The scatter in the relationship between redshift and the radio-to-submillimeter spectral index

We derive the scatter in the relationship between redshift and the radio-to -submillimeter spectral index, alpha(1.4)(350), using the observed spectral energy distributions of 17 low-redshift star-forming galaxies. A mean gala xy model is derived, along with the rms scatter in alpha(1.4)(350). The sca tter is roughly constant with redshift. Constant rms scatter, combined with the flattening of the mean alpha(1.4)(350)-z relationship with increasing redshift, leads to increasing uncertainty for redshift estimates at high re dshifts. Normalizing by the dust temperature in the manner proposed by Blai n decreases the scatter in alpha(1.4)(350) for most of the sample, but does not remove outliers, and free-free absorption at rest frequencies above 1. 4 GHz is not likely to be a dominant cause of scatter in the alpha(1.4)(350 )-z relationship. We rederive the cumulative redshift distribution of the 1 4 field galaxies in a recent submillimeter and radio source sample of Small et al. The most likely median redshift for the distribution is 2.7, with a conservative lower limit of z = 2, as was also found by Small et al. based on the original models. The normalization and shape of the redshift distri bution for the faint submillimeter sources are consistent with those expect ed for forming elliptical galaxies.