Analytic stellar structure

This paper continues to elaborate on analytic methods to construct models for the internal structure of solar-type stars. Since a detailed stellar model is desired, a nonlinear analytic density distribution in terms of a two-parameter family of models has been assumed. Hydrostatic equilibrium and energy conservation determine the conditions in the gravitationally stabilized stellar fusion reactor. The results show once more that methods of differential and integral calculus provide a laboratory for the application of special functions of mathematical physics in stellar structure.Paper presented at the Second International Conference on Industrial and Applied Mathematics, July 8–12 1991, Washington D.C., U.S.A.     

Gravitational collapse of a rotating iron stellar core and physical properties of the accompanying neutrino emission

We have ascertained an important role of rotation effects in a collapsing stellar core using a quasi-one-dimensional hydrodynamic model with a rigorous allowance for the neutrino energy losses including the neutrino opacity stage. However, the neutrino scattering processes are not considered in the neutrino emission kinetics as secondary compared to the absorption processes. The quasi-one-dimensional approximation (with averaging of the expression for the centrifugal force over the polar angle) allows numerical calculations to be performed relatively easily up to the formation of a hydrostatically equilibrium neutron star after a very long stage of collapsar cooling by neutrino emission (about 2 s). We present detailed results of our numerical solution, including the neutrino spectra, with electron neutrinos making a dominant contribution to them and the contribution from electron antineutrinos being smaller by an order of magnitude. In the model under consideration, we solve the equation of matter neutronization kinetics by taking into account the main process of nuclear reactions on free nucleons, although the contribution from iron and helium nuclei is included in the equation of state.     

Some electrically charged relativistic stellar models in general relativity

Some new families of electrically charged stellar models of ultra-compact star have been studied. With the help of particular form of one of the metric potentials the Einstein–Maxwell field equations in general relativity have been transformed to a system of ordinary differential equations. The interior matter pressure, energy–density, and the adiabatic sound speed are expressed in terms of simple algebraic functions. The constant parameters involved in the solution have been set so that certain physical criteria satisfied. Based on the analytic model developed in the present work, the values of the relevant physical quantities have been calculated by assuming the estimated masses and radii of some well known potential strange star candidates like X-ray pulsar Her X-1, millisecond X-ray pulsar SAX J 1808.4-3658, and 4U 1820-30. The analytical equations of state of the charged matter distribution may play a significant role in the study of the internal structure of highly compact charged stellar objects in general relativity.     

A non-parametric method of estimating the physical parameters of stellar atmosphere

The physical parameters of stellar atmosphere, e.g. the effective temperature, surface gravity and chemical abundance, are the main factors for the differences in stellar spectra, and the automatic measurement of these parameters is an important content in the automatic processing of the immense amount of spectral data provided by LAMOST and other patrol telescopes. Aiming at the estimation of the physical parameters for every star in large samples of stellar spectral data, a variable window-width algorithm is proposed in this article. It consists of the following three steps: (1) A PCA (principal component analysis) treatment of historical stellar spectral data is carried out to obtain a low-dimensional characteristic data of the spectra. (2) Establish the correlation between the characteristic data and the physical parameters using a non-parametric estimator with variable window-width. (3) By means of this estimator, the three physical parameters of the star are directly calculated. As shown by results of experiments, in comparison with the fixed window-width estimator and other algorithms reported in literature, our algorithm is more accurate and robust.     

Upper limits in the toroidal component of force-free magnetic fields in stellar atmospheres in the context of solar and stellar flares

Doing numerical calculations of axially symmetric force-free fields, Milsom and Wright (1976) have noticed that there seem to be no solutions if the toroidal component of the field exceeds a certain limit. In the present paper this problem is reexamined in the approximation of a plane stellar surface using a very simple analytic approximation. The results of Milsom and Wright (1976) are confirmed but, in contrast to their interpretation, it is shown that these limitations do not indicate the possibility of sudden changes of the topology of the magnetic field. This is because in a stellar atmosphere the toroidal component of the surface magnetic field is no independent quantity but is produced by shearing motions in the star which will prevent the toroidal magnetic field from exceeding its maximum value. To study the possibility of sudden changes in the magnetic field, which could cause stellar flares, the calculations are re-done prescribing the motion of the magnetic footpoints (shear in the stellar surface) instead of the toroidal component of the surface field. Using the same mathematical formalism it is found that no sudden changes can occur for configurations where all field lines connect to the stellar surface but that sudden changes may be possible for a more complicated field topology.     

