Radio sources in galaxy clusters at 28.5 GHz

We present serendipitous detections of radio sources at 28.5 GHz (1 cm), which resulted from our program to image the thermal Sunyaev-Zeldovich (SZ) effect in 56 galaxy clusters. In a total area of similar to 0.8 deg(2), we find 64 radio sources with fluxes down to similar to 0.4 mJy (greater than 4 sigma) and within 250 " from the pointing centers. The spectral indices (S proportional to nu(-alpha)) of 54 sources with published low-frequency flux densities lie in the range -0.6 less than or similar to alpha less than or similar to 2, with a mean of 0.77 +/- 0.06 and a median of 0.84. Extending low-frequency surveys of radio sources toward the galaxy clusters Cl 0016 + 16, Abell 665, and Abell 2218 to 28.5 GHz and selecting sources with S-1.4 GHz greater than or equal to 7 mJy to form an unbiased sample, we find a mean spectral index of 0.71 +/- 0.08 and a median of 0.71. We find 4 to 7 times more sources than predicted from a low-frequency survey in areas without galaxy clusters. This excess cannot be accounted for by gravitational lensing of a background radio population by cluster potentials, indicating that most of the detected sources are associated with galaxy clusters. The differential source count slope, gamma similar to 1.96 (dN/dS proportional to S-gamma), is flatter than what is expected for a nonevolving Euclidean population (gamma = 2.5). For the cluster Abell 2218, the presence of unsubtracted radio sources with S-28.5 GHz less than or equal to 0.5 mJy (similar to 5 sigma) can reduce the observed SZ temperature decrement by Delta T similar to 10 to 25 mu K. The corresponding overestimation of the Hubble constant derived through a combined analysis of 28.5 GHz SZ images and X-ray emission observations is less than 6%.