Spectral variations of the nova V2468 Cyg at various stages of the development of its outburst

Spectral variations of the nova V2468 Cyg were studied over 1.5 years following the beginning of its outburst, during its smooth fading and the star’s rebrightenings. Following the rebrightening on March 25, 2008, the profiles of H I lines had changed, from a two-component structure with peaks at ?220 and 670 km/s to a four-component structure with peaks at ?640, ?260, 255, and 620 km/s. The profiles of [N II] 5755 Å, [O III] 5007 Å, He II 4686 Å, and [Fe VII] 6086 Å lines varied throughout the interval of our observations. During rebrightenings, the lines profiles changed and the line intensities significantly decreased. The width of the [Fe VII] 6086 Å profile varied, in addition to its shape and intensity; this profile differed from the profiles of other lines during the nebular phase. Estimates of chemical-element abundances in the nova’s envelope indicate enhanced abundances of nitrogen and oxygen, compared to the Sun, and solar abundances of neon and argon. The helium abundance was somewhat higher than the solar value. The mass of the ejected envelope is estimated to be 5 × 10^?5 M _⊙.     

A study of the shell of Nova V2659 Cyg

Results of a study of the shell of Nova V2659 Cyg based on spectrophotometric observations carried out over a year and a half after its eruption are presented. The physical conditions in the nova shell have been studied. The electron temperature (9000 K) and density (5 × 10⁶ cm^?3) in the nebular stage have been estimated, together with the abundances of helium, oxygen, nitrogen, neon, argon, and iron. The abundances of nitrogen, oxygen, neon, and argon are enhanced relative to the solar values. The relative abundances are [N/H] = 2.26 ± 0.25 dex, [O/H] = 1.66 ± 0.35 dex, [Ne/H] = 0.78 ± 0.25 dex, and [Ar/H] = 0.32 ± 0.38 dex. The estimated mass of oxygen and total mass of the emitting shell are ≈1 × 10^?4M_⊙ and ≈3 × 10^?4M_⊙, respectively. In the period of chaotic brightness oscillations, the maximum velocity of the shell expansion derived from the radial velocities of the absorption components of the HI and FeII line profiles increased by ≈400 km/s 41 days after the maximum, and by ≈200 km/s 101 days after the maximum, reaching 1600 km/s in both cases.     

Multicolor photometry of CH Cygni in 1978–1998

We present the results of long-term (1978–1998) infrared and optical observations of the unique symbiotic system CH Cygni. The system’s IR brightness and color variations are generally consistent with a model in which the source is surrounded by a dust envelope with variable optical depth. There was evidence for a hot source in the CH Cyg system during the entire period from 1978 to 1998, with the exception of several hundred days in 1987–1989. Over the observation period, there was tendency for the system to gradually redden at 0.36–5 µm, accompanied by a brightness decrease at 0.36–2.2µm and a brightness increase at 3.5 and 5 µm. The “activation” of the cool sources in 1986–1989 nearly coincided with the disappearance of radiation from the hot source. The dust envelope of CH Cyg is not spherically symmetrical, and its optical depth along the line of sight is substantially lower than its emission coefficient, the mean values being τ_ex(L)～0.06 and τ_em(L)～0.16. We confirm the presence of a 1800-to 2000-day period in both the optical and IR, both accounting for, and not accounting for, a linear trend. The spectral type of the cool star varied between M5III and M7III. The spectral type was M5III during the phase of maximum activity of the system’s hot source, while the spectral type was M7III when the star’s optical radiation was almost completely absent. The luminosity of the cool giant varied from (6300–9100)L _⊙; its radius varied by approximately 30%. The ratio of the luminosities of the dust envelope and the cool giant varied from 0.08 to 0.5; i.e., up to 50% of the cool star’s radiation could be absorbed in the envelope. The temperature of dust particles in the emitting envelope varied from 550 to 750 K; the radius of the envelope varied by more than a factor of 2. The expansion of the emitting dust envelope observed in 1979–1988 accelerated: its initial velocity (in 1979) was ～8 km/s, while the maximum velocity (in 1987–1989) was ～180 km/s. Beginning in 1988, the radiation radius of the dust envelope began to decrease, first at ～45 km/s and then (in 1996–1998) at ～3 km/s. From 1979 until 1996, the mass of the emitting dust envelope increased by approximately a factor of 27 (the masses in 1979 and 1988 were ～1.4×10^?7 M _⊙ and ～3.8×10^?6 M _⊙, respectively), after which (by 1999) it decreased by nearly a factor of 7. The mass-loss rate of the cool star increased in 1979–1989, reaching ～3.5×10^?6 ～3.5×10^?6 M _⊙/yr in 1988. Subsequently (up to the summer of 1999), the envelope itself began to lose mass at a rate exceeding that of the cool star. The largest input of matter to the envelope occurred after the phase of optical activity in 1978–1985. If the envelope’s gas-to-dust ratio is ～100, the mass of matter ejected in 1988 was ～4×10^?4 M _⊙.     

