On broadened definitions of instability for stars in thermal imbalance

The classical theory of stability of dynamical systems is employed to demonstrate that traditional definitions of pulsational instability cannot be directly applied to stars in thermal imbalance. In particular, it is shown that, for the case of thermal imbalance, pulsational displacements and pulsational velocities have separate and distincte-folding times. This being true, a broadened set of definitions becomes necessary, and we formulate such a set, again with reference to the classical theory. In accordance with the new definitions, it is argued that the development of observable pulsations requires as a necessary condition infinitesimal instability of both absolute displacement and velocity. If either one is unstable without the other, this constitutes a class of (probably) non-pulsational instability, not previously treated in the astrophysical literature. Finally, it is shown that the stability of stars in thermal imbalance may be evaluated according to the present definitions by employing either of two existing theories — the energy approach due to Demaret 91974; 1975; 1976) or the small perturbation technique of Coxet al. (1973).     

Vibrational stability of stars in thermal imbalance: A solution in terms of asymptotic expansions

The solution of the partial differential equation describing the ‘non-isentropic’ oscillations of a star in thermal imbalance has been obtained in terms of asymptotic expansions up to the first order in the parameterII/t _s, whereII is the adiabatic pulsation period for the fundamental mode andt _s , a secular time scale of the order of the Kelvin-Helmholtz time. Use has been made of the zeroth order ‘isentopic’ solution derived in I. The solution obtained allows one to derive unambiguously a general integral expression for the coefficient of vibrational stability for arbitrary stellar models in thermal imbalance. The physical interpretation of this stability coefficient is discussed and its generality and its simplicity are stressed. Application to some simple analytic stellar models in homologous and nonhomologous contraction enables one to recover, in a more straightforward manner, results obtained by Coxet al. (1973). Aizenman and Cox (1974) and Davey (1974). Finally, we emphasize that the inclusion of the effects of thermal imbalance in the stability calculations of realistic evolutionary sequences of stellar models, not considered up to now by the other authors, is quite easy and straightforward with the simple formula derived here.     

The atmospheres of helium-deficient Bp stars

Based on spectra taken with a 6-m telescope, we analyzed the abundances of chemical elements in the He-weak stars HD 21699 and HD 217833, estimated their surface magnetic fields (B_s = 4000 and 4500 G, respectively) from the magnetic intensification of spectral lines, and determined their microturbulences (V _t = 0.80 and 0.75 km s⁻¹, respectively). The low values of V _t show that the stellar atmospheres are stabilized by a magnetic field, which explains the presence of diffusion processes that lead to chemical anomalies. Helium is strongly underabundant, and its deficiency is −1.50 and −1.81 dex in HD 21699 and HD 217833, respectively. We used model atmospheres to determine the effective temperatures, T _eff = 16 000 and 15 450 K, and surface gravities, log g = 4.15 and 3.88, for the stars from the Hδ line, implying that they lie on the main sequence near the stars of luminosity class V.     

Distribution of luminous blue stars in M33

M₃₃ luminous stars with M_V ≲ -7 and U--B < o are selected in this paper. The spatial distribution of the stars shows a good agrement with the associations and HII regions. However HII regions are absent in the three youngest associations in M₃₃ (t ≈ 5 ÷ 7 × 10yr). It is supposed that the true distance modulus of M₃₃ derived from the brightest blue stars is 24.2. An age gradient across the arms is absent. The spiral arms outlined by the luminous stars differ form those in M₃₁. They are diffuse and wide. The multiarm features of M₃₃ support the stochastic self-propagating model.     

Quasi-stellar objects as rotating magnetic superstars

In this paper the magnetic superstar model is used to discuss QSO luminosity and density evolution. Our main hypotheses are that (i) mass loss from old stars in massive galaxies cools and then falls into the centre to form a nuclear disc (Bailey, 1980); and (ii) magnetic superstars in galactic nuclei condense out of gaseous material at the centre of a supermassive-magnetised disc (Kundt, 1979). On this generalised model we find that the non-thermal (synchrotron) optical luminosity scales asL _opt L ³ t ^–7/3, whereL is the total blue luminosity of old stars in the galaxy and t is cosmic time. In addition we show that QSO co-moving density follows the lawD(t)exp-(t/t _Evol)^16/15 with an evolution timescalet _Evol = 1.95 × 10⁹ yr. The model as a whole is in good agreement with observations.     

