Models for highly flattened, rapidly rotating cool stars in a Newtonian approximation

We investigate the physical characteristics of single, rapidly rotating white dwarfs, which could form as a result of a merger of two white dwarfs with different masses and filled Roche lobes, due to the radiation of gravitational waves. When the merging of the binary components occurs without loss of mass and angular momentum, the merger products are subject to secular instability, and the density in their cores does not exceed ～10⁸ g/cm³. Models are constructed for rapidly rotating neutron stars, which could form after the collapse of rotating iron cores of evolved massive stars. Dynamically unstable neutron-star models are characterized by a shift of the maximum density from the rotational axis. The total momentum of such neutron stars is about half the maximum possible momentum for the evolved cores of massive stars.     

Formation and evolution of Ae and Be stars

Several scenarios for the formation of accretion and decretion disks in single and binary Ae and Be stars are proposed. It is shown that, in order for a rapidly rotating main-sequence Be star to lose mass via a disk, the star’s rotation must be quasi-rigid-body. Estimates show that such rotation can be maintained by the star’s magnetic field, which is probably a relict field. The evolution of single Be main-sequence stars is numerically simulated allowing for mass loss via the stellar wind and rotational mass loss assuming rigid-body rotation. The stellar wind is the factor that determines the maximum mass of Be stars, which is close to 30M _⊙. The evolution of Be stars in close binaries is analyzed in the approximation adopted in our scenario. Long gamma-ray bursts can be obtained as a result of the collapse of rapidly rotating oxygen—neon degenerate dwarfs—the accreting companions of Be stars—into neutron stars.     

Population synthesis of rapidly rotating main-sequence stars with companions

Usingthe “Scenario Machine” (a specialized numerical code formodeling the evolution of large ensembles of binary systems), we have studied the physical properties of rapidly rotating main-sequence binary stars (Be stars) with white-dwarf companions and their abundance in the Galaxy. The calculations are the first to take into account the cooling of the compact object and the effect of synchronization of the rotation on the evolution of Be stars in close binaries. The synchronization time scale can be shorter than the main-sequence lifetime of a Be star formed during the first mass transfer. This strongly influences the distribution of orbital periods for binary Be stars. In particular, it can explain the observed deficit of short-period Be binaries. According to our computations, the number of binary systems in the Galaxy containing a Be star and white dwarf is large: 70–80% of all Be stars in binaries should have degenerate dwarf companions. Based on our calculations, we conclude that the compact components in these systems have high surface temperatures. Despite their high surface temperatures, the detection of white dwarfs in such systems is hampered by the fact that the entire orbit of the white dwarf is embedded in the dense circumstellar envelope of the primary, and all the extreme-UV and soft X-ray emission of the compact object is absorbed by the Be star’s envelope. It may be possible to detect the white dwarfs via observations of helium emission lines of Be stars of not very early spectral types. The ultraviolet continuum energies of these stars are not sufficient to produce helium line emission. We also discuss numerical results for Be stars with other evolved companions, such as helium stars and neutron stars, and suggest an explanation for the absence of Be-black-hole binaries.     

Merging of components in close binaries: Type Ia supernovae,massive white dwarfs,and Ap stars

The “Scenario Machine” (a computer code designed for studies of the evolution of close binaries) was used to carry out a population synthesis for a wide range of merging astrophysical objects: main-sequence stars with main-sequence stars; white dwarfs with white dwarfs, neutron stars, and black holes; neutron stars with neutron stars and black holes; and black holes with black holes. We calculate the rates of such events, and plot the mass distributions for merging white dwarfs and main-sequence stars. It is shown that Type Ia supernovae can be used as standard candles only after approximately one billion years of evolution of galaxies. In the course of this evolution, the average energy of Type Ia supernovae should decrease by roughly 10%; the maximum and minimum energies of Type Ia supernovae may differ by no less than by a factor of 1.5. This circumstance must be taken into account at estimating the parameters of the Universe expansion acceleration. According to theoretical estimates, the most massive—as a rule, magnetic—white dwarfs probably originate from mergers of white dwarfs of lower mass. At least some magnetic Ap and Bp stars may form in mergers of low-mass main-sequence stars (M ? 1.5 M _⊙) with convective envelopes.     

