et al. (2004, Dokl. Phys., 315–317) found that the transverse force decreases with the increase of the distance between fragments, that is, fragments do not separate in a transverse direction under the action of constant repulsion force. This work on the decreasing transverse force uses the values of the transverse force coefficient by Zhdan et al. (2004, Dokl. Phys., 315–317) obtained from numerical modeling for spheres in a supersonic flow to derive the analytical solution of the dynamic equation for a fragment. The new model of layer-by-layer scattering of meteoroid fragments moving as a system of bodies is constructed on the basis of the analytical solutions derived in this work and the numerical data by Zhdan et al. (2005, Dokl. Phys., 514–518).     

Angular fluctuations in the cosmic microwave background owing to initial perturbations in the radiation temperature

A new method is proposed to account for multiple scattering by electrons in calculations of the correlation functions describing the angular fluctuations in the cosmic microwave background radiation (CMBR). The apparatus of the theory of radiative transport with Rayleigh scattering is used. The problem is reduced to solving an integral equation for the vector source function (dependent only on time), along with differential equations for the other quantities (scalar potentials, baryon velocities, etc.) which show up in the problem. The quantities which describe the angular fluctuations in the CMBR (in the temperature and in the polarization) are then calculated by integrating the vector source function along the line of sight. As an illustration, the correlation functions and power spectra are calculated for the case where the fluctuations are produced by some initial gaussian perturbations of the CMBR. __________ Translated from Astrofizika, Vol. 50, No. 4, pp. 621–631 (November 2007).     

Calculation of effective optical depth of absorption line formation in homogeneous semi-infinite planetary atmosphere during anisotropic scattering

The algorithm for determining effective optical thickness of absorption line formation in a plane-parallel homogeneous planetary atmosphere is presented. The case of anisotropic scattering is considered. The results of numerical calculations of τ _e (μ₀) at the scattering angle γ = π for some values of the single scattering albedo λ and the parameter of the Heyney-Greenstein scattering indicatrix g are given. The refined equation for the function T ^m (−μ, μ₀) is presented.     

PHOKA experiment: Description of the equipment and first results

The CORONAS-PHOTON Russian satellite intended to study the Sun was successfully launched into orbit on January 30, 2009. Scientific equipment of the satellite includes the PHOKA radiometer of soft X-ray and extreme UV radiation. The PHOKA instrument is intended to measure the absolute flux of solar electromagnetic radiation in the spectral windows of 0.5–7 nm, 0.5–11 nm, 27–37 nm, and 116–125 nm. When leaving and entering the Earth’s shadow, the instrument aboard the spacecraft measures absorption of radiation by various layers of the Earth’s atmosphere. Before the launch, photodiodes of the instrument had been calibrated using a synchrotron radiation source. In-flight stability of sensitivity of main channels is controlled using calibration channels. The paper describes the PHOKA instrument and presents its capabilities and main characteristics, as well as some results of its operation in orbit.     

Green’s function for the linear Kompaneets equation

Green’s function for the linear Kompaneets equation is calculated; it is expressed in terms of a Whittaker function W_2,iμ(Z) or a MacDonald function K_iμ(z) with a purely imaginary index. A method is proposed for calculating these functions. Langer’s asymptotic solution for large μ is refined in Cherry’s second approximation. With a series expansion for small values of the argument and the asymptotic form for large values, this approximation enables one to calculate Green’s function to five significant figures. Solutions of the Kompaneets equation will be used to estimate the accuracy of numerical methods and to calculate the evolution of the spectrum of a photon gas during Compton scattering, as well as the average frequencies and the dispersion of photon frequencies for different initial spectra. Translated from Astrofizika, Vol. 40, No. 1, pp. 97–116, January–March, 1997.     

