The SED fitting method

The SED fitting procedure to obtain photometric redshifts is based on the fit of the overall shape of the spectra and on the detection of strong spectral properties. To obtain more secure results, the filter set must be chosen in order to braket some of these features, as the 4000Å break or the Lyman break at 912Å. The observed photometric SEDs are compared to those obtained from a set of reference spectra, using the same photometric system. These template SEDs can be either observed or synthetic.

The photometric redshift of a given object corresponds to the best fit of its photometric SED by the set of template spectra, in general through a standard $\chi^2$ minimization procedure. The observed SED of a given galaxy is compared to a set of template spectra:

$$\chi^2(z)=\sum_{i=1}^{N_{\rm filters}} \left[{F_{{\rm obs},i}- b \times F_{{\rm temp},i}(z)\over \sigma_i} \right]^2 \:,$$ (1)

where $F_{{\rm obs},i}$, $F_{{\rm temp},i}$ and $\sigma_i$ are the observed and template fluxes and their uncertainty in filter $i$, respectively, and $b$ is a normalization constant.

A combination of this method with the Bayesian marginalization introducing an a priori probability was proposed by Benítez (2000): he demonstrated that in this case the dispersion of $z_{\rm phot}$ can be significantly improved. Despite of this result, we decided to not introduce such type of information, because the application of the Bayesian technique can introduce spurious effects in particular studies. However, this method can be regarded with interest when the goal is some specific application or when one is dealing with poor data, in such a way that the introduction of hints allows to obtain useful results. Alternatively, the photometric redshift estimate can be safely improved introducing the Bayesian inference when prior information is not related to the photometric properties of sources. Examples of such priors that could be combined with the $z_{\rm phot}$ technique are the morphology or the clues inferred from gravitational lensing modeling. In these cases, the user can easily introduce the interesting prior in the Fortran 77 code.

The major advantages of the SED fitting technique are its simplicity and the fact that it does not require any spectroscopic sample. Its weak point is mainly related to the need to choose fiducial spectral templates valid for all objects. We will discuss our choice in the following.
 

2000-12-10