We discuss low-frequency g modes excited by resonant couplings with weakly unstable oscillatory convective modes in the rotating convective core in early-type main-sequence stars. Our non-adiabatic pulsation analyses including the effect of Coriolis force for $2\,M_\odot$ main-sequence models show that if the convective core rotates slightly faster than the surrounding radiative layers, g modes in the radiative envelope are excited by a resonance coupling. The frequency of the excited g mode in the inertial frame is close to $|mΩ_{\rm c}|$ with $m$ and $Ω_{\rm c}$ being the azimuthal order of the g mode and the rotation frequency of the convective core, respectively. These g mode frequencies are consistent with those of photometric rotational modulations and harmonics observed in many early-type main-sequence stars.
Context: we study the convection-pulsation coupling that occurs in cold Cepheids close to the red edge of the classical instability strip. In these stars, the surface convective zone is supposed to stabilise the radial oscillations excited by the kappa-mechanism. Aims: we study the influence of the convective motions onto the amplitude and the nonlinear saturation of acoustic modes excited by kappa-mechanism. We are interested in determining the physical conditions needed to lead to a quenching of oscillations by convection. Methods: we compute two-dimensional nonlinear simulations (DNS) of th…
delta Scuti variables are stars which exhibit periodic changes in their luminosity through radial and non-radial pulsations. Internally, these stars have relatively small convective cores, and convective overshoot can significantly affect the size. Recently, models of radial pulsation in delta Scuti stars found a strong correlation between the pulsation constant (Q) as a function of effective temperature and the amount of convective overshoot within the star. However, only models with metallicities of Z = 0.02 were examined, leaving the dependence of this relationship on chemical composition u…
We investigate the pulsational stability of massive (M >~ 120 Msun) main sequence stars of a range of metallicities, including primordial, Population III stars. We include a formulation of convective damping motivated by numerical simulations of the interaction between convection and periodic shear flows. We find that convective viscosity is likely strong enough to stabilize radial pulsations whenever nuclear-burning (the epsilon-mechanism) is the dominant source of driving. This suggests that massive main sequence stars with Z <~ 2 x 10^-3 are pulsationally stable and are unlikely to experien…
The Blazhko-phenomenon, the modulation of the pulsation of RR Lyrae stars remains one of the most stubborn unsolved problems of stellar pulsation. The recent idea of Stothers proposes that periodic variations in the properties of the convective envelope may be behind the amplitude and phase modulation. In this work we approximated the mechanism by introducing variations in the convective parameters of the Florida-Budapest hydrodynamic code and also by means of amplitude equations. We found that the process is only effective for long modulation periods, typically for more than hundred days, in …
Despite the appearance of two- and three-dimensional models thanks to the rapid growth of computing performance, numerical hydrocodes used to model radial stellar pulsations still apply a one-dimensional stellar envelope model without any realistic atmosphere, in which a significant improvement was the inclusion of turbulent convection. However, turbulent convection is an inherently multi-dimensional physical process in the vicinity of the ionization zones that generate pulsation. The description of these processes in one dimension can only be approximated based on simplified theoretical consi…
(abridged) Recent work on several beta Cephei stars has succeeded in constraining both their interior rotation profile and their convective core overshoot. In particular, a recent study focusing on theta$ Oph has shown that a convective core overshoot parameter of alpha = 0.44 is required to model the observed pulsation frequencies, significantly higher than for other stars of this type. We investigate the effects of rotation and overshoot in early type main sequence pulsators, and attempt to use the low order pulsation frequencies to constrain these parameters. This will be applied to a few t…
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 have developed a three-dimensional radiation hydrodynamics code to simulate the interaction of convection and radial pulsation in classical variable stars. One key goal is the ability to carry these simulations to full amplitude in order to compare them with observed light curves. Previous multi-dimensional calculations were prevented from reaching full amplitude because of drift in the radial coordinate system, due to the algorithm defining radial movement of the coordinate system during the pulsation cycle. We have removed this difficulty by defining our radial coordinate flow algorithm t…
In cold Cepheids close to the red edge of the classical instability strip, a strong coupling between the stellar pulsations and the surface convective motions occurs. This coupling is by now poorly described by 1-D models of convection, the so-called "time-dependent convection models" (TDC). The intrinsic weakness of such models comes from the large number of unconstrained free parameters entering in the description of turbulent convection. A way to overcome these limits is to compute two-dimensional direct simulations (DNS), in which all the nonlinearities are correctly solved. Two-dimensiona…
