My collaborators and I have examined sites of ongoing clump formation in the VELA simulations, a large suite of high resolution cosmological simulations using the AMR code ART. Surprisingly, we find ongoing clump formation in regions with very high values of Q, often above Q~5. Such regions should be stable according to any existing version of Toomre theory. This presents a very interesting theoretical challenge, addressing the fundamental nature of VDI and clump formation.

 

I am attempting to resolve this issue by examining the nature of turbulence in proto-clump regions. In general, there are two modes of turbulence: solenoidal, which represents local rotation or shear and can stabilize a region against gravitational collapse, and compressive, which represents local convergent flows and may thus enhance instability. For isotropic turbulence, there is on average twice as much power in the solenoidal mode as in the compressive mode. However, tidal effects caused by galaxy mergers or the impact of dense gas streams may inverse this relation, causing the compressive modes to dominate. In this case, a region could undergo local collapse even if the turbulence is very high, in contradiction to Toomre theory. Preliminary results show a clear correlation between VDI and excess power in compressive turbulence, but work is still ongoing.

Roughly 60% of star forming galaxies at redshifts z~2-3 are clumpy (Guo et al 2015). In these clumpy galaxies, roughly 20% of the UV light is in several giant clumps, each containing a few percent of the total galaxy mass. This is robustly reproduced in high resolution cosmological simulations (e.g. Mandelker et al 2014), and is associated with a general state of violent disk instability (VDI).

 

The formation of giant clumps is commonly associated with Toomre instability. The high gas fractions and velocity dispersions in high-z disk galaxies induce collapse on scales comparable with the observed clumps. Furthermore, observations reveal the clumps to be located in regions where the Toomre Q parameter is below unity, and which are thus gravitationally unstable. 

 

However, such observations do not prove that the clumps were formed by Toomre instability. A collapsed clump is by construction a highly non-linear object with extremely high surface density, while Toomre Q is a linear concept.

 

The Origin of VDI

Right: Gas surface density for one of our simulated galaxies at redshift z~2. Left: Map of Toomre Q. The collapsed, non-linear clumps all have Q<1, as expected. However, the inter-clump medium, where new clumps are being formed, has high Q values.

(Figure by Shigeki Innoue)

Histograms showing Q values in all regions that will collapse into massive clumps within a free fall time, for three of our simulated galaxies. There are many massive clumps actively forming in high Q regions.

(Figure by Shigeki Innoue)

Left: Gas surface density for four of our simulated galaxies at redshift z~3. The two on the left are unstable for most of their evolution, continuously forming massive clumps. The two on the right are stable for most of their lifetime and do not form clumps. Right: Ratio of solenoidal to compressive turbulent energy for the four galaxies shown on the left, as a function of time (cosmic expansion factor). The unstable cases have systematically more power in compressive turbulence than the stable cases.