Variability of the photospheric radiation of active K-M dwarfs and their X-ray luminosities

Variability of the photospheric radiation of 40 (dKe-dMe) dwarfs in the solar neighborhood due to variations in the spottedness of their surfaces is analyzed based on the behavior of their mean annual brightnesses over long time intervals. The amplitudes and characteristic time scales of the variations of the mean annual brightness are taken to be indicators of photospheric activity and were used to infer the levels of photospheric activity in the stars studied. The influence of axial rotation on the development of cyclic activity in young red dwarfs and F-M main-sequence stars is analyzed. The durations and amplitudes of the photospheric variability of rapidly rotating (dK0e-dK5e) stars testifies to a higher level of photospheric activity among red dwarfs and solar-type stars. The X-ray luminosities of these stars grow with the amplitude of the variations of the mean annual brightness. However, this is not typical of rapidly rotating M dwarfs, for which the X-ray emission varies by more than two orders of magnitude, although their degrees of spottedness are all virtually the same. A linear relationship between the X-ray and bolometric luminosities is observed for young (dKe-dMe) stars, with their ratios log(L _x/L _bol) being about ?3. These properties can be used to determine whether a red dwarf is a young star or is already on the main sequence.     

Formation of planets during the evolution of single and binary stars

Current views of the origin and evolution of single and binary stars suggest that the planets can form aroundmain-sequence single and binary stars, degenerate dwarfs, neutron stars, and stellarmass black holes according to several scenarios. Planets can arise during the formation of a star mainly due to excess angular momentum leading to the formation of an accretion-decretion disk of gas and dust around a single star or the components of a binary. It is the evolution of such disks that gives rise to planetary systems. A disk can arise around a star during its evolution due to the accretion of matter from dense interstellar clouds of gas and dust onto the star, the accretion of mass froma companion in a binary system, and the loss of matter during the contraction of a rapidly rotating star, in particular, if the star rotates as a rigid body and the rotation accelerates with its evolution along the main sequence. The fraction of stars with planetary systems is theoretically estimated as 30–40%, which is close to the current observational estimate of ∼34%.     

Spots and activity of Pleiades stars from observations with the Kepler Space Telescope (K2)

Observations of the K2 continuation of Kepler Space Telescope program are used to estimate the spot coverage S (the fractional spotted area on the surface of an active star) for stars of the Pleiades cluster. The analysis is based on data on photometric variations of 759 confirmed clustermembers, together with their atmospheric parameters, masses, and rotation periods. The relationship between the activity (S) of these Pleiades stars and their effective temperatures shows considerable change in S for stars with temperatures T _eff less than 6100 K (this can be considered the limiting value for which spot formation activity begins) and a monotonic increase in S for cooler objects (a change in the slope for stars with Teff ~ 3700 K). The scatter in this parameter ΔS about its mean dependence on the (V ?Ks)0 color index remains approximately the same over the entire (V?K _s )0 range, including cool, fully convective dwarfs. The computated S values do not indicate differences between slowly rotating and rapidly rotating stars with color indices 1.1 < (V?K _s )0 < 3.7. The main results of this study include measurements of the activity of a large number of stars having the same age (759 members of the Pleiades cluster), resulting in the first determination of the relationship between the spot-forming activity and masses of stars. For 27 stars with masses differing from the solarmass by nomore than 0.1M⊙, themean spot coverage is S = 0.031±0.003, suggesting that the activity of candidate young Suns is more pronounced than that of the present-day Sun. These stars rotate considerably faster than the Sun, with an average rotation period of 4.3^d. The results of this study of cool, low-mass dwarfs of the Pleiades cluster are compared to results from an earlier study of 1570 M stars.     

Rotational mass loss by Be stars

We have carried out a numerical study of rotational mass loss by rapidly rotating Be stars assuming preservation of rigid-body rotation during their main-sequence evolution. Evolutionary models are computed for stars with solar chemical composition and initial masses of 3, 10 and M_⊙. As a result of their rapid initial rotation, these stars can lose one to four percent of their initial mass during the main-sequence stage. The amount of mass lost increases with the initial mass of the star. The matter lost by Be stars can form gas-dust disks with masses comparable to the masses of planets, which, in principle, makes possible the formation of planetary systems around such stars.     

