Convective energy transport in stellar atmospheres

The motion of convective cells in an environment which changes rapidly with depth is examined. In such an environment a cell may move through regions with different levels of ionization and with associated differences in heat capacity. The energy equation is cast in a manner which is independent of the history of these cells. The convective flux at a given level of the atmosphere is written as an average over an ensemble of cells originating at a range of other levels. A procedure for correcting the temperature gradient for these non-local effects is described and results for a model solar atmosphere are given. The principal results are: (1) The rms velocity varies smoothly and is non-zero well into the photosphere (e.g.,v _rsm=1.4 km/sec at =0.2); (2) Convective overshoot reduces the radiative flux to 60% and 90% of the total at =2.5 and 0.2 respectively; and (3) The interior adiabat of the convective envelope is less sensitive to the assumed value of the average cell size than in the usual treatment of convection.Supported in part by the National Science Foundation GP-9433, GP-9114], the Office of Naval Research Nonr-220(47)], and Air Force Grant AG-AFOSR-171-67.