Stellar structure model in hydrostatic equilibrium in the context of f(R)-gravity

In this work we present a stellar structure model from the f(R)-gravity point of view capable of describing some classes of stars(white dwarfs, brown dwarfs, neutron stars, red giants and the Sun). This model is based on f(R)-gravity field equations for f(R) = R + f_2R~2, hydrostatic equilibrium equation and a polytropic equation of state. We compare the results obtained with those found by Newtonian theory. It has been observed that in these systems, where high curvature regimes emerge,stellar structure equations undergo modifications. Despite the simplicity of this model, the results are satisfactory. The estimated values of pressure, density and temperature of the stars are within those determined by observations. This f(R)-gravity model has proved to be necessary to describe stars with strong fields such as white dwarfs, neutron stars and brown dwarfs, while stars with weaker fields, such as red giants and the Sun, are best described by Newtonian theory.     

Emulating the OPAL equation of state

The equation of state for the structure of the Sun and stars has to be precise to allow comparisons with observations, i.e., helioseismic inversions of thermodynamic quantities. Among the two of the most popular formalisms are (1) the OPAL equation of state developed at Livermore and (2) the Mihalas-Hummer-Däppen (MHD) equation of state. While OPAL has a solid theoretical foundation, and matches the observational data better, the MHD formalism is more intuitive, easy to realize, and has the possibility of adjustable parameters. Furthermore, it an open-source product in contrast to the proprietary OPAL. Recently a version of MHD has been obtained by including the so-called “Plank-Larkin partition function” and by adding scattering-state terms. The resulting formalism matches OPAL rather well. Here, we report on the next logical step, the implementation of this MHD upgrade into the simple and popular CEFF equation of state. Such an implementation will make it a flexible and convenient tool, allowing an approximative on-line implementation of OPAL in solar and stellar models.     

The Solar-Stellar Connection: Magneto-Acoustic Pulsations in 1.5M ⊙ – 2M ⊙ Peculiar A Stars

Stellar astronomers look on in envy at the wealth of data, the incredible spatial resolution, and the maturity of the theoretical understanding of the Sun. Yet the Sun is but one star, so stellar astronomy is of great interest to solar astronomers for its range of different conditions under which to test theoretical understanding gained from the study of the Sun. The rapidly oscillating peculiar A stars are of particular interest to solar astronomers. They have strong, global, dipolar magnetic fields with strengths in the range 1?–?25?kG, and they pulsate in high-overtone p modes similar to those in the Sun; thus they offer a unique opportunity to study the interaction of pulsation, convection, and strong magnetic fields, as is now done in the local helioseismology of sunspots. Some of them even pulsate in modes with frequencies above the acoustic cutoff frequency, in analogy with the highest frequency solar modes, but with mode lifetimes up to decades in the roAp stars, very unlike the short mode lifetimes of the Sun. They offer the most extreme cases of atomic diffusion, a small, but important ingredient of the standard solar model with wide application in stellar astrophysics. They are compositionally stratified and are observed and modelled as a function of atmospheric depth and thus can inform plans to expand helioseismic observations to have atmospheric depth resolution. Study of this unique class of pulsating stars follows the advanced state of studies of the Sun and offers more extreme conditions for the understanding of physics shared with the Sun.     

