The scale length over which convection mixes mass in a star can be calculated as the inverse of the vertical derivative of the unidirectional (up or down) mass flux. This is related to the mixing length in the mixing length theory of stellar convection. We give the ratio of mass mixing length to pressure scale height for a grid of 3D surface convection simulations, covering from 4300\,K to 6900\,K on the main-sequence, and up to giants at $\log g = 2.2$, all for solar composition. These simulations also confirm what is already known from solar simulations, that convection doesn't proceed by discrete convective elements, but rather as a continuous, slow, smooth, warm upflow and turbulent, entropy deficient, fast down drafts. This convective topology also results in mixing on a scale as that of the classic mixing length formulation, and is simply a consequence of mass conservation on flows in a stratified atmosphere.
We report the results of a magneto-hydrodynamic (MHD) simulation of a convective dynamo in a model solar convective envelope driven by the solar radiative diffusive heat flux. The convective dynamo produces a large-scale mean magnetic field that exhibits irregular cyclic behavior with oscillation time scales ranging from about 5 to 15 years and undergoes irregular polarity reversals. The mean axisymmetric toroidal magnetic field is of opposite signs in the two hemispheres and is concentrated at the bottom of the convection zone. The presence of the magnetic fields is found to play an important…
Tidally-excited inertial waves in stellar convective regions are a key mechanism for tidal dissipation in stars and therefore the evolution of close-in binary or planetary systems. As a first step, we explore here the impact of latitudinal differential rotation on the properties of free inertial modes and identify the different families of modes. We show that they differ from the case of solid-body rotation. Using an analytical approach as well as numerical calculations, we conclude that critical layers (where the Doppler-shifted frequency vanishes) could play a very important role for tidal d…
We present results of convective turbulent dynamo simulations including a coronal layer in a spherical wedge. We find an equatorward migration of the radial and azimuthal fields similar to the behavior of sunspots during the solar cycle. The migration of the field coexist with a spoke-like differential rotation and anti-solar (clockwise) meridional circulation. Even though the migration extends over the whole convection zone, the mechanism causing this is not yet fully understood.
The stratification near the base of the Sun's convective envelope is governed by processes of convective overshooting and element diffusion, and the region is widely believed to play a key role in the solar dynamo. The stratification in that region gives rise to a characteristic signal in the frequencies of solar p modes, which has been used to determine the depth of the solar convection zone and to investigate the extent of convective overshoot. Previous helioseismic investigations have shown that the Sun's spherically symmetric stratification in this region is smoother than that in a standar…
Recent spectropolarimetric observations of otherwise ordinary G, K, and M giants revealed localized magnetic strips in the HRD coincident with the regions where the first dredge-up and core He-burning occur. We seek to understand the origin of magnetic fields in such late-type giant stars. In analogy with late-type dwarf stars, we focus primarily on parameters known to influence the generation of magnetic fields in the outer convective envelope. We compute the classical dynamo parameters along the evolutionary tracks of low- and intermediate-mass stars at various metallicities using stellar mo…
The observed radii of M dwarfs in eclipsing binaries exceed predicted radii by ~ 5%. To investigate this anomaly, the structure of low-mass stars irradiated by a close companion is considered. Irradiation modifies the surface boundary conditions and thereby also the adiabatic constants of their outer convection zones. This changes the models' radii and luminosities. For short-period M dwarf binaries with components of similar mass, radius inflation due to their mutual irradiation is found to be < 0.4%. This is an order of magnitude too small to explain the observed anomaly. Although stronger i…
A calibration of the mixing-length parameter in the local mixing-length theory (MLT) is presented for the lower part of the convection zone in pure-hydrogen atmosphere white dwarfs. The parameterization is performed from a comparison of 3D CO5BOLD simulations with a grid of 1D envelopes with a varying mixing-length parameter. In many instances, the 3D simulations are restricted to the upper part of the convection zone. The hydrodynamical calculations suggest, in those cases, that the entropy of the upflows does not change significantly from the bottom of the convection zone to regions immediat…
Eruptive mass loss likely produces the energetic outbursts observed from some massive stars before they undergo core-collapse supernovae (CCSNe). The resulting dense circumstellar medium (CSM) may also cause the subsequent SNe to be observed as Type IIn events. The leading hypothesis of the cause of these outbursts is the response of the envelope of the red supergiant (RSG) progenitor to energy deposition in the months to years prior to collapse. Early theoretical studies of this phenomena were limited to 1D, leaving the 3D convective RSG structure unaddressed. Using FLASH's hydrodynamic capab…