Abundances of carbon,nitrogen, oxygen,and other elements in the atmospheres of the giants 25 Mon and HR 7389

An analysis of high-resolution CCD spectra of the giant 25 Mon, which shows signs of metallicity, and the normal giant HR 7389 is presented. The derived effective temperatures, gravitational accelerations, and microturbulence velocities are T_eff = 6700 K, log g = 3.24, and ξ _t = 3.1 km/s for 25 Mon and T_eff = 6630 K, log g = 3.71, and ξ _t = 2.6 km/s for HR 7389. The abundances (log ε) of nine elements are determined: carbon, nitrogen, oxygen, sodium, silicon, calcium, iron, nickel, and barium. The derived excess carbon abundances are 0.23 dex for 25 Mon and 0.16 dex for HR 7389. 25 Mon displays a modest (0.08 dex) oxygen excess, with the oxygen excess for HR 7389 being somewhat higher (0.15 dex). The nitrogen abundance is probably no lower than the solar value for both stars. The abundances of iron, sodium, calcium (for HR 7389), barium, and nickel exceed the solar values by 0.22–0.40 dex for both stars. The highest excess (0.62 dex) is exhibited by the calcium abundance for 25 Mon. Silicon displays a nearly solar abundance in both stars—small deficits of ?0.03 dex and ?0.07 dex for 25 Mon and HR 7389, respectively. No fundamental differences in the elemental abundances were found in the atmospheres of 25 Mon and HR 7389. Based on their T_eff and log g values, as well as theoretical calculations, A. Claret estimated the masses, radii, luminosities, and ages of 25 Mon (M/M_⊙ = 2.45, log(R/R_⊙) = 0.79, log(L/L_⊙) = 1.85, t = 5.3 × 10⁸ yr) and HR 7389 (M/M_⊙ = 2.36, log(R/R_⊙) = 0.50, log(L/L_⊙) = 1.24, t = 4.6 × 10⁸ yr), and also of the stars 20 Peg (M/M_⊙ = 2.36, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.79, t = 4.9 × 10⁸ yr) and 30 LMi (M/M_⊙ = 2.47, log(R/R_⊙) = 0.73, log(L/L_⊙) = 1.88, t = 4.8 × 10⁸ yr) studied by the author earlier.     

Partial mixing in early-type main-sequence B stars

Partial mixing of material in the radiative envelopes and convective cores of rotating main sequence stars with masses of 8 and 16 M _⊙ is considered as a function of the inital angular momentum of the stars. Losses of rotational kinetic energy to the generation of shear turbulence in the radiative envelope and the subsequent mixing of material in the envelope are taken into account. With an initial equatorial rotational velocity of 100 km/s, partial mixing develops in the upper part of the layer with variable chemical composition and the lower part of the chemically homogeneous radiative envelope. When the initial equatorial rotational velocity is 150–250 km/s, the joint action of shear turbulence and semi-convection leads to partial mixing in the radiative envelope and central parts of the star. The surface abundance of helium is enhanced, with this effect increasing with the angular momentum of the star. With an initial equatorial rotational velocity of 250 km/s, the ratio of the surface abundances of helium and hydrogen grows by ~30% and ~70% toward the end of the main-sequence evolution of an 8 M _⊙ and 16 M _⊙ star, respectively. The transformation of rotational kinetic energy into the energy of partial mixing increases with the angular momentum of the star, but does not exceed ~2%?3% in the cases considered.     