Tidal forces in eccentric binary stars known as heartbeat stars excite detectable oscillations that shed light on the processes of tidal synchronization and circularization. We examine the pulsation phases of tidally excited oscillations (TEOs) in heartbeat binary systems. The target list includes four published heartbeat binaries and four additional systems observed by {\it Kepler}. To the first order, the pulsation phases of TEOs can be explained by the geometric effect of the dominant $l=2$, $m=0$, or $\pm 2$ modes assuming pulsations are adiabatic. We found that this simple theoretical int…
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…
Harmonics as a Hidden Window into the Turbulent Convective Envelope of non-Blazhko RRab Stars
Institute of Theoretical Physics, Shanxi University（山西大学理论物理研究所）；State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（山西大学量子光学技术与器件国家重点实验室）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
Pulsation harmonics reveal the origin of the century-old Blazhko effect
Institute of Theoretical Physics, Shanxi University（山西大学理论物理研究所）；State Key Laboratory of Quantum Optics Technologies and Devices, Shanxi University（山西大学量子光学技术与器件国家重点实验室）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）
Three dimensional hydrodynamic simulations of full amplitude RR Lyrae stars have been computed for several models across the instability strip. The three dimensional nature of the calculations allows convection to be treated without reference to a phenomenological approach such as the local mixing length theory. Specifically, the time dependent interaction of the large scale eddies and the radial pulsation is controlled by the conservation laws, while the effects of smaller convective eddies are simulated by an eddy viscosity model. The light amplitudes for these calculations are quite similar…
We present results of the instability analysis of the post-main sequence massive star models against radial and nonradial pulsations. We confirm that both p- and g-modes can be excited by the $κ$-mechanism acting in the metal opacity bump. However, as opposed to the previous claims, we find that an intermediate convective zone (ICZ) related to the hydrogen burning shell is not necessary for excitation of g-modes. These modes can be reflected at a minimum of the Brunt-Väisälä frequency, located at the top of the chemical composition gradient region surrounding the radiative helium core. This mi…
We predict the flux and surface velocity perturbations produced by convectively excited gravity modes (g-modes) in main sequence stars. Core convection in massive stars can excite g-modes to sufficient amplitudes to be detectable with high precision photometry by Kepler and CoRoT, if the thickness of the convective overshoot region is < 30 per cent of a pressure scale height. The g-modes manifest as excess photometric variability, with amplitudes of ~ 10 micromagnitudes at frequencies ~ 10 microHz (0.8 1/d) near the solar metallicity zero-age main sequence. The flux variations are largest for …
Asteroseismology of non-radial pulsations in Hot B Subdwarfs (sdB stars) offers a unique view into the interior of core-helium-burning stars. Ground-based and space-borne high precision light curves allow for the analysis of pressure and gravity mode pulsations to probe the structure of sdB stars deep into the convective core. As such asteroseismological analysis provides an excellent opportunity to test our understanding of stellar evolution. In light of the newest constraints from asteroseismology of sdB and red clump stars, standard approaches of convective mixing in 1D stellar evolution mo…
Context: Observations of asymptotic giant branch (AGB) stars with increasing spatial resolution reveal new layers of complexity of atmospheric processes on a variety of scales. Aim: To analyze the physical mechanisms that cause asymmetries and surface structures in observed images, we use detailed 3D dynamical simulations of AGB stars; these simulations self-consistently describe convection and pulsations. Methods: We used the CO5BOLD radiation-hydrodynamics code to produce an exploratory grid of global "star-in-a-box" models of the outer convective envelope and the inner atmosphere of AGB sta…
As it is long known, the presence of a convective region creates a discontinuity in the chemical profile of a star, which in turn translates into a sharp variation of the adiabatic sound speed. This variation produces an oscillatory behavior of the pulsation frequencies, to which low degree p-modes are sensitive. We investigate the possibility of detecting the signature related to the presence of a convective core in the frequency spectrum of low-mass stars by means of suitable frequency combinations (such as separations and ratios)
We explore the role of mass loss and convective core overshoot in the evolution of Classical Cepheids. Stellar evolution models are computed with a recipe for pulsation-driven mass loss and it is found that mass loss alone is unable to account for the long-standing Cepheid mass discrepancy. However, the combination of mass loss and moderate convective core overshooting does provide a solution, bringing the amount of convective core overshooting in Cepheids closer to that found for other stars.