The lower temperature limit of accretors

There should be a universal correlation between the main observational parameters of magnetized accreting stars (neutron stars, white dwarfs, and possibly T Tauri stars): their luminosities, periods, and temperatures. To first approximation, such a dependence is obeyed reasonably well for X-ray pulsars, intermediate polars, and T Tauri stars. In contrast, the parameters of anomalous pulsars (so-called “magnetars”) and soft gamma-ray repeaters differ sharply from this dependence, and even occupy a “forbidden” region in the parameter space. This presents a serious argument against the idea that these are accretingneutron stars.     

Axially symmetrical models of the products of a conservative merger of a binary white dwarf with similar-mass components

The possibility of a conservative merger of a binary white dwarf whose components have similar masses is studied. Axially symmetrical models for single, rapidly rotating white dwarfs that are possible products of such mergers are constructed and their physical characteristics investigated. The merger products must be turbulent, and the viscosity of the electron gas is not sufficient to support the observed luminosities of massive, bright white dwarfs. The amount of dissipative energy and the timescale for its release are estimated.     

The activity of late-type stars: the Sun among stars with cyclic activity

The coronal and chromospheric emission of several hundred late-type stars whose activity was recently detected are analyzed. This confirms the previous conclusion for stars of HK project that there exist three groups of objects: active red M dwarfs, G-K stars with cyclic activity, and stars exhibiting high but irregular activity. The X-ray fluxes, EUV-spectra, and X-ray cycles can be used to study the main property of stellar coronas—the gradual increase in the number of high-temperature (T ≥ 10 MK) regions in the transition from the Sun to cyclically active K dwarfs and more rapidly rotating F and G stars with irregular activity. The level of X-ray emission is closely related to the spottedness of the stellar surface. The correlation between the chromospheric and coronal emission is weak when the cycles are well-defined, but becomes strong when the activity is less regular. Unexpectedly, stars whose chromospheric activity is even lower than that of the Sun are fairly numerous. Common and particular features of solar activity among the activity of other cyclically active stars are discussed. Our analysis suggests a new view of the problem of heating stellar coronas: the coronas of stars with pronounced cycles are probably heated by quasistationary processes in loops, while prolonged nonstationary coronal events are responsible for heating the coronas of F and G stars with high but irregular activity.     

Stellar activity observed by the Kepler Space Telescope. The M dwarf of the Kepler-32 system with five orbiting planets

The activity of the central star of the Kepler-32 planetary system is studied using continuous 1141-day observations with the Kepler Space Telescope. The Kepler-32 system includes a slowly rotating Mdwarf (rotational period of 37.8 d) with a mass of 0.54M _⊙ and five planets. One of the unique properties of the system is its compactness: the orbits of all five planets are less than a third of the size of the orbit of Mercury; the planet closest to the star is separated from it by only 4.3 stellar radii. Surface-temperature inhomogeneities of the central star are studied using precise photometric observations of Kepler-32, and their evolution traced. In total, 42 624 individual brightness measurements in the 1141-day (3.1-year) observing interval were selected for the analysis. The calculated amplitude power spectra for the first and second halves of the interval of the Kepler-32 observations indicate appreciable variability of the photometric period, corresponding to the evolution of active regions at various latitudes on the stellar surface. Evidence for the existence of two active regions on the stellar surface separated in phase by 0.42 has been found. Time intervals in which the longitudes of the active regions changed (“flip-flops”) with durations of the order of 200–300 days have been established. The spotted area of the star was, on average, about 1% of the total visible surface, and varied from 0.3 to 1.7%. The results for the dwarf Kepler-32 are compared with those from a spectropolarimetric survey of 23 M dwarfs, including both fully convective stars and stars with weakly radiative cores. For a more detailed comparison, temperature inhomogeneities on the surface of one of the survey stars, DS Leo, was reconstructed using the ground-based observations (316 individual measurements of the V-band brightness of the star during seven observing seasons in an all-sky automated survey). The general properties and evolution of the active regions on DS Leo and Kepler-32 are considered. The positions of the active regions on the surface of Kepler-32 yields no evidence for differential rotation of this star. The possibility of detecting the magnetic field of Kepler-32 is proposed. The analysis of the photometric data for Kepler-32 are also compared to the previous results for the fully convective, low-mass M dwarfs GJ 1243 and LHS 6351. This demonstrates that the observed manifestations of activity on Kepler-32 correspond to those for active G-K stars and to M dwarfs with masses of the order of 0.5M _⊙, rather than Mdwarfs with masses from 0.2 to 0.5M _⊙.     

