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Register a new userAsteroseismology of evolved stars with EGGMiMoSA I. Theoretical mixed-mode patterns from the subgiant to the RGB phase
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This study is the first of a series of papers that provide a technique to analyse the mixed-modes frequency spectra and characterise the structure of stars on the subgiant and red-giant branches. We define seismic indicators, relevant of the stellar structure and study their evolution on a grid of models. The proposed method, EGGMiMoSA, relies on the asymptotic description of mixed modes, defines initial guesses for the parameters, and uses a Levenberg-Marquardt technique to adjust the mixed-modes pattern efficiently. We follow the evolution of the mixed-modes parameters along a grid of models from the subgiant phase to the RGB bump and extend past works. We show the impact of the mass and composition on their evolution. The evolution of the period spacing $Deltapi_1$, pressure offset $epsilon_p$, gravity offset $epsilon_g$, and coupling factor $q$ as a function of $Delta u$ is little affected by the chemical composition and it follows two different regimes depending on the evolutionary stage. On the subgiant branch, the models display a moderate core-envelope density contrast. The evolution of $Delta pi_1$, $epsilon_p$, $epsilon_g$, and $q$ thus significantly changes with the mass. Also, we demonstrate that, at fixed Z/X and with proper measurements of $Deltapi_1$ and $Delta u$, we may unambiguously constrain the mass, radius and age of a subgiant star. Conversely, on the red-giant branch, the core-envelope density contrast becomes very large. Consequently, the evolution of $epsilon_p$, $epsilon_g$ and $q$ as a function of $Delta u$ becomes independent of the mass. This is also true for $Delta pi_1$ in stars with masses $lesssim 1.8M_odot$ because of core electron degeneracy. This degeneracy is lifted for higher masses, again allowing for a precise measurement of the age. Overall, our computations qualitatively agree with past observed and theoretical studies.
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Since few decades, asteroseismology, the study of stellar oscillations, enables us to probe the interiors of stars with great precision. It allows stringent tests of stellar models and can provide accurate radii, masses and ages for individual stars. Of particular interest are the mixed modes that occur in subgiant solar-like stars since they can place very strong constraints on stellar ages. Here we measure the characteristics of the mixed modes, particularly the coupling strength, using a grid of stellar models for stars with masses between 0.9 and 1.5 M_{odot}. We show that the coupling strength of the $ell = 1$ mixed modes is predominantly a function of stellar mass and appears to be independent of metallicity. This should allow an accurate mass evaluation, further increasing the usefulness of mixed modes in subgiants as asteroseismic tools.
Seismic observations by the space-borne mission emph{Kepler} have shown that the core of red giant stars slows down while evolving, requiring an efficient physical mechanism to extract angular momentum from the inner layers. Current stellar evolution codes fail to reproduce the observed rotation rates by several orders of magnitude, and predict a drastic spin-up of red giant cores instead. New efficient mechanisms of angular momentum transport are thus required. In this framework, our aim is to investigate the possibility that mixed modes extract angular momentum from the inner radiative regions of evolved low-mass stars. To this end, we consider the Transformed Eulerian Mean (TEM) formalism, introduced by Andrews & McIntyre (1978), that allows us to consider the combined effect of both the wave momentum flux in the mean angular momentum equation and the wave heat flux in the mean entropy equation as well as their interplay with the meridional circulation. In radiative layers of evolved low-mass stars, the quasi-adiabatic approximation, the limit of slow rotation, and the asymptotic regime can be applied for mixed modes and enable us to establish a prescription for the wave fluxes in the mean equations. The formalism is finally applied to a $1.3 M_odot$ benchmark model, representative of observed CoRoT and emph{Kepler} oscillating evolved stars. We show that the influence of the wave heat flux on the mean angular momentum is not negligible and that the overall effect of mixed modes is to extract angular momentum from the innermost region of the star. A quantitative and accurate estimate requires realistic values of mode amplitudes. This is provided in a companion paper.
