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).