A model for the population of helium stars in the Galaxy: Low-mass stars

We model the Galactic ensemble of helium stars using population synthesis techniques, assuming that all helium stars are formed in binaries. In this picture, single helium stars are produced by mergers of helium remnants of the components of close binaries (mainly, the merging of helium white dwarfs) or in the disruption of binaries with helium components during supernova explosions. The estimated total birthrate of helium stars in the Galaxy is 0.043 yr^?1; the total number is 4 × 10⁶; and the binarity rate is 76%. We construct a subsample of low-mass (M_He ? 2M_⊙) helium stars defined by observational selection effects: the limiting magnitude (V_He ≤ 16), ratio of the magnitudes of the components in binaries (V_He ≤ V_comp), and lower limit for the semiamplitude of the radial velocity required for detecting binarity (K_min = 30 km s^?1). The parameters of this subsample are in satisfactory agreement with observations of helium subdwarfs. In particular, the binarity rate in the selection-limited sample is 58%. We analyze the relations between the orbital periods and masses of helium subdwarfs and their companions in systems with various combinations of components. We predict that the overwhelming majority (～97%) of unobserved companions to helium stars will be white dwarfs, predominantly, carbon-oxygen white dwarfs.     

太阳系演化中的地球和月球起源(英文)

宇宙中恒星的演化始于巨星的形成 ,后者的质量是太阳系的数百倍 ,寿命估计为数百万年。重元素合成于巨星的内部。它们控制了巨星爆炸过程中 (超新星 )形成的气态云和盘状物的冷凝加速度。冷凝和旋转的加速导致后代恒星质量越来越小 ,寿命越来越长 ,直到形成像太阳这样的小星体 ,其质量为 1.989× 10 30 kg ,寿命已有几十亿年。这些小恒星的形成是冷凝过程中产生的水成冰氢星子不断聚集的结果。上一代巨星的原始星盘中的物质只有一小部分参与了冰氢星子的形成。这些星体形成于致密、高速旋转的原始恒星星盘中 ,周围环绕着巨行星和褐矮星。由于星体达到恒星状态 ,它们开始影响原恒星盘 ,结果导致星体相互分散 ,同时 ,最近的巨星发生表面去气作用。后者可以从巨星到恒星的质量衰减得到证实。UpsilonAndromedae、5 5Cancri和HD16 84 4 3等天体的巨行星记载了这样的事实。太阳系中的表面去气作用主要反映在近太阳巨星的流体外壳完全消失。由于流体外壳消失 ,铁硅酸盐熔融核暴露地表 ,形成小的类地行星。木星也经历过表面去气作用 ,依据是木星具有很高的平均密度 (1.3g cm3) ,几乎是土星密度 (0 .7g cm3)的两倍。因此 ,类地行星的形成经历了两个阶段 :原行星 (其父巨星具有重的熔融核 )和正常行星 (在其父行星     

Evolution of close binaries and gamma-ray bursts

We analyze the late stages of evolution of massive (M ₀ ? 8 M _⊙) close binaries, from the point of view of possible mechanisms for the generation of gamma-ray bursts. It is assumed that a gamma-ray burst requires the formation of a massive (～1 M _⊙), compact (R ? 10 km) accretion disk around a Kerr black hole or neutron star. Such Kerr black holes are produced by core collapses of Wolf-Rayet stars in very close binaries, as well as by mergers of neutron stars and black holes or two neutron stars in binaries. The required accretion disks can also form around neutron stars that were formed via the collapse of ONeMg white dwarfs. We estimate the Galactic rate of events resulting in the formation of rapidly rotating relativistic objects. The computations were carried out using the “Scenario Machine.”     