Photometric parameters of the dwarf nova SS Cygni in the quiescent state

The mean 1983–1996 UBV light curves of the dwarf nova SS Cyg are used to derive the binary parameters in the quiescent state. Solutions are obtained for a classical hot-spot model and a model with an energy source lying outside the accretion disk. Photometric and spectroscopic data are combined to infer the masses and radii of the binary components. The white dwarf in SS Cyg is one and a half times as massive as the red dwarf, q=M _wd /M _rd ～1.45, M _rd ～0.46M _⊙ and M _wd ～0.66M _⊙. The orbital inclination of the system is i?51°–54°. The contribution of the accretion disk to the total flux in the quiescent state is estimated to be ～47–49% and ～54% in the VU and B filters, respectively. The hot spot contributes less than ～3% to the total optical flux. In the “non-classical” hot-spot model, the disk and bulge contributions are 27 and 2–8%, respectively, depending on the orbital phase. The shape of the mean light curves of SS Cyg suggests asymmetric heating of the red-dwarf surface in the quiescent state by high-temperature radiation generated in the hot-spot region.     

The evolutionary status of ultraluminous X-ray sources

We analyze models for quasi-stationary, ultraluminous X-ray sources (ULXs) with luminosities 10³⁸–10⁴⁰ erg/s exceeding the Eddington limit for a ～1.4M_⊙ neutron star. With the exception of relatively rare stationary ULXs that are associated with supernova remnants or background quasars, most ULXs are close binary systems containing a massive stellar black hole (BH) that accretes matter donated by a stellar companion. To explain the observed luminosities of ～10⁴⁰ erg/s, the mass of the BH must be ～40M_⊙ if the accreted matter is helium and ～60M_⊙ if the accreted matter has the solar chemical composition. We consider donors in the form of main-sequence stars, red giants, red supergiants, degenerate helium dwarfs, heavy disks that are the remnants of disrupted degenerate dwarfs, helium nondegenerate stars, and Wolf-Rayet stars. The most common ULXs in galaxies with active star formation are BHs with Roche-lobe-filling main-sequence companions with masses ～7M_⊙ or close Wolf-Rayet companions, which support the required mass-exchange rate via their strong stellar winds. The most probable candidate ULXs in old galaxies are BHs surrounded by massive disks and close binaries containing a BH and degenerate helium-dwarf, red-giant, or red-supergiant donor.     

Radial pulsations of helium stars and a model for BX CIR

The results of hydrodynamical calculations of radially pulsating helium stars with masses 0.5M_⊙≤M≤0.9M_⊙, bolometric luminosities 600L_⊙≤5×10³L_⊙, and effective temperatures 1.5×10⁴ K≤T_eff≤3.5×10⁴ K are presented. The pulsation instability of these stars is due to the effects of ionization of iron-group elements in layers with temperatures T～2×10⁵ K. The calculations were carried out using opacities for the relative mass abundances of hydrogen and heavy elements X=0 and Z=0.01, 0.015, and 0.02. Approximate formulas for the pulsation constant Q over the entire range of pulsation instability of the hot helium stars in terms of the mass M, radius R, effective temperature T_eff, and heavy-element abundance Z are derived. The instability of BX Cir to radial pulsations with the observed period Π=0.1066 d occurs only for a mass M≥0.55M_⊙, effective temperature T_eff≥23000 K, and heavy-element abundance Z≥0.015. The allowed mass of BX Cir is in the range 0.55M_⊙≤M≤0.8M_⊙, which corresponds to luminosities 800L_⊙≤M≤1400L_⊙ and mean radii 1.7R_⊙?R?2.1R_⊙.     

