Formation of P Cygni profiles with limb darkening of the stellar core

In the framework of the Sobolev approximation, we investigate the effects of limb darkening of the stellar core onto the formation of line profiles in rapidly expanding envelopes.For the case of outward-accelerating envelopes, it is shown that the P Cygni profiles, calculated with and without limb darkening, do appear almost identical as long as the size of the envelope remains large with respect to the radius of the star. As the extent of the envelope decreases, the resulting profiles are found to differ appreciably close to the line center.When considering outward-decelerating (or equivalently inward-accelerating) envelopes, calculations with the limb darkening effects reveal that the P Cygni profiles are more strongly affected than in the previous case. These effects are specially important in the blue wing and near the center of the resulting line profiles, irrespective of the size of the envelope.Chargé de Recherches au Fonds National de la Recherche Scientifique, Belgium.     

A possible interpretation of the optical spectrum for BL Lac-type objects

On the basis of Sobolev's method, the population of 30 levels of hydrogen atom is determined allowing for the radiative and collision processes of the heating and ionization of the medium with velocity gradient gradv=10^–9–10^–11s^–1, electron temperatureT _e=10⁴ K-2×10⁴ K and electron densityN _e=10¹⁰ cm^–3–10¹¹ cm^–3. The central source radiation is characterized by a power spectrum with spectral indices varying from 0 to 2. A region of possible physical conditions is found where the thermal diffuse radiation of the envelope exceeds the emission in the Balmer H line.     

Hydrogen ionization and n=2 population for model spicules and prominences

Using slab model atmospheres that are irradiated from both sides by photospheric, chromospheric, and coronal radiation fields we have determined the ionization and excitation equilibrium for hydrogen.The model atom consists of two bound levels (n = 1 and n = 2) and a continuum. Ly- was assumed to be optically thick with the transition in detailed radiative balance. The Balmer continuum was assumed to be optically thin with the associated radiative ionization dominated by the photospheric radiation field (T _rad = 5940 K). The ionization equilibrium was determined from an exact treatment of the radiative transfer problem for the internally generated Ly-c field and the impressed chromospheric and coronal field (characterized by T _rad = 6500K).Our calculations corroborate the hypothesis that N₂, the n = 2 population density, is uniquely determined by the electron density N _e. We also present ionization curves for 6000K, 7500K, and 10000K models ranging in total hydrogen density from 1 × 10¹⁰/cm³ to 3 × 10¹²/cm³. Using these curves it is possible to obtain the total hydrogen density from the n = 2 population density in prominences and spicules.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Determination of mass-loss rates from the first order momentW 1 of unsaturated P Cygni line profiles

The escape probability method introduced by Sobolev to treat the transfer of line photons is used in order to derive the expressions of thenth order momentW _n (E()/E _c –1)(–₁₂) ⁿ ·d of a P Cygni profile formed in rapidly expanding envelopes around a central point-like source under various physical and geometrical conditions.With the only assumption that there is mass-conservation of the species in the flow, we state for the case of optically thin lines that the relation between the first order momentW ₁ and the quantityM _n (level), first established by Castoret al. (1981) under more restrictive conditions, is in fact independent of the type of velocity fieldv(r) and a fortiori of the distribution adopted for the radial opacity ₁₂ ^r (X). These results also remain unchanged when including collisions (0) and/or an additional rotational velocity fieldv (r) in the expanding atmosphere. We investigate the presence of an underlying photospheric absorption line and conclude that for realistic cases, neglecting this boundary condition to the radiative transfer leads to an underestimate of the mass-loss rate by a factor of about 20%. By means of a three-level atom model, we demonstrate that all results derived for a single line transition equally apply for an unresolved doublet profile providedW ₁ andM _n (level) are calculated with the weighted wavelength _D and total oscillator strengthf _D of the doublet.Considering the occultation and inclination effects caused by the finite size of the central core, we refine the value of the multiplicative constant fixing the ratio ofW ₁ toM _n (level). We show that this relation allows a determination of the mass-loss rate with an uncertainly less than 30%, irrespective of the sizeL _max of the atmosphere and of the limb-darkening affecting the stellar core. Reviewing all possible sources of error, we finally conclude that this method of deriving a mass-loss rate from the analysis of an unsaturated P Cygni profile is very powerful. The total uncertainty affecting the determination ofM _n (level) from the measurement ofW ₁ should be smaller than 60%.     