Activity cycles of M dwarfs

We have determined activity cycles for coolest M dwarfs using photometry from the ASAS survey. The time scales of brightness variations were determined for the program stars using calculated amplitude power spectra and wavelet spectra. Most of ther program stars display periodicities in their light-curve variations, with periods from hundreds of days to years. Analysis of diagrams plotting P _cyc/P _rot versus 1/P _rot in logarithmic coordinates shows that the data for all our program objects fit the general relation quite well. No differences in the activity cycles are found for our sample stars, which have different masses and thus internal structures, some having convective envelopes and others being totally convective. Our analysis indicates that the slope i of this relation is close to unity, regardless of whether it is determined from all data, from data for the shortest cycles, or from data for the longest cycles. This value of i differs from values in the literature for stars of other spectral types. Our analysis of the P _cyc-P _rot relation indicates that the activity cycles for the studied sample of M dwarfs do not depend on the rotation periods of these objects. The data for the studied objects do not agree with any of the relations for relatively young (active) stars or older (less active) stars. The studied M dwarfs probably form another branch of low-mass stars that display more random, irregular magnetic activity on their surfaces, which is generated and supported by the distributed dynamo mechanism or a small-scale dynamo mechanism.     

A search for FK Com candidates using Kepler Space Telescope observations: Analogs of HD 199178

Analysis of collected photometric observations obtained with the Kepler Space Telescope were used to select and study 33 objects with parameters corresponding to those of the FK Com starHD199178; these can be considered candidate stars of this type. In this final study, the four objects with the best light curves, which show the properties of their regular rotational modulation most clearly, were selected for detailed studies. The photometric analysis is based on all data currently available in the Kepler archive (covering almost four years). The rotational periods and estimated parameters of the objects’ differential rotation are determined, and the longitudes of the dominant active regions on the surfaces found. For all four stars, the spot coverage is approximately 1% of the visible stellar surface area. The rotational periods and data on the stars’masses and radii fromtheMAST catalog are used to determine the rotation velocities projected onto the line of sight, which ranged from 12 to 21 km/s. Further studies will enable definite conclusions about how these stars are related to FK Com stars. If they are ultimately classified as FK Com stars, this will considerably increase the number of this rare type of star and the also number of rapidly rotating, single, late-type giants.     

The Spots and Activity of Stars in the Beehive Cluster Observed by the Kepler Space Telescope (K2)

The spottedness parameters S (the fraction of the visible surface of the star occupied by spots) characterizing the activity of 674 stars in the Beehive Cluster (age 650 Myr) are estimated, together with variations of this parameter as a function of the rotation period, Rossby number Ro and other characteristics of the stars. The activity of the stars in this cluster is lower than the activity of stars in the younger Pleiades (125 Myr). The average S value for the Beehive Cluster stars is 0.014, while Pleiades stars have the much higher average value 0.052. The activity parameters of 61 solar-type stars in the Beehive Cluster, similar Hyades stars (of about the same age), and stars in the younger Pleiades are compared. The average S value of such objects in the Beehive Cluster is 0.014± 0.008, nearly coincident with the estimate obtained for solar-type Hyades stars. The rotation periods of these objects are 9.1 ± 3.4 day, on average, in agreement with the average rotation period of the Hyades stars (8.6 ^d ). Stars with periods exceeding 3–4 ^d are more numerous in the Beehive Cluster than in the Pleiades, and their periods have a larger range, 3–30 ^d . The characteristic dependence with a kink at Ro (saturation) = 0.13 is not observed in the S–Rossby number diagram for the Beehive and Hyades stars, only a clump of objects with Rossby numbers Ro > 0.7. The spottedness data for the Beehive Cluster and Hyades stars are in good agreement with the S values for dwarfs with ages of 600–700 Myr. This provides evidence for the reliability of the results of gyrochronological calibrations. The data for the Beehive and Pleiades stars are used to analyze variations in the spot-forming activity for a large number of stars of the same age that are members of a single cluster. A joint consideration of the data for two clusters can be used to draw conclusions about the time evolution of the activity of stars of different masses (over a time interval of the order of 500 Myr).     

Elliptical motion of a star in a close binary system

The motion of a rotating star in a close binary system with conservative mass exchange is considered. In contrast to the Paczyński-Huang model, the new model applied examines the relative motion of a star along an elliptical orbit in a close binary system, taking into account the mutual gravitation between the stars, reactive forces, the gravitation exered on the stars by the mass-transfer stream, and perturbations due to the rotation of the accreting star. The variations of the semi-major axis and eccentricity of the orbit and the orbital angular velocity of the accreting star as a function of the component-mass ratio q are determined. The results are applied to the BF Aurigae system.