Study Of Stellar Structure Research Articles

Study of stellar structures in f(ℛ,𝒯μν𝒯μν) theory

This paper deals with the dynamics of cylindrical collapse with anisotropic fluid distribution in the framework of [Formula: see text] gravity. For this purpose, we consider non-static and static cylindrical spacetimes in the inner and outer regions of a star, respectively. To match both geometries at the hypersurface, we consider the Darmois junction conditions. We use the Misner–Sharp technique to examine the impacts of correction terms and effective fluid parameters on the dynamics of a cylindrical star. A correlation between the Weyl tensor and physical quantities is also developed. The conformally flat condition is not obtained due to the influence of anisotropic pressure and higher-order nonlinear terms. Further, we assume isotropic fluid and specific model of this theory which yields the conformally flat spacetime and inhomogeneous energy density. We conclude that the collapse rate reduces as compared to general relativity due to the inclusion of effective pressure and additional terms of this theory.

Asteroseismology of High-Mass Stars: New Insights of Stellar Interiors With Space Telescopes

Massive stars are important metal factories in the Universe. They have short and energetic lives, and many of them inevitably explode as a supernova and become a neutron star or black hole. In turn, the formation, evolution and explosive deaths of massive stars impact the surrounding interstellar medium and shape the evolution of their host galaxies. Yet the chemical and dynamical evolution of a massive star, including the chemical yield of the ultimate supernova and the remnant mass of the compact object, strongly depend on the interior physics of the progenitor star. We currently lack empirically calibrated prescriptions for various physical processes at work within massive stars, but this is now being remedied by asteroseismology. The study of stellar structure and evolution using stellar oscillations -- asteroseismology -- has undergone a revolution in the last two decades thanks to high-precision time series photometry from space telescopes. In particular, the long-term light curves provided by the MOST, CoRoT, BRITE, Kepler/K2 and TESS missions provided invaluable data sets in terms of photometric precision, duration and frequency resolution to successfully apply asteroseismology to massive stars and probe their interior physics. The observation and subsequent modelling of stellar pulsations in massive stars has revealed key missing ingredients in stellar structure and evolution models of these stars. Thus asteroseismology has opened a new window into calibrating stellar physics within a highly degenerate part of the Hertzsprung--Russell diagram. In this review, I provide a historical overview of the progress made using ground-based and early space missions, and discuss more recent advances and breakthroughs in our understanding of massive star interiors by means of asteroseismology with modern space telescopes.

How Much do we Trust StellarModels?

Figure 1: A Tribute to Arlette by her longtime friend Annie Baglin 1. Conference rationale Eighty years ago, Paul Ledoux, then in Chicago, published with Chaim Leib Pekeris the now famous work entitled Radial Pulsations of Stars. Stellar evolution was still in its infancy, numerical model were not computed on a massive scale as today. With the advent of computers and the improvement of observational data, the study of stellar structure and evolution has now become a central field of astrophysics, and pulsations have become the prime method to learn about the internal structure of stars. In the last fifteen years space telescopes provided us a tremendous amount of data, opening the way to test stellar models with unprecedented thoroughness. It is now up to theoretical stellar physi-cists to use these observations to improve stellar models and provide accurate stellar properties to fields such as exoplanetary science and Galactic archeology. The last decades were also marked by the achievements of a remarkable scientist, an inspiring col-league, a patient teacher and a friend, who devoted herself to our field of research and who celebrated her 75th birthday in August 2018, Arlette Grotsch-Noels. This conference is a tribute to Arlette. The aim of this workshop was to bring together experts of theoretical stellar physics and Galactic archeology to discuss the current issues connected to stellar structure and evolution. Topics ranged from microphysical ingredients such as atomic

Insights from the APOKASC determination of the evolutionary state of red-giant stars by consolidation of different methods

ABSTRACTThe internal working of low-mass stars is of great significance to both the study of stellar structure and the history of the Milky Way. Asteroseismology has the power to directly sense the internal structure of stars and allows for the determination of the evolutionary state – i.e. has helium burning commenced or is the energy generated only by the fusion in the hydrogen-burning shell? We use observational data from red-giant stars in a combination (known as APOKASC) of asteroseismology (from the Kepler mission) and spectroscopy (from SDSS/APOGEE). The new feature of the analysis is that the APOKASC evolutionary state determination is based on the comparison of diverse approaches to the investigation of the frequency-power spectrum. The high level of agreement between the methods is a strong validation of the approaches. Stars for which there is not a consensus view are readily identified. The comparison also facilitates the identification of unusual stars including those that show evidence for very strong coupling between p and g cavities. The comparison between the classification based on the spectroscopic data and asteroseismic data have led to a new value for the statistical uncertainty in APOGEE temperatures. These consensus evolutionary states will be used as an input for methods that derive masses and ages for these stars based on comparison of observables with stellar evolutionary models (‘grid-based modelling’) and as a training set for machine-learning and other data-driven methods of evolutionary state determination.