The stellar populations of spiral galaxies

We have used a large sample of low-inclination spiral galaxies with radially resolved optical and near-infrared photometry to investigate trends in star formation history with radius as a function of galaxy structural parameters. A maximum-likelihood method was used to match all the available photometry of our sample to the colours predicted by stellar population synthesis models. The use of simplistic star formation histories, uncertainties in the stellar population models and considering the importance of dust all compromise the absolute ages and metallicities derived in this work; however, our conclusions are robust in a relative sense. We find that most spiral galaxies have stellar population gradients, in the sense that their inner regions are older and more metal rich than their outer regions. Our main conclusion is that the surface density of a galaxy drives its star formation history, perhaps through a local density dependence in the star formation law. The mass of a galaxy is a less important parameter; the age of a galaxy is relatively unaffected by its mass; however, the metallicity of galaxies depends on both surface density and mass. This suggests that galaxy‐mass-dependent feedback is an important process in the chemical evolution of galaxies. In addition, there is significant cosmic scatter suggesting that mass and density may not be the only parameters affecting the star formation history of a galaxy.     

Amplification of stellar background by circumstellar masers

The calculations with the use of simple maser model show that the stellar background contributes negligibly to the mean peak intensities at 1612 MHz. Under some conditions, however, the contribution from the central star may constitute a few percent of the mean peak intensity. Such possibility may occur when the thick and large OH envelope is illuminated by very luminous and extended central star. To compare the theoretical results with observations a sample of 55 OH/IR stars with best known parameters is analyzed. The ratio of the blue-shifted to the red-shifted 1612 MHz peak slightly increases in objects with the largest OH radii. This relation is interpreted in terms of amplification of the stellar photons.     

Analysis of the structure and dynamics of the stellar tails of open star clusters

We have analyzed the formation, structure, and dynamical evolution of the population of stars that escaped from open clusters by numerical simulations using S. Aarseth’s modified NBODY6 code. In the Galactic tidal field, the population of stars that escaped from a cluster is shown to be elongated along the orbit of the cluster symmetrically about its core in the form of stellar tails of increasing sizes. We analyze the parameters of stellar tails as a function of such initial simulation conditions as the number of stars, the cluster density, the eccentricity of the Galactic cluster orbit in the plane of the Galactic disk, and the z velocity component. As a result, we constructed a grid of model stellar tails of open clusters. The grid includes such time-dependent parameters of the stellar tails as the length, the cross section, the number of stars, the velocity distribution, etc. Our simulations allow us to clarify the origin of moving clusters and stellar streams and to assess the role of star clusters in forming the stellar velocity field in the solar neighborhood.     

Effect of rotational and tidal distortions on the periods of small adiabatic oscillations of stellar models

Kopal's method of representing the inner structure of a rotationally and tidally-distorted star by a rotationally-and tidally-distorted Roche model has been used in conjunction with an averaging concept introduced by Kippenhahn and Thomas of representing the equipotential surfaces of a rotationally and tidally distorted stellar model by the equipotential surfaces of an equivalent spherical model to determine the combined effects of rotation and tidal distortion on the periods of small adiabatic oscillations of a stellar model.     