Time dependent monochromatic scattering of radiation in one dimensional media: Analytical and numerical solutions

In order to choose a numerical method for solving the time dependent equations of radiative transport, we obtain an exact solution for the time dependent radiation field in a one dimensional infinite medium with monochromatic, isotropic scattering for sources with an arbitrary spatial distribution and an arbitrary time variation of their power. The Lax-Wendroff method seems to be the most suitable. Because it is assumed that radiation delay is caused by the finite speed of light, the following difficulty arises when the numerical method is used: the region of variation of the variables (position τ and time t) is triangular (the inequality τ ≤ t). This difficulty is overcome by expanding the unknown functions in series in terms of small values of the time and position. By comparing the numerical and exact solutions for a point source with a given time dependence for its power and with pure scattering, the number of steps in the variables required to obtain a desired accuracy is estimated. This numerical method can be used to calculate the intensity and polarization of the radiation from sources in the early universe during epochs close to the recombination epoch. __________ Translated from Astrofizika, Vol. 51, No. 1, pp. 109–123 (February 2008).     

Direct and Indirect Thermospheric Heating Sources for Solar Cycles 21–23

Solar variability is often cast in terms of radiative emission and the associated long-term climate response; however, growing societal reliance on technology is creating more interest in day-to-day solar variability. This variability is associated with both solar radiative and solar wind emissions. In this paper we explore the combined effects of radiative and solar wind fluctuations at Earth. The fluctuations in radiative and geomagnetic power create an extended interval of solar maximum for the upper atmosphere. We use a trio of empirical models to estimate, over the last three solar cycles, the relative contributions of solar extreme ultraviolet (UV) power, Joule power, and particle kinetic power to the Earth’s upper atmosphere energy budget. Daily power values are derived from three source models. The SOLAR2000 solar irradiance specification model provides estimates of the daily extreme and far UV solar power input. Geomagnetic power is derived from a combination of satellite-estimated particle precipitation power and an empirical model of Joule power from hemispherically integrated estimates of high-latitude energy deposition. During the interval 1975 to 2003, the average daily contributions were: particles – 36 GW, Joule – 95 GW and solar – 464 GW for a total of 595 GW. Solar wind-driven geomagnetic power provided 22% of the total global upper atmospheric energy. In the top 15 power events, geomagnetic power contributed two-thirds of the total power budget. In each of these events, Joule power alone exceeded solar power. With rising activity, Joule power becomes the most variable element of solar upper atmosphere interactions.     

Relaxation time of the superfluid core of a neutron star

The superconducting proton condensate in the “npe” phase of a neutron star is considered. It is shown to be a type II superconductor in the outer layer of the “npe” phase and a type I superconductor in the inner layer. Relaxation times are found for elastic scattering of normal relativistic electrons from the magnetic fields of proton vortex clusters in the case of a type II superconductor and elastic scattering from the magnetic field at the center of a neutron vortex in the case of a superconductor of the first kind. The dynamical relaxation times obtained for the angular velocity of the pulsar PSR 0833—45 vary, as a function of the density of the layers taking part in the relaxation process, within a fairly wide range: from several hours to l0⁹ years. This means that the characteristic times of variation of pulsar angular velocity may be observed to lie in the indicated time range. Translated from Astrofizika, Vol. 40, No. 4, op. 497–506, October–December, 1997.     

Meteoroid ablation models

The fate of entering meteoroids in atmosphere is determined by their size, velocity and substance properties. Material from ablation of small-sized meteors (roughly R≤0.01–1 cm) is mostly deposited between 120 and 80 km altitudes. Larger bodies (up to meter sizes) penetrate deeper into the atmosphere (down to 20 km altitude). Meteoroids of cometary origin typically have higher termination altitude due to substance properties and higher entry velocity. Fast meteoroids (V>30–40 km/s) may lose a part of their material at higher altitudes due to sputtering. Local flow regime realized around the falling body determines the heat transfer and mass loss processes. Classic approach to meteor interaction with atmosphere allows describing two limiting cases: – large meteoroid at relatively low altitude, where shock wave is formed (hydrodynamical models); – small meteoroid/or high altitudes – free molecule regime of interaction, which assumes no collisions between evaporated meteoroid particles. These evaporated particles form initial train, which then spreads into an ambient air due to diffusion. Ablation models should make it possible to describe physical conditions that occur around meteor body. Several self-consistent hydrodynamical models are developed, but similar models for transition and free molecule regimes are still under study. This paper reviews existing ablation models and discusses model boundaries.     

