A special case of analyzing SEDs of extragalactic sources is the problem of redshift estimation, a topic that is usually refered to as photometric redshifts (hereafter photo-z). This problem is distinct from all other estimates of physical properties because independent and more precise measurements of the same property are available for large samples in the form of spectroscopic redshifts. The method can thus be tested extensively and even calibrated empirically. It is also one of the earliest forms of SED fitting, having been suggested as a manner to go beyond the limits of early spectroscopy (Baum 1957).
For a working definition, Koo (1999) suggests the following: “photometric redshifts are those derived from only images or photometry with spectral resolution λ∕Δλ ≲ 20. This choice of 20 is intended to exclude redshifts derived from slit and slitless spectra, narrow band images, ramped-filter imager, Fabry-Perot images, Fourier transform spectrometers, etc.” This definition leaves room for a wide variety of approaches that are actively being explored by members of the community. While today most studies build on a set of magnitudes or colors, recently other observables have been utilized with good success, e.g., in the work by Wray and Gunn (2008). However, all methods depend on strong features in the SEDs of the objects, such as the Balmer break or even PAH features (Negrello et al. 2009).
Traditionally, photometric redshift estimation is broadly split into two areas: empirical methods and the template-fitting approach. Empirical methods use a subsample of the photometric survey with spectroscopically-measured redshifts as a ‘training set’ for the redshift estimators. This subsample describes the redshift distribution in magnitude and colour space empirically and is used then to calibrate this relation. Template methods use libraries of either observed spectra of galaxies exterior to the survey or model SEDs (as described in Section 2). As these are full spectra, the templates can be shifted to any redshift and then convolved with the transmission curves of the filters used in the photometric survey to create the template set for the redshift estimators.
Both methods then use these training sets as bases for the redshift estimating routines, which include χ2-fitting and various machine learning algorithms (e.g. artificial neural networks, ANNs). The most popular combinations are χ2-fitting with templates and machine learning with empirical models. For a review of the ideas and history of both areas, see Koo (1999).
The preference of one over the other is driven by the limitations of our understanding of the sources and the available observations. Template models are preferred when exploring new regimes since their extrapolation is trivial, if potentially incorrect. Empirical models are preferred when large training sets are available and great statistical precision is required. Here we review these techniques and estimators, concentrating predominantly on the template method which is closer to the idea of SED fitting as discussed in the previous section.