The Radio-to-Submillimeter Flux Density Ratio of Galaxies as a Measure of Redshift

We re-examine the technique of determining the redshifts of galaxies from theratio of the submillimeter-to-radio continuum flux densities based on arecently published catalog of 850~$\mu$m sources. We derived the expectedvariation of this ratio as a function of redshift incorporating the expectedaverage luminosity and the spectral energy distribution (SED) of dust emissionand the radio continuum. We find that the existing data for most of the highredshift ($z \gtsim 1$) sources correspond to our new calculation. Amongst thewell-identified sources, there is none with an index significantly higher thanpredicted. Sources which have an index lower than predicted are either withinthe error zone or much lower, the latter presumably having AGN-dominatedradio-continuum emission. We find the median redshift to be $\sim 2$, which isconsistent with that deduced by previous work ($\sim 3$) within the error. Wealso discuss the various systematic effects that can affect the accuracy of theredshift estimate. We examine other methods of redshift estimation, likephotometric ratio in the submillimeter and locating the peak of the SED in therest system of the objects. We conclude that while the various methods arehelpful in identifying high-redshift objects and making a crude estimate of theredshift, they are not, at present, accurate enough for a detailed study ofredshift distribution of the submillimeter galaxies.Comment: 6 pages LaTeX, PASJ in pres