Stellar masses from granulation and oscillations of 23 bright red giants observed by BRITE-Constellation

Context. The study of stellar structure and evolution depends crucially on accurate stellar parameters. The photometry from space telescopes has provided superb data that enabled the asteroseismic characterisation of thousands of stars. However, typical targets of space telescopes are rather faint and complementary measurements are difficult to obtain. On the other hand, the brightest, otherwise well-studied stars, are lacking seismic characterization. Aims. Our goal is to use the granulation and/or oscillation timescales measured from photometric time series of bright red giants (1.6 ≤ V mag ≤ 5.3) observed with BRITE-Constellation to determine stellar surface gravities and masses. Methods. We used probabilistic methods to characterise the granulation and/or oscillation signal in the power density spectra and the autocorrelation function of the BRITE-Constellation time series. Results. We detect a clear granulation and/or oscillation signal in 23 red giant stars and extract the corresponding timescales from the power density spectra as well as the autocorrelation function of the BRITE-Constellation time series. To account for the recently discovered non-linearity of the classical seismic scaling relations, we used parameters from a large sample of Kepler stars to re-calibrate the scalings of the high- and low-frequency components of the granulation signal. We developed a method to identify which component is measured if only one granulation component is statistically significant in the data. We then used the new scalings to determine the surface gravity of our sample stars, finding them to be consistent with those determined from the autocorrelation signal of the time series. We further used radius estimates from the literature to determine the stellar masses of our sample stars from the measured surface gravities. We also defined a statistical measure for the evolutionary stage of the stars. Conclusions. Our sample of stars covers low-mass stars on the lower giant branch to evolved massive supergiants and even though we cannot verify our mass estimates with independent measurements from the literature, they appear to be at least good enough to separate high-mass from low-mass stars. Given the large known but usually not considered systematic uncertainties in the previous model-based mass estimates, we prefer our model-independent measurements.

Study of stellar structures in f(R,T) gravity

This paper is devoted to study the compact objects whose pressure and density are related through polytropic equation-of-state (EoS) and MIT bag model (for quark stars) in the background of [Formula: see text] gravity. We solve the field equations together with the hydrostatic equilibrium equation numerically for the model [Formula: see text] and discuss physical properties of the resulting solution. It is observed that for both types of stars (polytropic and quark stars), the effects of model parameters [Formula: see text] and [Formula: see text] remain the same. We also obtain that the energy conditions are satisfied and stellar configurations are stable for both EoS.

Grand challenges in the physics of the sun and sun-like stars

The study of stellar structure and evolution is one of the main building blocks of astrophysics, and the Sun has an importance both as the star that is most amenable to detailed study and as the star that has by far the biggest impact on the Earth and near-Earth environment through its radiative and particulate outputs. Over the past decades, studies of stars and of the Sun have become somewhat separate. But in recent years, the rapid advances in asteroseismology, as well as the quest to better understand solar and stellar dynamos, have emphasized once again the synergy between studies of the stars and the Sun. In this article I have selected two grand challenges both for their crucial importance and because I thnk that these two problems are tractable to significant progress in the next decade. They are (i) understanding how solar and stellar dynamos generate magnetic field, and (ii) improving the predictability of geo-effective space weather.

Chandrasekhar’s book An Introduction to the Study of Stellar Structure

For me, and for many astrophysicists of my generation, Chandrasekhar’s book An Introduction to the Study of Stellar Structure was very important. I could not have done my PhD (1962–1965) without it. Much more recently (1998) I realized that I could not have written my lecture course on thermodynamics and statistical mechanics without much of it, particularly the first chapter. I shall present anecdotal evidence that the influence of his discussion on the second law of thermodynamics has been important not just for astrophysics but for a much wider range of physics. Chandrasekhar’s discussion of polytropes was masterly. Even today polytropes play an important role as an aid for understanding stellar structure. I believe that to the list of analytic solutions of the polytrope only one more has to be added: a curious n = 5 model of Srivastava (1962). Stellar structure is nowadays a very computationally intensive subject. I shall illustrate this with a couple of topics from my experience with Djehuty, a supercomputer code for modelling stars in 3D. Nevertheless it remains true, I believe, that analytical mathematical entities like polytropes are fundamental as aids for understanding what the computers churn out. How close are we to seeing a book with the title ‘The Last Word on the Study of Stellar Structure’? Not very, although much has been learned in 70 years. I shall discuss a few of the aspects of stellar evolution that are problematic today. I shall discuss a couple of aspects where I believe analysis of ‘piecewise polytropic’ structures sheds light on the question ‘Why do stars become red giants?’

