Intensity Fluctuations of Radiation Escaping from a Multicomponent Stochastic Atmosphere. I

This is the first part of a paper devoted to a theoretical investigation of intensity fluctuations of radiation at the frequencies of a spectral line formed in a multicomponent stochastic atmosphere. It is assumed that the optical depth of structural elements and the power of the energy sources contained in them undergo random variations. The frequency dependence of the relative mean-square deviation of the intensity of radiation escaping from the atmosphere is determined. Two special cases are considered and it is shown that the behavior of this quantity is different, depending on which of the indicated characteristics of the medium undergoes random variations. The results make it possible to judge the character of random variations in the fine structure of a radiating medium from observations of it in the cores and wings of spectral lines. Recent observations of prominences made using the SUMER spectrometer in the SOHO international project served as the specific motivation for the work.     

Fluctuations in the Intensity of Radiation Emerging from a Multicomponent Stochastic Atmosphere. II

This part of a series of papers examines the more general problem in which it is assumed that the fluctuations in the intensity of radiation emerging from a medium are caused by random variations in both the optical thickness of the structural elements and the power of the energy sources contained in them. The frequency dependence of the relative mean square deviation (RelMSD) is investigated for different possible relationships among the parameters of the fine structure components. It is shown that the level of fluctuations at the central frequencies of a line can be greater than or smaller than in the far wings. The dependence of the RelMSD on the number of components and the number of possible realizations of their optical properties is discussed. The influence of random variations in the scattering coefficient on the observed integral intensity of a spectrum line is also examined. Observations of several relatively strong EUV lines from the SOHO/ SUMER space program are presented for comparison. These data indicate that there is a correlation between the frequency dependence of the RelMSD and the characteristic temperature for formation of these lines.__________Translated from Astrofizika, Vol. 48, No. 2, pp. 303–313 (May 2005).     

Polarized line formation by resonance scattering: Lorentz profile

Multiple resonance scattering of spectral line radiation is examined in atmospheres with uniformly distributed sources of unpolarized radiation. It is assumed that the profile of the absorption coefficient is lorentzian and that scattering involves complete frequency redistribution. The polarization characteristics of the emerging radiation are determined by iterative solution of a nonlinear Ambartsumyan-Chandrasekhar matrix integral equation. In particular, it is found that for pure scattering the maximum polarization at the limb of the disk is 5.421%. The polarization characteristics of the emerging radiation are compared for three different absorption profiles: Lorentz, Doppler, and rectangular (monochromatic radiation). __________ Translated from Astrofizika, Vol. 50, No. 2, pp. 199–217 (May 2007).     

Effects of high velocities on photoionization lines

We have treated formation of spectral lines in a commoving frame where photoionization is predominant over collisional processes. We have assumed that the radiation field for causing photoionization is a function of Planck function. We have also considered the situation in which the continuum contributes to the radiation in the line. In all the models the quantityB/A (ratio of outer to inner radii) is kept equal to 10 and the total optical depth is taken to be 10³. The velocity is assumed to be varying according to the lawdV/dτ ∼ < 1/τ whereτ is the optical depth (τ > 0) in the given shell. The velocities at the innermost radius (r =A) are set equal to 0 and at the outermost radius (r =B), the maximum velocities are taken to be 0, 1, 3 and 10 Doppler units. The calculated line profiles are those seen by an observer at infinity.P Cygni-type profiles are observed in the case of a medium with no continuum absorption. For a medium with continuum absorption double peaked asymmetric profiles are noticed when the velocities are small; the two emission peaks merge into a single asymmetric peak for larger velocities.     

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).     

Analytical solutions for saturated P Cygni type profiles

Analytical formulae for single P Cygni type saturated resonance line profiles in stellar winds have been derived. The limbdarkening and presence of underlying intrinsic atmospheric profile have been ignored. The Sobolev approximation for radiative transfer has been used and the general velocity law has been specified by widely used β parameter. The analytical formulae for the saturated resonance line profiles can be found for cases when 2β is an integer. The formulae for 2β = 1,2, 3 and 4 have been found by us. Also the formulae for calculating the line profiles in the cases of external and internal sharp truncation (cutoff) of the scattering shell have been given. Some characteristic line profiles have been presented. It has been shown that the turbulence-generated isotropic dominant backscattering of radiation in stellar winds generates wide dark plateaux in the blue wings of spectral lines, and the slopes of plateaux are shaped by turbulence. This revised version was published online in July 2006 with corrections to the Cover Date.     