Atmospheric Losses Under Dust Bombardment in the Ancient Atmospheres

We have considered the new process of atmospheric losses - “sputtering” under bombardment by interplanetary dust. It is demonstrated that “sputtering” due to collisions with the interplanetary dust is an effective way of atmospheric gas loss (10^–4–10^–3 of the dust particles' accreting mass) and that it changes the composition of the atmospheric gases. In calculations we have taken that the dust particles collide elastically with the atoms and molecules of the atmosphere. Estimation of the effects of inelastic collisions was also considered. As a result of these collisions a part of the atmospheric atoms and molecules will have “upward” velocity and enough energy to escape. It was considered that escaping atoms can collide with the atoms of the “main” gas of the upper atmosphere. The atmospheric gas composition is assumed to be just as in the modern Martian atmosphere - the “main” gases in the upper atmosphere were taken to be O and CO₂. In our computations we pay particular attention to the abundance of noble gases in planetary atmospheres since these gases are very important for theories of atmospheric origin. We computed that under “sputtering” by the interplanetary dust, atmospheres were enriched by the “heavy” elements and isotopes in the wide range of the upper atmospheric parameters O/CO₂, T/g (O/CO₂– on the level of homosphere;T is temperature of the exosphere,g is gravitational acceleration). However the loss efficiency for “heavy” gases is relatively high compared to other known gas loss processes. In the case of noble gases for the specific parameters of the upper atmosphere (small T/g ratio; high O/CO₂ on the level of homosphere) we have got the unique result: despite the diffusion separation in the upper atmosphere the loss efficiency of Xe > Kr > Ar. The effect of “sputtering” of the planetary atmospheres was strongest during the early stages of the planetary evolution - when the rate of the dust accretion was intrinsically higher than now because of collisions of planetesimals. In light of the new escape process, the main peculiarities of the noble gases abundance in the planetary atmospheres could be explained. This revised version was published online in July 2006 with corrections to the Cover Date.     

A one-dimensional numerical model of H<Subscript>2</Subscript>O cloud formation in the Martian atmosphere

A one-dimensional numerical model with a size distribution of aerosol particles in Martian atmosphere is developed. The model incorporates detailed microphysics and turbulent transport. Dust particles suspended in the Martian atmosphere play a role of cloud condensation nuclei. Diurnal cycle of condensational processes is obtained on the basis of GCM temperature profiles. An effective radius of ice particles is 1–2 μm near the lower boundary of cloud layer and 0.2–0.3 μm at the altitude of 50–60 km. These results are consistent with solar infrared occultations by SPICAM experiment on Mars-Express. Near-surface fogs may form under specific conditions. The connections of condensational processes and cloud macroscopic parameters on microphysical properties of aerosol particles are main focus of this paper. In particular, the dependence on variations of cloud condensation nuclei contact parameter is analyzed, taking into account new experimental data of adsorption properties of minerals at low temperatures.     

Statistical description of the radiation field in a homogeneous medium of finite optical thickness

The problem of finding statistical averages which characterize the radiation field in a semi-infinite atmosphere has been discussed by the author in a series of papers. In this paper some of the results obtained there are generalized to media of finite optical thickness. The average number of scattering events undergone by a photon during its random walk in an atmosphere and the average time required for this are determined. Three different types of averages are considered, depending on the photon characteristics over which the averages are taken. Special attention is devoted to the asymptotic behavior of these quantities for media with large optical depths taking the influence of continuum absorption into account. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 263–275 (May 2006).     

Radio synthesis imaging of anisotropic angular broadening in the solar wind

We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2–16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2–16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R⊙, the major axis scattering angle is ∼ 0.7" atλ= 6 cm and it varies with heliocentric distance asR ^-1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized toλ = 20 cm, has a value 20 ± 7 at 5R⊙and varies with heliocentric distance asR ^-3. Comparison with earlier resu lts suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8–3.4 for scale sizes between 2–35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are l k m at 2R⊙ and 4 km at 13R⊙. These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum.     

