The relation of period spacing ($ΔP$) versus period ($P$) of dipole prograde g modes is known to be useful to measure rotation rates in the g-mode cavity of rapidly rotating $γ$ Dor and slowly pulsating B (SPB) stars. In a rapidly rotating star, an inertial mode in the convective core can resonantly couple with g modes propagative in the surrounding radiative region. The resonant coupling causes a dip in the $P$-$ΔP$ relation, distinct from the modulations due to the chemical composition gradient. Such a resonance dip in $ΔP$ of prograde dipole g modes appears around a frequency corresponding to a spin parameter $2f_{\rm rot}{\rm(cc)}/ν_{\rm co-rot} \sim 8-11$ with $f_{\rm rot}$(cc) being the rotation frequency of the convective core and $ν_{\rm co-rot}$ the pulsation frequency in the co-rotating frame. The spin parameter at the resonance depends somewhat on the extent of core overshooting, central hydrogen abundance, and other stellar parameters. We can fit the period at the observed dip with the prediction from prograde dipole g modes of a main-sequence model, allowing the convective core to rotate differentially from the surrounding g-mode cavity. We have performed such fittings for 16 selected $γ$ Dor stars having well defined dips, and found that the majority of $γ$ Dor stars we studied rotate nearly uniformly, while convective cores tend to rotate slightly faster than the g-mode cavity in less evolved stars.
We investigate the pulsation properties of stellar models representative of $δ$ Scuti and $γ$ Doradus variables. We have calculated a grid of stellar models from 1.2 to 2.2 M$_{\odot}$, including the effects of both rotation and convective overshoot using MESA, and we investigate the pulsation properties of these models using GYRE. We discuss observable patterns in the frequency spacing for $p$ modes and the period spacings for g modes. Using the observable patterns in g mode period spacings, it may be possible to observationally constrain the convective overshoot and rotation of a model. We a…
Gamma Doradus stars present an incredibly rich pulsation spectra, with gravito-inertial modes, in some cases supplemented with delta Scuti-like pressure modes and in numerous cases with Rossby modes. The present paper aims at showing that, in addition to these modes established in the radiative envelope, pure inertial modes, trapped in the convective core, can be detected in Kepler observations of gamma Doradus stars, thanks to their resonance with the gravito-inertial modes. We start by using a simplified model of perturbations in a full sphere of uniform density. Under these conditions, the …
Recent asteroseismic observations by the $\it Kepler$ space mission have revealed the dip fine structure in the period-spacing versus period diagram of rapidly rotating $γ$ Doradus stars. Following the successful reproduction of the dip structure by numerical calculations in previous studies, we present in this paper the physical mechanism of how the dip is formed as a result of the interaction between the gravito-inertial waves in the radiative envelope and the pure inertial waves in the convective core. We analytically describe the wave solutions in both of the radiative envelope and the con…
We computed a grid of theoretical models to fit the $δ$ Scuti frequencies of CoRoT 100866999 detected earlier from the CoRoT timeserials. The pulsating primary star is determined to be a main sequence star with a rotation period of $4.1^{+0.6}_{-0.5}$ days, rotating slower than the orbital motion. The fundamental parameters of the primary star are determined to be $M$ = $1.71^{+0.13}_{-0.04}$ $M_{\odot}$, $Z=0.012^{+0.004}_{-0.000}$, $f_{\rm ov}$ = $0.02^{+0.00}_{-0.02}$, $T_{\rm eff}$ = $8024^{+249}_{-297}$ K, $L$ = $11.898^{+2.156}_{-1.847}$ $L_{\odot}$, $\log g$ = $4.166^{+0.013}_{-0.002}$,…
If Gamma Dor-type pulsations are driven by the convective blocking mechanism, a convective envelope at a sufficient depth is essential. There are several hot Gamma Dor and hybrid star candidates in which there should not be an adequate convective envelope to excite theγDor-type oscillations. The existence of these hot objects needs an explanation. Therefore, we selected, observed and studied 24 hotγDor and hybrid candidates to investigate their properties. The atmospheric parameters, chemical abundances and vsini values of the candidates were obtained using medium-resolution (R= 46 000)spectra…
We use photometry from the Kepler Mission to study oscillations in gamma Doradus stars. Some stars show remarkably clear sequences of g modes and we use period echelle diagrams to measure period spacings and identify rotationally split multiplets with l=1 and l=2. We find small deviations from regular period spacings that arise from the gradient in the chemical composition just outside the convective core. We also find stars for which the period spacing shows a strong linear trend as a function of period, consistent with relatively rapid rotation. Overall, the results indicate it will be possi…