Over time, tides synchronize the rotation periods of stars in a binary system to the orbital period. However, if the star exhibits differential rotation then only a portion of it can rotate at the orbital period, so the rotation period at the surface may not match the orbital period. The difference between the rotation and orbital periods can therefore be used to infer the extent of the differential rotation. We use a simple parameterization of differential rotation in stars with convective envelopes in circular orbits to predict the difference between the surface rotation period and the orbit…
The treatment of convective boundaries remains an important source of uncertainty within stellar evolution, with drastic implications for the thermally-pulsing stars on the Asymptotic Giant Branch (AGB). Various sources are taken as motivation for the incorporation of convective boundary mixing during this phase, from s-process nucleosynthesis to hydrodynamical models. In spite of the considerable evidence in favour of the existence of convective boundary mixing on the pre-AGB evolution, this mixing is not universally included in models of TP-AGB stars. The aim of this investigation is to asce…
Recent 3D-simulations have shown that the turbulent kinetic flux (TKF) is significant. We discuss the effects of TKF on the size of convection zone and find that the TKF may help to solve the solar abundance problem. The solar abundance problem is that, with new abundances, the solar convection zone depth, sound speed in the radiative interior, the helium abundance and density in the convective envelope are not in agreement with helioseismic inversions. We have done Monte Carlo simulations on solar convective envelope models with different profile of TKF to test the effects. The solar abundanc…
We describe a 3D finite-difference spherical anelastic MHD (FSAM) code for modeling the subsonic dynamic processes in the solar convective envelope. A comparison of this code with the widely used global spectral anlastic MHD code, ASH (Anelastic Spherical Harmonics), shows that FSAM produces convective flows with statistical properties and mean flows similar to the ASH results. Using FSAM, we first simulate the rotating solar convection in a partial spherical shell domain and obtain a statistically steady, giant-cell convective flow with a solar-like differential rotation. We then insert buoya…
Results of evolutionary modelling of subdwarf B stars are presented. For the first time, we explore the core and near-core mixing in the subdwarf B stars using new algorithms available in the MESA code: the predictive mixing scheme and the convective premixing scheme. We show how both methods handle the problems with determination of convective boundary, discrepancy between core masses obtained from asteroseismology and evolutionary models, and long-standing problems related to the core-helium-burning phase such as splitting of the convective core and the occurrence of breathing pulses. We fin…
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 report on the results of four convective dynamo simulations with an outer coronal layer. The magnetic field is self-consistently generated by the convective motions beneath the surface. Above the convection zone, we include a polytropic layer that extends to 1.6 solar radii. The temperature increases in this region to $\approx8$ times the value at the surface, corresponding to $\approx1.2$ times the value at the bottom of the spherical shell. We associate this region with the solar corona. We find solar-like differential rotation with radial contours of constant rotation rate, together with…
We present the evolution of a 6M$_{\odot}$ star, of solar-like initial metallicity, and investigate the effects of key nuclear reaction rates, as well as the treatment of the convective mixing on its evolution along the Cepheid instability strip. In particular, we study the effect of recent estimates of the $^{14}$N(p,γ)$^{15}$O reaction on the formation and extension of the blue loop during core helium burning. We also investigate the effects induced on this blue loop by the adoption of non-standard convective mixing prescriptions, as well as the implications of modifying the Mixing Length Th…
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）
The $s$-process nucleosynthesis in Asymptotic Giant Branch (AGB) stars depends on the modeling of convective boundaries. We present models and s-process simulations that adopt a treatment of convective boundaries based on the results of hydrodynamic simulations and on the theory of mixing due to gravity waves in the vicinity of convective boundaries. Hydrodynamics simulations suggest the presence of convective boundary mixing (CBM) at the bottom of the thermal pulse-driven convective zone. Similarly, convection-induced mixing processes are proposed for the mixing below the convective envelope …
We explore the effects of an outer stably stratified coronal envelope on rotating turbulent convection, differential rotation, and large-scale dynamo action in spherical wedge models of the Sun. We solve the compressible magnetohydrodynamic equations in a two-layer model with unstable stratification below the surface, representing the convection zone, and a stably stratified coronal envelope above. The interface represents a free surface. We compare our model to models that have no coronal envelope. The presence of a coronal envelope is found to modify the Reynolds stress and the $Λ$ effect re…
