Far-infrared Photometric Redshifts: A New Approach to a Highly Uncertain Enterprise

Abstract

This paper presents a new approach to deriving far-infrared (FIR) photometric redshifts for galaxies based on their reprocessed emission from dust at rest-frame FIR through millimeter wavelengths. FIR photometric redshifts ("FIR-z") have been used over the past decade to derive redshift constraints for highly obscured galaxies that lack photometry at other wavelengths like the optical/near-IR. Most literature FIR-z fits are performed through ${\chi }^{2}$ minimization to a single galaxy's FIR template spectral energy distribution (SED). The use of a single galaxy template, or modest set of templates, can lead to an artificially low uncertainty estimate on FIR-z's because real galaxies display a wide range in intrinsic dust SEDs. I use the observed distribution of galaxy SEDs (for well-constrained samples across $0\lt z\lt 5$ ) to motivate a new FIR through millimeter photometric redshift technique called MMpz. The MMpz algorithm asserts that galaxies are most likely drawn from the empirically observed relationship between rest-frame peak wavelength, ${\lambda }_{\mathrm{peak}}$ , and total IR luminosity, L ${}_{\mathrm{IR}}$ ; the derived photometric redshift accounts for the measurement uncertainties and intrinsic variation in SEDs at the inferred L ${}_{\mathrm{IR}}$ , as well as heating from the cosmic microwave background at $z\gtrsim 5$ . The MMpz algorithm has a precision of ${\sigma }_{{\rm{\Delta }}z/(1+z)}\approx 0.3\mbox{--}0.4$ , similar to single-template fits, while providing a more accurate estimate of the FIR-z uncertainty with reduced chi-squared of order ${ \mathcal O }({\chi }_{\nu }^{2})=1$ , compared to alternative FIR photometric redshift techniques (with ${ \mathcal O }({\chi }_{\nu }^{2})\approx 10\mbox{--}{10}^{3}$ ).