Radiation pressure effects in the oscillations of compressible rotating homogeneous spheroids

Earlier models of compressible, rotating, and homogeneous ellipsoids with gas pressure are generalized to include the presence of radiation pressure. Under the assumptions of a linear velocity field of the fluid and a bounded ellipsoidal surface, the dynamical behaviour of these models can be described by ordinary differential equations. These equations are used to study the finite oscillations of massive radiative models with masses 10M and 30M in which the effects of radiation pressure are expected to be important.Models with two different degrees of equilibrium are chosen: an equilibrium (i.e., dynamically stable) model with an initial asymmetric inward velocity, and a nonequilibrium model with a nonequilibrium central temperature and which falls inwards from rest. For each of these two degrees of equilibrium, two initial configurations are considered: rotating spheroidal and nonrotating spherical models.From the numerical integration of the differential equations for these models, we obtain the time evolution of their principal semi-diametersa ₁ anda ₃, and of their central temperatures, which are graphically displayed by making plots of the trajectories in the (a ₁,a ₃) phase space, and of botha ₁ and the total central pressureP _c against time.It is found that in all the equilibrium radiative models (in which radiation pressure is taken into account), the periods of the oscillations of botha ₁ andP _c are longer than those of the corresponding nonradiative models, while the reverse is true for the nonequilibrium radiative models. The envelopes of thea ₁ oscillations of the equilibrium radiative models also have much longer periods; this result also holds for the nonequilibrium models whenever the envelope is well defined. Further, as compared to the nonradiative models, almost all the radiative models collapse to smaller volumes before rebouncing, with the more massive model undergoing a larger collapse and attaining a correspondingly larger peakP _c.When the mass is increased, the dynamical behavior of the radiative model generally becomes more nonperiodic. The ratio of the central radiation pressure to the central gas pressure, which is small for low mass models, increases with mass, and at the center of the more massive model, the radiation pressure can be comparable in magnitude to the gas pressure. In all the radiative models, the average periods as well as the average amplitudes of both thea ₁ andP _c oscillations also increase with mass.When either rotation or radiation pressure effects or both are included in the equilibrium nonradiative model, the period of the envelope of thea ₁ oscillations is increased. The presence of rotation in the equilibrium radiative model, however, decreases this period.Some astrophysical implications of this work are briefly discussed.     

Structure of envelopes ejected by Novae

The paper contains an analysis of the structure of envelopes ejected during the outbursts of Novae. The data used for this purpose: (a) Direct photographs of envelopes and the photographs taken with the use of different colour filters; (b) Spectra of envelopes. The envelope of DQ Her is studied most carefully. The analysis of all available data for the envelopes around DQ Her and V 603 Aql permits us to outline a morphological model of these envelopes, see Figure 3. It appears, that the structure of both these envelopes is approximately identical and that the difference in the observed properties of the photographic images of the nebulae (Figure 2 and Figure 4) is connected with a difference in the orientation of the polar axes of the envelopes relative to the line of sight. The envelope ejected during the outburst of T Aur (Figure 5) reveals the same properties, which are characteristic for the envelopes of DQ Her and V 603 Aql.From this we conclude that the distribution of gases inside the envelopes of the majority of Novae is approximately of the same character. This speaks in favour of the presence of certain forces around many Novae, which guide the motion of ejected plasma along some quite definite directions inside rather small solid angles. It seems that the only conceivable forces of this type may be the forces of a magnetic nature. This hypothesis for example permits us to explain the difference between the envelope of GK Per (Figure 1) and the envelopes of DQ Her, V 603 Aql, T Aur (Figures 2, 4 and 5).Comparing the velocity of expansion of the envelope of DQ Her and the rate of change of its angular size we computed that the distance to DQ Her is equal to 320 pc.On the base of photographs of the envelope of DQ Her it is found that in 1968 the fluxF _H of radiation in the H-line was equal to (6±2)×10^–12 ergs/cm²sec, whereas the mass of the envelope was equal to 10²⁹ G and its electronic concentrationn _e to 2×10³ cm^–3. Several hypotheses, which may explain the stratification of emission from different elements inside the envelope are discussed.     