Acceleration of particles in the vicinity of a massive black hole

Recent results of the gamma-ray Cherenkov astronomy definitely prove the existence of fast variability in the very high energy (V.H.E.) gamma-ray flux of some active galactic nuclei. The BL Lac PKS 2155-304 for instance showed variations down to a few minutes time scale. From standard light travel time argument, these variations put extremely strong constraints on the size of the TeV emitting zone, which has to be of the order of a few Schwarzschild radius, even for high values of the relativistic Doppler factor of the emitting jets. Such discovery is a challenge for particle acceleration scenarios, which have to imagine efficient acceleration processes at work in a very compact zone. Eventually, the immediate vicinity of the central black hole appears as the most conservative choice for the location of the TeV emission region of active galactic nuclei. In this paper, we propose a two-step mechanism for charged particle acceleration in the magnetosphere of a massive black hole surrounded by an accretion disk. Particles first gain energy by a stochastic process during the accretion phase. It is shown that effective proton acceleration up to energies 10¹⁷–10¹⁹ eV is possible in a low-luminosity magnetized accretion disk with 2D turbulent motion. The distribution function of energetic protons over energies is a power law function with typical index ≃−1. Here electrons are not very efficiently accelerated because of their drastic losses by synchrotron radiation. In a second time, part of the fast particles escape from the disk and are then entrained by the magnetic structure above the disk, in the rotating black hole magnetosphere. They thus gain additional energy by direct centrifugal mechanism, up to about 10²⁰ eV for the protons and to 10–100 TeV for the electrons when they cross the light cylinder surface. Such energetic particles can further radiate in the TeV spectral range observed by Cherenkov experiments as HESS, MAGIC and VERITAS. Energetic protons can produce γ-radiation in the energy band 1 GeV–100 TeV and above mainly by nuclei collisions with the disk matter, clouds, or ambient low energy photons. Energetic electrons can also reach the required spectral range by inverse Compton emission. However their acceleration is less efficient due to heavy radiation losses, and only gained by centrifugal process during the second phase of the whole mechanism we describe. Our present analysis would therefore favor hadronic scenarios for TeV emission of active galactic nuclei. It is tempting to relate long term variability over years of TeV active galactic nuclei to the first stochastic acceleration phase, which also provides the needed power law particle distributions, while short term variability over minutes is more likely due to perturbations of the second fast direct acceleration phase.     

Correlation between the Gamma-ray and the Near-infrared Emissions from Gamma-ray-loud Blazars in the Low State

We have studied the correlations between the near-IR and the γ-ray bands using 29 observed γ-ray-loud blazars (16 BL Lac objects and 13flat-spectrum radio quasars (FSRQs)) with near-IR and γ-ray spectralindices and fluxes. The results show that there are very strong correlations between near-IR mean spectral index α_IR and γ-ray mean spectral index α_γ and between near-IR and γ-ray fluxes. Which means that γ-ray radiation from the blazars should be mainly produced by the synchrotron self-Compton process. In addition, the γ-ray emission of BL Lac objects may be somewhat different from flat-spectrum radio quasars. This revised version was published online in July 2006 with corrections to the Cover Date.     

Multiwavelength focusing with the Sun as gravitational lens

The light deviation caused by the gravitational potential in the vicinity of the sun could be used as a means of focussing radiation that cannot be focussed easily otherwise. The gravitational lens formed by the sun is not stigmatic, but does have the advantage of being achromatic and acts identically on all types of mass-less radiations. For a source at infinity, its geometrical characteristics present a “caustic” line starting at 550 astronomical units (UA) downstream from the sun. In a plane perpendicular to that caustic line, images of distant objects are formed.The perturbations by the solar corona plasma will significantly blur electromagnetic radiation for wavelengths longer than those of the IR domain. At shorter wavelengths, for example the γ domain, the focussing process could lead to 10⁸ amplification factors. In order to reach the regions where images are formed, long distance space missions are necessary. Once launched, missions of this type would be dedicated to a single field. Some possible targets are considered, such as Sagitarius A observed in X and γ rays.In this paper we study the point spread function (PSF) of the sun as a gravitational lens. Taking into account perturbations by the planets, the non sphericity of the sun and coronal plasma index, we derive limits within which such observations could be possible.     

