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

I present a new approach at deriving far-infrared photometric redshifts for galaxies based on their reprocessed emission from dust at rest-frame far-infrared through millimeter wavelengths. Far-infrared 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-infrared. Most literature FIR-z fits are performed through $χ^2$minimization to a single galaxy's far-infrared 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 $0<z<5$) to motivate a new far-infrared 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, $λ_{\rm peak}$, and total IR luminosity, L$_{\rm IR}$; the derived photometric redshift accounts for the measurement uncertainties and intrinsic variation in SEDs at the inferred L$_{\rm IR}$, as well as heating from the CMB at $z>5$. The MMpz algorithm has a precision of $σ_{Δz/(1+z)}\approx0.3-0.4$, similar to single-template fits, while providing a more accurate estimate of the FIR-$z$ uncertainty with reduced chi-squared of order $\mathcal{O}(χ^2_ν)=1$, compared to alternative far-infrared photometric redshift techniques (with $\mathcal{O}(χ^2_ν)\approx10-10^{3}$).