Gravitational collapse of a rotating iron stellar core: The limiting case of transparency to neutrino emission

A quasi-one-dimensional hydrodynamic model for the collapse of a rotating iron stellar core is used to determine the neutrino spectra in the limiting case of total transparency to neutrino emission (without any deposition effect). The derived spectra allow the previously constructed spectra used to theoretically estimate the number of events in the LSD underground neutrino detector from SN 1987A to be refined. At typical iron stellar core parameters, including those that characterize the core rotation specified in the initial conditions of the model, this number has turned out to be 1.6, which is close in order of magnitude to its experimental value of 5. Here, we compare in detail these results by assuming that the transparency of the collapsing iron core itself could be attributable to the development of its three-dimensional dynamical instability—the subject of future theoretical studies. The physical formulation of the problem coincides closely with the collapse model proposed in our previous paper, where the above number of events turned out to be 0.5. We have confirmed the previously published results with regard to the neutrino spectra, including the significant superiority of electron neutrinos over electron antineutrinos in them. The hydrostatically equilibrium configuration (a rotating collapsar) obtained in our model calculation is discussed in comparison with self-similar solutions that are close in physical formulation of the problem. This result seems a nontrivial consequence of the included rotation effects that hinder nonstop collapse established in the mentioned self-similar solutions.     

On stellar encounters and their effect on cometary orbits in the Oort cloud

We systematically investigate the encounters between the Sun and neighbouring stars and their effects on cometary orbits in the Oort cloud, including the intrinsic one with the star Gl 710 (HIP 89 825), with some implications to stellar and cometary dynamics. Our approach is principally based on the combination of a Keplerian‐rectilinear model of stellar passages and the Hipparcos Catalogue (ESA 1997). Beyond the parameters of encounter, we pay particular attention to the observational errors in parallaxes and stellar velocities, and their propagation in time. Moreover, as a special case of this problem, we consider the collision probability of a star passing very closely to the Sun, taking also into account the mutual gravitational attraction between the stars. In the part dealing with the influence of stellar encounters on the orbital elements of Oort cloud comets, we derive new simple formulae calculating the changes in the cometary orbital elements, expressed as functions of the Jeans impulse formula. These expressions are then applied to calculate numerical values of the element changes caused by close encounters of neighbouring stars with some model comets in the Oort cloud. Moreover, the general condition for an ejection of comets from the cloud effected by a single encounter is derived and discussed.     

Lepton loss and entropy generation in stellar collapse

The effects of uncertainties in determining the loss of neutrinos and the generation of entropy during the collapse of a stellar core are studied using a simple spherically-symmetric homologous collapse model with an improved treatment for the excited nuclei. It is found that the neutrino loss and entropy generation are not altogether insensitive to most variations of the assumptions regarding the input physics, collapse rate and initial conditions and in particular the need to determine accurately beta capture rates in stellar collapse is pointed out.     

The effects of ion screening on neutrino-nucleus interactions in core-collapse supernova explosions

The effects of ion screening in stellar core collapses are investigated based on a new progenitor star model.Simulation results show that ion screening slightly affects the leptons and decreases explosion energy,which is a negative factor for energy transfer supernova explosions.We also investigate the effect on type Ⅱ-supernova explosions of neutrino-nucleus elastic scattering based on the new progenitor star model.It is shown that,compared with the previously calculated results,neutrinos-nucleus elastic scattering in stellar core collapses is more severe,leading to an obvious reduction of the neutrino leakage energy loss and an increase of supernova explosion energy.     

The neutrino radiation of collapsing stellar cores and the neutrino burst detected from SN 1987 A

The properties of the neutrino burst generated by massive 1.5–2M collapsing stellar iron-oxygen cores are discussed. Special attention is given to the neutrino heat conductivity theory which allows us to calculate the transport of neutrinos through the collapsing stellar core up to the formation and during the first seconds of cooling of a hot hydrostatic neutron star. The theoretical predictions seem to be in good agreement with both the KAMIOKANDE II and IMB data on the neutrino burst detected from SN 1987A. The most reliable constraint on the neutrino rest mass is shown to bem _v <20–30eV, while the safest upper limit on the neutrino magnetic moment, µ _v < 10^–11 Bohr magnetons, results rather from the cooling of white dwarfs than from the SN 1987A neutrino data.Presented to the 13th International Conference Neutrino-88, Boston, U.S.A., 5–11 June, 1988.     

A note on the linear stellar model

For a purely gaseous self-gravitating stellar configuration with linear matter density distribution the total power generated by nuclear reactions is considered. The analytic connection between physical parameters of the macroscopic and microscopic levels of the stellar equilibrium configuration is revealed.     

