Selection of ULIRGs in infrared and submm surveys

We examine the selection characteristics of infrared and submm surveys with IRAS, Spitzer, BLAST, Herschel and SCUBA, and identify the range of dust temperatures these surveys are sensitive to, for galaxies in the ultraluminous IR galaxy (ULIRG) luminosity range [12 < log (L-IR/L-circle dot) < 13], between z = 0 and 4. We find that the extent of the redshift range over which surveys are unbiased is a function of the wavelength of selection, flux density limit and ULIRG luminosity. Short wavelength (lambda less than or similar to 200 mu m) surveys with IRAS, Spitzer/MIPS and Herschel/PACS are sensitive to all spectral energy distribution (SED) types in a large temperature interval (17-87 K), over a substantial fraction of their accessible redshift range. On the other hand, long wavelength (lambda greater than or similar to 200 mu m) surveys with BLAST, Herschel/SPIRE and SCUBA are significantly more sensitive to cold ULIRGs, disfavouring warmer SEDs even at low redshifts. In order to evaluate observations in the context of survey selection effects, we examine the temperature distribution of four ULIRG samples from IRAS, Spitzer/MIPS, BLAST and SCUBA. We find that the lack of cold ULIRGs in the local (z < 0.1) Universe is not a consequence of the selection and that the range of ULIRG temperatures seen locally is only a subset of a much larger range which exists at high redshift. We demonstrate that the local luminosity-temperature (L-T) relation, which indicates that more luminous sources are also hotter, is not applicable in the distant Universe when extrapolated to the ULIRG regime, because the scatter in observed temperatures is too large. Finally, we show that the difference between the ULIRG temperature distributions locally and at high redshift is not the result of galaxies becoming colder due to an L-T relation which evolves as a function of redshift. Instead, they are consistent with a picture where the evolution of the infrared luminosity function is temperature dependent, i.e. cold galaxies evolve at a faster rate than their warm counterparts.