We have developed a multidimensional radiation hydrodynamics code to simulate the interaction of radial stellar pulsation and convection for full amplitude pulsating models. Convection is computed using large eddy simulations. Here we perform three-dimensional simulations of RR Lyrae stars for comparison with previously reported two-dimensional simulations. We find that the time dependent behavior of the peak convective flux on pulsation phase is very similar in both the two-dimensional and three-dimensional calculations. The growth rates of the pulsation in the two-dimensional calculations ar…
We present a grid on non-linear convective type-II Cepheid models. The dense model grids are computed for 0.6M_Sun and a range of metallicities ([Fe/H]=-2.0,-1.5,-1.0), and for 0.8M_Sun ([Fe/H]=-1.5). Two sets of convective parameters are considered. The models cover the full temperature extent of the classical instability strip, but are limited in luminosity; for the most luminous models violent pulsation leads to the decoupling of the outermost model shell. Hence, our survey reaches only the shortest period RV Tau domain. In the Hertzsprung-Russel diagram we detect two domains in which perio…
Opacity enhancements for stellar interior conditions have been explored to explain observed pulsation frequencies and to extend the pulsation instability region for B-type main-sequence variable stars. For these stars, the pulsations are driven in the region of the opacity bump of Fe-group elements at $\sim$200,000 K in the stellar envelope. Here we explore effects of opacity enhancements for the somewhat cooler main-sequence A-type stars, in which $p$-mode pulsations are driven instead in the second helium ionization region at $\sim$50,000 K. We compare models using the new LANL OPLIB vs. LLN…
This article reviews our current understanding of modelling convection dynamics in stars. Several semi-analytical time-dependent convection models have been proposed for pulsating one-dimensional stellar structures with different formulations for how the convective turbulent velocity field couples with the global stellar oscillations. In this review we put emphasis on two, widely used, time-dependent convection formulations for estimating pulsation properties in one-dimensional stellar models. Applications to pulsating stars are presented with results for oscillation properties, such as the ef…
Classical Cepheids are powerful probes of both stellar evolution and near-field cosmology thanks to their high luminosities, pulsations, and that they follow the Leavitt (Period-Luminosity) Law. However, there still exist a number of questions regarding their evolution, such as the role of rotation, convective core overshooting and winds. ln particular, how do these processes impact Cepheid evolution and the predicted fundamental properties such as stellar mass. In this work, we compare a sample of period change that are real-time observations of stellar evolution with new evolution models to …
IM Per is a triple star system whose eclipsing pair masses and radii are accurate to within 1 \%. The TESS light curve of the program target exhibits partial eclipses and multiple oscillations with mmag-level amplitudes. It is found that the oscillations affect eclipse timing measurements. Binary modeling of the high-quality TESS data indicates that the eclipsing components of the triple system are twin dwarfs with parameters of $M_2$/$M_1$ = 0.995, $R_2$/$R_1$ = 0.901, and $Δ$($T_{\rm eff,1}$--$T_{\rm eff,2}$) = 12 K in an eccentric ($e$ = 0.049), detached configuration. The third light of $l…
Hot DQ white dwarfs constitute a new class of white dwarf stars, uncovered recently within the framework of the SDSS project. Recently, three hot DQ white dwarfs have been reported to exhibit photometric variability with periods compatible with pulsation g-modes. Here, we present a nonadiabatic pulsation analysis of the recently discovered carbon-rich hot DQ white dwarf stars. One of our main aims is to test the convective-mixing picture for the origin of hot DQs through the pulsational properties. Our study relies on the full evolutionary models of hot DQ white dwarfs recently developed by Al…
