With the simple energy equation employed in these simulations there are two interesting limits: the adiabatic and the isothermal equations of state. Over the long term these two equations of state should lead to divergent evolutions as the adiabatic disk heats up. The present comparison has the modest goal of investigating whether the equation of state has an impact over a relatively brief period of initial evolution in the cylindrical disk.
Run CK7b is a repeat of CK7a using an isothermal equation of state.
The initial linear growth phase in the two runs is essentially
identical. Once turbulence sets in the runs vary in detail, but not in
any systematic way. In particular there are no significant differences
between the two runs in terms of stress at rms or the change in
between rms and the inner boundary. Although the accretion
rates in both runs differ from each other, they both also vary strongly
in time, and the average difference between the two runs is less than
the fluctuations level seen in either run alone.
The main differences observed in these two runs are consistent with
what would be expected for the these equations of state. In CK7a
the temperature varies with radius, rising over the course of the
simulation by as much as 30% inside of R=10, while falling rapidly
inside of rms. The temperature has also declined slightly outside
of R=25 due to expansion of the disk off the outer boundary. The
density fluctuations (8) in the isothermal run CK7b are
larger on average over the whole disk: the mean
is
0.73 versus 0.60 in CK7a.
Title Page
|
3.4 Influence of phi domain
|
4. A Hydrodynamic Disk