Simulations from Waters & Proga (2019a)
Non-isobaric Thermal Instability
(Accepted to ApJ)
Figure 4 simulations
Part 1: first 1200 cooling times
These simulations reveal the basic dynamics of single non-isobaric clouds:
increasingly stronger oscillations as the cloud size increases that
get damped over time scales that are long compared to the cloud formation timescale.
The unit of time (the cooling time) in these simulations is about 17 hours, as appropriate for the broad
line region clouds in AGN, so this first movie shows
two years of evolution, while the next shows an additional five.
Numerical details: These simulations use the same physical parameters and numerical setup
as in the work by
Proga & Waters (2015), but here radiation forces are neglected and we employ
the new code Athena++.
A uniform resolution of 256 zones per thermal length is used, so the small cloud (black) has 4,096 zones
and the larger cloud (red) 16,384 zones. The initial conditions consist of a single perturbation
of the entropy mode with amplitude 0.01. The boundary conditions are periodic.
(Accepted to ApJ)
Part 2: 1200-4000 cooling timesSince the velocity is getting very small as the solution approaches a steady state, we now zoom-in by a factor of about 50 on the velocity panel, and also reduce the range on the density and pressure panels. The final steady state solution is plotted in Figure 5.
'Numerical shattering'If we run this same simulation but reduce the amplitude of the larger perturbation by two orders of magnitude to A=1e-4, a numerical effect is revealed (here the y-ranges are dynamic, as we are following the linear solution as it grows in amplitude): McCourt et al. (2018). It cannot be, however, since it occurs in the linear regime where the perturbation is 'unaware' that it is large and any other perturbations in the system evolve independently because the superposition principle holds. Thus, there must be small isobaric perturbations in the system that overtook this very slow growing entropy mode. All of our numerical inputs have a precision down to 1e-10, but it is easy to show that exponential growth of small scale perturbations of this magnitude can catch up with the intended perturbation with A = 1e-4. This effect could be easily mistaken for 'shattering' in multi-dimensional simulations, even for non-isobaric clouds put in 'by hand'. It can occur in any part of the flow that is thermally unstable by the isobaric criterion.
Part 2 of this simulation is presented on the webpage of our companion paper.