Atmospheric chemical abundances and the evolutionary status of the spectroscopic and speckle-interferometric binary 9 Cyg

We have performed speckle interferometry with the 6-m telescope of the Special Astrophysical Observatory and spectroscopy (at 3700–9200 Å) with the 2-m telescope at Peak Terskol of the spectroscopic and interferometric binary 9 Cyg, which is a composite-spectrum star with an orbital period of 4.3 yrs. The atmosphere of the system’s primary component is analyzed in detail. The luminosities of both components estimated to be L ₁ = 103.8 L _⊙, L ₂ = 55.2 L _⊙, where L _⊙ is the solar luminosity, and their effective temperatures to be T _e (1) = 5300 K and T _e (2) = 9400 K. The abundances of C, N, O, Fe, and other elements in the primary’s atmosphere have been derived. The chemical composition shows signatures of mixing of material from its atmosphere and the region of nuclear reactions. The evolutionary status of 9 Cyg has been determined. The binary’s age is about 400 million years; the brighter star is already in the transition to becoming a red giant, while the secondary is still in the hydrogen-burning stage near the zero-age main sequence. We suggest an evolutionary model for the binary’s orbit that explains the high eccentricity, e = 0.79.     

Interpretation of the light curve of the eclipsing binary V444 Cyg on the set of convexo-concave functions

The narrow-band λ4244 Å continuum light curve of the eclipsing binary V444 Cyg, which has a Wolf-Rayet component, is interpreted assuming that the brightness distribution and absorption in the WN5 star's disk are monotonic, non-increasing, convexo-concave, non-negative functions. The convex and concave parts of these functions correspond to the core of the WN5 star and its extended photosphere and atmosphere, respectively. The radius and brightness temperature of the opaque core of the WN5 star are r _WN5 ^core ? 4R _⊙ and T _br ^core >52000 K, respectively. The stellar wind is characterized by an accelerated radial outflow. Acceleration of the wind persists at large distances from the center of the star. A crude Lamers-law fit to the reconstructed velocity field in the wind yields an acceleration parameter β=1.58–1.82.     

Enhancement of surface helium abundance in intermediate-mass main-sequence stars

The evolution of rapidly rotating 8, 4, and 2 M _⊙ main-sequence stars is considered together with hydrodynamical transfer in their interiors. The conditions under which turbulent erosion, semiconvection, and shear turbulence lead to partial mixing of the matter in the radiative envelope and central regions of the stars are determined. The enhancement of the surface helium abundance with time depends on both the intensity of partial mixing in their interiors and mass loss by the stellar wind. The ratio of the number densities of helium and hydrogen at the surface can rise by the end of main-sequence stage by ～30% for a 8 M _⊙ star and ～10?20% for a 4 M _⊙ star, depending on the mass-loss rate. Partial mixing of the matter in the radiative envelope and in the central region of the star can provide an explanation for the observed enhancement of the atmospheric helium abundances of early B stars toward the end of their main-sequence evolution. The enhancement of the surface helium abundance in a 2 M _⊙ star is so small that it cannot be detected, and is appreciably lower than the enhancement beneath the surface.     

