Semi-convection: What is the underlying physical context?
Arlette Noels
备注：
12 pages, 6 figures, in "Studying stellar Rotation and Convection", Lecture Notes in Physics (Springer Verlag, Berlin), M.J. Goupil, K. Belkacem, C. Neiner, F. Lignières, and J. J. Green (eds)
Stellar conditions leading to a possible semi-convective mixing are discussed in three relevant cases: (1) low mass MS stars in which the CNO cycle takes progressively the lead over the PP chain due to the increase in temperature as core hydrogen burning proceeds, (2) massive MS stars which experience a large contri- bution of the radiation pressure to the total pressure and (3) core helium burning stars for which the production of carbon in the core increases the opacity. A short discussion of semi-convection in terms of instability of non radial modes follows.
Properties of semi-convection and core convective overshooting of stars with 15 $M_{\odot}$ and 30 $M_{\odot}$ are calculated in the present paper. New methods are used to deal with semi-convection. Different entropy gradient is used when adopting the Schwarzschild method and the Ledoux method which are used to confine the convective boundary and to calculate the turbulent quantities: $\frac{\partial \overline{s}}{\partial r}=-\frac{c_{p}}{H_P}(\nabla-\nabla_{\rm ad})$ when the Schwarzschild method is adopted and $\frac{\partial \overline{s}}{\partial r}=-\frac{c_{p}}{H_P}(\nabla-\nabla_{\rm a…
Semi-convection is a slow mixing process in chemically-inhomogeneous radiative interiors of stars. In massive OB stars, it is important during the main sequence. However, the efficiency of this mixing mechanism is not properly gauged yet. Here, we argue that asteroseismology of $β$ Cep pulsators is capable of distinguishing between models of varying semi-convection efficiencies. We address this in the light of upcoming high-precision space photometry to be obtained with the Kepler two-wheel mission for massive stars along the ecliptic.
We report on modelling in stellar astrophysics with the ANTARES code. First, we describe properties of turbulence in solar granulation as seen in high-resolution calculations. Then, we turn to the first 2D model of pulsation-convection interaction in a cepheid. We discuss properties of the outer and the HEII ionization zone. Thirdly, we report on our work regarding models of semiconvection in the context of stellar physics.
When a planet falls onto the surface of its host star, the added high-metallicity material does not remain in the surface layers, as often assumed, but is diluted into the interior through fingering (thermohaline) convection. Until now, however, the timescale over which this process happens remained very poorly constrained. Using recently-measured turbulent mixing rates for fingering convection, I provide reliable numerical and semi-analytical estimates for the rate at which the added heavy elements drain into the interior. I find that the relative metallicity enhancement post-infall drops by …
The recent progress in high-spatial-resolution techniques, spanning wavelengths from the visual to the radio regime, is leading to new valuable insights into the complex dynamical atmospheres of Asymptotic Giant Branch (AGB) stars and their wind forming regions. Striking examples are images of asymmetries and inhomogeneities in the photospheric and dust-forming layers which vary on time-scales of months. These features are probably related to large-scale convective flows predicted by 3D star-in-a-box models. Furthermore, high-resolution observations make it possible to measure dust condensatio…
In a rigidly-rotating magnetohydrodynamic (MHD) system with convective turbulence, a large-scale dynamo, categorized as the $α^2$-type, can be excited when the spin rate is large enough. In this paper, the rotational dependence of the $α^2$-type dynamo and the cause of it are explored by mean-field (MF) dynamo models coupled with direct numerical simulations (DNSs) of MHD convections. Bearing the application to the solar/stellar dynamo in mind, we adopt a strongly-stratified polytrope as a model of the convective atmosphere. Our DNS models show that the $α^2$-type dynamo is excited when ${\rm …
The modelling of massive star evolution is a complex task, and is very sensitive to the way physical processes (such as convection, rotation, mass loss, etc.) are included in stellar evolution code. Moreover, the very high observed fraction of binary systems among massive stars makes the comparison with observations difficult. In this paper, we focus on discussing the uncertainties linked to the modelling of convection and rotation in single massive stars.