We explore the three-dimensional properties of convective, luminous ($L\approx10^{4.5}-10^{5}L_\odot$), Hydrogen-rich envelopes of Red Supergiants (RSGs) based on radiation hydrodynamic simulations in spherical geometry using $\texttt{Athena++}$. These computations comprise $\approx30\%$ of the stellar volume, include gas and radiation pressure, and self-consistently track the gravitational potential for the outer $\approx 3M_\odot$ of the simulated $M\approx15M_\odot$ stars. This work reveals a radius, $R_\mathrm{corr}$, around which the nature of the convection changes. For $r>R_\mathrm{corr…
Mixing in the convective core is quite uncertain in core helium burning stars. In order to explore the overshooting mixing beyond the convective core, we incorporated the $k$-$ω$ proposed by Li (2012, 2017) into MESA, and investigated the overshooting mixing in evolution of sdB models. We found that the development of the convective core can be divided into three stages. When the radiative temperature gradient $\nabla_{\rm rad}$ monotonically decreases from the stellar center, the overshooting mixing presents a behaviour of exponential decay similar with Herwig (2000), and the overshooting dis…
We review the current state of knowledge of magnetic fields inside stars, concentrating on recent developments concerning magnetic fields in stably stratified (zones of) stars, leaving out convective dynamo theories and observations of convective envelopes. We include the observational properties of A, B and O-type main-sequence stars, which have radiative envelopes, and the fossil field model which is normally invoked to explain the strong fields sometimes seen in these stars. Observations seem to show that Ap-type stable fields are excluded in stars with convective envelopes. Most stars cont…
The evolution of stars born with a convective core is highly dependent on the efficiency and extent of near core mixing processes, which effectively increases both the core mass and main-sequence lifetime. We investigate to what extent gravity-mode period spacings in slowly pulsating B-type stars observed by the Kepler mission can be used to constrain both the shape and extent of convective core overshoot and additional mixing in the radiative envelope. We compute grids of 1D stellar structure and evolution models for two different shapes of convective core overshooting and three shapes of rad…
Observations indicate that the convective cores of stars must ingest a substantial amount of material from the overlying radiative zone, but the extent of this mixing and the mechanism which causes it remain uncertain. Recently, Anders et al. (2021) developed a theory of convective penetration and calibrated it with 3D numerical hydrodynamics simulations. Here we employ that theory to predict the extent of convective boundary mixing in early-type main-sequence stars. We find that convective penetration produces enough mixing to explain core masses inferred from asteroseismology and eclipsing b…
Convective boundary mixing is one of the major uncertainties in stellar evolution. In order to study its dependence on boundary properties and turbulence strength in a controlled way, we computed a series of 3D hydrodynamical simulations of stellar convection during carbon burning with a varying boosting factor of the driving luminosity. Our 3D implicit large eddy simulations were computed with the PROMPI code. We performed a mean field analysis of the simulations within the Reynolds-averaged Navier-Stokes framework. Both the vertical RMS velocity within the convective region and the bulk Rich…
Star-planet tidal interactions may result in the excitation of inertial waves in the convective region of stars. In low-mass stars, their dissipation plays a prominent role in the long-term orbital evolution of short-period planets. Turbulent convection can sustain differential rotation in their envelope, with an equatorial acceleration (as in the Sun) or deceleration, which can modify the waves' propagation properties. We explore in this first paper the general propagation properties of free linear inertial waves in a differentially rotating homogeneous fluid inside a spherical shell. We assu…
We calculate overstable convective (OsC) modes of $2M_\odot$, $4M_\odot$, and $20M_\odot$ main sequence stars. To compute non-adiabatic OsC modes in the core, we assume $(\nabla\cdot\vec{F}_C)^\prime=0$ as a prescription for the approximation called frozen-in convection in pulsating stars where $\vec{F}_C$ is the convective energy flux and the prime $^\prime$ indicates Eulerian perturbation. We find that the general properties of the OsC modes are roughly the same as those obtained by Lee \& Saio (2020) who assumed $δ(\nabla\cdot\vec{F}_C)=0$, except that no OsC modes behave like inertial mode…
Massive ($M >30\,$M$_{\odot}$) stars exhibit luminosities that are near the Eddington-limit for electron scattering causing the increase in opacity associated with iron at $T\approx180,000\,$K to trigger supersonic convection in their outer envelopes. Three dimensional radiative hydrodynamics simulations by Jiang and collaborators with the Athena++ computational tool have found order of magnitude density and radiative flux fluctuations in these convective regions, even at optical depths $\gg100$. We show here that radiation can diffuse out of a parcel during the timescale of convection in thes…