Stars resembling the Sun

Summary. This review is primarily directed to the question whether photometric solar analogues remain such when subjected to detailed spectroscopic analyses and interpreted with the help of internal stucture models. In other words, whether the physical parameters: mass, chemical composition, age (determining effective temperature and luminosity), chromospheric activity, equatorial rotation, lithium abundance, velocity fields etc., we derive from the spectral analysis of a photometric solar analogue, are really close to those of the Sun. We start from 109 photometric solar analogues extracted from different authors. The stars selected had to satisfy three conditions: i) their colour index must be contained in the interval: –0.69, ii) they must possess a trigonometric parallax, iii) they must have undergone a high resolution detailed spectroscopic analysis. First, this review presents photometric and spectrophotometric researches on solar analogues and recalls the pionneering work on these stars by the late Johannes Hardorp. After a brief discussion on low and high resolution spectroscopic researches, a comparison is made between effective temperatures as obtained, directly, from detailed spectral analyses and those obtained, indirectly, from different photometric relations. An interesting point in this review is the discussion on the tantalilizing value of the of the Sun, and the presentation of a new reliable value of this index. A short restatement of the kinematic properties of the sample of solar analogues is also made. And, finally, the observational diagram, obtained with 99 of the initially presented 109 analogues, is compared to a theoretical diagram. This latter has been constructed with a grid of internal structure models for which, (very important for this investigation), the Sun was used as gauge. In analysing the position, with respect to the Sun, of each star we hoped to find a certain number of stars tightly neighbouring the Sun in mass, chemical composition and state of evolution. The surprising result is that the stars occupy in this HR Diagram a rather extended region around the Sun, many of them seem more evolved and older than the Sun, and only 4 of the evolved stars seem younger. The age of some stars in the sample is also discussed in terms of chromospheric activity and Li-content. Our conclusion is much the same as that contained in previous papers we have written on the subject: in spite of a much larger number of stars, we have not been able to nominate a single star of the sample for a “perfect good solar twin”. Another aim in beginning, 25 years ago, this search for solar analogues, was to have ready a bunch of stars resembling the Sun and analysed spectroscopically in detail, in order that, when planets hunters of solar type stars, finally would have found such a specimen, we would have been able to immediately compare the physical parameters of this star to those of the Sun. We have been lucky enough: one of the good solar analogues we present herewith, is 51 Pegasi (HD 217014) which, according to the very recent observations by Mayor and Queloz (1995), has a planet orbiting around it. And what is more: two other stars possessing planets: 47 Ursae Majoris (HD 95128) and 70 Virginis (HD 117176), have just been discovered by Marcy and Butler (187 Meeting of the AAS, January 1996). One of them, 47 Ursae Majoris, is also included in the list of photometric solar analogues. The other star, 70 Virginis, has only been included after the “Planets News”, because the colour index of this star is slightly higher than the prescribted limit of the selection, (, instead, 0.69). It would have been a pity to leave the third ” planet star out of the competition.     

The fractional kinetic equation and thermonuclear functions

The paper discusses the solution of a simple kinetic equation of thetype used for the computation of the change of the chemical compositionin stars like the Sun. Starting from the standard form of the kineticequation it is generalized to a fractional kinetic equation and itssolutions in terms of H-functions are obtained. The role of thermonuclearfunctions, which are also represented in terms of G- and H-functions,in such a fractional kinetic equation is emphasized. Results containedin this paper are related to recent investigations of possibleastrophysical solutions of the solar neutrino problem.     

Encounters of the Sun with nearby stars in the past and future

The relative space motions of the Sun and nearby stars are considered. The coordinates and velocities of the stars are taken from the Catalogue of Nearby Stars by Gliese and Jahreiss (1991). The minimum space separation between the Sun and every star as well as the corresponding moment of time are calculated by two ways. Firstly, the straight line motions are considered. Secondly, the effect of the Galaxy potential is taken into account. The Galaxy model proposed by Kutuzov and Ossipkov (1989) is used. Twenty five stars approaching the Sun closer than two parsecs are selected. The effects of the uncertainties in the observational data are studied. The influence of the encounters to the Oort cloud is discussed.     

Reflection of Alfven waves and plasma turbulization in solar corona

The continuous reflection of Alfven waves in the coronae of the Sun and stars is considered. Based on the WKB approximation, the solution to the linear wave equation in the case of a stratified isothermal atmosphere has been obtained. A critical analysis of results obtained by Ferraro and Plumpton (1958) and Hollweg (1972), as well as the relations in the Elsasser variables has been carried out. It has been shown that Alfven disturbances do not undergo a continuous reflection within the accepted model and are transformed into intermediate-type modes that possess the properties of vibrations and travelling waves. The problem of the turbulization of corona plasma is discussed. The origin of the Alfven waves that propagate toward the Sun is related to the development of parametric instability.     

Encounters of the Sun with nearby stars in the past and future

The relative space motions of the Sun and nearby stars are considered. The coordinates and velocities of the stars are taken from the Catalogue of Nearby Stars by Gliese and Jahreiss (1991). The minimum space separation between the Sun and every star as well as the corresponding moment of time are calculated by two ways. Firstly, the straight line motions are considered. Secondly, the effect of the Galaxy potential is taken into account. The Galaxy model proposed by Kutuzov and Ossipkov (1989) is used. Twenty five stars approaching the Sun closer than two parsecs are selected. The effects of the uncertainties in the observational data are studied. The influence of the encounters to the Oort cloud is discussed.     

