Convective core entrainment in 1D main sequence stellar models

3D hydrodynamics models of deep stellar convection exhibit turbulent entrainment at the convective-radiative boundary which follows the entrainment law, varying with boundary penetrability. We implement the entrainment law in the 1D Geneva stellar evolution code. We then calculate models between 1.5 and 60 M⊙ at solar metallicity (Z = 0.014) and compare them to previous generations of models and observations on the main sequence. The boundary penetrability, quantified by the bulk Richardson number, RiB, varies with mass and to a smaller extent with time. The variation of RiB with mass is due to the mass dependence of typical convective velocities in the core and hence the luminosity of the star. The chemical gradient above the convective core dominates the variation of RiB with time. An entrainment law method can therefore explain the apparent mass dependence of convective boundary mixing through RiB. New models including entrainment can better reproduce the mass dependence of the main sequence width using entrainment law parameters A ∼ 2 × 10−4 and n = 1. We compare these empirically constrained values to the results of 3D hydrodynamics simulations and discuss implications.

Comparison of 2D and 3D compressible convection in a pre-main sequence star

Context. A 1D description of stellar dynamics is at the basis of stellar evolution modeling. Designed to investigate open problems in stellar evolution, the MUltidimensional Stellar Implicit Code expands a realistic 1D profile of a star’s internal structure to examine the interior dynamics of a specific star through either 2D or 3D hydrodynamic simulations. Aims. Extending our recent studies of 2D stellar convection to 3D stellar convection, we aim to compare 3D hydrodynamic simulations to identically set-up 2D simulations, for a realistic pre-main sequence star. Methods. We compare statistical quantities related to convective flows including: average velocity, vorticity, local enstrophy, and penetration depth beneath a convection zone. These statistics were produced during stationary, steady-state compressible convection in the star’s convection zone. Results. Our simulations confirm the common result that 2D simulations of stellar convection have a higher magnitude of velocity on average than 3D simulations. Boundary conditions and the extent of the spherical shell can affect the magnitude and variability of convective velocities. The difference between 2D and 3D velocities is dependent on these background points; in our simulations this can have an effect as large as the difference resulting from the dimensionality of the simulation. Nevertheless, radial velocities near the convective boundary are comparable in our 2D and 3D simulations. The average local enstrophy of the flow is lower for 2D simulations than for 3D simulations, indicating a different shape and structuring of 3D stellar convection. We performed a statistical analysis of the depth of convective penetration below the convection zone using the model proposed in our recent study (Pratt et al. 2017, A&A, 604, A125). That statistical model was developed based on 2D simulations, which allowed us to examine longer times and higher radial resolution than are possible in 3D. Here, we analyze the convective penetration in 3D simulations, and compare the results to identically set-up 2D simulations. In 3D simulations, the penetration depth is as large as the penetration depth calculated from 2D simulations.

Asymmetric shocks in χ Cygni observed with linear spectropolarimetry

Aims. We derive information about the dynamics of the stellar photosphere, including pulsation, from a coherent interpretation of the linear polarisation detected in the spectral lines of the Mira star χ Cyg. Methods. From spectropolarimetric observations of χ Cyg, we performed a careful analysis of the polarisation signals observed in atomic and molecular lines, both in absorption and emission, using radiative transfer in the context of polarisation produced through two mechanisms: intrinsic polarisation and continuum depolarisation. We also explain the observed line doubling phenomenon in terms of an expanding shell in spherical geometry, which allows us to pinpoint the coordinates over the stellar disc with enhanced polarisation. Results. We find that the polarised spectrum of χ Cyg is dominated by intrinsic polarisation and has a negligible continuum depolarisation. The observed polarised signals can only be explained by assuming that this polarisation is locally enhanced by velocity fields. During the pulsation, radial velocities are not homogeneous over the disc. We map these regions of enhanced velocities. Conclusions. We set an algorithm to distinguish the origin of this polarisation in any stellar spectra of linear polarisation and to find a way to increase the signal by coherently adding many lines with an appropriated weight. Applied to the Mira star χ Cyg, we reached the unexpected result that during the pulsation, velocities are radial but not homogeneous over the disc. The reason for these local velocity enhancements are probably related to the interplay between the atmospheric pulsation dynamics and the underlying stellar convection.