Regions of stellar and planetary interiors that are unstable according to the Schwarzschild criterion, but stable according to the Ledoux criterion, are subject to a form of oscillatory double-diffusive (ODD) convection often called "semi-convection". In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and composition by ODD convection, and ultimately propose a new 1D prescription that can be used in stellar and planetary structure and evolution models. The first paper in this series demonstrated that under certa…
We present the atmospheric structure and the fundamental parameters of three red supergiants, increasing the sample of RSGs observed by near-infrared spectro-interferometry. Additionally, we test possible mechanisms that may explain the large observed atmospheric extensions of RSGs. We carried out spectro-interferometric observations of 3 RSGs in the near-infrared K-band with the VLTI/AMBER instrument at medium spectral resolution. To comprehend the extended atmospheres, we compared our observational results to predictions by available hydrostatic PHOENIX, available 3-D convection, and new 1-D…
We study low frequency waves that propagate in a region of layered semi-convection. Layered semi-convection is predicted to be present in stellar and planetary interiors and can significantly modify the rate of thermal and compositional mixing. We derive a series of analytical dispersion relations for plane-parallel layered semi-convection in the Boussinesq approximation using a matrix transfer formalism. We find that like a continuously stratified medium, a semi-convective staircase -- in which small convective regions are separated by sharp density jumps -- supports internal gravity waves (g…
The process referred to as "semi-convection" in astrophysics and "double-diffusive convection in the diffusive regime" in Earth and planetary sciences, occurs in stellar and planetary interiors in regions which are stable according to the Ledoux criterion but unstable according to the Schwarzschild criterion. In this series of papers, we analyze the results of an extensive suite of 3D numerical simulations of the process, and ultimately propose a new 1D prescription for heat and compositional transport in this regime which can be used in stellar or planetary structure and evolution models. In …
The convective kissing instability in low-mass M-dwarf models: convective overshooting, semi-convection, luminosity functions, surface abundances and star cluster age dating
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…
Oscillatory double-diffusive convection (ODDC) (also known as semi- convection) refers to a type of double diffusive instability that occurs in regions of planetary and stellar interiors which have a destabilizing thermal stratification and a stabilizing mean molecular weight stratification. In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and chemical species by ODDC. Rosenblum et al. (2011) first showed that ODDC can either spontaneously form layers, which significantly enhance the transport of heat and chem…
Stars are changing entities in a constant evolution during their lives. At non-secular time scales (from seconds to years) the effect of dynamical processes such as convection, rotation, and magnetic fields can modify the stellar oscillations. Convection excites acoustic modes in solar-like stars, while rotation and magnetic fields can perturb the oscillation frequencies lifting the degeneracy in the azimuthal component m of the eigenfrequencies. Moreover, the interaction between rotation, convection, and magnetic fields can produce magnetic dynamos, which sometimes yield to regular magnetic a…
Many helioseismic measurements suffer from substantial systematic errors. A particularly frustrating one is that time-distance measurements suffer from a large center to limb effect which looks very similar to the finite light travel time, except that the magnitude depends on the observable used and can have the opposite sign Zhao et al. (2012). This has frustrated attempts to determine the deep meridional flow in the solar convection zone, with Zhao et al. (2012) applying an ad hoc correction with little physical basis to correct the data. In this letter we propose that part of this effect ca…
The solar convection zone exhibits a strong level of differential rotation, whereby the rotation period of the polar regions is about 25-30% longer than the equatorial regions. The Coriolis force associated with these zonal flows perpetually "pumps" the convection zone fluid, and maintains a quasi-steady circulation, poleward near the surface. What is the influence of this meridional circulation on the underlying radiative zone, and in particular, does it provide a significant source of mixing between the two regions? In Paper I, we began to study this question by assuming a fixed meridional f…
We have implemented open boundary conditions into the ANTARES code to increase the realism of our simulations of stellar surface convection. Even though we greatly benefit from the high accuracy of our fifth order numerical scheme (WENO5), the broader stencils needed for the numerical scheme complicate the implementation of boundary conditions. We show that the effective temperature of a numerical simulation cannot be changed by corrections at the lower boundary since the thermal stratification does only change on the Kelvin-Helmholtz time scale. Except for very shallow models, this time scale…
Iron-rich layers are known to form in the stellar subsurface through a combination of gravitational settling and radiative levitation. Their presence, nature and detailed structure can affect the excitation process of various stellar pulsation modes, and must therefore be modeled carefully in order to better interpret Kepler asteroseismic data. In this paper, we study the interplay between atomic diffusion and fingering convection in A-type stars, and its role in the establishment and evolution of iron accumulation layers. To do so, we use a combination of three-dimensional idealized numerical…
Both observations and numerical simulations show that stellar convective motions are composed of semi-regular flows of convective rolling cells and the fully developed turbulence. Although the convective rolling cells are crucial for the properties of the stellar convection that transports heat and mixes materials in the stellar interior, their contributions have not been included in turbulent convection models proposed up to now. We simplify the structure of the convective rolling cells as a cellular pattern moving circle by circle with different angular velocities around the center, estimati…
