The GOODS-N Jansky VLA 10 GHz Pilot Survey: Sizes of Star-forming μJY Radio Sources

Our sensitive (σ_n ≈ 572 nJy beam^(-1)), high-resolution (FWHM θ_(1/2) = 0.”22 ≈ 2 kpc at z ≳ 1), 10 GHz image covering a single Karl G. Jansky Very Large Array (VLA) primary beam (FWHM Θ_(1/2) ≈ 4.’25) in the GOODS-N field contains 32 sources with S_p ≳ 2 µJy beam^(-1) and optical and/or near-infrared (OIR) counterparts. Most are about as large as the star-forming regions that power them. Their median FWHM major axis is 〈Θ_M〉= 167 ± 32 mas ≈ 1.2 ± 0.28 kpc, with rms scatter ≈ 91 mas ≈ 0.79 kpc. In units of the effective radius r_e that encloses half their flux, these radio sizes are 〈r_e〉≈ 69 ± 13 mas ≈ 509 ± 114 pc, with rms scatter ≈ 38 mas ≈ 324 pc. These sizes are smaller than those measured at lower radio frequencies, but agree with dust emission sizes measured at mm/sub-mm wavelengths and extinction-corrected Hα sizes. We made a low-resolution (θ_(1/2) = 1.”0) image with ≈ 10x better brightness sensitivity, in order to detect extended sources and measure matched-resolution spectral indices α^(10 Ghz)_(1.4 Ghz). It contains six new sources with S_p ≳ 3.9 µJy beam^(-1) and OIR counterparts. The median redshift of all 38 sources is 〈z〉= 1.24 ± 0.15. The 19 sources with 1.4 GHz counterparts have a median spectral index of 〈α^(10 Ghz)_(1.4 Ghz)〉= -0.74 ± 0.10, with rms scatter ≈ 0.35. Including upper limits on α for sources not detected at 1.4 GHz flattens the median to 〈α^(10 Ghz)_(1.4 Ghz)〉≳ -0.61, suggesting that the μJy radio sources at higher redshifts—and hence those selected at higher rest-frame frequencies—may have flatter spectra. If the non-thermal spectral index is α_(NT) ≈ -0.85, the median thermal fraction of sources selected at median rest-frame frequency ≈ 20 GHz is ≳ 48%