Modelling differential rotation of red giants: the case of the evolved sun

ABSTRACT Asteroseismology has revealed that cores of red giants rotate about one order of magnitude faster than their convective envelopes. This paper attempts an explanation for this rotational state in terms of the theory of angular momentum transport in stellar convection zones. A differential rotation model based on the theory is applied to a sequence of evolutionary states of a red giant of one solar mass. The model computations show a rotation of about ten times faster in the cores compared to the stellar surface. This rotational state is caused by the non-diffusive downward convective transport of angular momentum. The contrast in rotational rates between core and envelope increases with the radius (age) of the star. Seismologically detected scaling for the spin-down of the giants’ cores is also reproduced.

A well-balanced scheme for the simulation tool-kit A-MaZe: implementation, tests, and first applications to stellar structure

Characterizing stellar convection in multiple dimensions is a topic at the forefront of stellar astrophysics. Numerical simulations are an essential tool for this task. We present an extension of the existing numerical tool-kit A-MaZe that enables such simulations of stratified flows in a gravitational field. The finite-volume based, cell-centered, and time-explicit hydrodynamics solver of A-MaZe was extended such that the scheme is now well-balanced in both momentum and energy. The algorithm maintains an initially static balance between gravity and pressure to machine precision. Quasi-stationary convection in slab-geometry preserves gas energy (internal plus kinetic) on average, despite strong local up- and down-drafts. By contrast, a more standard numerical scheme is demonstrated to result in substantial gains of energy within a short time on purely numerical grounds. The test is further used to point out the role of dimensionality, viscosity, and Rayleigh number for compressible convection. Applications to a young sun in 2D and 3D, covering a part of the inner radiative zone, as well as the outer convective zone, demonstrate that the scheme meets its initial design goal. Comparison with results obtained for a physically identical setup with a time-implicit code show qualitative agreement.

Turbulence, magnetism, and transport inside stars

We present recent progress made in modelling stars and their turbulent magnetized dynamics in 3-D. This work is inspired by many years of discussion with Jean-Paul Zahn. I (ASB) first met him as a professor of astrophysical fluid dynamics (AFD) at the Paris-Meudon observatory's graduate school of astrophysics in 1994–1995. He made me the honor of accepting to be my PhD's advisor (1995–1998). He then supported me during my postdoc years in Boulder with his long time friend Prof. Juri Toomre between January 1999 and December 2002 and through the difficult process of getting a tenure position, and then since as a tenure researcher in Department of Astrophysics at CEA Paris-Saclay. I have been fortunate and lucky to share so many years discussing and doing scientific projects with Jean-Paul. As I was getting more experienced and started supervising my own students, he was always available, guiding us with his acute scientific vista and encouraging them. Antoine Strugarek, who co-author this paper, was like me fortunate to share Jean-Paul's knowledge. The three of us published several papers together during Antoine's PhD (2009–2012) addressing the dynamics of the solar tachocline and its interplay with convection. We miss him greatly. In this paper, we discuss mainly two topics that benefited from Jean-Paul's deep understanding of AFD: a) the dynamics of the solar tachocline and angular momentum transport in stellar interior and b) turbulent convection and dynamo action in stellar convection zones.

On long-duration 3D simulations of stellar convection using ANTARES

We present initial results from three-dimensional (3-D) radiation hydrodynamical simulations for the Sun and targeted Sun-like stars. We plan to extend these simulations up to several stellar days to study p-mode excitation and damping processes. The level of variation of irradiance on the time scales spanned by our 3-D simulations will be studied too. Here we show results from a first analysis of the computational data we produced so far.