Frequency modulation and stochastic variability of the elatina varve record: A proxy for solar cyclicity?

A sequence of 1337 laminae of cyclically varying thickness, interpreted as periglacial varves, obtained from drill cores of the late Precambrian Elatina Formation may record by proxy an ancient solar activity cycle similar to that of the present epoch Sun. This inferred ancient activity cycle, represented by a sequence of 110 varve-cycles, has a variable period which approximates a normal distribution (chi square = 3.5), with mean and median values of 12 varve years, standard deviation 1.6 varve years, and maximum variability of ± 4 varve years. The time-sequence of varve-cycle periods consists of both deterministic and stochastic elements. The intrinsic period of the varve-cycle is modulated principally by a longer period of 160 varve years, during which the varve-cycle period displays superimposed stochastic variation. The power spectral density of the varve thickness sequence is endowed with a strong multiplet of spectral lines centered on the median period, a second weaker multiplet at 22–25 varve years, and several very long periods. The line spacing within the multiplets favors a separation of period mainly of about 160 varve years, while the superimposed random variability of the varve-cycle period is expressed in the amplitude of the sideband envelope. Running autocorrelation of the varve sequence supports the interpretation of frequency modulation (deviation ratio 1.5) of the late Precambrian solar activity cycle principally by a period of 160 varve years.     

Stochastic and dynamic temperature changes in the interplanetary gas

Exact solutions have been found to the Fokker-Planck equations, incorporating stochastic velocity changes and modelling particles moving in an inverse square central force field under an inverse square collision frequency. The solutions for the velocity distribution contain a combination of collisional and dynamical (reversible) heating. At a general position, there are two populations each with three distinct temperatures, one normal to the orbital plane and the others closely parallel and perpendicular to the mean orbit. Collisional heating is strong and most readily detected in the secondary component of gas which reaches upstream directions along indirect orbits (attractive central force). For interplanetary helium gas reaching 1 a.u., the collisional heating ranges from effective transverse increase of 200 K and radial increase of 1500 K in the downstream wake, to several thousand K increase in radial temperature of the secondary component transverse to the initial gas stream. In interpreting 584 Å sky background radiation observations, the dynamical changes in the velocity spread have to be taken into account for helium gas that is initially hot, when Doppler shifts relative to the solar emission line are significant; the present solutions being the thermal approximations to the distribution function reveal the appropriate radial temperature as a function of space.     

Determining the Physical Parameters of the System V1413 Aql in Its Quiescent and Active States in 20122017

We present the results of our spectroscopic observations for the classical symbiotic star V1413 Aql in 20122017. In this period the system was in both active and rare (for it) quiescent states. In 2012 the optical spectrum was dominated by the radiation from the erupted hot component of spectral type F47 III. In 2017 the system passed to a quiescent state that lasted at least three months. In this period lines of ions with high ionization potentials, such as He II 4686 Å and CIV 5802 Å, appeared in the spectrum. The temperature and luminosity of the hot component in this period were $$T_{\textrm{hot}}\approx 90\,000$$ K and $$L_{\textrm{hot}}\approx 1800L_{\odot}$$. We show that the quiescent state in 2017 differs little in its time and energy characteristics from the previous active state observed in 1993.     

