Radio Confusion on Cluster Sunyaev-Zel'dovich Effect

We examine the expected radio confusion on the thermal Sunyaev-Zel'dovich (SZ) effect of galaxy clusters at 28.5 GHz and 90 GHz based on the cluster radio luminosity function (CRLF) at 1.4 GHz. With the observationally determined spectral index (${\alpha}$, where $S_{\rm\nu}\propto\nu^{-\alpha}$) distribution, instead of a single average index $<\alpha>$, we convert the cluster radio luminosity function at 1.4 GHz to the high frequency ones and estimate the total radio flux in a cluster. At 28.5 GHz, radio confusion is up to 10~100% for small clusters ($M\sim 2\times 10^{14}M_{\odot}$) below redshift z=1, with more severe confusion for smaller and lower redshift clusters. By contrast, at 90 GHz the confusion is less than 10% for small clusters even at low redshifts.