Seismological studies of ZZ Ceti stars - I. The model grid and the application to individual stars

We calculate and explore an extensive adiabatic model grid for pulsating white dwarfs with hydrogen-dominated atmospheres, the ZZ Ceti stars. We also compared the computed modes with the observed ones for five ZZ Ceti stars that are a representative sample of the whole class of pulsators. We describe our new approach for seismological studies, using the relative observed amplitudes to give weights for the periods in the fit and the external mass and temperature determinations as a guide. Our seismological study is clear evidence that seismology is indeed a powerful tool in the study of stellar structure and evolution.

Estimating stellar parameters from spectra

Estimating stellar parameters from spectrophotometric data is a key tool in the study of stellar structure and stellar evolution. Although many methods have been proposed to estimate stellar parameters from ultraviolet (UV), optical and infrared (IR) data using low, medium or high-resolution observational data of the target(s), only a few address the problem of the uncertainties in the stellar parameters. This information is critical for a meaningful comparison of the derived parameters with results obtained from other data and/or methods. Here we present a frequentist method to estimate these uncertainties. We demonstrate that the combined use of both a local and a global goodness-of-fit parameter alters the uncertainty intervals as determined from the use of only one of these deviation estimating parameters. This technique using both goodness-of-fit parameters is applied to the infrared 2.38-4.08 μ m ISO-SWS data (Infrared Space Observatory – Short Wavelength Spectrometer) of α Boo, yielding an effective temperature range from 4160 K to 4300 K, a logarithm of the gravity range from 1.35 to 1.65 dex and a metallicity from -0.30 to 0.00 dex. However, using a lack-of-fit test, it is shown that even the “best” theoretical models are still not capable of capturing all the structure in the data, and this is due to our incomplete knowledge and modelling of the full physical stellar structure or due to problems in the data reduction process.

Extragalactic eclipsing binaries: astrophysical laboratories

Extragalactic eclipsing binaries open a new perspective on the study of stellar structure and evolution. Stars in different galaxies have formed and evolved in environments with chemical histories that may differ from those of the solar neighborhood. For example, the LMC and SMC contain low-metallicity, young massive stars that are no longer found in our Galaxy. Eclipsing binaries, yielding accurate determinations of masses, radii and temperatures, allow for critical tests of, e.g., convective overshooting, mass loss, and internal structure. In addition, they provide an empirical calibration of the mass-luminosity relationship. In this paper, I present some results from ongoing programs on the determination of physical properties and distances to eclipsing binaries in the LMC, the SMC, and M31. In particular, I focus on aspects relevant to stellar astrophysics, and on the contributions of these eclipsing binaries to our understanding of the structure and chemical evolution of the host galaxies.

Stars: Their structure and evolution

The subject of astrophysics began with the study of the stars. It may be recalled that the positivist philosophers who were so influential in European thinking had asserted that it was in the nature of things that one can never know what the stars are. And yet, with Fraunhofer’s discovery of dark lines in the spectrum of the Sun and the stars, and their subsequent explanation in terms of atomic absorption lines, a major scientific revolution had occurred – a question that appeared meaningless within the premise of science had acquired a meaning. Lane, Kelvin and Helmholtz laid the foundations for the theory of stars towards the end of the 19th century. But the credit for constructing a remarkably successful theory of the stability and equilibrium of stars must go to Sir Arthur Eddington. His book The Internal Constitution of the Stars published in 1926 is undoubtedly one of the greatest masterpieces of the 20th century. It is from this book that young Chandrasekhar learnt about the theory of the stars. The year was 1928, and he was an undergraduate student in the Presidency College in Madras. The newly discovered Compton Effect was much in the news, and was the subject of his first scientific publication entitled Thermodynamics of the Compton Effect with reference to the Interior of the Stars (Chandrasekhar 1928). He was 18 years old then. That same year he learnt about the discovery of the Fermi-Dirac statistics from Arnold Sommerfeld who happened to visit Madras. Straightaway he applied the new statistics to Compton scattering, and this paper was communicated to the Royal Society by R. H. Fowler (Chandrasekhar 1929). During the next ten years he made monumental contributions to the theory of stellar structure and stellar evolution. Much of it is summarized in his classic book entitled An Introduction to the Study of Stellar Structure published in 1939. Almost immediately after writing this book he decided to leave the field, and turned his attention to problems in Stellar Dynamics. This decision was primarily due to the fact that his epoch making discoveries, instead of being lauded, stirred up a great controversy largely on account of Eddington rejecting them. In this article we shall attempt to recall some of his pioneering contributions to the theory of the stars. This is undoubtedly a daunting task. Fortunately, Chandrasekhar himself had made a selection of his most important papers from this period for inclusion in Volume I of his Selected Papers. We shall choose a few of them, explain their content, and trace their impact on subsequent developments.