Magnetodynamic phenomena in the solar and stellar outer atmospheres

Magnetic effects causing anomalous heating and drastic flarings in the atmospheres of various types of stars are discussed. The best studied examples of these magnetic effects with spatially resolved observations are those in the case of the Sun, but no simple application of the solar knowledge to the stellar cases is allowed, since there are generally very large differences in the physical conditions between the Sun and other types of stars. We examine possible effects of the magnetic field in the respective situations of several types of stars which show X-ray and radio emissions indicating the presence of such activities, and it is concluded that the magnetic field may be playing important roles in producing anomalous heating and drastic flarings also in those stars having very different physical conditions, in ways seemingly very different from, but intrinsically closely related to, those in the case of the Sun.Invited review paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Magnetic cycles of Sun-like stars with different levels of coronal and chromospheric activity——comparison with the Sun

The atmospheric activity of the Sun and Sun-like stars is analyzed involving observations from the HK-project at the Mount Wilson Observatory, the California and Carnegie Planet Search Program at the Keck and Lick Observatories and the Magellan Planet Search Program at the Las Campanas Observatory.We show that for stars of F, G and K spectral classes, the cyclic activity, similar to the 11-yr solar cycle, is different: it becomes more prominent in K-stars. Comparative study of Sun-like stars with different levels of chromospheric and coronal activity confirms that the Sun belongs to stars with a low level of chromospheric activity and stands apart among these stars by its minimum level of coronal radiation and minimum level of variations in photospheric flux.     

Rotation Profiles of Solar-like Stars with Magnetic Fields

We investigate the rotation profile of solar-like stars with magnetic fields. A diffu-sion coefficient of magnetic angular momentum transport is deduced. Rotating stellar models with different mass incorporating the coefficient are computed to give the rotation profiles. The total angular momentum of a solar model with only hydrodynamic instabilities is about 13 times larger than that of the Sun at the age of the Sun, and this model can not reproduce quasi-solid rotation in the radiative region. However, the solar model with magnetic fields not only can reproduce an almost uniform rotation in the radiative region, but also a total angular momentum that is consistent with the helioseismic result at the 3 σ level at the age of the Sun. The rotation of solar-like stars with magnetic fields is almost uniform in the radiative region, but for models of 1.2-1.5 M⊙, there is an obvious transition region between the convective core and the radiative region, where angular velocity has a sharp radial gradient, which is different from the rotation profile of the Sun and of massive stars with magnetic fields. The change of angular velocity in the transition region increases with increasing age and mass.     

Variations in surface activity of the sun and solar-type stars

Twenty-five-year records of relative Caii H and K emission fluxes of lower Main-Sequence stars have been measured at Mount Wilson Observatory and reveal surface activity in most of the older G- and K-type dwarf stars that is similar to the aperiodical activity cycle of the contemporary Sun (i.e., the cyclic and the occasional episode of reduced activity in the past few centuries). We find an inverse relationship between the amplitude of the activity cycle and the length of the cycle for the ensemble of those solar-type stars. We also find a similar relationship using the 250-year sunspot record (Cycles 1 to 21). The similarity between the two inverse relationships for the solar-type stars observed for 25 years and the Sun for a longer interval of time may suggest one common underlying physical mechanism that is responsible for the variations in surface activity ranging from decades to centuries.Also at Center for Excellence in Information Systems at Tennessee State University.     

Are stars with planets anomalous?

The chemical-dynamical properties of stars with giant planets are compared to those of a nearby star sample within the framework of a stellar orbital diffusion model. The stars-with-planets sample includes recently discovered extrasolar planets and the Sun. We find that the planet-bearing stars, 14 Her, ρ ¹ Cnc and τ Boo, are much more metal-rich than stars of similar age and this cannot be easily explained by orbital diffusion. We also confirm previous claims that the motion of the Sun relative to the local standard of rest is very small compared to other G dwarfs of similar age, and we offer a possible explanation for this apparent anomaly.     

Gamma rays from halos around stars and the Sun

Inverse Compton (IC) scattering by relativistic electrons produces a major component of the diffuse emission from the Galaxy. The photon fields involved are the cosmic microwave background and the interstellar radiation field (ISRF) from stars and dust. Calculations of the inverse Compton distribution have usually assumed a smooth ISRF, but in fact a large part of the Galactic luminosity comes from the most luminous stars, which are rare. Therefore we expect the ISRF, and hence the inverse Compton emission, to be clumpy at some level, which could be detectable by instruments such as GLAST. Even individual nearby luminous stars could be detectable assuming just the normal cosmic-ray electron spectrum. We present the basic formalism required and give possible candidate stars to be detected and make predictions for GLAST. Then we apply the formalism to the OB associations and the Sun, showing that the IC emission produced is not negligible compared to the sensitivity of current or coming detectors. We estimate that the gamma-ray flux from the halo around the Sun contributes to the diffuse background emission at the few percent level.     

Non-Axisymmetric Magnetic Fields and Flip-Flops on the Sun and Cool Stars

The modulation of solar activity closely follows the solar rotation period suggesting the existence of long-lived active regions at preferred longitudes. For instance, two preferred active longitudes in both southern and northern hemispheres are found to be persistent at the century time scale. These regions migrate with differential rotation and periodically alternate their activity levels showing a flip-flop cycle. The pattern and behaviour of active longitudes on the Sun is similar to that on cool, rapidly rotating stars with outer convective envelopes. This suggests that the magnetic dynamo, including non-axisymmetric magnetic fields and flip-flop cycles, is also similar in these stars. This allows us to overview the phenomenon of stellar magnetic activity and to study it in detail on the Sun.     