More than 1500 exoplanets have been discovered around a large diversity of host stars (from M- to A-type stars). Tidal dissipation in their convective envelope is a key actor that shapes the orbital architecture of short-period systems and that still remains unknown. Using a simplified two-layer assumption and grids of stellar models, we compute analytically an equivalent modified tidal quality factor, which is proportional to the inverse of the frequency-averaged dissipation due to the viscous friction applied by turbulent convection on tidal waves. It leads the conversion of their kinetic en…
Stellar convection is customarily described by Mixing-Length Theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and at all evolutionary phases. The aim o…
We re-analysed the carbon and oxygen isotopic ratios in the atmospheres of the two bright K giants Arcturus and Aldebaran. Previous determinations of their 16O/18O ratios showed a rough agreement with FDU expectations; however, the estimated 16O/17O and 12C/13C ratios were lower than in the canonical predictions. These anomalies are interpreted as signs of the occurrence of non-convective mixing episodes. We re-investigated this issue in order to verify whether the observed data can be reproduced in this hypothesis and if the well determined properties of the two stars can help us in fixing th…
Convective-core overshoot mixing is a significant uncertainty in stellar evolution. Because numerical simulations and turbulent convection models predict exponentially decreasing radial rms turbulent velocity, a popular treatment of the overshoot mixing is to apply a diffusion process with exponentially decreasing diffusion coefficient. It is important to investigate the parameters of the diffusion coefficient because they determine the efficiency of the mixing in the overshoot region. In this paper, we have investigated the effects of the core overshoot mixing on the properties of the core in…
Context. Convective regions in stellar models are always associated with uncertainties, for example due to extra-mixing or the possible inaccurate position of the transition from convective to radiative transport of energy. These have a strong impact on stellar models and their fundamental parameters. The most promising method to reduce these uncertainties is to use asteroseismology to derive diagnostics probing the structural characteristics of these regions. Aims. We wish to use custom-made integrated quantities to improve the capabilities of seismology to probe convective regions in stellar…
The spectral distribution of field white dwarfs shows a feature called the "non-DA gap". As defined by Bergeron et al., this is a temperature range (5100K--6100K) where relatively few non-DA stars are found, even though such stars are abundant on either side of the gap. It is usually viewed as an indication that a significant fraction of white dwarfs switch their atmospheric compositions back and forth between hydrogen-rich and helium-rich as they cool. In this paper, we present a Monte Carlo model of the Galactic disk white dwarf population, based on the spectral evolution model of Chen and H…
Twists in the flow: revisiting convective mixing in rotating stellar models. I. Effect on the stellar structure
Dartmouth College（达特茅斯学院）；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，天体物理学与分子间介质实验室）；KU Leuven（荷语鲁汶大学）；Radboud University Nijmegen（奈梅亨拉德堡德大学）；Max Planck Institute for Astronomy（马克斯·普朗克天文学研究所）
We revisit the problem of the formation of DB white dwarfs, as well as the origin of hydrogen in DBA stars, using a new set of envelope model calculations with stratified and mixed hydrogen/helium compositions. We first describe an approximate model to simulate the so-called convective dilution process, where a thin, superficial hydrogen radiative layer is gradually eroded by the underlying and more massive convective helium envelope, thus transforming a DA white dwarf into a DB star. We show that this convective dilution process is able to account for the large increase in the number of DB wh…
Since 1995, more than 1500 exoplanets have been discovered around a large diversity of host stars (from M- to A-type stars). Tidal dissipation in stellar convective envelopes is a key actor that shapes the orbital architecture of short-period systems. Our objective is to understand and evaluate how tidal dissipation in the convective envelope of low-mass stars (from M to F types) depends on their mass, evolutionary stage and rotation. Using a simplified two-layer assumption, we compute analytically the frequency-averaged tidal dissipation in their convective envelope. This dissipation is due t…
We present here, for the first time, a 2D study of the overshoot convective mechanism in nova outbursts for a wide range of possible compositions of the layer underlying the accreted envelope. Previous surveys studied this mechanism only for solar composition matter accreted on top of carbon oxygen (C-O) white dwarfs. Since, during the runaway, mixing with carbon enhances the hydrogen burning rates dramatically, one should question whether significant enrichment of the ejecta is possible also for other underlying compositions (He, O, Ne, Mg), predicted by stellar evolution models. We simulated…