A search for the age-dependency of Ap star parameters

Some observational data of the sample of the magnetic chemically peculiar stars (MCP stars) are investigated statistically. For the MCP stars of spectral types later than A2 both the frequency distribution and the R ⋅ sin i-values suggest the existence of a linear relation between stellar diameter and rotation period. The MCP stars of spectral types earlier than B9 show an overpopulation of small R ⋅ sin i which may indicate the existence of a second group with smaller radius in this sample. The equatorially symmetric rotator is used as the magnetic model. With respect to its temporal behaviour the effective magnetic field is separated into dipolar and quadrupolar contribution. Both signs of the axisymmetric quadrupole moment appear with equal frequency. The dipole moment which produces the amplitude of the B_eff(t) curve forms for longer periods two groups which are separated by a distinct gap. Both of the groups exhibit magnetic fields which are the stronger the greater the stellar radius is, contrary to what is expected for frozen-in fields. The dominance of magnetic curves without polarity reversal for longer-period stars is in accordance with predictions of the dynamo theory.     

Observational manifestations of early mixing in B- and O-type stars

The helium and nitrogen enrichment of the atmospheres of early B-type stars during the main sequence (MS) evolutionary phase is re-analysed. It is confirmed that the effect depends on both the aget and the stellar massM. For example, the helium abundanceHe/H increases by 0.04 (60–70% of initial value) for stars withM=8–13M and by 0.025 (about 30%) for stars withM=6M . The nitrogen abundance rises by three times forM=14M and by, two times forM=10M . According to the latest theoretical computations, the observed appearance of CNO-cycled material in surface layers of the stars can be a result of the rotationally induced mixing, in particular, of the turbulent diffusion. Carbon is in deficiency in B stars, but unexpectedly does not show any correlation with the stellar age. However it is shown that the total C+N abundance derived for early B stars conflicts with the theory.Basing on modern data the helium enrichment is first examined in O-type MS stars, as well as in components of binaries. As compared with early B stars, the He abundance for more massive O stars and for components of binaries show a different relation with the relative aget/t _MS . Namely during short time betweent/t _MS 0.5 and 0.7 a sharp jump is observed up toHe/H=0.2 and more. In particular, such a jump is typical for fast rotating O stars (v sini200 km s^–1),. Therefore the effect of mixing depends on massM, relative aget/t _MS , rotational velocityv and duplicity.The mass problem (the discrepancy betweenM _ev andM _sp ) is also analysed, because some authors consider it as a possible evidence of early mixing, too. It is shown that the accurate data for components of binaries lead to the conclusion that the discrepancy is less than 30%. Such a difference can be removed at the expense of theM _ev lowering, if the displacement of evolutionary tracks, owing to the rotationally induced mixing is taken into consideration.     

Stars outside the Hipparcos list closely encountering the Solar system

Based on currently available kinematic data, we have searched for stars outside the Hipparcos list that either closely encountered in the past or will encounter in the future the Solar system within several parsecs. For the first time, we have identified two single stars, GJ 3379 (G 099-049) and GJ 3323 (LHS 1723), as candidate for a close encounter with the solar orbit. The star GJ 3379 could encounter the Sunmore closely to aminimumdistance d _min = 1.32±0.03 pc at time t _min = −163 ± 3 thousand years. We have found two potential candidates for a close encounter that have only photometrical distances: the white dwarf SSSPM J1549-3544 without any data on its radial velocity and the L-dwarf SDSS J1416+1348. The probabilities of their penetration into the Oort cloud region are 0.09 (at a model radial velocity <V _r < = 50 km s⁻¹) and 0.05, respectively.     

Some results of the cooperative photometric observations of the UV Cet-type flare stars in the years 1967–71

The list of the cooperative photometric observations of the UV Cet-type flare stars that have been organized during the years 1967 to 1971 by the Working Group on Flare Stars of the IAU Commission 27 is given. The completeness and reliability of the data obtained are evaluated by comparing simultaneous observations at different observatories. the statistical analysis of the UV Cet, YZ CMi, EV Lac and AD Leo flares observed in the B-band is carried out. The flare energy spectrum in the energy range where observational selection effects are small is found to be d lnv/d lnE _B=–1.4 to –1.9,v is an occurrence of flares with radiation energy ofE _B. The total flares' radiation is equal to 1.7%, 1.2%, 0.3% and 0.4% of the quiet radiation in the B-band of the stars listed, and the main part of this total radiation is due to the strongest flares. Distributions of flare rise times (t _r) and of rates of flare absolute luminosity increase (d² E _B/dt _r ²Ë _r) are considered; these parameters of flare are independent statistically for all stars studied. Correlation coefficientsr (E _B,t _r) andr (E _B,r(E _B,Ë _r)) are rather small except r (E _B,t _r)=0.86 for the AD Leo flares. Contradictory conclusions on temporal distribution of flares infered by different investigators are noted.     