The space-borne missions CoRoT and Kepler opened up a new opportunity for better understanding stellar evolution by probing stellar interiors with unrivalled high-precision photometric data. Kepler has observed stellar oscillation for four years, which gave access to excellent frequency resolution that enables deciphering the oscillation spectrum of evolved red giant branch and asymptotic giant branch stars. The internal structure of stars in the upper parts of the red and asymptotic giant branches is poorly constrained, which makes the distinction between red and asymptotic giants difficult. We perform a thorough seismic analysis to address the physical conditions inside these stars and to distinguish them. We studied the oscillation mode properties of about 2.000 evolved giants in a model described by the asymptotic pressure-mode pattern of red giants, which includes the signature of the helium second-ionisation zone. We extracted the mode properties up to the degree l = 3 and investigated their dependence on stellar mass, metallicity, and evolutionary status. We identify a clear difference in the signature of the helium second-ionisation zone between red and asymptotic giants. We also detect a clear shortage of the energy of l = 1 modes after the core-He-burning phase. Furthermore, we note that the mode damping observed on the asymptotic giant branch is similar to that observed on the red giant branch. We highlight that the signature of the helium second-ionisation zone varies with stellar evolution. This provides us with a physical basis for distinguishing red giant branch stars from asymptotic giants. Here, our investigation of stellar oscillations allows us to constrain the physical processes and the key events that occur during the advanced stages of stellar evolution, with emphasis on the ascent along the asymptotic giant branch, including the asymptotic giant branch bump.
The existence of mixed modes in stars is a marker of stellar evolution. Their detection serves for a better determination of stellar age. The goal of this paper is to identify the dipole modes in an automatic manner without human intervention. I use the power spectra obtained by the Kepler mission for the application of the method. I compute asymptotic dipole mode frequencies as a function of coupling factor and dipole period spacing, and other parameters. For each star, I collapse the power in an echelle diagramme aligned onto the monopole and dipole mixed modes. The power at the null frequency is used as a figure of merit. Using a genetic algorithm, I then optimise the figure of merit by adjusting the location of the dipole frequencies in the power spectrum}. Using published frequencies, I compare the asymptotic dipole mode frequencies with published frequencies. I also used published frequencies for deriving coupling factor and dipole period spacing using a non-linear least squares fit. I use Monte-Carlo simulations of the non-linear least square fit for deriving error bars for each parameters. From the 44 subgiants studied, the automatic identification allows to retrieve within 3 $mu$Hz at least 80% of the modes for 32 stars, and within 6 $mu$Hz at least 90% of the modes for 37 stars. The optimised and fitted gravity-mode period spacing and coupling factor agree with previous measurements. Random errors for the mixed-mode parameters deduced from Monte-Carlo simulation are about 30-50 times smaller than previously determined errors, which are in fact systematic errors. The period spacing and coupling factors of mixed modes in subgiants are confirmed. The current automated procedure will need to be improved using a more accurate asymptotic model and/or proper statistical tests.
The Li enrichment in the Universe still presents various puzzles to astrophysics. One open issue is that of obtaining estimates for the rate of e-captures on 7Be, for T and rho conditions different from solar. This is important to model the Galactic nucleosynthesis of Li. In this framework, we present a new theoretical method for calculating the e-capture rate in conditions typical of evolved stars. We show how our approach compares with state-of-the-art techniques for solar conditions, where various estimates are available. Our computations include: i) traditional calculations of the electronic density at the nucleus, to which the e-capture rate for 7Be is proportional, for different theoretical approaches including the Thomas--Fermi, Poisson--Boltzmann and Debye--Hueckel (DH) models of screening, ii) a new computation, based on a formalism that goes beyond the previous ones, adopting a mean-field adiabatic approximation to the scattering process. The results obtained with our approach as well as with the traditional ones and their differences are discussed in some detail, starting from solar conditions, where our method and the DH model converge to the same solution. We then analyze the applicability of the various models to a rather broad range of T and rho values, embracing those typical of red giant stars. We find that, over a wide region of the parameter space explored, the DH approximation does not stand, and the more general method we suggest is preferable. We then briefly reanalyze the 7Li abundances in RGB and AGB stars of the Galactic Disk using the new Be-decay rate. We also underline that the different values of the electron density at the nucleus we find should induce effects on electron screening (for p-captures on Li itself, as well as for other nuclei) so that our new approach might have wide astrophysical consequences.
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