The Radio-to-Submillimeter Spectral Index as a Redshift Indicator

We present models of the 1.4 GHz to 350 GHz spectral index, alpha(350/1.4),for starburst galaxies as a function of redshift. The models include asemi-analytic formulation, based on the well quantified radio-to-far infraredcorrelation for low redshift star forming galaxies, and an empiricalformulation, based on the observed spectrum of the starburst galaxies M82 andArp 220. We compare the models to the observed values of alpha(350/1.4) forstarburst galaxies at low and high redshift. We find reasonable agreementbetween the models and the observations, and in particular, that an observedspectral index of alpha(350/1.4) > +0.5 indicates that the target source islikely to be at high redshift, z > 1. The evolution of alpha(350/1.4) withredshift is mainly due to the very steep rise in the Raleigh-Jeans portion ofthe thermal dust spectrum shifting into the 350 GHz band with increasingredshift. We also discuss situations where this relationship could be violated.We then apply our models to examine the putative identifications of submmsources in the Hubble Deep Field, and conclude that the submm sources reportedby Hughes et al. are likely to be at high redshifts, z > 1.5.Comment: standard LATEX file plus 1 postscript figure. Added references and revised figure. second figure revision. Final Proof version. to appear in Astrophysical Journal Letter