Spectral Line and Continuum Radiation Propagation in a Clumpy Medium

We discuss the propagation of spectral line and continuum radiation in a clumpy medium and give general expressions for the observed absorption or emission from a cloud population. We show that the affect of the medium clumpiness can usually be characterised by a single number multiplying the mean column opacity. Our result provides a simpler proof and generalization of the result of Martin et al. (1984). The formalism provides a simple way to understand the effects of clumping on molecular line profiles and ratios; for example, how clumping effects the interpretation of ¹³CO(1–0) to ¹²CO(1–0) line ratios. It also can be used as a propagation operator in physical models of clumpy media where the incident radiation effects the spectral line emissivity. We are working to extend the formalism to the propagation of masers in a clumpy medium, but in this case, there are special difficulties because formal expectation values are not characteristic of observations because they are biased by rare events.     

Ionization structure of the atmospheres and line profiles in the spectra of Wolf-Rayet stars

The ionization structure of the atmospheres of Wolf-Rayet (WR) and WC stars is studied. The stellar atmospheres were assumed to consist of helium, hydrogen, and carbon. Profiles of the C III l 5696 line are calculated, both for a spherically symmetric atmosphere with a density that decreases monotonically outward and for an atmosphere containing a dense condensation (inhomogeneity). The dependence of line profiles on the parameters of the inhomogeneity is investigated. It is shown that profiles of the C III λ 5696 line calculated assuming no inhomogeneities in the atmosphere are too weak, whereas assuming the existence of inhomogeneities enables one to reconcile the observed and calculated profiles. An equation is obtained relating the mass of an inhomogeneity to the flux in the detail of the total profile of the CIII λ 5696 line formed by that inhomogeneity. This equation is used to construct a stochastic cloud model of the atmosphere of a WR star, consisting of a large number of inhomogeneities in a homogeneous, spherically symmetric stellar wind. In the proposed model, the formation of inhomogeneities was treated as a random process. It is shown that in this model it is possible both to obtain an average line profile corresponding to the observed one and to reproduce the amplitude and overall pattern of variability of profiles in the spectra of Wolf-Rayet stars. Translated from Astrofizika, Vol. 42, No. 3, pp. 373–398, July–September, 1999.     

Gravitational radiation from differentially rotating and oscillating white dwarfs

We examine the possible emission of gravitational waves from white dwarfs undergoing self-similar oscillations driven by the energy released during relaxation of their differential rotation. Two distributions of the initial angular momentum are considered. It is assumed that 1% of the energy dissipated by a rotating white dwarf is converted into the energy of self-similar oscillations and, therefore, into gravitational radiation. The relative amplitude of the gravitational radiation from an isolated white dwarf at a distance of 50 pc is found to be less than 10⁻²⁷. The emission from the galactic population of white dwarfs may create a background which overlaps the random cosmological background of gravitational radiation for the improved decihertz detectors currently being proposed. __________ Translated from Astrofizika, Vol. 49, No. 2, pp. 231–242 (May 2006).     

B and Be-stars in the young open stellar clusters NGC 659 and NGC 7419

The populations of B and Be-stars in the young open clusters NGC 7419 and NGC 659 are studied. Lowresolution spectral observations in the region of the Hα line are used to study 34 members of NGC 7419 and additional spectra in the range λ3700-6200 ? are obtained for 12 stars. During the period of our observations, four previously identified Be-stars manifested an absorption profile for the Hα line. Emission in the Hα line is observed in the spectra of 21 objects. The members of the cluster NGC 7419 are classified as to spectral type. The position of the Be-stars on a two-color IR diagram and a comparison with the position of the objects in other clusters with similar ages cast doubt on the existence of two starformation waves. Moderate resolution spectra were obtained for 22 stars in the cluster NGC 659 over wavelengths of λ4050-5200 ? and for 7 objects in the neighborhood of the Hα line. Emission is observed in both the Hα and Hβ lines for two of the five Be-stars that were studied, while faint emission appears only in the Hα line in one of the stars. The other members of the cluster show no signs of emission in these spectra. T_eff, log g, and Vsini are estimated for the observed stars. It is found that 5 of the objects are not members of the cluster.     