Using K2 data, we have identified 23 very low mass members of the $ρ$ Oph and Upper Scorpius star-forming region as having periodic photometric variability not easily explained by well-established physical mechanisms such as star spots, eclipsing binaries, or pulsation. All of these unusual stars are mid-to-late M dwarfs without evidence of active accretion, and with photometric periods generally $<$1 day. Often the unusual light curve signature takes the form of narrow flux dips; when we also have rotation periods from star spots, the two periods agree, suggesting that the flux dips are due t…
The γ Dor pulsating stars present high-order gravity modes, which make them important targets in the intermediate-and low-mass main-sequence region of the Hertzsprung-Russell diagram. Whilst we have only access to rotation in the envelope of the Sun, the g modes of γ Dor stars can in principle deliver us constraints on the inner layers. With the puzzling discovery of unexpectedly low rotation rates in the core of red giants, the γ Dor stars appear now as unique targets to explore internal angular momentum transport in the progenitors of red giants. Yet, the γ Dor pulsations remain hard to dete…
The short-period (P $\approx1.7$ d), Algol-type eclipsing binary KIC 7385478 consists of an F-type primary star ($M_1 \approx 1.71M_{\odot}$) and an evolved K-type secondary ($M_2 \approx 0.37M_{\odot}$) (Ozdarcan \& Ali Dal 2017). We study the variability of the {\it Kepler} light curve and attribute many frequency peaks in the Fourier spectrum to the spot modulation. These frequencies are in the form of orbital harmonics and are highly variable in amplitude. They are most likely from the mass-accreting primary star. In addition, we identify a series prograde dipole g-modes from the primary s…
Observations of the pulsations of stars can be used to infer their interior structure and test theoretical models. The main sequence $γ$ Doradus (Dor) and $δ$ Scuti (Sct) stars with masses 1.2-2.5 $M_{\sun}$ are particularly useful for these studies. The $γ$ Dor stars pulsate in high-order $g$ modes with periods of order 1 day, driven by convective blocking at the base of their envelope convection zone. The $δ$ Sct stars pulsate in low-order $g$ and $p$ modes with periods of order 2 hours, driven by the $κ$ mechanism operating in the Heii ionization zone. Theory predicts an overlap region in t…
CONTEXT. Gamma Doradus stars (hereafter gamma Dor stars) are known to exhibit gravity- and/or gravito-intertial modes that probe the inner stellar region near the convective core boundary. The non-equidistant spacing of the pulsation periods is an observational signature of the stars' evolution and current internal structure and is heavily influenced by rotation. AIMS. We aim to constrain the near-core rotation rates for a sample of gamma Dor stars, for which we have detected period spacing patterns. METHODS. We combined the asymptotic period spacing with the traditional approximation of stell…
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 $Π_0$), 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 $γ~$Doradus ($γ~$Dor) stars whose rotation frequency has been derived from $\textit{Kepler}$ photometry. We make use of two 6D grids of stellar models, one with s…
Convective envelopes in stars on the main sequence are usually connected only with stars of spectral types F5 or later. However, observations as well as theory indicate that the convective outer layers in earlier stars, despite being shallow, are still effective and turbulent enough to stochastically excite oscillations. Because of the low amplitudes, exploring stochastically excited pulsations became possible only with space missions such as Kepler and CoRoT. Here I review the recent results and discuss among others, pulsators such as delta Scuti, gamma Doradus, roAp, beta Cephei, Slowly Puls…
We present multidimensional modeling of convection and oscillations in main-sequence stars somewhat more massive than the Sun, using three separate approaches: 1) Using the 3-D planar StellarBox radiation hydrodynamics code to model the envelope convection zone and part of the radiative zone. Our goals are to examine the interaction of stellar pulsations with turbulent convection in the envelope, excitation of acoustic modes, and the role of convective overshooting; 2) Applying the spherical 3-D MHD ASH (Anelastic Spherical Harmonics) code to simulate the core convection and radiative zone. Ou…
We present the characterization of KIC 4142768, an eclipsing binary with two evolved A-type stars in an eccentric orbit with a period of 14 days. We measure the fundamental parameters of the two components ($M_1=2.05M_{\odot}, R_1=2.96R_{\odot}$ and $M_2=2.05M_{\odot}, R_2=2.51R_{\odot}$) by combining {\it Kepler} photometry and spectra from {\it Keck} HIRES. The measured surface rotation rates are only one-fifth of the pseudo-synchronous rate of the eccentric orbit. Fourier spectrum of the light curve reveals hybrid pulsations of $δ$ Scuti and $γ$ Doradus type, with pulsation frequencies at a…