Astrometric modeling of unresolved variable binary systems. II. Application to Gaia epoch astrometry of nearby pulsating and convective red giants
KU Leuven（荷语鲁汶大学）；Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS（巴黎天文台，巴黎文理研究大学，索邦大学，巴黎西岱大学，塞吉-蓬图瓦兹大学，法国国家科学研究中心）；French-Chilean Laboratory for Astronomy, IRL 3386, CNRS and U. de Chile（法智利天文学联合实验室，法国国家科学研究中心和智利大学）
Within the framework of non-local time-dependent stellar convection theory, we study in detail the effect of turbulent anisotropy on stellar pulsation stability. The results show that anisotropy has no substantial influence on pulsation stability of g modes and low-order (radial order $n_\mathrm{r}<5$) p modes. The effect of turbulent anisotropy increases as the radial order increases. When turbulent anisotropy is neglected, most of high-order ($n_\mathrm{r}>5$) p modes of all low-temperature stars become unstable. Fortunately, within a wide range of the anisotropic parameter $c_3$, stellar pu…
The envelopes of stars near the Eddington limit are prone to various instabilities. A high Eddington factor in connection with the Fe opacity peak leads to convective instability, and a corresponding envelope inflation may induce pulsational instability. Here, we investigate the occurrence and consequences of both instabilities in models of Wolf-Rayet stars. We determine the convective velocities in the sub-surface convective zones to estimate the amplitude of the turbulent velocity at the base of the wind that potentially leads to the formation of small-scale wind structures, as observed in s…
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…
Realistic stellar models are essential to the forward modelling approach in asteroseismology. For practicality however, certain model assumptions are also required. For example, in the case of subdwarf B stars, one usually starts with zero-age horizontal branch structures without following the progenitor evolution. We analyse the effects of common assumptions in subdwarf B models on the g-mode pulsational properties. We investigate if and how the pulsation periods are affected by the H-profile in the core-envelope transition zone. Furthermore, the effects of C-production and convective mixing …
Kepler observations of the star HD 187091 (KID 8112039, hereafter KOI-54) revealed a remarkable light curve exhibiting sharp periodic brightening events every 41.8 days with a superimposed set of oscillations forming a beating pattern in phase with the brightenings. Spectroscopic observations revealed that this is a binary star with a highly eccentric orbit, e=0.83. We are able to match the Kepler light curve and radial velocities with a nearly face-on (i=5.5 degree) binary star model in which the brightening events are caused by tidal distortion and irradiation of nearly identical A stars dur…
Non-local, time-dependent convection models have been used to explain the location of double-mode pulsations in Cepheids in the HR diagram as well as the existence and location of the red edge of the instability strip. These properties are highly sensitive to model parameters. We use 2D radiation hydrodynamical simulations with realistic microphysics and grey radiative-transfer to model a short period Cepheid. The simulations show that the strength of the convection zone varies significantly over the pulsation period and exhibits a phase shift relative to the variations in radius. We evaluate …
We present Kepler photometry and ground based spectroscopy of KIC 4544587, a short-period eccentric eclipsing binary system with self-excited pressure and gravity modes, tidally excited modes, tidally influenced p modes, and rapid apsidal motion of 182 y per cycle. The primary and secondary components of KIC 4544587 reside within the delta Scuti and gamma Dor instability region of the Hurtzsprung-Russell diagram, respectively. By applying the binary modelling software PHOEBE to prewhitened Kepler photometric data and radial velocity data obtained using the William Herschel Telescope and 4-m Ma…
HD49330 is a Be star that underwent an outburst during its five-month observation with the CoRoT satellite. An analysis of its light curve revealed several independent p and g pulsation modes, in addition to showing that the amplitude of the modes is directly correlated with the outburst. We modelled the results obtained with CoRoT. We modelled the flattening of the structure of the star due to rapid rotation in two ways: Chandrasekhar-Milne's expansion and 2D structure computed with ROTORC. We then modelled kappa-driven pulsations. We also adapted the formalism of the excitation and amplitude…