Candidate red clump giants in the PPMX catalogue

This paper presents the RCGP catalogue of more than 0.5 million candidate red clump stars with the limiting magnitude K _s = 9.5 ^m . These stars are selected from the PPMX catalogue as the most probable red clump members by analyzing the color-reduced proper motion diagrams built from the proper motions given in PPMX and J, K _s -photometry given in the 2MASS catalogue. Reddening of the selected stars is used to find extinction in the K _s -band and to consider it in the further analysis. The two-dimensional galactic rotation model generalized by Ogorodnikov is used to investigate the tangential velocity field of the selected red clump members, most of which are thin disk stars located within 1.5 kpc from the sun. The values of kinematic parameters and solar components are determined as a function of stellar heights above the galactic equatorial plane and their heliocentric distances.     

Comprehensive study of the magnetic stars HD 5797 and HD 40711 with large chromium and iron overabundances

We present the results of a comprehensive study of the chemically peculiar stars HD 5797 and HD 40711. The stars have the same effective^temperature, T _eff = 8900 K, and a similar chemical composition with large iron (+1.5 dex) and chromium (+3 dex) overabundances compared to the Sun. The overabundance of rare-earth elements typically reaches +3 dex. We have measured the magnetic field of HD 5797. The longitudinal field component B _e has been found to vary sinusoidally between −100 and +1000 G with a period of 69 days. Our estimate of the evolutionary status of the stars suggests that HD 5797 and HD 40711, old objects with an age t ≈ 5 × 10⁸ yr, are near the end of the core hydrogen burning phase.     

Discussion of infrared measurements of T Tauri stars and related objects

It is at first reported that certain kinds of stars which have been classified as T Tauri stars or related objects are in reality not of this type. After the exclusion of those objects, the infrared measurements accessible in the literature permit to draw some astrophysical inferences. It is then possible to distinguish three classes of light variations. All T Tauri stars have an infrared excess. From the colour indices H – K and K – L it can be deduced that the infrared excess for more than one half of the objects is due to the thermal radiation of the circumstellar dust envelope; for the remaining stars also free-free radiation from the gas envelope can play an essential part. The largest infrared excesses E_H–K were found with the hotter stars (spectral type A) and the strongest emission lines with the cooler stars (spectral types G, K, M). This can finally be explained by the fact that the convection zone in cooler stars reaches far down into their interior than in hotter stars.     

Main sequence for rotating stars of intermediate mass

We have investigated the evolutionary behaviour of intermediate mass (2, 3, 4, 5, and 7M ) Population I stars, assuming two different rates of rotation at the threshold of stability.In the first part of the study, stars are assumed to start with a critical rotation (fast rotation model) and to progress to the point of rotational instability. The stars evolve by losing mass and become rotationally unstable before they reach the zero-age Main Sequence. It is argued that multiple star systems might be formed through the evolution of rapidly rotating stars. An expression for the rotational mass loss rate is derived as a function of the physical parameters of stars.In the second part of the study, stars are assumed to rotate at a rate below the critical value (slow rotation model). The evolution of slowly rotating stars is followed as far as zero-age Main Sequence on the theoretical Hertzsprung-Russell diagram and compared with that of normal stars. The evolutionary paths are found to be more or less similar to those of normal stars; but their positions on the Main Sequence are characterized by effective temperatures and luminosities lower than those of normal stars. The zero-age Main-Sequence times of these stars are longer than those of normal stars. The rotational rates obtained for the zero-age Main Sequence are in good agreement with observed values.     

Semi-regular and alternating pulsations in hydrodynamical models for low-mass giants

On the basis of hydrodynamical simulations the semi-regular and alternating pulsations of the W Vir and RV Tau stars are studied including non-steady radiative transfer effects in gray sphericalsymmetric atmospheres. It is shown that the transition from regular to semi-regular oscillations occurs at periodsP13–15 days due to pulsation energy imbalance provoqued by strong radiating shocks. The differences between the periods and amplitudes of W Vir and RV Tau variables are explained as a result of this imbalance. It is suggested that the semi-regular alternating pulsations of the RV Tau stars appear following a period-doubling phenomenon, which can be also understood in terms of the pulsation energy variations between odd and even fundamental cycles. The pulsational characteristics of the period-doubled models are in general accordance with those observed in the RV Tau stars. On the basis of numberical results, a theoretical estimation of the upper limit for the luminosity of the RV Tau stars is derived asL10³ L .     