Infrared photometry of the unique object FG Sge in 1985–2001

Our analysis of many years of infrared photometry of the unique object FG Sge indicates that the dust envelope formed around the supergiant in August 1992 is spherically symmetrical and contains compact, dense dust clouds. The emission from the spherically symmetrical dust envelope is consistent with the observed radiation from the star at 3.5–5 µm, and the presence of the dust clouds can explain the radiation observed at 1.25–2.2 µm. The mean integrated flux from the dust envelope in 1992–2001 was ～(1.0±0.2)×10^?8 erg s^?1cm^?2. The variations of its optical depth in 1992–2001 were within 0.5–1.0. The maximum density of the dust envelope was recorded in the second half of 1993 and corresponded to mean optical depths as high as unity. Several times in the interval from 1992 to 2001, the dusty material of the envelope partially dissipated and was then replenished. For example, the optical depth of the dust cloud at λ=1.25 µm during the last brigthness minimum in the J band was τ_1.25≈4.3, which is much higher than the optical depth of the dust envelope of FG Sge. During maxima of the J brightness, the mean spectral energy distribution at 0.36–5 µm can be represented as a combination of radiation from a G0 supergiant that is attenuated by a dust envelope with a mean optical depth of 0.65±0.15 and emission from the spherically symmetrical dust envelope itself, with the temperature of the graphite grains being 750±150 K. At minima of the J brightness, only radiation from the dust envelope is observed at 1.65–5 µm, with the radiation from the supergiant barely detectable at 1.25 µm. As a result, the integrated flux during J minima is almost half that during J maxima. The mean mass of the spherically symmetrical dust envelope of FG Sge in 1992–2001 was (3 ± 1) × 10^?7M_⊙. This envelope’s mass varied by nearly a factor of two during 1992–2001, in the range (2 – 4) × 10^?7M_⊙. In Autumn 1992, the mass-loss rate from the supergiant exceeded 2 × 10^?7M_⊙/yr. The average rate at which matter was injected into the envelope during 1993–2001 was 10^?8M_⊙/yr. The mean rate of dissipation of the dust envelope was about 1 × 10^?8M_⊙/yr. During 1992–2001, the supergiant lost about 8.7 × 10^?7M_⊙. The parameters of the dust envelope were relatively constant from 1999 until the middle of 2001.     

IR photometry and models for the dust envelopes of two carbon stars

The results of JHKLM photometry of two carbon stars are presented: the irregular variable NQ Cas and the Mira star BD Vul. Data on the mean fluxes supplemented with mid-IR observations with the IRAS, AKARI, andWISE satellites are used to compute spherically symmetrical model dust envelopes for the stars, consisting of particles of amorphous carbon and silicon carbide. The optical depth in the visible for the comparatively cool dust envelope of BD Vul, with a dust temperature at its inner boundary T₁ = 610 K, is fairly low: τ_V = 0.13. The dust envelope of NQ Cas is appreciably hotter (T₁ = 1550 K), and has τ_V = 0.32. The estimated mass-loss rates are 1.5 × 10^?7M_⊙/yr for NQ Cas and 5.9 × 10^?7M_⊙/yr for BD Vul.     

The relation between the observed mass distribution for compact stars and the mechanism for supernova explosions

The observed mass distribution for the compact remnants of massive stars (neutron stars and black holes) and its relationship to the possible mechanism of ejection of the envelopes of type II and Ib/c supernovae are analyzed. The observed lack of compact remnants with masses 1.5–3 M _⊙ suggests a magneto-rotational mechanism for the supernovae, and a soft equation of state for neutron stars with limiting masses near 1.5 M _⊙. The observational consequences of this hypothesis are discussed.     

The dust envelope of the symbiotic nova V1016 Cyg

Brightness and color variations of V1016 Cyg are studied using many years of UBVRJHKLM photometric observations and information about its spectral energy distribution in the intermediate IR (7.7 to 22.7 µm) obtained with the IRAS and ISO low-resolution spectrometers. Models for its stationary, spherically symmetrical, extended dust envelope are computed for two cases of heating: by the radiation of the cool component only and by the combined radiation from both components. Model fitting of the IRAS and ISO observations shows that the model with a single central source—the Mira star—provides a better fit to the data, indicating that the hot component’s radiation is appreciably reprocessed by the ambient gas medium and has almost no direct influence on the IR spectrum of the symbiotic nova. The mean spectral energy distributions measured by IRAS in 1983 and ISO on October 1, 1996, differ considerably. The observed evolution of the envelope’s spectrum probably reflects an increasing grain concentration and decreasing grain temperature at the inner edge of the envelope, associated with decreased luminosity and increased temperature of the hot component. The total mass-loss rate, gas-expansion velocity at the outer edge of the envelope, and upper limit to the mass of the central radiation source are estimated.     

