Bayesian Photometric Redshifts: Introduction

Precise spectroscopic redshifts are ideal, but they can be time consuming to obtain and altogether unattainable for objects fainter than about 24th magnitude AB.  For objects without spec-z, we rely on photo-z.

Photometric redshifts rely on multiband photometry with broad to medium filters.  The more filters the better, but 3-4 are recommended at minimum.  Robust photometry is essential for robust photo-z, including identical apertures in all images and corrections for different PSFs (e.g., ColorPro or TFIT).

Photo-z analysis consists of fitting the input photometry various SEDs (Spectral Energy Distributions for ellipticals, spirals, and starbursts) redshifted by different amounts.  For an animated illustration, click here (14M gif; Safari chokes on this, but Firefox handles it well).  A grid of fit choices is attempted, varying both redshift and spectral type.  The fits yield a likelihood distribution P(z,t).

BPZ (Benitez00) introduced the use of Bayesian inference and priors to photometric redshift estimation.  For example, bright objects and ellipticals are assumed unlikely to be at high redshift.  Benitez00 derived a prior based on objects with spec-z in the HDF-N and demonstrated that this yields superior photo-z results to assuming no prior (a "flat" prior), which is unphysical.

After adopting the prior P(z,t | m) based on the i-band magnitude m, the SED types are marginalized over, and BPZ outputs a likelihood function P(z).  BPZ further summarizes this as a most likely redshift with uncertainties, including how degenerate the best fit is to other redshift,type combinations, and how good the best fit is.

Again, for an animated illustration of SED fitting, click here (14M gif; Safari chokes on this, but Firefox handles it well).sed animation frame z=3.50