Size scaling of clump instabilities in turbulent, feedback-regulated disks

We explore the scaling between the size of star-forming clumps and rotational support in massively star-forming galactic disks. The analysis relies on simulations of a clumpy galaxy at z = 2 and the observed DYnamics of Newly Assembled Massive Objects (DYNAMO) sample of rare clumpy analogs at z approximate to 0.1 to test a predictive clump size scaling proposed by Fisher et al. in the context of the violent disk instability (VDI) theory. We here determine the clump sizes using a recently presented two-point estimator, which is robust against resolution/noise effects, hierarchical clump substructure, clump-clump overlap and other galactic substructure. After verifying Fisher's clump scaling relation for the DYNAMO observations, we explore whether this relation remains characteristic of the VDI theory, even if realistic physical processes, such as local asymmetries and stellar feedback, are included in the model. To this end, we rely on hydrodynamic zoom-simulations of a Milky Way-mass galaxy with four different feedback prescriptions. We find that, during its marginally stable epoch at z = 2, this mock galaxy falls on the clump scaling relation, although its position on this relation depends on the feedback model. This finding implies that Toomre-like stability considerations approximately apply to large (similar to kpc) instabilities in marginally stable turbulent disks, irrespective of the feedback model, but also emphasizes that the global clump distribution of a turbulent disk depends strongly on feedback.