Our sensitive ( \sigma _ { \mathrm { n } } \approx 572 \mathrm { nJy beam } ^ { -1 } ) , high-resolution ( FWHM \theta _ { 1 / 2 } = 0 \farcs 22 \approx 2 \mathrm { kpc~ { } at~ { } } z \gtrsim 1 ) 10 GHz image covering a single Karl G. Jansky Very Large Array ( VLA ) primary beam ( FWHM \Theta _ { 1 / 2 } \approx 4 \farcm 25 ) in the GOODS-N field contains 32 sources with S _ { \mathrm { p } } \gtrsim 2 \mu \mathrm { Jy~ { } 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 \langle \theta _ { \mathrm { M } } \rangle = 167 \pm 32 \mathrm { mas } \approx 1.2 \pm 0.28 % \mathrm { kpc } with rms scatter \approx 91 \mathrm { mas } \approx 0.79 \mathrm { kpc } .
In units of the effective radius r _ { e } that encloses half their flux , these radio sizes are \langle r _ { e } \rangle \approx 69 \pm 13 \mathrm { mas } \approx 509 \pm 114 % \mathrm { pc } and have rms scatter \approx 38 \mathrm { mas } \approx 324 \mathrm { 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 H \alpha sizes .
We made a low-resolution ( \theta _ { 1 / 2 } = 1 \farcs 0 ) image with \approx 10 \times better brightness sensitivity to detect extended sources and measure matched-resolution spectral indices \alpha _ { 1.4 GHz } ^ { 10 GHz } .
It contains 6 new sources with S _ { \mathrm { p } } \gtrsim 3.9 \mu \mathrm { Jy~ { } beam } ^ { -1 } and OIR counterparts .
The median redshift of all 38 sources is \langle z \rangle = 1.24 \pm 0.15 .
The 19 sources with 1.4 GHz counterparts have median spectral index \langle \alpha _ { 1.4 GHz } ^ { 10 GHz } \rangle = -0.74 \pm 0.10 with rms scatter \approx 0.35 .
Including upper limits on \alpha for sources not detected at 1.4 GHz flattens the median to \langle \alpha _ { 1.4 GHz } ^ { 10 GHz } \rangle \gtrsim - 0.61 , suggesting that the \mu Jy radio sources at higher redshifts , and hence selected at higher rest-frame frequencies , may have flatter spectra .
If the non-thermal spectral index is \alpha _ { NT } \approx - 0.85 , the median thermal fraction of sources selected at median rest-frame frequency \approx 20 GHz is \gtrsim 48 % .