An analytic model for disc disruption by strong stellar magnetic fields

An analytic model is presented for the inner structure of an accretion disc in the presence of a strong stellar magnetic field. The model is valid inside the radius at which the electron scattering opacity starts to exceed the Kramers opacity. It illustrates how the increasing stellar poloidal field leads to an elevated disc temperature, ultimately causing a breakdown in the vertical equilibrium owing to rapidly increasing radiation pressure which cannot be balanced by the vertical stellar gravity. Viscous instability also occurs. The solution gives an accurate representation of numerical results, and enables useful expressions to be derived for the radius at which the disc is marginally thin and the radius at which viscous instability occurs. The disruption mechanism appears to have general validity for accretion discs around strongly magnetic stars.     

Recent advances in modeling stellar interiors

Advances in stellar interior modeling are being driven by new data from large-scale surveys and high-precision photometric and spectroscopic observations. Here we focus on single stars in normal evolutionary phases; we will not discuss the many advances in modeling star formation, interacting binaries, supernovae, or neutron stars. We review briefly: (1) updates to input physics of stellar models; (2) progress in two and three-dimensional evolution and hydrodynamic models; (3) insights from oscillation data used to infer stellar interior structure and validate model predictions (asteroseismology). We close by highlighting a few outstanding problems, e.g., the driving mechanisms for hybrid γ Dor/δ Sct star pulsations, the cause of giant eruptions seen in luminous blue variables such as η Car and P Cyg, and the solar abundance problem.     

The OSCROX stellar oscillaton code

This paper describes the OSCROX stellar oscillation code for the calculation of the adiabatic oscillations of low degree ? of a spherical star. There are two principal versions: one in Lagrangian variables (oscroxL), the second in Eulerian variables (oscroxE). The Lagrangian code does not require values of the Brunt Väisälä frequency or equivalently the density gradient. For ?=1 the oscillation equations have both an exact integral and an exact partial wave solution, and codes oscroxL1 and oscroxE1 incorporate these exact solutions. The difference in the frequencies obtained with the various codes gives some estimate of the uncertainty in the results due both to limited accuracy of hydrostatic support of the stellar model, and the limited accuracy of the integration of the oscillation equations. We compare the results of the different methods by calculating the frequencies in the range 20–2500 μHz of a model of a 1.5 M_⊙ main-sequence star (ModelJC) kindly provided by J. Christensen-Dalsgaard for the purposes of cross comparison of codes, a modified version of this model (ModelJCA) with improved hydrostatic support, and of a highly accurate n=3 polytropic model of a star with the same mass and radius. For the polytropic model the frequencies as calculated by all codes agree to within 0.001 μHz, whereas for the 1.5 M_⊙ main sequence model the frequency differences reach a maximum of 0.04 μHz, due primarily to the limited accuracy of hydrostatic support in the model; this is reduced to 0.01 μHz for ModelJCA.     

Recurrent gas accretion by massive star clusters, multiple stellar populations and mass thresholds for spheroidal stellar systems

We explore the gravitational influence of pressure-supported stellar systems on the internal density distribution of a gaseous environment. We conclude that compact massive star clusters with masses  ≳10⁶ M_⊙  act as cloud condensation nuclei and are able to accrete gas recurrently from a warm interstellar medium which may cause further star formation events and account for multiple stellar populations in the most massive globular and nuclear star clusters. The same analytical arguments can be used to decide whether an arbitrary spherical stellar system is able to keep warm or hot interstellar material or not. These mass thresholds coincide with transition masses between pressure supported galaxies of different morphological types.     

Relaxational effects in radiating stellar collapse

Relaxational effects in stellar heat transport can in many cases be significant. Relativistic Fourier–Eckart theory is inherently quasi-stationary, and cannot incorporate these effects. The effects are naturally accounted for in causal relativistic thermodynamics, which provides an improved approximation to kinetic theory. Recent results, based on perturbations of a static star, show that relaxation effects can produce a significant increase in the central temperature and temperature gradient for a given luminosity. We use a simple stellar model that allows for non-perturbative deviations from staticity, and confirms qualitatively the predictions of the perturbative models.