The time-scale for core collapse in spherical star clusters

The collapse time for a cluster of equal-mass stars is usually stated to be either 330 central relaxation times (t_rc) or 12-19 half-mass relaxation times (t_rh). But the first of these times applies only to the late stage of core collapse, and the second only to low-concentration clusters. To clarify how the time depends on the density profile, the Fokker-Planck equation is solved for the evolution of a variety of isotropic cluster models, including King models, models with power-law density cusps of ρ ∼ r^−γ, and models with nuclei. The collapse times for King models vary considerably with the cluster concentration when expressed in units of t_rc or t_rh, but vary much less when expressed in units of t_rc divided by a dimensionless measure of the temperature gradient in the core. Models with cusps have larger temperature gradients and evolve faster than King models, but not all of them collapse: those with 0 < γ < 2 expand because they start with a temperature inversion. Models with nuclei collapse or expand as the nuclei would in isolation if their central relaxation times are short; otherwise their evolution is more complicated. Suggestions are made for how the results can be applied to globular clusters, galaxies, and clusters of dark objects in the centers of galaxies.Scott D. Tremaine     

On the relation between the peak frequency and the corresponding rise time of solar microwave impulsive bursts and the height dependence of magnetic fields

In the present paper we report the results of a correlation analysis for 57 microwave impulsive bursts observed at six frequencies in which we have obtained a regression line between the peak frequency and the corresponding rise time of microwave impulsive bursts: {ie361-01} (with a correlation coefficient of - 0.43). This can be explained in the frame of a thermal model. The magnetic field decrease with height has to be much slower than in a dipole field in order to explain the weak dependence of f _p on t _r . This decrease of magnetic field with height in burst sources is based on the relationship between f _p and t _r found by assuming a thermal flare model with a collisionless conduction front.On leave from Beijing Observatory, Academia Sinica, Beijing, China.     

Radii of some Ap,Am and A stars

Based on the observed energy curves of nine Ap stars, three Am stars, four normal A stars and one F0 V magnetic star, their radii have been estimated.Thence, the bolometric magnitudesM _bo1 have been obtained and a plot between logT _e andM _bo1 of these stars shows that a majority of Ap and Am stars are a little above the zero-age Main-Sequence, suggesting that they are slightly more evolved as compared to the normal A stars.The bolometric corrections derived from the aboveM _bo1 are much closer to those computed by Mihalas than to the ones given by Davis and Webb, the latter being about O ^m 1 more negative than the former.     

The Crust Properties and Cooling of Strange Stars

We investigate the influence of the following parameters on the crust properties of strange stars: the strange quark mass (m _s), the strong coupling constant (α_c) and the vacuum energy density (B). It is found that the mass density at the crust base of strange stars cannot reach the neutron drip density. For a conventional parameter set of m _s=200 MeV, B ^1/4 = 145 MeV and α_c = 0.3, the maximum density at the crust base of a typical strange star is only 5.5 × 10¹⁰ gcm^-3, and correspondingly the maximum crust mass is 1.4 ×10^-6 M_⊙. Subsequently, we present the thermal structure and the cooling behavior of strange stars with crusts of different thickness, and under different diquark pairing gaps. Our work might provide important clues for distinguishing strange stars from neutron stars.     

Disintegration process of hierarchical triple systems. I. Small-mass planet orbiting equal-mass binary

The stability of hierarchical triple system is studied in the case of an extrasolar planet or a brown dwarf orbiting a pair of main sequence stars. The evolution of triple system is well modelled by random walk (RW) diffusion, particularly in the cases where the third body is small and tracing an orbit with a large eccentricity. A RW model neglects the fact that there are many periodic orbits accompanied by stability islands, and hence inherently overestimates the instability of the system. The present work is motivated by the hope to clarify how far the RW model is applicable. Escape time and the surface section technique are used to analyse the outcome of numerical integrations. The analysis shows that the RW-like model explains escape of the third body if the initial configuration is directly outside of the KAM tori. A small gap exists in (q ₂/a ₁, e ₂)-plane between locations of the stability limit curves based on our numerical study and on RW-model (the former is shifted by –1.4 in q ₂/a ₁ direction from the latter).     

Intrinsic colour indices of Be stars obtained from 2MASS photometry

This paper is based on 2MASS photometry (J H K_s magnitudes) of 1172 Be stars. The observed mean intrinsic colours have been derived with aid of two‐colour diagrams for Be stars of luminosity classes Ie‐IIe, IIIe and IVe‐Ve. The obtained results are the first determinations of their intrinsic colours in the astronomical literature. The smoothed infrared colours are compared with those obtained for “normal” B stars. Several two‐colour diagrams and plots of observed and smoothed intrinsic colour versus spectral type of luminosity classes Ie‐IIe, IIIe and IVe‐Ve are presented. Generally the determined infrared intrinsic colours of Be stars (V – J)₀, (V – H)₀, and (V – K_s)_o differ substantially from those of “normal” B stars. It is found that the intrinsic colours of B stars are generally bluer than Be stars of corresponding spectral type and luminosity class. The mean absolute visual magnitude M_v of 528 Be stars for luminosity classes Iae, Ibe‐Iabe, IIe, IIIe and IVe‐Ve is derived from HIPPARCOS parallaxes. The M_v calibration is compared with the existing ones. The Be stars are generally brighter than “normal” B stars of corresponding spectral types. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)