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The high-frequency radio sky has historically remained largely unexplored dueto the typical faintness of sources in this regime, and the modest survey speedcompared to observations at lower frequencies. However, high-frequency radiosurveys present an invaluable tracer of high-redshift star-formation, as theydirectly target the faint radio free-free emission. We present deep continuumobservations at 34 GHz in the COSMOS and GOODS-North fields from the Karl G.Jansky Very Large Array (VLA), as part of the COLDz survey. The deep COSMOSmosaic spans $\sim10\text{arcmin}^2$ down to $\sigma=1.3\mu\text{Jybeam}^{-1}$, while the wider GOODS-N observations cover $\sim50\text{arcmin}^2$to $\sigma=5.3\mu\text{Jy beam}^{-1}$. We present the deepest 34 GHz radionumber counts to date, with five and thirteen continuum detections in COSMOSand GOODS-N, respectively. Nine galaxies show 34 GHz continuum emission that isoriginating from star-formation, although for two sources this is likely due tothermal emission from dust. Utilizing deep ancillary radio data at 1.4, 3, 5and 10 GHz, we decompose the spectra of the remaining seven star-forminggalaxies into their synchrotron and thermal free-free components, findingtypical thermal fractions and synchrotron spectral indices comparable to thoseobserved in local star-forming galaxies. Using calibrations from theliterature, we determine free-free star-formation rates (SFRs), and show thatthese are in agreement with SFRs from spectral energy distribution fitting andthe far-infrared/radio correlation. Our observations place strong directconstraints on the high-frequency radio emission in typical galaxies athigh-redshift, and provide some of the first insight in what is set to become akey area of study with future radio facilities as the Square Kilometer ArrayPhase 1 and next-generation VLA.

COLDz: Deep 34 GHz Continuum Observations and Free-free Emission in High-redshift Star-forming Galaxies