Gravitational lensing limits on the average redshift of submillimeter sources

The submillimeter universe has now been explored with the Submillimeter Com mon-User Bolometer Array camera on the James Clerk Maxwell Telescope, and a claim has been made to the presence of a new population of optically unide ntified star-forming galaxies at high redshifts (z greater than or similar to 3). Such a population dramatically alters current views on the star form ation history of the universe as well as galaxy formation and evolution. Re cently, new radio identifications of the Hubble Deep Field submillimeter so urces have led to the suggestion that some of these sources are at low reds hifts; however, the submillimeter source redshift distribution is still not well determined. Here we present an upper limit to the average redshift (z ) by comparing the expected number of gravitationally lensed submillimeter sources that are due to foreground cluster potentials with the current obse rved statistics of such lensed sources. The upper limit depends on the cosm ological parameters, and at the 68% confidence level, (z)< 3.1, 4.8, 5.2, o r 8.0 for (Omega(in) Omega(Lambda)) values of (0.3, 0.7), (0.5, 0.5), (0.3, 0.0), or (1.0, 0.0), respectively. These upper limits are consistent with the redshift distribution for 850 mu m sources implied by star formation hi story models that are based on measured background radiation at far-infrare d and submillimeter wavelengths.