太阳大气铍丰度的衰减

Li和Be轻元素在温度仅几百万度时就因核反应而遭毁坏,因此它们是恒星演化过程的外层对流混合延伸程度很好的一种示踪。基于这种考虑,我们曾计算过太阳包层模型Li的衰减,得到一个同时满足日震学太阳对流区深度和太阳Li丰度观测要求的非局部太阳对流包层模型[1].Li丰度给出了一个非局部对流混合延伸程度的上限。     

Habitable zones around main sequence stars

A one-dimensional climate model is used to estimate the width of the habitable zone (HZ) around our Sun and around other main sequence stars. Our basic premise is that we are dealing with Earth-like planets with CO2/H2O/N2 atmospheres and that habitability requires the presence of liquid water on the planet's surface. The inner edge of the HZ is determined in our model by loss of water via photolysis and hydrogen escape. The outer edge of the HZ is determined by the formation of CO2 clouds, which cool a planet's surface by increasing its albedo and by lowering the convective lapse rate. Conservative estimates for these distances in our own Solar System are 0.95 and 1.37 AU, respectively; the actual width of the present HZ could be much greater. Between these two limits, climate stability is ensured by a feedback mechanism in which atmospheric CO2 concentrations vary inversely with planetary surface temperature. The width of the HZ is slightly greater for planets that are larger than Earth and for planets which have higher N2 partial pressures. The HZ evolves outward in time because the Sun increases in luminosity as it ages. A conservative estimate for the width of the 4.6-Gyr continuously habitable zone (CHZ) is 0.95 to 1.15 AU. Stars later than F0 have main sequence lifetimes exceeding 2 Gyr and, so, are also potential candidates for harboring habitable planets. The HZ around an F star is larger and occurs farther out than for our Sun; the HZ around K and M stars is smaller and occurs farther in. Nevertheless, the widths of all of these HZs are approximately the same if distance is expressed on a logarithmic scale. A log distance scale is probably the appropriate scale for this problem because the planets in our own Solar System are spaced logarithmically and because the distance at which another star would be expected to form planets should be related to the star's mass. The width of the CHZ around other stars depends on the time that a planet is required to remain habitable and on whether a planet that is initially frozen can be thawed by modest increases in stellar luminosity. For a specified period of habitability, CHZs around K and M stars are wider (in log distance) than for our Sun because these stars evolve more slowly. Planets orbiting late K stars and M stars may not be habitable, however, b ecause they can become trapped in synchronous rotation as a consequence of tidal damping. F stars have narrower (log distance) CHZ's than our Sun because they evolve more rapidly. Our results suggest that mid-to-early K stars should be considered along with G stars as optimal candidates in the search for extraterrestrial life.     

Numerical simulations of the Hyades dynamics and the nature of the moving Hyades cluster

We present our numerical simulations of the dynamical evolution of the Hyades open cluster. The simulations were performed usinga modified NBODY6 algorithm that included tidal forces and a realistic orbit of the cluster in a gravitational field described by the Miyamoto-Nagai potential. Our goal was to study the nature of movingclu sters. We show that the stars that were earlier cluster members could be later identified within a sphere of 50 pc in diameter around the Sun. The number of such stars for the chosen initial mass and virial radius of the cluster does not exceed ten. The maximum space velocity of these stars relative to the core of the current cluster does not exceed 3 km s^?1. Our numerical simulations confirm the assumption that some of the moving clusters near the Sun could consist of stars that have escaped from open clusters in the course of their dynamical evolution.     

Red giant clump in the Tycho-2 catalogue

The Tycho-2 proper motions and Tycho-2 and 2MASS photometry are used to select 97348 red giant clump (RGC) stars. The interstellar extinction and photometric distance are calculated for each of the stars. The selected stars are shown to form a selection-unbiased sample of RGC stars within about 350 pc of the Sun with the addition of more distant stars. The distribution of the selected stars in space and their motion are consistent with the assumption that the RGC contains Galactic disk stars with various ages and metallicities, including a significant fraction of stars younger than 1 Gyr with masses of more than 2M _⊙. These young stars show differences of their statistical characteristics from those of older RGC stars, including differences in the variations of their distribution density with distance from the Galactic plane and in the dispersion of their velocities found using radial velocities and proper motions. The Sun has been found to rise above the Galactic plane by 13 ± 1 pc. The distribution density of the stars under consideration in space is probably determined by the Local Spiral Arm and the distribution of absorbing matter in the plane of the Gould Belt.