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We present Very Large Array observations of the 33 GHz radio continuumemission from 22 local ultraluminous and luminous infrared (IR) galaxies(U/LIRGs). These observations have spatial (angular) resolutions of 30--720 pc(0.07"-0.67") in a part of the spectrum that is likely to be optically thin.This allows us to estimate the size of the energetically dominant regions. Wefind half-light radii from 30 pc to 1.7 kpc. The 33 GHz flux density correlateswell with the IR emission, and we take these sizes as indicative of the size ofthe region that produces most of the energy. Combining our 33 GHz sizes withunresolved measurements, we estimate the IR luminosity and star formation rateper area, and the molecular gas surface and volume densities. These quantitiesspan a wide range (4 dex) and include some of the highest values measured forany galaxy (e.g., $\mathrm{\Sigma_{SFR}^{33GHz} \leq 10^{4.1} M_{\odot} yr^{-1}kpc^{-2}}$). At least $13$ sources appear Compton thick ($\mathrm{N_{H}^{33GHz}\geq 10^{24} cm^{-2}}$). Consistent with previous work, contrasting these datawith observations of normal disk galaxies suggests a nonlinear and likelymulti-valued relation between SFR and molecular gas surface density, thoughthis result depends on the adopted CO-to-H$_{2}$ conversion factor and theassumption that our 33 GHz sizes apply to the gas. 11 sources appear to exceedthe luminosity surface density predicted for starbursts supported by radiationpressure and supernovae feedback, however we note the need for more detailedobservations of the inner disk structure. U/LIRGs with higher surfacebrightness exhibit stronger [{\sc Cii}] 158$\mu$m deficits, consistent with thesuggestion that high energy densities drive this phenomenon.

astrophysical journal/the astrophysical journal

A 33 GHz Survey of Local Major Mergers: Estimating the Sizes of the  Energetically Dominant Regions from High Resolution Measurements of the Radio  Continuum