Simulations from Waters & Proga (2019b)

Cloud coalescence:
a dynamical instability affecting mulitphase environments
(Accepted to ApJ Letters)
arXiv posting

TI Simulations

'Numerical shattering' - Part 2

This simulation reveals the nonlinear outcome of the 'numerical shattering' experiment from the Paper 1 webpage. The short wavelength isobaric perturbations that overtook the large entropy mode perturbation have already saturated into clouds and they now proceed to coalesce. While the small isobaric perturbations were unintentionally introduced (due to truncating our numerical inputs at ⁓10^-10), the resulting clouds are nevertheless fully resolved. This simulation nicely captures the overall dynamics of coalesecence: cloud mergers occur rapidly when clouds are undergoing oscillations (here induced by the formation dynamics), aided by the small separation distances. Once the oscillations settle down, the advective flows outside the clouds become very small and coalescence becomes a very slow process. While it is not shown here, the final steady state is a single cloud.

The cooling time in these simulations is evaluated in the cold gas (note: in Paper 1, we measured this quantity instead in the initial thermally unstable gas) and is about 1.7 hours, as appropriate for the broad line region clouds in AGN, so this movie shows about 70 days of evolution.

isobaric_takeover_part2 from UNLV Astronomy on Vimeo.

Figure 1 Simulation

This simulation was designed to establish coalescence as a dynamical instability: steady state solutions arise whenvever cloud spacings are perfectly symmetric, but these steady states are unstable. That is, the slightest spatial perturbation introduced in the initial conditions will lead to the clouds instead coalescing.

TI_4and8P_p1 from UNLV Astronomy on Vimeo.

Here we adjust the plot limits to show that only very small pressure gradients are involved in the lead up to coalescence. We speculate that this process can occur much faster if the clouds are subjected to continual thermal disturbances, as this will induce oscillations that 'revive' the large advective flows outside the clouds.

TI_4and8P_p2 from UNLV Astronomy on Vimeo.

Pre-existing cloud Simulations

Fiducial run

Here is the evolution of our fiducial 2D run, showing that two spatially well-separated 'pre-existing' clouds will coalesce. The main image is a density map showing the full domain, while the lower panels zoom-in on the rectangular region. The bottom panel is a map of vorticity and corresponds to the lower colorbar.

To induce oscillations, we initialized the temperature of the clouds to 0.8 T_0, where T_0 is the equilibrium value on the S-curve. The clouds undergo 'spreading' as they re-equlibriate; similar behavior can be seen in the TI simulations above. We ran control runs with perfectly symmetric spacings (i.e. domain sizes with gaps between cloud edges that are the same as the cloud spacing) to verify that this spreading alone will not result in coalescence.

We refer to the 'dark spots' inside the clouds in these simulations as entrained vortex bubbles. They are underdense pockets of high vorticity gas that form at the cloud interfaces and then maintain their structure as they propagate deep inside the cloud.

L15R45 from UNLV Astronomy on Vimeo.

Self-consistent formation of cloud interfaces

It appears that this work is the first to self-consistently form cloud interfaces beginning with 'standard' pre-existing clouds initialized in pressure equilibrium. Here is a movie showing this early evolution, which occurs on a timescale short compared to the oscillation timescale of the clouds in the movie above.

L15R45_0-20t_cool from UNLV Astronomy on Vimeo.


We thank Jim Stone and the other developers of Athena++ for sharing this excellent code. These simulations were run on the institutional computing clusters at LANL. TW is partially supported by the LANL LDRD Exploratory Research Grant 20170317ER.