Abstract
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.
| Original language | English (US) |
|---|---|
| Article number | 169 |
| Journal | Astrophysical Journal |
| Volume | 926 |
| Issue number | 2 |
| DOIs | |
| State | Published - Feb 1 2022 |
Funding
We thank Keaton Burns, Matt Browning, Matteo Cantiello, Geoff Vasil, and Kyle Augustson for useful discussions and/or questions that improved the content of this manuscript. Ben Brown thanks Jeffrey Oishi for many years of discussions about overshooting convection. We thank the anonymous referee for carefully reading our manuscript, engaging with our science, and helping identify places where our descriptions of our simulations were confusing. EHA is funded as a CIERA Postdoctoral fellow and would like to thank CIERA and Northwestern University. We acknowledge the hospitality of Nordita during the program “The Shifting Paradigm of Stellar Convection: From Mixing Length Concepts to Realistic Turbulence Modeling,” where the groundwork for this paper was set. This work was supported by NASA HTMS grant 80NSSC20K1280 and NASA SSW grant 80NSSC19K0026. Computations were conducted with support from the NASA High End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center on Pleiades with allocation GID s2276. The Flatiron Institute is supported by the Simons Foundation.
ASJC Scopus subject areas
- Astronomy and Astrophysics
- Space and Planetary Science