A Method for Incorporating the Effects of Large-Scale Magnetic Fields in the Study of Stellar Structure and Variability

A Method for Incorporating the Effects of Large-Scale Magnetic Fields in the Study of Stellar Structure and Variability

Has rapid solar core rotation been observed?

Internal rotation and gravitational quadropole moment of the Sun are of interest to solar physics, the study of stellar structure and to investigations related to the test of gravitational theories. High precision measurements of fluctuations in the limb darkening function and in the spectral line shifts have raised the possibility that the interior of the Sun may be studied more directly than had previously been possible. Recently, Claverie et al.1 argued that their detection of a 13.1±0.2 day velocity signal give further experimental evidence that the solar core is rotating more rapidly than the observable surface. We show here that the phase as well as the magnitude of the observed signal amplitude may be predicted without any rapid core rotation by taking into account the presence of sunspots and their contribution to the spectral line profile as integrated over the disk of the Sun. Hence, we conclude that the existence of a 13.1–day apparently periodic velocity signal with amplitude 6.5 m s−1 during the 88 days observing period cannot be taken as evidence for a rapidly rotating solar core.

General calibration problems

During this symposium we have already heard papers which have dealt with the calibration of certain spectral parameters. In this session we turn to the matter of calibrating luminosity criteria in terms of absolute magnitude. This is a central problem in studies of our Galaxy and it finds in this topic its widest application. At the same time we remind ourselves that the determination of absolute magnitude is necessary in studies of stellar structure and stellar evolution since this information tells us about the radiation passing through the stellar interior and the stellar atmosphere and of the amount of energy generated by the star. The luminosity also allows us to calculate the size of a star and to estimate its surface gravity.

Hydrogen Content of the Sun and of Stars of Small Masses

THE simple Cowling model of a star of small mass with a convective core and radiative envelope is of considerable importance in view of Bethe's theory of energy generation, which demands a stellar model of the convective radiative type. It appears possible to use this simple model so as to conform to Bethe's formula of energy generation on one hand and furnish an approximate value of the hydrogen content of a star of small mass on the other. For formulae relating to the Cowling model we shall refer to Chandrasekhar's "Introduction to the Study of Stellar Structure", pp. 351–54. The constant x0 in Kramers' opacity formula will be taken as 3.9 × 1025 (1 – x2)/t, where tmacr; is the mean guillotine factor, and x the hydrogen content; helium content being assumed zero.

An Introduction to the Study of Stellar Structure

EDDINGTON'S “Internal Constitution of the Stars” was published in 1926 and gives what now ranks as a classical account of his own researches and of the general state of the theory at that time. Since then, a tremendous amount of work has appeared. Much of it has to do with the construction of stellar models with different equations of state applying in different zones. Other parts deal with the effects of varying chemical composition, with pulsation and tidal and rotational distortion of stars, and with the precise relations between the interior and the atmosphere of a star. The striking feature of all this work is that so much can be done without assuming any particular mechanism of stellar energy-generation. Only such very comprehensive assumptions are made about the distribution and behaviour of the energy sources that we may expect future knowledge of their mechanism to lead mainly to more detailed results within the framework of the existing general theory. An Introduction to the Study of Stellar Structure By S. Chandrasekhar. (Astrophysical Monographs sponsored by The Astrophysical Journal.) Pp. ix+509. (Chicago: University of Chicago Press; London: Cambridge University Press, 1939.) 50s. net.

Static Solutions of Einstein's Field Equations for Spheres of Fluid

A method is developed for treating Einstein's field equations, applied to static spheres of fluid, in such a manner as to provide explicit solutions in terms of known analytic functions. A number of new solutions are thus obtained, and the properties of three of the new solutions are examined in detail. It is hoped that the investigation may be of some help in connection with studies of stellar structure. (See the accompanying article by Professor Oppenheimer and Mr. Volkoff.)