We presented an innovative method that performs a multi-color classification and redshift estimation of astronomical objects in a unifying approach. The method is essentially based on templates and evaluates the statistical consistency of a given measurement with a database of spectral knowledge, serving as a second, very crucial input to the algorithm.
The introduction of this method is motivated by the quest for a statistically correct extraction of the information present in the color vectors of surveys with many filters. The method is derived from basic statistical principles and calculates probability density functions for each survey object telling us two different results simultaneously: the class membership and redshift estimates according to the Maximum Likelihood (ML) and Minimum Error Variance (MEV) estimators. We add our own version of the MEV technique featuring improved handling of bimodalities in the probability function.
Our choice for the database is a large, systematically ordered library containing templates for stars, galaxies and quasars, which are supposed to cover virtually all but some unusual members among each of the three object classes. The libraries were established from a few model assumptions and templates published by various authors and extracted from the literature.
The method can be implemented in a computationally very efficient way, by using directly color indices as object features. We showed that our color-based approach is expected to deliver results consistent with those from flux-based template-fitting algorithms.
The accuracy of the data calibration is a very important issue, constraining the design of the libraries and limiting the maximum achievable performance of the method via the effective photometric quality. Calibration errors can distort results and shrink the information output.
We carried out Monte-Carlo simulations for three model surveys using the same total exposure time but different filter sets. One of them is a UBVRI broad-band survey, while the other two expose two third of the time in various medium-band filters. Altogether, the performance of all three setups was rather similar despite the quite different numbers of collected photons. So it appears, that medium-band filters obtain more information per photon and thereby compensate the loss of depth in terms of flux detection, from which they suffer in comparison to broad bands. Among the differences, medium-band surveys performed better than the broad-band survey for finding quasars, and they provided much higher redshift resolution in their estimates. Also, in the presence of calibration errors or uncorrected reddening effects, bright objects are not easier to classify than faint ones, and a large number of shallow filters might provide more information than a small number of deeply exposed filters.
Based on simple analytic assumptions, we have discussed the relative information content of surveys with different characteristic filter width. All surveys using the same amount of total telescope time and filter sets stretching over the entire spectral range of interest, should perform equal in terms of classification. This theoretical conclusion depends on perfect calibration and perfect template knowledge.
In practice, the classification should reach deeper in medium-band surveys than in broad-band surveys, because the former are less affected by inaccuracies in the calibration and in the template library. Furthermore, the filters can be chosen to avoid noise from strong night sky emission lines which is not possible with broad-band filters.
In particular, using the proposed statistical classification approach in a suitable medium-band survey it should be possible
for z>2-quasars, and on the order of
for galaxies.
This method should be very suitable for many survey-type applications, which usually require only low spectral resolution and finite accuracy in the derivation of physical parameters, but aim for large samples to feed statistical studies and to search for rare and unusual objects. Of course, if you need a 100% sure confirmation on the nature of an individual object, or if you aim for high resolution studies, it gives you only a preselection of candidates.
In Paper II we show, that this method is very powerful and indeed of great practical relevance for multi-color surveys with many filters like in the case of CADIS. The results of our shown simulations compare well with the performance of a real survey, and therefore, they can in fact be used for testing the performance of future survey designs.
Acknowledgements
The authors thank H. H. Hippelein for helpful discussions on template fits and H.-M. Adorf for some on classification methods and their fine-tuning. We also thank D. Calzetti for kindly making available the galaxy templates in digital form. We would finally like to thank the referee, Dr. S. C. Odewahn, for detailed comments improving the paper. This work was supported by the DFG (Sonderforschungsbereich 439).
Copyright ESO 2001