Long-Term Spectral Variability of the Herbig Ae-Star HD 179218

The results of high-resolution long-term spectral monitoring of Herbig Ae star HD 179218 in the region of emission H line and the sodium resonance doublet Na I D are presented. The received data show the existence of short-term variability (about 10 days) and long-term wave-like variability of equivalent width EW, intensity of circumstellar (CS) emission I and parameters of H emission profile. The analysis of these data allows us to suppose the existence of the global variability of parameters of accretion disk.     

Helium radiation diffusion in prominences

The following is shown on the basis of a solution of the integral diffusion equations for radiation in a multilevel helium atom under low-temperature plasma conditions (T _e = 7000 K) in the Vertical slab model: (a) Neutral helium is ionized by coronal radiation mainly in the 100–300 Å spectral region; the degree of helium ionization is maximum at the boundary planes, (b) The photorecombinations to the 2³ S and 2¹ S levels and the photoionizations by the Balmer continuum of the Sun are very nearly balanced and this determines the population of these levels. The 2³ S level is destroyed by electron impacts (this reduces the brightness of the triplet lines), and the 2¹ S level decays via the escape of the quanta of 584 through the 2¹ P level, (c) Emission in the resonance line 584 (2¹ P 1¹ S) occurs due to recombination to 2¹ S with subsequent absorption of quanta of infrared radiation 20581. This is a rare case. (d) The radiation of helium is generated in the vicinity of the boundary planes in the region of penetration of radiation with 200 Å, where the density of matter decreases gradually down to the coronal value. In the subordinate lines, the radiation is conditioned by the quasi-resonance scattering of photospheric radiation, (e) The calculated absolute values of the intensities of the helium and hydrogen lines are in good agreement with the observations (see Figure 6).The helium to hydrogen number ratio is close to 0.05.     

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 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,kT _emc ², |–s _B|kT _e/mc ² )^1/2|cos|, whereT _e is the electron plasma temperature, _B=eB/mc the electron cyclotron frequency,s=1,2,... the number of cyclotron harmonic and 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.     

On the Thermochemical Instability of an Ionized Plasma Cooled by Oxygen Forbidden Lines

The thermal stability of an ionized hydrogen plasma in which the reaction OIII + (h) OIV + e^- proceeds is analyzed. The gas is assumed to be heated by a diluted stellar radiation of effective temperature T_*. The stability analysis is carried out taking into account the chemical relaxation time effects from which a fifth order dispersion relation is obtained instead the fourth order polynomial obtained when such effects are neglected. The effects of the thermal conduction are also considered.     

Circumstellar clouds derived from the 2800 Mgii data

As a result of the analysis of the observed interstellar 2800 Mgii absorption line data, an empirical relationship — a positive correlation — between the equivalent widthW(2800) and the effective temperature of the starT was discovered (Figure 1). However, in the case when this doublet is of stellar (photospheric) origin, only a negative correlation betweenW(2800) andT exists. Hence, the existence itself of such a positive correlation betweenW(2800) andT may be viewed as incomprehensible for the present influence of the star on the strength of the absorption line 2800 Mgii of nonstellar origin.On the other hand, we have evidence that the ionizing radiation of hot stars cannot provide for the observed very high degree of ionization of the interstellar magnesium. In particular, the observations give for interstellar magnesium the ratioN ⁺/N ₁ 1000, while in the case of ionization under the action of stellar radiation only we haveN ⁺/N ₁ 10.The assumption that circumstellar clouds surround hot stars can naturally explain these and other similar facts. A method for the determination of the general parameters-size, concentration, mass etc. — of the circumstellar clouds is developed. The main results of the application of this method to the relation of more than 20 hot stars are:(1) The circumstellar clouds surround almost (70%) all hot giants and subgiants. In the remaining (30%) cases, the absence of circumstellar envelopes requires additional evidence. (2) The linear sizes of circumstellar clouds vary within wide ranges — from 0.002 pc up to 1 pc. Most frequent are clouds with size of 0.1 pc. (3) The main concentration of hydrogen atoms (electrons) in circumstellar clouds is of the order of 100 cm^–3; the minimum value is 20–30 cm^–3, the maximum 10⁴ cm^–3. In one case (Deneb) the electron concentration rises up to 10⁵ cm^–3 for the size of the cloud 0.001 pc=3×10¹⁵ cm. (4) Stars of the same spectral and luminosity classes may possess circumstellar clouds characterized by quite different parameters. (5) Hydrogen in circumstellar clouds is completely ionized; for these clouds the optical depth _c 1; on the average,T _c 0.005. (6) The integrated brightness of circumstellar clouds is substantially fainter (by 8–10^m) than that of the central star. This is the reason why these clouds cannot be detected by ground-based observations. (7) The masses of individual circumstellar clouds vary from 1 down to 10^–4 . This gives for the mass ejection rate from 10^–10 to 10^–6 per year in case if these clouds are formed by the braking and accumulation of the ejected mass.The method of 2800 Mgii seems very convenient, fruitful and promising for the detection and study of circumstellar envelopes. Also, this method is very sensitive for a determination of the general parameters of such clouds, and concerns practically all their geometric, physical, kinematic and other properties.     

