OVERSHOOTING FROM CONVECTIVE CORES - THEORY AND NUMERICAL-SIMULATION

Authors
Citation
Iw. Roxburgh, OVERSHOOTING FROM CONVECTIVE CORES - THEORY AND NUMERICAL-SIMULATION, Space science reviews, 66(1-4), 1993, pp. 299-308
Citations number
11
Categorie Soggetti
Astronomy & Astrophysics
Journal title
ISSN journal
00386308
Volume
66
Issue
1-4
Year of publication
1993
Pages
299 - 308
Database
ISI
SICI code
0038-6308(1993)66:1-4<299:OFCC-T>2.0.ZU;2-T
Abstract
Convective overshooting increases the fraction of the star which is ef fectively mixed, thus altering models of stellar evolution. If the fee d back of overshooting on the structure of the star is neglected the e stimated extent of overshooting is very small. If the feed back is inc luded in these estimates then the adiabatic core is extended by a dist ance comparable to a substantial fraction of the radius of the unstabl e region. An upper limit on convective overshooting is given by the in tegral constraint (Roxburgh 1978,1989) with viscous dissipation neglec ted. If this constraint is applied to small convective cores then the maximum extent of the penetration region is shown to be at most about 0.18 times the radius of the core independent of the details of energy generation and opacity. The ratio of the maximum penetration distance to the scale height at the edge of the ''classical boundary'' varies very strongly with core size, and modelling overshooting by taking the penetration distance as a multiple of the scale height is likely to g ive misleading results. Numerical simulations of two-dimensional compr essible convection in a fluid where the central regions are naturally convectively unstable, and the surrounding layers are stable, have bee n undertaken for different values of the Prandtl number. The results i ndicate that for low Prandtl numbers viscous dissipation is of decreas ing importance and the simple integral condition gives a reasonable es timate of the extent of overshooting. Stellar seismology offers the po ssibility of detecting the location of the core - envelope interface t hrough a periodic variation of the small frequency separation with