Determining Total Infrared Luminosities from Submm Measurements of High Redshift Galaxies

Determining total infrared luminosities for very high redshift galaxies is important to estimate the rate of star formation in heavily dust-embedded environments. It is also challenging because the most sensitive far infrared observatory, Herschel, was limited in sensitivity and its deepest measurements are subject to confusion noise. Thus, these determinations largely depend on ALMA, observing in the mm- and/or submm-wavelengths, which sample only the long-wavelength part of the spectral energy distributions (SEDs). Luminosities are conventionally estimated with modified blackbody fits to these measurements, but do not include the emission in the mid-infrared by warmer dust; there is evidence that this mid-IR component may be relatively strong in very high-redshift galaxies compared with local ones. A correction factor must be applied to the modified black body luminosities to derive the total infrared luminosity. We study infrared SEDs using simulations tuned to galactic conditions typical of high-z galaxies. We find that the different behaviors of infrared SEDs are dominated by a single key physical parameter, the luminosity density. This allows us to estimate the corrections for the missing mid-infrared luminosity in a general way. We find that a factor of 1.6 - 1.7 (0.2 dex) is appropriate in most circumstances, with a larger factor of 1.75 - 1.85 (0.25 dex) up to 2 (0.3 dex) necessary for high redshift (z > 4) galaxies at the highest luminosities, > 10 12 Lsun. These corrections are needed to estimate star formation rates based on total infrared luminosity.