On radiative dissipation of sinusoidal compressive waves in the chromosphere

A first-order theory is developed for the radiative dissipation of compressive waves in the chromosphere above T _min, where line radiation becomes dominant. The radiative relaxation time, which is the key to dissipation, is shown to depend on wave amplitude, falling greatly for amplitudes 2 km s^–1 or more. For a given amplitude, dissipation is greatest for high frequencies, 0.1 s^–1, periods 1 min. The observed short-period r.m.s. velocities ~2.4 km s^–1 at the D₁, level are adequate to provide dissipation balancing chromospheric emission losses.Predictions for the temperature-velocity phase difference and the phase velocity are compatible with observations.     

Atlas of spectra of selected stars in ground-based ultraviolet

We present an atlas of spectra of high signal-to-noise ratio and high spectral resolution (R ≥ 60000) in a poorly studied short-wavelength region up to 3055 Å. The spectra of well-studied stars of close temperatures (β Ori, α Lyr and α Cyg) are compared with the spectrum of a low-metallicity A-type supergiant KSPer, the atmosphere of which is poor in hydrogen, H/He = 3 × 10^?5.We study the velocity field in the expanding atmospheres and envelopes of these stars. A complete atlas and detailed identification of spectral features are available in the Internet.     

A generalized method for deriving mass-loss rates: The first order moment of unsaturated P Cygni line profiles

For the case of optically thin lines, we show that the relation existing between the first order momentW ₁ (E()/E _c –1)(–₁₂)d of a P Cygni profile and the quantityMn(level), whereM is the mass-loss rate of the central star andn(level) the fractional abundance of the ion under study, is in fact independent of any Sobolev-type approximations used for the transfer of line radiation, contrary to what has been assumed in some previous works (Castoret al., 1981; Surdej, 1982). Consequently, all results established in the context of very rapidly expanding atmospheres and mainly referring to the non-dependence ofW ₁ vs various physical (underlying photospheric absorption line, limb darkening, etc.) and geometrical (velocity fieldv(r), etc.) effects remain unchanged for arbitrary (e.g non-Sobolev type) outward-accelerating velocity laws.Whenever applied with caution, Equation (50) thus provides a very powerful means of deriving mass-loss rates—with a total uncertainty less than 60 percent—from the measurementW ₁ of unsaturated P Cygni profiles observed in the spectrum of early—as well as late—type stars, quasars, etc.     

Resonance line radiation originating from a region with well-developed plasma turbulence

This study considers the influence of the effects of scattering due to Langmuir turbulent pulsations in the transfer of radiation in the spectral lines. The transfer equation of radiation in spectral lines, by taking into account scattering due to Langmuir turbulent pulsations, is written in a form convenient for application by numerical methods.The profile's intensity for a plane-parallel finite isothermal slab of a turbulent plasma in the case of complete redistribution of scattering by an atom are obtained. Numerical studies show that in this case with the broadening of spectral lines and the decreasing of self-reversal, the Langmuir frequency _pe is of the same order as the electronic Doppler width _De. Creation of the line satellites when _pe is larger than the line width is shown with the aid of numerical methods.     