The analysis of XUV emission lines

A technique for analyzing measurements of XUV spectral line intensities is described. Application of the technique to OSO-4 and OSO-6 spectra indicates that the mean coronal temperature is 2.1 × 10⁶ K in typical active solar regions and that the mean coronal temperature in typical quiet regions ranges from 1.5 × 10⁶ to 2.1 × 10⁶ K. One active region spectrum shows evidence for substantial quantities of coronal material with 2 × 10⁶ < T < 3.5 × 10⁶ K. Measurements from limb spectra show evidence that (1) coronal abundances of N and O are low relative to heavier elements; or (2) that the ionization equilibrium calculations used may contain systematic errors; or (3) that the XUV intensity measurements may be incorrectly calibrated.     

Particle Acceleration and High-Frequency (X-ray and γ-ray) Emission in the Jets of Active Galactic Nuclei

It is suggested that the outflowing plasma in the jets of active galactic nuclei (AGNs) is inhomogeneous and consists of separate clouds. These clouds are strongly magnetized and move away from the central engine at relativistic speeds. The clouds interact with an ambient medium which is assumed to be at rest. In the process of this interaction, particles of the ambient medium are accelerated to high energies at the cloud front and flow ahead of the front. It is shown that the radiation of the accelerated particles may be responsible for the X-ray and γ-ray emission from AGN jets. TeV γ-ray emission is generated in the inner parts of AGN jets where the Lorentz factor of the cloud fronts is Γ0≥ 30, while GeV γ-ray emission emanates from the outer parts of AGN jets where Γ0 is ∼ 10. This revised version was published online in July 2006 with corrections to the Cover Date.     

Continuous absorption and depression in the solar spectrum at wavelengths from 650 to 820 nm

Results of calculations of the cross-sections of the basic processes forming continuous absorption in the photospheres of solar-type stars in the visible and infrared spectral ranges are reported. (These processes are photoionization of H^– ions and excited hydrogen atoms, as well as absorption of photons by “free” electrons being in the partially ionized plasma of the photosphere.) The effective cross-section of hydrogen satisfying the observational data or the results of laboratory experiments was introduced, and its nonmonotonic behavior caused by photoionization of excited hydrogen atoms was ascertained in the spectral range of λ from 650 to 820 nm. For a plane-parallel model of the Sun, the continuous absorption coefficient κ _c (λ|z) was calculated as a function of the wavelength and coordinate. Its spectral features caused by the effective cross-section structure in the above-mentioned spectral range were for the first time analyzed. The spectral dependence of the radiation intensity in the solar disk center in the continuous spectral range of λ from 600 to 900 nm was studied. The calculation results were compared to the currently available data of observations. It has been shown that the deviation of the observed radiation intensity from the Planck distribution (i.e., the depression) is caused by the processes of photoionization of the excited hydrogen atoms in the states with a principal quantum number n = 3. In the range of λ from 650 to 820 nm, the mean relative deviation is approximately 4%. It has been established that the magnitude of the depression effect significantly depends on the effective temperature of the photosphere of a solar-type star.     

The Influence of Fluctuations of the Solar Emission Line Profileon the Doppler Shift of Interplanetary HLyα Lines Observed by the Hubble–Space–Telescope

In an earlier research the employment of a radiation transport model with angle-dependent partial frequency redistribution, self-absorption by interplanetary hydrogen, realistic solar H_Lyαemission profile, and a time dependent `hot' hydrogen model to analyze 5 interplanetary H_Lyα glow spectra obtained with theHubble–Space–Telescope–GHRS spectrometer, has not resulted in unequivocal determination of a set of thermodynamical parameters of the interstellar hydrogen The residual discrepancies between the model and the data concern the observations performed within an interval of 1 year close to the solar minimum from very similar lines of sight. In this paper we investigate by calculating interplanetary H_Lyα lines with the use of a one hydrogen distribution and several solar H_Lyα line profiles whether this residual may be caused by possible variations in time of the shape of the solar H_Lyα emission line profile which cause variable illuminations of the interplanetary gas. These variations of illuminations cause variations in Doppler shift of the resonant interplanetary H_Lyα line that can amount to ≃ 4 km s^-1in the line peak. Consequently we conclude that without adequate knowledge of the solar H_Lyα emission line profile during spectral observations of the interplanetary hydrogen gas it is impossible to obtain an agreement between models and observations better than by this value. This revised version was published online in July 2006 with corrections to the Cover Date.