Gravitational Lensing Limits on the Average Redshift of Submillimeter Sources

Abstract

The submillimeter universe has now been explored with the Submillimeter Common User Bolometer Array (SCUBA) camera on the James Clerk Maxwell Telescope, and a claim has been made to the presence of a new population of optically unidentified starforming galaxies at high redshifts (z \gtrsim 3). Such a population dramatically alters current views on the star formation history of the universe as well as galaxy formation and evolution. Recently, new radio identifications of the Hubble Deep Field submm sources have led to the suggestion that some of these sources are at low redshifts, however, submm 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 submm sources due to foreground cluster potentials to current observed statistics of such lensed sources. The upper limit depends on the cosmological parameters, and at the 68% confidence level, <z> < 3.1, 4.8, 5.2, or 8.0 for (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 redshift distribution for 850 micron sources implied by starformation history models based on measured background radiation at far-infrared and submm wavelengths.