We investigate the pulsation driving mechanism responsible for the long-period photometric variations observed in LS IV-14°116, a subdwarf B star showing a He-enriched atmospheric composition. To this end, we perform detailed nonadiabatic pulsation computations over fully evolutionary post He-core-flash stellar structure models, appropriate for hot subdwarf stars at evolutionary phases previous to the He-core burning stage. We found that the variability of LS IV-14°116 can be attributed to nonradial g-mode pulsations excited by the ε-mechanism acting in the He-burning shells that appear before…
Long period variables, among them Miras, are thought to be pulsating. Under this approach the whole star inflates and deflates along a period that can vary from 100 to 900 days; that pulsation is assumed to produce shock waves on the outer layers of the star that propagate into the atmosphere and could account for the increase in luminosity and the presence of emission lines in the spectra of these stars. However, this paradigm can seriously be questioned from a theoretical point of view. First, in order to maintain a radial pulsation, the spherical symmetry of the star must be preserved: how …
Motivated by the recent detection of stochastically excited modes in the massive star V1449 Aql (Belkacem et al., 2009b), already known to be a $β$ Cephei, we theoretically investigate the driving by turbulent convection. By using a full non-adiabatic computation of the damping rates, together with a computation of the energy injection rates, we provide an estimate of the amplitudes of modes excited by both the convective region induced by the iron opacity bump and the convective core. Despite uncertainties in the dynamical properties of such convective regions, we demonstrate that both are ab…
We determine instability domains on the Hertzsprung-Russel diagram for rotating main sequence stars with masses 2-20 $\mathrm M_\odot$. The effects of the Coriolis force are treated in the framework of the traditional approximation. High-order g-modes with the harmonic degrees, $\ell$, up to 4 and mixed gravity-Rossby modes with $|m|$ up to 4 are considered. Including the effects of rotation results in wider instability strips for a given $\ell$ comparing to the non-rotating case and in an extension of the pulsational instability to hotter and more massive models. We present results for the fi…
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…
The recent analyses of the light curves provided by CoRoT have revealed pulsation spectra of unprecedented richness and precision, in particular, thousands of pulsating modes, and a clear distribution of amplitudes with frequency. In the community, some scientists have started doubting about the validity of the classical tools to analyze these very accurate light curves. This work provides the asteroseismic community with answers to this question showing that (1) it is physically possible for a star to excite at a time and with the observed amplitudes such a large number of modes; and (2) that…
We discuss non-linear excitation and amplitude saturation of $g$-modes, $r$-modes and overstable convective (OsC) modes in early type main sequence stars, taking account of the effects of three-mode couplings on amplitude evolutions. OsC modes are rotationally stabilized convective modes in the convective core and they resonantly excite low frequency $g$-modes to obtain large amplitudes in the envelope when the rotation rate of the core is larger than critical rates. We use, for a network of three-mode couplings, amplitude equations governing the time evolution of the mode amplitudes where eac…
We present the analysis of KIC 8164262, a heartbeat star with a high-amplitude (~1 mmag), tidally resonant pulsation (a mode in resonance with the orbit) at 229 times the orbital frequency and a plethora of tidally induced g-mode pulsations (modes excited by the orbit). The analysis combines Kepler light curves with follow-up spectroscopic data from the Keck telescope, KPNO (Kitt Peak National Observatory) 4-m Mayal telescope and the 2.7-m telescope at the McDonald observatory. We apply the binary modelling software, PHOEBE, to the Kepler light curve and radial velocity data to determine a det…