Evolution of planetary-nebula envelopes and determination of their distances

Evolutionary properties of the radial distribution of the gas density in the envelopes of 12 Galactic planetary nebulae are discussed. An evolutionary relationship between the maximum gas density n(r)_max and the radius of the ionized segment of the nebula r _c is derived. The ionized-gas masses in the envelopes of these nebulae M _i /M _⊙ are determined. The relationship between the mass M _i /M _⊙ and radius of the nebula is derived. The value of M _i /M _⊙ changes by approximately a factor of 275 during a nebula’s evolution, ranging from 0.0038M _⊙ for “young” nebulae (IC 5117) to 1.05M _⊙ for “old” nebulae (NGC 7293). Distances to the nebulae are determined based on calculated photoionization models. These distances are in good agreement with those obtained independently byMalkov and with the distance to the planetary nebula K648 in the Galactic star cluster M15.     

Masses of RR Lyrae Stars with Different Chemical Abundances in the Galactic Field

The surface gravities and effective temperatures have been added to a compilative catalog published earlier, which includes the relative abundances of several chemical elements for 100 field RR Lyrae stars. These atmoshperic parameters and evolutionary tracks from the Dartmouth database are used to determine the masses of the stars and perform a comparative analysis of the properties of RR Lyrae stars with different chemical compositions. The masses of metal-rich ([Fe/H] > −0.5) RR Lyrae stars with thin disk kinematics are in the range (0.51−0.60)M_⊙. Only stars with initial masses exceeding 1M_⊙ can reach the horizontal branch during the lifetime of this subsystem. To become an RR Lyrae variable, a star must have lost approximately half of its mass during the red-giant phase. The appearance of such young, metal-rich RR Lyrae stars is possibly due to high initial helium abundances of their progenitors. According to the Dartmouth evolutionary tracks for Y = 0.4, a star with an initial mass as low as 0.8 M_⊙ could evolve to become an RR Lyrae variable during this time. Such stars should have lost (0.2−0.3)M_⊙ in the red-giant phase, which seems quite realistic. Populations of red giants and RR Lyrae stars with such high helium abundances have already been discovered in the bulge; some of these could easily be transported to the solar neighborhood as a consequence of perturbations due to inhomogeneities of the Galaxy’s gravitational potential.

     

Stellar sources of the short-lived radionuclides in the early solar system

We discuss the possible stellar sources of short-lived radionuclides (SLRs) known to have been present in the early solar system (²⁶Al, ³⁶Cl, ⁴¹Ca, ⁵³Mn, ⁶⁰Fe, ¹⁰⁷Pd, ¹²⁹I, ¹⁸²Hf, ²⁴⁴Pu). SLRs produced primarily by irradiation (⁷Be, ¹⁰Be) are not discussed in this paper. We evaluate the role of the galactic background in explaining the inventory of SLRs in the early solar system. We review the nucleosynthetic processes that produce the different SLRs and place the processes in the context of stellar evolution of stars from 1 to 120 M_⊙. The ejection of newly synthesized SLRs from these stars is also discussed. We then examine the extent to which each stellar source can, by itself, explain the relative abundances of the different SLRs in the early solar system, and the probability that each source would have been in the right place at the right time to provide the SLRs. We conclude that intermediate-mass AGB stars and massive stars in the range from ∼20 to ∼60 M_⊙ are the most plausible sources. Low-mass AGB stars fail to produce enough ⁶⁰Fe. Core-collapse Type II supernovae from stars with initial masses of <20 M_⊙ produce too much ⁶⁰Fe and ⁵³Mn. Sources such as novae, Type Ia supernovae, and core-collapse supernovae of O-Ne-Mg white dwarfs do not appear to provide the SLRs in the correct proportions. However, intermediate-mass AGB stars cannot provide ⁵³Mn or the r-process elements, so if an AGB star provided the ⁴¹Ca, ³⁶Cl, ²⁶Al, ⁶⁰Fe, and ¹⁰⁷Pd, and if a late stellar source is required for ⁵³Mn and the r-process elements, then two types of sources would be required. A separate discussion of the production of r-process elements highlights the difficulties in modeling their production. There appear to be two sources of r-process elements, one that produces the heavy r-process elements, including the actinides, and one that produces the elements from N to Ge and the elements ∼110 < A < ∼130. These can be assigned to SNII explosions of stars of ?11 M_⊙ and stars of 12-25 M_⊙, respectively. More-massive stars, which leave black holes as supernova remnants, apparently do not produce r-process elements.     