The hydrogen emission spectrum of a shock wave in a stellar atmosphere

Based on a self-consistent solution of the equations of gas dynamics, kinetics of hydrogen atomic level populations, and radiative transfer, we analyze the structure of a shock wave that propagates in a partially ionized hydrogen gas. We consider the radiative transfer at the frequencies of spectral lines by taking into account the effects of a moving medium in the observer's frame of reference. The flux in Balmer lines is shown to be formed behind the shock discontinuity at the initial hydrogen recombination stage. The Doppler shift of the emission-line profile is approximately one and a half times smaller than the gas flow velocity in the Balmer emission region, because the radiation field of the shock wave is anisotropic. At Mach numbers M₁?10 and unperturbed gas densities σ₁=10^?10 g cm^?3, the Doppler shift is approximately one third of the shock velocity U₁. The FWHM of the emission-line profile δ _? is related to the shock velocity by δ _? ≈ k _? U₁, where k _? = 1, 0.6, and 0.65 for the Hα, Hβ, and Hγ lines, respectively.     

Radiation hydrodynamics of high-luminosity accretion into black holes

To extend Shapiro's (1973a, b) calculations of black hole accretion to the regimes of interstellar gas densities and of black hole masses for which emergent luminosities are expected to be high, the radiation hydrodynamics of spherically symmetric gas flows in static isotropic metrics is discussed. Since for the more luminous objects the optical depth of the accretion volume becomes large, particular attention has to be paid to radiative transfer through non-Euclidean spaces, and a method for solving the full transfer problem is presented. The method is applied to accretion into black holes of mass between 10M and 10⁵ M , under the conservative assumption that all other heat sources, like dissipation of magnetic or turbulent energy, can be neglected in comparison to the compressional work term,p dV. In the interstellar gas parameter range of interest, the radiation field is then dominated by emission and absorption of synchrotron radiation from inner zones of the flow. Temperature stratifications, luminosities and emergent spectra resulting from these processes are calculated.     

On the theory of the light curves of supernovae

An account of the theory of the light curves of supernovae is presented, based on certain assumptions concerning the passage through the stellar atmosphere of powerful shock waves. The investigation is based on numerical integration of appropriate equations of gas dynamics and radiative heat-conductivity. The calculations substantially involve the ionization and recombination of hydrogen in the envelope of a supernova. Changes are traced in the curves arising from the transition from compact stars with small radius (10R ), to stars with very extensive envelopes (10000R ). The light curves for compact stars agree well with observations of the peculiar supernovae in NGC 5457, NGC 6946 and NGC 5236. The characteristics of the light curves with the passage of shock waves through the extended atmosphere coincide within an order of magnitude with observations of the supernovae of type II and type I near their maximum brightness. A powerful heat-wave propagates before the shock-front in the extensive atmosphere which gives rise to a detached supernova envelope in the form of a thin spherical layer. We investigated the condition in an ascending wave of cooling and recombination in the supernova envelope. It is shown that part of the hydrogen may recombine to attain full transparency for radiation passing through it. The observations are compared with the results of the theory of radioactive decay of the elements. This explanation of the light curves by the passage of shock waves requires energies of 10⁵⁰ to 10⁵² ergs, which are in agreement with mechanisms of thermonuclear explosions.Translated from the Russian by E. Budding.     

Linear waves in a radiating and scattering grey medium

The problem on linear waves in a radiating and scattering grey medium is studied using Whitham's method. Analysis of the basic equations distinguishes two limiting cases: the one is theequilibrium case in which the energy exchange between the gas and radiation plays an essential role, and the other is theScattering case in which the effect of energy exchange is negligible. A new type ofradiation acoustic wave with the speed is found in the scattering case. The governing equations for linearized one-dimensional flow are reduced to one equation of radiative acoustics valid to order 1/c, and the criterion for the two limiting cases is derived from studying this equation. The harmonic solution is analytically studied to show that theeffective optical depth corresponding to the wavelength of perturbation gives the measure of the interaction between the gas and radiation. When _eff1, the sound speeda _g ² =P _g / and the propagating speed of radiative disturbancea _f ² =fc ² appear as the modified classical and radiation-induced modes respectively, wheref is the Eddington factor. When _eff1, the isentropic sound speeda _s ² =(P _g +P _r / appears in the equilibrium case, and the radiation acoustic speeda _A ² appears in the scattering case. The dispersion relation of the harmonic solution is numerically calculated. The result shows that the wave pattern depends critically on the ratio=P _g /(P _g +P _r ). When , the speeda _S anda _A arise from the modified classical mode, and when , they originate from the radiation-induced mode.