Context: Internal chemical mixing in intermediate- and high-mass stars represents an immense uncertainty in stellar evolution models.In addition to extending the main-sequence lifetime, chemical mixing also appreciably increases the mass of the stellar core. Several studies have made attempts to calibrate the efficiency of different convective boundary mixing mechanisms, with sometimes seemingly conflicting results. Aims: We aim to demonstrate that stellar models regularly under-predict the masses of convective stellar cores. Methods: We gather convective core mass and fractional core hydrogen…
After off-center C ignition in the cores of super-AGB stars the C flame propagates all the way down to the center, trailing behind it the C-shell convective zone, and thus building a degenerate ONe core. This standard picture is obtained in stellar evolution simulations if the bottom C-shell convection boundary is assumed to be a discontinuity associated with a strict interpretation of the Schwarzschild condition for convective instability. However, this boundary is prone to additional mixing processes, such as thermohaline convection and convective boundary mixing. Using hydrodynamic simulati…
We use a thin flux tube model in a rotating spherical shell of turbulent convective flows to study how active region scale flux tubes rise buoyantly from the bottom of the convection zone to near the solar surface. We investigate toroidal flux tubes at the base of the convection zone with field strengths ranging from 15 kG to 100 kG at initial latitudes ranging from 1 degree to 40 degrees with a total flux of 10^22 Mx. We find that the dynamic evolution of the flux tube changes from convection dominated to magnetic buoyancy dominated as the initial field strength increases from 15 kG to 100 kG…
Convection plays a key role in the evolution of stars due to energy transport and mixing of composition. Despite its importance, this process is still not well understood. One longstanding conundrum in all 1D stellar evolution codes is the treatment of convective boundaries. In this study we compare two convective uncertainties, the boundary location (Ledoux versus Schwarzschild) and the amount of extra mixing, and their impact on the early evolution of massive stars. With increasing convective boundary mixing (CBM), we find a convergence of the two different boundary locations, a decreasing b…
The red-giant branch bump provides valuable information for the investigation of the internal structure of low-mass stars. Because current models are unable to accurately predict the occurrence and efficiency of mixing processes beyond convective boundaries, one can use the luminosity of the bump --- a diagnostic of the maximum extension of the convective envelope during the first-dredge up --- as a calibrator for such processes. By combining asteroseismic and spectroscopic constraints, we expand the analysis of the bump to masses and metallicities beyond those previously accessible using glob…
In solar-type stars (with radiative cores and convective envelopes), the magnetic field powers star spots, flares and other solar phenomena, as well as chromospheric and coronal emission at ultraviolet to X-ray wavelengths. The dynamo responsible for generating the field depends on the shearing of internal magnetic fields by differential rotation. The shearing has long been thought to take place in a boundary layer known as the tachocline between the radiative core and the convective envelope. Fully convective stars do not have a tachocline and their dynamo mechanism is expected to be very dif…
Based on the turbulent convection model (TCM), we investigate chemical mixing in the bottom overshooting region of the convective envelope of intermediate-mass stars, focusing on its influence on the formation and extension of blue loops in the Hertzsprung-Russell (HR) diagram. A diffusive mixing model is adopted during the Red Giant Branch (RGB) phase. The properties of the blue loop are changed by modification of the element profiles above the H-burning shell, which results from the incomplete mixing in the bottom overshooting region when stellar model evolves up along the RGB. Such modifica…
The helioseismic observations of the internal rotation profile of the Sun raise questions about the two-dimensional (2D) nature of the transport of angular momentum in stars. Here we derive a convective prescription for axisymmetric (2D) stellar evolution models. We describe the small scale motions by a spectrum of unstable linear modes in a Boussinesq fluid. Our saturation prescription makes use of the angular dependence of the linear dispersion relation to estimate the anisotropy of convective velocities. We are then able to provide closed form expressions for the thermal and angular momentu…
Recent hydrodynamical simulations of convection in a solar-like model suggest that penetrative convective flows at the boundary of the convective envelope modify the thermal background in the overshooting layer. Based on these results, we implement in one-dimensional stellar evolution codes a simple prescription to modify the temperature gradient below the convective boundary of a solar model. This simple prescription qualitatively reproduces the behaviour found in the hydrodynamical simulations, namely a local heating and smoothing of the temperature gradient below the convective boundary. We…
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…
