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Register a new userAsteroseismic masses, ages, and core properties of $gamma$ Doradus stars using gravito-inertial dipole modes and spectroscopy
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The asteroseismic modelling of period spacing patterns from gravito-inertial modes in stars with a convective core is a high-dimensional problem. We utilise the measured period spacing pattern of prograde dipole gravity modes (acquiring $Pi_0$), in combination with the effective temperature ($T_{rm eff}$) and surface gravity ($log g$) derived from spectroscopy, to estimate the fundamental stellar parameters and core properties of 37 $gamma~$Doradus ($gamma~$Dor) stars whose rotation frequency has been derived from $textit{Kepler}$ photometry. We make use of two 6D grids of stellar models, one with step core overshooting and one with exponential core overshooting, to evaluate correlations between the three observables $Pi_0$, $T_{rm eff}$, and $log g$ and the mass, age, core overshooting, metallicity, initial hydrogen mass fraction and envelope mixing. We provide multivariate linear model recipes relating the stellar parameters to be estimated to the three observables ($Pi_0$, $T_{rm eff}$, $log g$). We estimate the (core) mass, age, core overshooting and metallicity of $gamma~$Dor stars from an ensemble analysis and achieve relative uncertainties of $sim!10$ per cent for the parameters. The asteroseismic age determination allows us to conclude that efficient angular momentum transport occurs already early on during the main sequence. We find that the nine stars with observed Rossby modes occur across almost the entire main-sequence phase, except close to core-hydrogen exhaustion. Future improvements of our work will come from the inclusion of more types of detected modes per star, larger samples, and modelling of individual mode frequencies.
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Aims: We investigate the thermal and chemical structure in the near-core region of stars with a convective core by means of gravito-inertial modes. We do so by determining the probing power of different asteroseismic observables and fitting methodologies. We focus on the case of the B-type star KIC$,$7760680, rotating at a quarter of its critical rotation velocity. Methods: We compute grids of 1D stellar structure and evolution models for two different prescriptions of the temperature gradient and mixing profile in the near-core region. We determine which of these prescriptions is preferred according to the prograde dipole modes detected in 4-yr $textit{Kepler}$ photometry of KIC$,$7760680. We consider different sets of asteroseismic observables and compare the outcomes of the regression problem for a $chi^2$ and Mahalanobis Distance merit function, where the latter takes into account realistic uncertainties for the theoretical predictions and the former does not. Results: Period spacings of modes with consecutive radial order offer a better diagnostic than mode periods or mode frequencies for asteroseismic modelling of stars revealing only high-order gravito-inertial modes. We find KIC$,$7760680 to reveal a radiative temperature gradient in models with convective boundary mixing, but less complex models without such mixing are statistically preferred for this rotating star, revealing extremely low vertical envelope mixing. Conclusions: Our results strongly suggest the use of measured individual period spacing values for modes of consecutive radial order as an asteroseismic diagnostic for stellar modelling of B-type pulsators with gravito-inertial modes.
With four years of nearly-continuous photometry from Kepler, we are finally in a good position to apply asteroseismology to $gamma$ Doradus stars. In particular several analyses have demonstrated the possibility to detect non-uniform period spacings, which have been predicted to be directly related to rotation. In the present work, we define a new seismic diagnostic for rotation in $gamma$ Doradus stars that are too rapidly rotating to present rotational splittings. Based on the non uniformity of their period spacings, we define the observable $Sigma$ as the slope of the period spacing when plotted as a function of period. We provide a one-to-one relation between this observable $Sigma$ and the internal rotation, which applies widely in the instability strip of $gamma$ Doradus stars. We apply the diagnostic to a handful of stars observed by Kepler. Thanks to g-modes in $gamma$ Doradus stars, we are now able to determine the internal rotation of stars on the lower main sequence, which is still not possible for Sun-like stars.
The search for twins of the Sun and Earth relies on accurate characterization of stellar and exoplanetary parameters: i.e., ages, masses, and radii. In the modern era of asteroseismology, parameters of solar-like stars are derived by fitting theoretical models to observational data, which include measurements of their oscillation frequencies, metallicity [Fe/H], and effective temperature Teff. Combining this information with transit data furthermore yields the corresponding parameters for their exoplanets. While [Fe/H] and Teff are commonly stated to a precision of ~0.1 dex and ~100 K, the impact of errors in their measurement has not been studied in practice within the context of the parameters derived from them. Here we use the Stellar Parameters in an Instant (SPI) pipeline to estimate the parameters of nearly 100 stars observed by Kepler and Gaia, many of which are confirmed planet hosts. We adjust the reported spectroscopic measurements of these stars by introducing faux systematic errors and artificially increasing the reported uncertainties, and quantify the differences in the resulting parameters. We find that a systematic error of 0.1 dex in [Fe/H] translates to differences of only 4%, 2%, and 1% on average in the resulting stellar ages, masses, and radii, which are well within their uncertainties (~11%, 3.5%, 1.4%) as derived by SPI. We also find that increasing the uncertainty of [Fe/H] measurements by 0.1 dex increases the uncertainties by only 0.01 Gyr, 0.02 M_sun, and 0.01 R_sun, which are again well below their reported uncertainties (0.5 Gyr, 0.04 M_sun, 0.02 R_sun). The results for Teff at 100 K are similar. Stellar parameters from SPI are unchanged within uncertainties by errors of up to 0.14 dex or 175 K, and are even more robust to errors in Teff than the seismic scaling relations. Consequently, the parameters for their exoplanets are robust as well.
Oscillations have been detected in a variety of stars, including intermediate- and high-mass main sequence stars. While many of these stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study on axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. These modes probe the deep layers of the star around its convective core. We consider a simplified model where the radiative zone of a star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral simulations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire shell and those that are restricted to a subdomain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We characterise these attractors by the dependence of their Lyapunov exponent with the BV frequency of the background and the oscillation frequency of the mode. Finally, we note that, as modes associated with short-period attractors form dissipative structures, they could play an important role for tidal interactions but should be dismissed in the interpretation of observed oscillation frequencies.
While many intermediate- and high-mass main sequence stars are rapidly and differentially rotating, the effects of rotation on oscillation modes are poorly known. In this communication we present a first study of axisymmetric gravito-inertial modes in the radiative zone of a differentially rotating star. We consider a simplified model where the radiative zone of the star is a linearly stratified rotating fluid within a spherical shell, with differential rotation due to baroclinic effects. We solve the eigenvalue problem with high-resolution spectral computations and determine the propagation domain of the waves through the theory of characteristics. We explore the propagation properties of two kinds of modes: those that can propagate in the entire shell and those that are restricted to a subdomain. Some of the modes that we find concentrate kinetic energy around short-period shear layers known as attractors. We describe various geometries for the propagation domains, conditioning the surface visibility of the corresponding modes.
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