arXiv subjects

A. B. Gorshkov

Publications and source records attributed to A. B. Gorshkov.

5 recordsLinked to original sources

arXiv2026

A mapping method of age estimation for binary stars: Application to the $α$ Centauri system A and B

Given the wealth of data provided by Gaia and the upcoming PLATO mission, it is essential to improve stellar models to obtain accurate stellar ages. Our objective is to apply a mapping technique to estimate the age of a system and the initial chemical composition. We also evaluate the influence of observational uncertainties in mass and heavy-element mixtures on results. We applied an inverse calibration method to the evolution of a multiple stellar system, assuming that the stars share the same age and initial chemical composition. This approach determines age, the initial mass fractions of helium ($Y_{ini}$) and heavy elements ($Z_{ini}$), as well as the convective mixing-length parameters ($α_A $ and $α_B$). It uses the observed luminosities ($L_A$ and $L_B$), radii ($R_A$ and $R_B$), and surface chemical compositions ($Z/X_A$ and $Z/X_B$). We used the most recent observational data for $M$, $R$, $L$, and $[Fe/H]$ of $α$ Centauri A and B as input data for our method. We compared two assumptions for the $Z/X$ ratio, following the results for the solar composition. For an assumed high solar $Z/X_\odot =0.0245$, we obtain an age of $7.8 \pm 0.6$ Ga, $Y_{ini} = 0.284 \pm 0.004$, and $Z_{ini} = 0.0335 \pm 0.0015$. For a low solar $Z/X_\odot = 0.0181$, the derived age is $8.7 \pm 0.6$ Ga, $Y_{ini} = 0.267 \pm 0.008$, and $Z_{ini} = 0.025 \pm 0.002$. Observational errors in the stellar masses of $\pm$0.002 lead to an age error of 0.6 Ga. Overshooting of $0.05-0.20H_p$ at the boundary of the convective core increases the age by $0.6-2.1$ Ga. Models with higher $Z/X$ and radiative cores, with ages of $7.2-7.8$ Ga, appear preferable and show better agreement with the observed asteroseismic frequencies.

astro-ph.SR↗

arXiv2024

Hydrogen Ionization Inside the Sun

Hydrogen is the main chemical component of the solar plasma, and H-ionization determines basic properties of the first adiabatic exponent $Γ_1$. Hydrogen ionization remarkably differs from the ionization of other chemicals. Due to the large number concentration, H-ionization causes a very deep lowering of $Γ_1$, and the lowering profile appears to be strongly asymmetric and extends over almost the entire solar convective zone. The excited states in the hydrogen atom are modelled with the help of a partition function, which accounts the internal degrees of freedom of the composed particle. A temperature-dependent partition function with an asymptotic cut-off tail is deduced from a solution of the quantum mechanical problem of the hydrogen atom in the plasma. We present a numerical simulation of hydrogen ionization, calculated with two expressions for the partition function, Planck-Larkin (PL) and Starostin-Roerich (SR), respectively. The Hydrogen ionization is shifted toward higher temperature in the SR-case compared to the PL-case. Different models for excited states of the hydrogen atom may change $Γ_1$ by as much as $10^{-2}$. The behavior of the $Γ_1$ profiles for pure hydrogen resembles `twisted ropes' for the two considered models. This significantly affects the helium ionization and the position of the helium hump. This entanglement of H and He effect gives us a chance to study a role of excited states in the solar plasma.