Gravito-acoustic modes in the Sun and other stars propagate in resonant cavities with a frequency below a given limit known as the cut-off frequency. At higher frequencies, waves are no longer trapped in the stellar interior and become traveller waves. In this article we study six pulsating solar-like stars at different evolutionary stages observed by the NASA Kepler mission. These high signal-to-noise targets show a peak structure that extends at very high frequencies and are good candidates for studying the transition region between the modes and the interference peaks or pseudo-modes. Follo…
Recent observation of the tidally-excited stellar oscillations in the main-sequence binary KOI-54 by the KEPLER satellite provides a unique opportunity for studying dynamical tides in eccentric binary systems. We develop a general theory of tidal excitation of oscillation modes of rotating binary stars, and apply our theory to tidally excited gravity modes (g-modes) in KOI-54. The strongest observed oscillations, which occur at 90 and 91 times the orbital frequency, are likely due to prograde m=2 modes (relative to the stellar spin axis) locked in resonance with the orbit. The remaining flux o…
We review the main results obtained from our seismic studies of B-type main sequence pulsators, based on the ground-based, MOST, Kepler and BRITE observations. Important constraints on stellar opacities, convective overshooting and rotation are derived. In each studied case, a significant modification of the opacity profile at the depths corresponding to the temperature range $\log{T}\in (5.0-5.5)$ is indispensable to explain all pulsational properties. In particular, a huge amount of opacity (at least 200\%) at the depth of the temperature $\log T = 5.46$ (the "nickel" opacity) has to be adde…
Evolutionary tracks and pulsational analysis of models with masses of 13-18 $M_\odot$ are presented. We address two important questions. The first one deals with one of the most unresolved problems in astrophysics, i.e., the existence of a blue loop after core helium ignition; the so called "to loop or not to loop" problem. We show that inward overshooting from the outer convective zone in the red giant phase is prerequisite for the development of the blue loop. Our second question concerns pulsational instability of models in the core helium burning phase. We present for the first time that m…
We present results from a detailed analysis of theoretical and observed light curves of classical Cepheid variables in the Galaxy and the Magellanic Clouds. Theoretical light curves of Cepheid variables are based on non-linear convective hydrodynamical pulsation models and the observational data are taken from the ongoing wide-field variability surveys. The variation in theoretical and observed light curve parameters as a function of period, wavelength and metallicity is used to constrain the input physics to the pulsation models, such as the mass-luminosity relations obeyed by Cepheid variabl…
We have computed linear non-adiabatic oscillations of luminous red giants using a non-local and anisotropic time-dependent theory of convection. The results show that low-order radial modes can be self-excited. Their excitation is the result of radiation and the coupling between convection and oscillations. Turbulent pressure has important effects on the excitation of oscillations in red variables.
After an optical peak, a classical or recurrent nova settles into a brief (days to years) period of quasi-stable thermonuclear burning in a compact configuration nearly at the white dwarf (WD) radius. During this time, the underlying WD becomes visible as a strong emitter of supersoft X-rays. Observations during this phase have revealed oscillations in the X-ray emission with periods on the order of tens of seconds. A proposed explanation for the source of these oscillations are internal gravity waves excited by nuclear reactions at the base of the hydrogen-burning layer. In this work, we pres…