We report the discovery of a post-mass transfer Gamma Doradus/Delta Scuti hybrid pulsator in the eclipsing binary KIC~9592855. This binary has a circular orbit, an orbital period of 1.2 days, and contains two stars of almost identical masses ($M_1=1.72M_{\odot}, M_2=1.71M_{\odot}$). However, the cooler secondary star is more evolved ($R_2=1.96R_{\odot}$) while the hotter primary is still on the zero-age-main-sequence ($R_1=1.53R_{\odot}$). Coeval models from single star evolution cannot explain the observed masses and radii, and binary evolution with mass-transfer needs to be invoked. After su…
Slowly pulsating B stars (SPB) and $γ$ Dor stars pulsate in high-order gravity (g-) modes. The frequencies of g-modes are sensitive to the detailed structure and evolution history of stars having convective cores. Receding convective cores in OB-type stars leave behind a chemically inhomogenous $\nabla_μ>0$ radiative zone. Once a g-mode has radial nodes near the boundaries of these layers, the mode gets trapped and its period deviates from asymptotic period spacing. Careful study of such trapped modes allows constraining the extent of such layers by fitting individual pulsation frequencies. We…
Core-envelope coupling of gravito-inertial waves in pre-main-sequence solar-type stars
INAF – Osservatorio Astrofisico di Catania（意大利国家天体物理研究所卡塔尼亚天文台）；STAR Institute, Université de Liège（列日大学STAR研究所）；Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM（巴黎萨克雷大学、巴黎西岱大学、法国原子能和替代能源委员会、法国国家科学研究中心、天体物理学和分子生物学研究所）；Institute of Science and Technology Austria (ISTA)（奥地利科学与技术研究所）；INAF – IAPS, Istituto di Astrofisica e Planetologia Spaziali（意大利国家天体物理研究所空间天体物理学和行星学研究所）；Universität Innsbruck, Institut für Astro- und Teilchenphysik（因斯布鲁克大学天体与粒子物理研究所）
The Kepler spacecraft is providing time series of photometric data with micromagnitude precision for hundreds of A-F type stars. We present a first general characterization of the pulsational behaviour of A-F type stars as observed in the Kepler light curves of a sample of 750 candidate A-F type stars. We propose three main groups to describe the observed variety in pulsating A-F type stars: gamma Dor, delta Sct, and hybrid stars. We assign 63% of our sample to one of the three groups, and identify the remaining part as rotationally modulated/active stars, binaries, stars of different spectral…
KIC 7760680 is so far the richest slowly pulsating B star, by exhibiting 36 consecutive dipole ($\ell=1$) gravity (g-) modes. The monotonically decreasing period spacing of the series, in addition to the local dips in the pattern confirm that KIC 7760680 is a moderate rotator, with clear mode trapping in chemically inhomogeneous layers. We employ the traditional approximation of rotation to incorporate rotational effects on g-mode frequencies. Our detailed forward asteroseismic modelling of this g-mode series reveals that KIC 7760680 is a moderately rotating B star with mass $\sim3.25$ M$_\odo…
We find that low-degree low-order g-modes become unstable in metal-poor low-mass stars due to the $\varepsilon$-mechanism of the pp-chain. Since the outer convection zone of these stars is limited only to the very outer layers, the uncertainty in the treatment of convection does not affect the result significantly. The decrease in metallicity leads to decrease in opacity and hence increase in luminosity of a star. This makes the star compact and results in decrease in the density contrast, which is favorable to the $\varepsilon$-mechanism instability. We find also instability for high order g-…
We present the analysis of an eccentric, partially eclipsing long-period ($P=19.23$ d) binary system KIC 9777062 that contains main sequence stars near the turnoff of the intermediate age open cluster NGC 6811. The primary is a metal-lined Am star with a possible convective blueshift to its radial velocities, and one star (probably the secondary) is likely to be a $γ$ Dor pulsator. The component masses are $1.603\pm0.006$(stat.)$\pm0.016$(sys.) and $1.419\pm0.003\pm0.008 M_\odot$, and the radii are $1.744\pm0.004\pm0.002$ and $1.544\pm0.002\pm0.002 R_\odot$. The isochrone ages of the stars are…
Context: the theory of stellar evolution presents shortcomings when confronted with asteroseismic probes of interior physical properties. The differences between observations and theory are often great because stellar models have mainly been calibrated from observables connected to the surface of stars. Period-spacing patterns caused by gravity modes are a particularly powerful asteroseismic tool that are useful for probing the near-core rotation and mixing of chemical elements in main-sequence stars with convective cores. Aims: we aim to compose a catalog of intermediate-mass stars in the TES…
A scheme of Bayesian rotation inversion, which allows us to compute the probability of a model of a stellar rotational profile, is developed. The validation of the scheme with simple rotational profiles and the corresponding sets of artificially generated rotational shifts has been successfully carried out, and we can correctly distinguish the (right) rotational model, prepared beforehand for generating the artificial rotational shifts, with the other (wrong) rotational model. The Bayesian scheme is applied to a gamma Dor-delta Sct type hybrid star, KIC 11145123, leading to a result that the c…
