Stellar Convective Penetration: Parameterized Theory and Dynamical Simulations

Most stars host convection zones in which heat is transported directly by fluid motion, but the behavior of convective boundaries is not well-understood. Here, we present 3D numerical simulations that exhibit penetration zones: regions where the entire luminosity could be carried by radiation, but w...

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Bibliographic Details
Published in:The Astrophysical journal Vol. 926; no. 2; pp. 169 - 186
Main Authors: Anders, Evan H., Jermyn, Adam S., Lecoanet, Daniel, Brown, Benjamin P.
Format: Journal Article
Language:English
Published: Philadelphia The American Astronomical Society 01.02.2022
IOP Publishing
Subjects:
Adiabatic flow
Astrophysical fluid dynamics
Astrophysics
Boussinesq equations
Convection
Convection heating
Fluid motion
Hydrodynamical simulations
Hydrodynamics
Luminosity
Mathematical models
Mixing length
Numerical simulations
Parameterization
Penetration
Radiation
Simulation
Solar convective zone
Stellar convection
Stellar convection envelopes
Stellar convective shells
Stellar convective zones
Stellar evolution
Stellar interiors
Stellar models
Stellar structures
Stiffness
Temperature gradients
ISSN:0004-637X, 1538-4357
Online Access:Get full text
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Summary:Most stars host convection zones in which heat is transported directly by fluid motion, but the behavior of convective boundaries is not well-understood. Here, we present 3D numerical simulations that exhibit penetration zones: regions where the entire luminosity could be carried by radiation, but where the temperature gradient is approximately adiabatic and convection is present. To parameterize this effect, we define the “penetration parameter”  , which compares how far the radiative gradient deviates from the adiabatic gradient on either side of the Schwarzschild convective boundary. Following Roxburgh and Zahn, we construct an energy-based theoretical model in which  controls the extent of penetration. We test this theory using 3D numerical simulations that employ a simplified Boussinesq model of stellar convection. The convection is driven by internal heating, and we use a height-dependent radiative conductivity. This allows us to separately specify  and the stiffness  of the radiative–convective boundary. We find significant convective penetration in all simulations. Our simple theory describes the simulations well. Penetration zones can take thousands of overturn times to develop, so long simulations or accelerated evolutionary techniques are required. In stars, we expect  ≈ 1 , and in this regime, our results suggest that convection zones may extend beyond the Schwarzschild boundary by up to ∼20%–30% of a mixing length. We present a MESA stellar model of the Sun that employs our parameterization of convective penetration as a proof of concept. Finally, we discuss prospects for extending these results to more realistic stellar contexts.
Bibliography:Stars and Stellar Physics
AAS33752
ObjectType-Article-1
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ISSN:0004-637X
1538-4357
DOI:10.3847/1538-4357/ac408d