Velocity dispersion in the interstellar medium of early galaxies

We study the structure of spatially resolved, line-of-sight velocity dispersion for galaxies in the Epoch of Reionization (EoR) traced by [CII] $158\mu\rm{m}$ line emission. Our laboratory is a simulated prototypical Lyman-break galaxy, "Freesia", part of the SERRA suite. The analysis encompasses the redshift range 6 < z < 8, when Freesia is in a very active assembling phase. We build velocity dispersion maps for three dynamically distinct evolutionary stages (Spiral Disk at z=7.4, Merger at z=8.0, and Disturbed Disk at z=6.5) using [CII] hyperspectral data cubes. We find that, at a high spatial resolution of 0.005" ($\simeq 30 pc$), the luminosity-weighted average velocity dispersion is $\sigma_{\rm{CII}}$~23-38 km/s with the highest value belonging to the highly-structured Disturbed Disk stage. Low resolution observations tend to overestimate $\sigma_{\rm CII}$ values due to beam smearing effects that depend on the specific galaxy structure. For an angular resolution of 0.02" (0.1"), the average velocity dispersion is 16-34% (52-115%) larger than the actual one. The [CII] emitting gas in Freesia has a Toomre parameter $\mathcal{Q}$~0.2 and a rotational-to-dispersion ratio of $v_{\rm c}/\sigma$~ 7 similar to that observed in z=2-3 galaxies. The primary energy source for the velocity dispersion is due to gravitational processes, such as merging/accretion events; energy input from stellar feedback is generally subdominant (< 10%). Finally, we find that the resolved $\sigma_{\rm{CII}} - {\Sigma}_{\rm SFR}$ relation is relatively flat for $0.02<{\Sigma}_{\rm SFR}/{{\rm M}_{\odot}} \mathrm{yr}^{-1} {\mathrm kpc}^{-2} < 30$, with the majority of data lying on the derived analytical relation $\sigma \propto \Sigma_{\rm SFR}^{5/7}$. At high SFR, the increased contribution from stellar feedback steepens the relation, and $\sigma_{\rm{CII}}$ rises slightly.