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Convective Boundary Mixing in Stars

Periodic Reporting for period 2 - COBOM (Convective Boundary Mixing in Stars)

Reporting period: 2020-03-01 to 2021-08-31

The heart of the COBOM project is to develop a global physical picture of fundamental instabilities and mixing processes in stellar and planetary environments. One major goal is to derive robust and predictive stellar evolution models, which are fundamental to nearly all fields of astrophysics, from exoplanet to galactic and extra-galactic research. The complex dynamics of flows at convective boundaries is a key process in stellar interiors that drives the transport of chemical species and heat, strongly affecting the structure and the evolution of many types of stars, including our Sun. The same physical processes can also drive transport of angular momentum, affecting the rotation evolution and the generation of magnetic field of stars. The treatment of mixing processes at convective boundaries (also referred to as overshooting) is currently one of the major uncertainties in stellar evolution theory. This mixing can dramatically affect the size of a convective core, the lifetime of major burning phases or the surface chemistry over a wide range of stellar masses. Many observational constraints indicate that convective boundary mixing process strongly affects the evolution of stars, but no robust description exists so far. Similar instabilities and mixing processes are also found in very different environments, namely giant planet interiors or in a geophysical context (e.g. Earth's core or oceans). The main objectives of this project are to (1) develop a global theoretical framework to describe mixing and heat transport at convective boundaries in stellar interiors, (2) derive new physically-based transport coefficients and parametrizations for one-dimensional stellar evolution models, (3) test the new formalisms against a wide range of observations and (4) extend our approach and framework to hydrodynamical process in planetary and geophysical environments. We will accomplish these goals by performing the most comprehensive study ever performed of mixing processes in different environments using a fundamentally new approach based on multi-dimensional fully compressible time implicit magneto-hydrodynamic simulations.
The first step of our project is to perform a systematic numerical analysis of envelope convection and convective boundary mixing in solar like models, including our own Sun. Our first achievement is the ability to perform fully compressible time implicit simulations with a new numerical tool, namely the MUSIC code developed by our team, for a wide range of stellar interiors and based on realistic geometries and stellar structures. Our numerical approach is novel compared to more conventional works based on ideal setups (cartesian box, ideal physics) and/or on assumptions and simplifications regarding the resolution of the hydrodynamical equations. We also combine the power of such numerical simulations with a novel approach to analyse the results, namely using rare event statistics to analyse penetrative plumes responsible for mixing. This statistical method is usually applied in finance or climate science.
Our first results for solar-like models that will be published in several papers are "non conventional", since they are not obtained within the usual "ideal" framework. As a major finding, our results highlight the importance of the impact of penetrative downflows on the thermal background below the convective boundary. They reveal a modification of the thermal background by penetrative down-flows and a local heating in the overshooting layer. This is a new feature that could have significant impacts on stellar structures and is subject to follow-up analyses.

We have also applied the same approach to the study of convective cores for a wide range of stellar masses. We can successfully apply the same statistical analysis based on rare events to convective cores. As found for penetrative down-flows for convective envelopes, we can confirm the existence of extreme and rare events of penetrating up-flows that penetrate much further than the average penetrating flow. Our first results show that the efficiency of the overshooting process above the convective core increases with stellar mass and stellar luminosity, as suggested by observations. We provide a numerically calibrated relationship describing the overshooting width as a function of the stellar luminosity. Such a relationship can be implemented in stellar evolution codes and is very much needed by the stellar community.
Our numerical approach is able to describe convection and convective boundary mixing in a range of stellar models under realistic stellar conditions. Our numerical simulations for a solar-like model are new compared to what has been done so far, because they are able to generate convection for a realistic stratification and without having to use common artefacts, namely drastically increasing the solar luminosity and/or modifying the thermal diffusivity. Our approach is therefore powerful as it allows to explore physical processes under more realistic stellar conditions. In addition, we have been successful in applying the same methods for convective envelopes and cores to analyse rare events. The novel extreme plume event paradigm that we developed can thus be generalised to a range of stellar models, providing a general and powerful framework for the analysis of convective boundary mixing.
A new result is the identification of a process of local heating in the overshooting layer of solar-like models. This local modification of the thermal stratification could provide a solution to a long standing problem in stellar physics, known as the "solar modelling problem" which points to a well-known discrepancy between solar models and helioseismology data. We are performing follow-up studies to confirm this result. This discovery was unexpected and, if confirmed, opens a wide range of implications for stellar structures in general.
The next steps involve the analysis of the effect of dimensionality (3D versus 2D), rotation and magnetic field on the efficiency of the overshooting process for convective envelopes and cores in order to provide the most comprehensive analysis of convective boundary mixing in stars ever performed. We are also expecting to demonstrate by the end of the project the success of applying our numerical framework to applications under very different conditions characterising planetary interiors and geophysical problems.
Radial velocity in the convective envelope of a giant star with MUSIC