Hydrodynamical simulations with MUSIC
The MUlti-dimensional Stellar Implicit Code (MUSIC) is a time implicit numerical code that solves the fully compressible equations of hydrodynamics in multi-dimension. It has been designed to allow for the description of a complete stellar (or planetary) interior over timescales relevant to the study of evolutionary phases. The scientific motivation is to adress some fundamtental questions in stellar structure and evolution theories, like convective boudary mixing, angular momentum transport and turbulent convection.
Two-dimensional simulations of internal gravity waves in a 5 solar mass ZAMS model
Le Saux A. et al. (2023), MNRAS 522, 2
Main-sequence intermediate-mass stars present a radiative envelope that supports internal gravity waves (IGWs). Excited at the boundary with the convective core, IGWs propagate towards the stellar surface and are suspected to impact physical processes such as rotation and chemical mixing. Our results show that low-frequency waves excited by core convection are strongly impacted by radiative effects as they propagate. This impact depends on the radial profile of radiative diffusivity which increases by almost 5 orders of magnitude between the centre of the star and the top of the simulation domain. In the upper layers of the simulation domain, we observe an increase of the temperature. Our study suggests that this is due to heat added in these layers by IGWs damped by radiative diffusion. We show that non-linear effects linked to large amplitude IGWs may be relevant just above the convective core. Our results also highlight that direct comparison between numerical simulations with enhanced luminosity and observations must be made with caution. Finally, our work suggests that thermal effects linked to the damping of IGWs could have a non-negligible impact on stellar structure.
A study of convective core overshooting as a function of stellar mass based on 2D hydrodynamical simulations
Baraffe I., [...], Le Saux A. et al. (2023), MNRAS 519, 4
We perform two-dimensional (2D) numerical simulations of core convection for zero-age main-sequence stars covering a mass range from 3 to 20 solar masses. We study the efficiency of overshooting, which describes the ballistic process of convective flows crossing a convective boundary, as a function of stellar mass and luminosity. Applying the framework of extreme plume events previously developed for convective envelopes (see Pratt et al. 2017), we derive overshooting lengths as a function of stellar masses. We find that the overshooting distance scales with the stellar luminosity and the convective core radius. We derive a scaling law which is implemented in a one-dimensional stellar evolution code and the resulting stellar models are compared to observations. The scaling predicts values for the overshooting distance that significantly increase with stellar mass, in qualitative agreement with observations. Quantitatively, however, the predicted values are underestimated for masses larger 10 solar masses. Our 2D simulations show the formation of a nearly adiabatic layer just above the Schwarzschild boundary of the convective core, as exhibited in recent three-dimensional simulations of convection (see Anders et al. 2019).
Impact of radial truncation on solar-like models
Vlaykov D., [...], Le Saux A. et al. (2022), MNRAS 514, 1
The steep stratification in stellar interiors suggests that the radial extent of global simulations can affect the convection dynamics, the IGWs in the stably stratified radiative zone, and the depth of the overshooting layer. We investigate these effects using 2D simulations and compare eight different radial truncations of the same solar-like stellar model. We find that the location of the inner boundary has an insignificant effect on the convection dynamics, the convective overshooting, and the travelling IGWs. However, we find that extending the outer boundary by only a few per cent of the stellar radius significantly increases the velocity and temperature perturbations in the convection zone, the overshooting depth, the power and the spectral slope of the IGWs. The effect is related to the background conditions at the outer boundary, which are determined in essence by the hydrostatic stratification and the given luminosity.
Local heating due to convective overshooting and the solar modelling problem
Baraffe I., [...], Le Saux A. et al. (2022), A&A 659, A53
In this project we use results from our 2D simulations of solar-like models to face the solar modelling problem in 1D stellar evolution codes. We implement in 1D codes a simple prescription to modify the temperature gradient below the convective boundary of a solar model, similarly to what is observed in MUSIC simulations. We show that introducing local heating in the overshooting layer can reduce the sound-speed discrepancy usually reported between solar models and the structure of the Sun inferred from helioseismology.
Solar-like models is artifically enhanced luminosity
Hydrodynamical simulations can serve as alternative laboratory to study complex physical phenomena that are inherently 3D, non-linear and anisotropic. However, the wide range of time and length scales as well as the complex regime of parameters that characterise stellar interiors is a real challenge for numerical simulations. Typical timescales range from a couple of minutes for waves propagation, to billion of years for stellar lifetime. Characteristic lengthscales near the surface are of the order of a couple of meters whereas stellar radii can reach billions of meters. On an other side, some challenges are numerical such as computational time, temporal and spatial resolutions or numerical stability. Consequently, it is necessary to make approximations when setting up a new numerical model. This means approximations in how the equations are solved, what spatial geometry to use as well as how realistic the system will be. In numerical simulations of convection that use realistic stellar conditions a common tactic adopted is to artificially increase the luminosity and the thermal diffusivity of a model. In a serie of two papers we have study the impact of the method on convective penetration and on internal gravity waves. We performed two-dimensional simulations of solar-like stars and compare three models with different luminosity enhancement factors to a reference model.
I - Impact on convective penetration
Baraffe I., Pratt J., […], Le Saux A. et al. (2021), A&A 654, A126
In this first study we confirm the increase in the characteristic overshooting depth with the increase in the energy input, as suggested by analytical models and by previous numerical simulations. As a major finding, our results highlight the importance of the impact of penetrative downflows on the thermal background below the convective boundary. The artificial increase in the energy flux intensifies the heating process by increasing the velocities in the convective zone and at the convective boundary, revealing a subtle connection between the local heating of the thermal background and the plume dynamics. This heating also increases the efficiency of heat transport by radiation which may counterbalance further heating and helps to establish a steady state. We suggest that the modification of the thermal background by penetrative plumes impacts the width of the overshooting layer. Additionally, our results suggest that an artificial modification of the radiative diffusivity in the overshooting layer, rather than only accelerating the thermal relaxation, could also alter the dynamics of the penetrating plumes and thus the width of the overshooting layer.
II - Impact on internal gravity waves
Le Saux A. Guillet T., Baraffe I. et al. (2022), A&A 660, A51
In this second study we confirm that an increase in the stellar luminosity yields a decrease in the bulk convective turnover timescale and an increase in the characteristic frequency of excitation of the internal waves. We also show that a higher energy input in a model, corresponding to a larger luminosity, results in higher energy in high frequency waves. Across our tests with the luminosity and thermal di usivity enhanced together by up to a factor of 104, our results are consistent with theoretical predictions of radiative damping. Increasing the luminosity also has an impact on the amplitude of oscillatory motions across the convective boundary. One must use caution when interpreting studies of internal gravity waves based on hydrodynamical simulations with artificially enhanced luminosity.