Master's thesis presentation: Hydrodynamic simulations with a radiative surface
by
Atefeh Barekat
→
Europe/Stockholm
FB53
FB53
Description
We solve the equations of radiation hydrodynamics to compute the time evolution toward
one-dimensional equilibrium solutions using a generalized Kramers opacity, κ = κ_0 ρ^a T^b,
with adjustable exponents a and b on density ρ and temperature T, respectively, and
prefactor κ_0. We choose our initial conditions to be isothermal and find that the early
time evolution away from the isothermal state is fastest near the height where the optical
depth is unity. In all cases where the quantity n = (3 − b)/(1 + a) is larger than −1, we
find a nearly polytropic solution with ρ ∝ T^n in the lower part and a nearly isothermal
solution in the upper part with a radiating surface in between, where the optical depth is
unity. In the lower part, the radiative diffusivity is found to be approximately constant,
while in the upper optically thin part it increases linearly. Interestingly, solutions with
different parameter combinations a and b that result in the same value of n are rather
similar, but not identical. Increasing the prefactor increases the temperature contrast and
lowers the value of the effective temperature. We find that the Peclet number based on
sound speed and pressure scale height exceeds numerically manageable values of around 10^4
when the prefactor κ_0 is chosen to be approximately six orders of magnitude below the
physically correct value. In the special case where a = −1 and b = 3, the value of n is
undetermined and the radiative diffusivity is strictly constant everywhere. In that case we
find a stratification that is approximately adiabatic. Finally, exploratory two-dimensional
calculations are presented where we include turbulent values of viscosity and diffusivity and
find that onset of convection occurs when these values are around 3 × 10^13 cm^2 s^(−1). The
addition of an imposed horizontal magnetic field suppresses small-scale convection, but has
not led to instability in the cases investigated so far.
