MERIDIONAL CIRCULATION AND DIFFUSION IN A-STARS AND EARLY F-STARS

Time-dependent, two-dimensional calculations of diffusion in presence of meridional circulation and/or turbulence have been carried out, in order to investigate in detail the effects of these competing processes on the development of abundance anomalies in the effective temperature range of FmAm stars. Once the helium superficial convection zone has disappeared, as required to obtain underabundances of calcium and scandium characteristic of FmAm stars, it is shown that meridional circulation has little influence on chemical separation. This is in agreement with the weak correlation observed between the magnitudes of abundance anomalies and projected rotational velocities in FmAm stars. It also implies that meridional circulation is not the process reducing the amplitude of abundance anomalies predicted by diffusion theory to the level at which they are observed. In stars rotating too rapidly to become FmAm stars (v(e) greater-than-or-equal-to 100 km s-1), chemical separation remains possible under the helium superficial convection zone. Calculations show that for most chemical elements, meridional circulation can considerably reduce the abundance anomalies predicted from diffusion in nonrotating models, yet, below rotational velocities of 200 km s-1, overabundances by factors of up to 5 still develop in many cases. Contrary to an often-held belief, meridional circulation does not completely wipe out chemical separation for v(e) greater-than-or-equal-to 100 km s-1. This is in agreement with the increasing amount of moderate abundance anomalies observed in chemically "normal" A and early F stars. Our results also show that in stars rotating above the cutoff velocity for FmAm stars, meridional circulation cannot by itself lead to the abundance patterns characteristic of lambda-Booti stars. A proper explanation for these in the framework of diffusion theory seems to require the presence of mass loss. Our models are also used to set upper limits to turbulence. In the presence of meridional circulation, helium settling in stars rotating at the observed cutoff for FmAm stars remains possible for values of vertical turbulent diffusion coefficients of order 10(3) cm2 s-1 under the helium superficial convection zone. This is lower by nearly two orders of magnitude than the upper limit obtained in nonrotating models, and sets extremely tight constraints on turbulence in stars having equatorial rotational velocities of 100 km s-1 and less. The effects of anisotropic turbulence on particle transport are also investigated; the presence of strong horizontal turbulence and negligible vertical turbulence is found to increase the efficiency of chemical separation in presence of meridional circulation; however, this appears only possible for prohibitively large values of horizontal turbulent diffusion coefficients. These calculations are demanding from the numerical standpoint. The use of upwind finite elements for spatial discretization proved to yield sufficiently accurate solutions while requiring reasonable amounts of computing time, and has made it possible to tackle problems having resisted prior attempts with more conventional finite difference-based numerical schemes.