# Simulations from Waters & Proga (2018)

### Non-isobaric Thermal Instability

(Submitted to ApJ)

arXiv posting

## 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.

fig4_p1 from UNLV Astronomy on Vimeo.

### Part 2: 1200-4000 cooling times

Since 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.fig4_p2 from UNLV Astronomy on Vimeo.

## Supplemental simulations

### '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):isobaric_takeover from UNLV Astronomy on Vimeo.

It appears that some sort of fragmentation is taking place, akin to the hypothetical 'shattering' process proposed by 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.