Although playing a key role in the understanding of the supernova phenomenon, the evolution of massive stars still suffers from uncertainties in their structure, even during their "quiet" main sequence phase and later on during their subgiant and helium burning phases. What is the extent of the mixed central region? In the local mixing length theory (LMLT) frame, are there structural differences using Schwarzschild or Ledoux convection criterion? Where are located the convective zone boundaries? Are there intermediate convection zones during MS and post-MS phase, and what is their extent and l…
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 di…
Double-diffusive convection, often referred to as semi-convection in astrophysics, occurs in thermally and compositionally stratified systems which are stable according to the Ledoux-criterion but unstable according to the Schwarzchild criterion. This process has been given relatively little attention so far, and its properties remain poorly constrained. In this paper, we present and analyze a set of three-dimensional simulations of this phenomenon in a Cartesian domain under the Boussinesq approximation. We find that in some cases the double-diffusive convection saturates into a state of homo…
Layered semi-convection is a possible candidate to explain Saturn's luminosity excess and the abnormally large radius of some hot Jupiters. In giant planet interiors, it could lead to the creation of density staircases, which are convective layers separated by thin stably stratified interfaces. We study the propagation of internal waves in a region of layered semi-convection, with the aim to predict energy transport by internal waves incident upon a density staircase. The goal is then to understand the resulting tidal dissipation when these waves are excited by other bodies such as moons in gi…
Much progress has recently been made in understanding and quantifying vertical mixing induced by double-diffusive instabilities such as fingering convection (usually called thermohaline convection) and oscillatory double-diffusive convection (a process closely related to semiconvection). This was prompted in parts by advances in supercomputing, which allow us to run Direct Numerical Simulations of these processes at parameter values approaching those relevant in stellar interiors, and in parts by recent theoretical developments in oceanography where such instabilities also occur. In this paper…
Meridional circulation in stellar convection zones is not generally well observed, but may be critical for MHD dynamos. Coriolis forces from differential rotation (DR) play a large role in determining what the meridional circulation is. Here we consider whether a stellar DR that is constant on cylinders concentric with the rotation axis can drive a meridional circulation.Conventional wisdom says that it can not. Using two related forms of governing equations that respectively estimate the longitudinal components of the curl of meridional mass flux and the vorticity, we show that such DR will d…
Continued progress in observational stellar astrophysics requires a deep understanding of the underlying convection dynamics. We present results of realistic 3D radiative hydrodynamic simulations of the outer layers of a moderate mass star (1.47 Msun), including the full convection zone, the overshoot region, and the top layers of the radiative zone. The simulation results show that the surface granulation has a broad range of scales, from 2 to 12 Mm, and that large granules are organized in well-defined clusters, consisting of several granules. Comparison of the mean structure profiles from 3…
The standard theory of pulsations deals with the frequencies and growth rates of infinitesimal perturbations in a stellar model. Modes which are calculated to be linearly driven should increase their amplitudes exponentially with time; the fact that nearly constant amplitudes are usually observed is evidence that nonlinear mechanisms inhibit the growth of finite amplitude pulsations. Models predict that the mass of convection zones in pulsating hydrogen-atmosphere (DAV) white dwarfs is very sensitive to temperature (i.e., $M_{\rm CZ} \propto T_{\rm eff}^{-90}$), leading to the possibility that…
Convective overshooting in super asymptotic giant branch stars has been suggested to lead to the formation of hybrid white dwarfs with carbon-oxygen cores and oxygen-neon mantles. As the white dwarf cools, this core-mantle configuration becomes convectively unstable and should mix. This mixing has been previously studied using stellar evolution calculations, but these made the approximation that convection did not affect the temperature profile of the mixed region. In this work, we perform direct numerical simulations of an idealized problem representing the core-mantle interface of the hybrid…
Aims: We aim at characterizing the inward transition from convective to radiative energy transport at the base of the convective envelope of the solar-like oscillator HD 52265 recently observed by the CoRoT satellite. Methods: We investigated the origin of one specific feature found in the HD 52265 frequency spectrum. We modelled the star to derive the internal structure and the oscillation frequencies that best match the observations and used a seismic indicator sensitive to the properties of the base of the envelope convection zone. Results: The seismic indicators clearly reveal that to best…
We seek to understand the transition from nearly axisymmetric configurations at solar rotation rates to nonaxisymmetric configurations for rapid rotation using 3D numerical simulations of turbulent convection and considering rotation rates between 1 and 30 times the solar value. We find a transition from axi- to nonaxisymmetric solutions at around 1.8 times the solar rotation rate. This transition coincides with a change in the rotation profile from antisolar- to solar-like differential rotation with a faster equator and slow poles. In the solar-like rotation regime, the field configuration co…
We conduct one-dimensional stellar evolution simulations in the mass range $13-20 M_{\odot}$ to late core collapse times and find that an inner vigorous convective zone with large specific angular momentum fluctuations appears at the edge of the iron core during the collapse. The compression of this zone during the collapse increases the luminosity there and the convective velocities, such that the specific angular momentum fluctuations are of the order of j_{conv}~5x10^15cm^2/sec. If we consider that three-dimensional simulations show convective velocities that are three to four times larger …
