Radio Sources from a 31 GHz Sky Survey with the Sunyaev-Zel'dovich Array

We present the first sample of 31 GHz selected sources to flux levels of 1 mJy. From late 2005 to mid-2007, the Sunyaev-Zel'dovich Array observed 7.7 deg(2) of the sky at 31 GHz to a median rms of 0.18 mJy beam(-1). We identify 209 sources at greater than 5 sigma significance in the 31 GHz maps, ranging in flux from 0.7 mJy to similar to 200 mJy. Archival NVSS data at 1.4 GHz and observations at 5 GHz with the Very Large Array are used to characterize the sources. We determine the maximum-likelihood integrated source count to be N(>S) = (27.2 +/- 2.5) deg(-2) x (S(mJy))(-1.18 +/- 0.12) over the flux range 0.7-15 mJy. This result is significantly higher than predictions based on 1.4 GHz selected samples, a discrepancy which can be explained by a small shift in the spectral index distribution for faint 1.4 GHz sources. From comparison with previous measurements of sources within the central arcminute of massive clusters, we derive an overdensity of 6.8 +/- 4.4, relative to field sources.