How the Cookie Crumbles: A Model for Star-forming Clumps in High-redshift Disk Galaxies

TL;DR

This paper develops a simple theoretical model predicting the distribution of star-forming clumps in high-redshift disk galaxies, aligning well with recent observations and highlighting differences between rotation-supported and dispersion-supported galaxies.

Contribution

It introduces a novel model linking gravitational stability, star formation efficiency, and gas profiles to the distribution of star-forming clumps in high-redshift galaxies.

Findings

Model predicts $N_c(> \\dot M_\star) \\propto \\dot M_\star^{-4/3}$ for clump distribution.

Good agreement with observed clump star formation rates and counts.

Rotation-supported galaxies have more clumps than dispersion-supported ones at similar mass.

Abstract

We present a simple model for the number distribution of maximally star-forming clumps in rotating disk galaxies, at high-$z$ with high gas surface densities. By combining assumptions surrounding marginal stability of disks against gravitational fragmentation and collapse (i.e., Toomre's $Q\approx 1$), star cluster formation efficiency scaling with local gas surface density, and star formation rates being tied to the relevant local dynamical/free-fall times, we find a star-forming clump distribution of $N_c(> \dot M_\star) \propto \dot M_\star^{-4/3}$ when assuming a power-law form for the gas surface density profile, and a numerically integrable relation for arbitrary gas disk profiles. We compare this model with recent high-redshift observations of lensed clumpy star-forming rotation-dominated galaxies, and find good agreement with the distribution of clump star formation rates and number of clumps. Moreover, we argue that any rotation-supported galaxy should have a significantly higher number of identifiable star-forming clumps relative to dispersion supported objects at a similar mass as $N_c \sim (V_c/\sigma)^2$.