astro-ph.SR↗

arXiv2022

Ionization of heavy elements and the adiabatic exponent in the solar plasma

Context. The adiabatic exponent $Γ_1$ is studied as a thermodynamic quantity in the partially ionized plasma of the solar convection zone. Aims. The aim of this study is to understand the impact of heavy elements on the $Γ_1$ profile. We calculated $Γ_1$ with the SAHA-S equation of state for different chemical compositions of plasma, and we analyzed contributions of individual elements to $Γ_1$. Methods. We studied the decrease in $Γ_1$ due to the ionization of heavy elements in comparison with the value obtained for a pure hydrogen-helium plasma. These types of differences are denoted as "Z contributions", and we analyzed them for eight elements (C, N, O, Ne, Mg, S, Si, and Fe) as well as for a mixture of elements corresponding to the solar chemical composition. We compared linear combinations of individual Z contributions with the exact Z contribution. Applying a least-squares technique to the decomposition of the full Z contribution to a basis of individual-element contributions, we obtained the mass fractions of the heavy elements. Results. The Z contribution of heavy elements can be described by a linear combination of individual-element Z contributions with a high level of accuracy of 5e-6 . The inverse problem of estimating the mass fractions of heavy elements from a given $Γ_1$ profile was considered for the example of solar-type mixtures. In ideal numerical simulations, the mass fractions of the most abundant elements could be determined with a relative accuracy better than a few tenths of a percent. In the presence of random or systematic errors in the $Γ_1$ profile, abundance estimations become remarkably less accurate. If the amplitude of the errors does not exceed 1e-4, we can expect a determination of at least the oxygen abundance with a relative error of about 10%.

astro-ph.SR↗

arXiv2019

Interpolation of equation-of-state data

Aims. We use Hermite splines to interpolate pressure and its derivatives simultaneously, thereby preserving mathematical relations between the derivatives. The method therefore guarantees that thermodynamic identities are obeyed even between mesh points. In addition, our method enables an estimation of the precision of the interpolation by comparing the Hermite-spline results with those of frequent cubic (B-) spline interpolation. Methods. We have interpolated pressure as a function of temperature and density with quintic Hermite 2D-splines. The Hermite interpolation requires knowledge of pressure and its first and second derivatives at every mesh point. To obtain the partial derivatives at the mesh points, we used tabulated values if given or else thermodynamic equalities, or, if not available, values obtained by differentiating B-splines. Results. The results were obtained with the grid of the SAHA-S equation-of-state (EOS) tables. The maximum $lg P$ difference lies in the range from $10^{-9}$ to $10^{-4}$, and $Γ_1$ difference varies from $10^{-9}$ to $10^{-3}$. Specifically, for the points of a solar model, the maximum differences are one order of magnitude smaller than the aforementioned values. The poorest precision is found in the dissociation and ionization regions, occurring at $T \sim 1.5\cdot 10^3 - 10^5$ K. The best precision is achieved at higher temperatures, $T>10^5$ K. To discuss the significance of the interpolation errors we compare them with the corresponding difference between two different equation-of-state formalisms, SAHA-S and OPAL 2005. We find that the interpolation errors of the pressure are a few orders of magnitude less than the differences from between the physical formalisms, which is particularly true for the solar-model points.

astro-ph.SR↗

arXiv2016

Evolution of lithium abundance in the Sun and solar twins

Evolution of the 7Li abundance in the convection zone of the Sun during different stages of its life time is considered to explain its low photospheric value in comparison with that of the solar system meteorites. Lithium is intensively and transiently burned in the early stages of evolution (pre-main sequence, pMS) when the radiative core arises, and then the Li abundance only slowly decreases during the main sequence (MS). We study the rates of lithium burning during these two stages. In a model of the Sun, computed ignoring pMS and without extra-convective mixing (overshooting) at the base of the convection zone, the lithium abundance does not decrease significantly during the MS life time of 4.6 Gyr. Analysis of helioseismic inversions together with post-model computations of chemical composition indicates the presence of the overshooting region and restricts its thickness. It is estimated to be approximately half of the local pressure scale height 0.5Hp) which corresponds to 3.8 % of the solar radius. Introducing this extra region does not noticeably deplete lithium during the MS stage. In contrast, at the pMS stage, an overshooting region with a value of approximately 0.18Hp is enough to produce the observed lithium depletion. If we conclude that the dominant lithium burning takes place during the pMS stage, the dispersion of the lithium abundance in solar twins is explained by different physical conditions, primarily during the early stage of evolution before the MS.

astro-ph.SR↗