Three-dimensional hydrodynamical modeling of mass transfer in the close binary system β Lyr

We present a three-dimensional hydrodynamical modeling of mass transfer in the close binary system β Lyr taking radiative cooling into account explicitly. The assumed mass-transfer rate through the first Lagrangian point L₁ is 3.0 × 10^?5 M _⊙/yr. A flow with a radius of 0.14–0.16 (in units of orbital separation) is formed in the vicinity of L₁. This flow forms an accretion disk with a radius close to 23 R _⊙ and a thickness of about 10 R _⊙. The accretion disk is surrounded by an outer envelope that extends beyond the computational domain. A spiral shock forms at the outer boundary of the disk at orbital phase 0.25. Geometrically, the disk is toruslike, while the outer envelope is cylinder-like. In this model, which has low temperatures inside the computational domain, no jetlike structures form in the disk. It is possible that the jetlike structure in β Lyr arises due to the interaction of radiative wind from the accretor with the flow from L₁. In the model considered, a hot region exists over the poles of the accretor at a height of about 0.21. The amount of matter lost by the system is close to 10% of the mass flowing through L₁; i.e., the mass transfer in the system is almost conservative. For a mass-transfer rate of 3.0 × 10^?5 M _⊙/yr, the orbital period varies by 40.4 s/yr. This means that the observed variation of the orbital period of 19 s/yr should correspond to a mass-transfer rate close to 1.0 × 10^?5 M _⊙/yr.     

Nonlinear radial pulsations of Wolf-Rayet stars

The evolution of Population I stars with initial masses 60 M _⊙ ≤ M _ZAMS ≤ 120 M _⊙ is computed up to the Wolf-Rayet stage, when the central helium abundance decreases to Y _c ≈ 0.05. Several models from evolutionary sequences in the core helium-burning stage were used as initial conditions when solving the equations of radiative hydrodynamics for self-exciting stellar radial pulsations. The low-density envelope surrounding the compact core during the core helium burning is unstable against radial oscillations in a wide range of effective temperatures extending to T _eff ～ 10⁵ K. The e-folding time of the amplitude growth is comparable to the dynamical time scale of the star, and, when the instability ceases growing, the radial displacement of the outer layers is comparable to the stellar radius. Evolutionary changes of the stellar radius and luminosity are accompanied by a decrease in the amplitude of radial pulsations, but, at the effective temperature T _eff ≈ 10⁵ K, the stellar oscillations are still nonlinear, with a maximum expansion velocity of the outer layers of about one-third the local escape velocity. The period of the radial oscillations decreases from 9 hr to 4 min as stellar mass decreases from M = 28 M _⊙ to M = 6 M _⊙ in the course of evolution. The nonlinear oscillations lead to a substantial increase of the radii of the Lagrangian mass zones compared to their equilibrium radii throughout the instability region. The instability of Wolf-Rayet stars against radial oscillations is due to the action of the κ mechanism in the iron-group ionization zone, which has a temperature of T ～ 2 × 10⁵ K.