Time-domain demodulation of RHESSI light curves

This paper presents an algorithm to decompose the modulated RHESSI light curves into periodic functions and a smooth function, representing the true (demodulated) time profile of an impulsive source. The decomposition is achieved by optimizing a trade-off between the Poisson likelihood, a smoothness constraint, and conditions on the average grid transmission and the (modulating or non-modulating) background. The algorithm, which operates on the level of count rates and does not require imaging information, is verified by numerical simulations and applied to some early RHESSI data, where – as a preliminary result – several impulsive features on time scales < 4 s may have been identified.     

Spectral variability of LBV star V 532 (Romano’s star)

We present the results of studying the spectral and photometric variability of the luminous blue variable star V532 in M33. The photometric variations are traced from 1960 to 2010, spectral variations—from 1992 to 2009. The star has revealed an absolute maximum of visual brightness (1992–1994, high/cold state) and an absolute minimum (2007–2008, low/hot state) with a brightness difference of ΔB ≈ 2.3 ^m . The temperature estimates in the absolute maximum and absolute minimum were found to be T ∼ 22000 K and T ∼ 42000 K, respectively. The variability of the spectrum of V532 is fully consistent with the temperature variations in its photosphere, while both permitted and forbidden lines are formed in an extended stellar atmosphere. Broad components of the brightest lines were found, the broadening of these components is due to electron scattering in the wind parts closest to the photosphere. We measured the wind velocity as a difference between the emission and absorption peaks in the PCyg type profiles. The wind velocity clearly depends on the size of the stellar photosphere or on the visual brightness, when brightness declines, the wind velocity increases. In the absolute minimum a kinematic profile of the V532 atmosphere was detected. The wind velocity increases and its temperature declines with distance from the star. In the low/hot state, the spectral type of the star corresponds to WN8.5h, in the high/cold state—to WN11. We studied the evolution of V532 along with the evolution of AGCar and the massive WR binary HD5980 in SMC. During their visual minima, all the three stars perfectly fit with the WNL star sequence by Crowther and Smith (1997). However, when visual brightness increases, all the three stars form a separate sequence. It is possible that this reflects a new property of LBV stars, namely, in the high/cold states they do not pertain to the bona fide WNL stars.     

Quasiperiodic oscillations in the active solar regionsfrom the data of nobeyama radioheliograph

The use of integral characteristics of radio spots showed that in addition to the known 3–5-min oscillations, the above-spot regions of sunspots exhibit quasiperiodic oscillations of intensity, perimeter, sectional area, and area of the surface of the above-spot source radio image with periods in the ranges of 25–80, 90–110, 120–140, and 160–210 min. These periods are observed for all spots studied using the different characteristics of a radio source, which does not contradict the interpretation of these low-frequency oscillations as natural oscillations of spots near a certain position of stable equilibrium.     

X-ray observation of XTE J2012+381 during the 1998 outburst

The outburst of X-ray transient source XTE J2012+381 was detected by the RXTE All-Sky Monitor on 1998 May 24th. Following the outburst, X-ray observations of the source were made in the 2–18 keV energy band with the Pointed Proportional Counters of the Indian X-ray Astronomy Experiment (IXAE) on-board the Indian satellite IRS-P3 during 1998 June 2nd–10th. The X-ray flux of the source in the main outburst decreased exponentially during the period of observation. No large amplitude short-term variability in the intensity is detected from the source. The power density spectrum obtained from the timing analysis of the data shows no indication of any quasi-periodic oscillations in 0.002–0.5 Hz band. The hardness ratio i.e. the ratio of counts in 6–18 keV to 2–6 keV band, indicates that the X-ray spectrum is soft with spectral index >2. From the similarities of the X-ray properties with those of other black hole transients, we conclude that the X-ray transient XTE J2012+381 is likely to be a black hole.