5 Conclusions for real multi-color applications

  
5.1 Calibration of colors

Obviously, the measurements also need a careful calibration among the wavebands. A large erroneus offset can be disastrous for the photometric classification of narrow class structures in color space. If, e.g., true stars were measured with shifted colors, the classification would potentially find it rather in the location of library galaxies or quasars, and vice versa. Also, the redshift estimates would be thrown off by color offsets.

Calibration problems are of greatest concern, when rare objects are searched and their class gets contaminated. Especially, when class volumes are almost touching in color space, already small calibration errors can push objects into the wrong class. E.g., in many filter sets the quasar class is not well separated from stars and galaxies. In the presence of a calibration error, abundant galaxies can be pushed into the quasar class potentially making up the largest population among the precious candidates. The shape of class volumes is likely to cause quite some redshift dependence for the contamination. Then objects in some redshift range can become virtually unidentifiable, if they are overwhelmed by contaminants.

If calibration errors were known and quantified, they could as well be removed. If they were present but not realized, the measurements would look too accurate and a seemingly faithful classification would be derived, which is potentially wrong. Thus, as long as the calibration errors are unknown, it is still important to take their potential size into account for the error estimates on which the classification is based. As a result, the performance of the classification for bright objects is indeed limited by the calibration error. We assume calibration errors on the order of 3% for the colors in our surveys, which implies that the quality of the classification saturates for objects that are more than $1\hbox{$.\!\!^{\rm m}$ }5$ brighter than the 10-$\sigma$-limits of the survey. On the other hand, if we assume for the moment poor data reduction or uncorrected galactic reddening changing the colors by, e.g., 10%, this would turn an entire survey catalog into a collection of "less-than-10-$\sigma$-objects'' -- a devastating effect for the survey quality.

An accurate relative calibration among many wavebands is best ensured by establishing a few spectrophotometric standard stars in each of the survey fields, a successful approach that we have made into a standard procedure in CADIS. This task can be carried out in a photometric night by taking spectra of the new standards and connecting these to published standard stars (Oke 1990). This way, spectrophotometric standards are available in every one of the survey exposures, which will not require any further calibartion efforts regardless of the conditions under which the regular imaging is carried out. Obviously, standard star spectra are supposed to cover the entire filter set, but if a mixture of (e.g. optical and infrared) instruments is used, the calibration will involve different procedures to be matched.

5.2 The optimum survey strategy

The most basic result of our study on the performance of different multi-color surveys is, that even for small systematic errors in the color indices of $s_{g-h} = 0\hbox{$.\!\!^{\rm m}$ }03$, a survey with 17 bands performs better in classification and redshift estimation than one with only few bands. For the 17 band case we found that the limiting magnitude for reasonable performance is reached when the typical statistical (i.e. photon noise) errors are on the order of 10%. It is obvious, that larger systematic errors will worsen the performance and will allow even higher statistical errors before the survey deteriorates significantly. For the survey strategy this implies that pushing the statistical errors in each band well below the systematic errors will add nothing to the survey performance. When $\Delta t_{{\rm int}}$is the integration time required to reach $\sigma \approx 1/2 s_{g-h}$, the optimum number of bands N for a given amount of total time $t_{{\rm tot}}$ is roughly

$$N = t_{{\rm tot}} / \Delta t_{{\rm int}} .$$ (31)

Although our present study has been confined to the wavelengths region attainable by optical CCDs and did not address the total wavelength coverage of the survey explicitely, it is predictable that further bands extending the wavenlength coverage (e.g. by adding NIR bands) will have a larger effect than splitting the optical bands. In particular, the maximum redshift for a reliable galaxy classification will be extended.

As the color indices are the prime observables entering the classification and redshift estimation process, it is clear that any multi-color survey has to be processed such, that these indices are measured in an optimum way. For ground-based observations it is of great importance to avoid that variable observing conditions introduce systematic offsets between bands when the observations are taken sequentially. First of all, this requires to assess the seeing point spread function on every dataset very carefully. Second, one has to correct for the effect of variable seeing which might influence the flux measurement of star-like and extended objects in a different way.

In CADIS, we essentially convolve each image to a common effective point spread function and measure the central surface brightness of each object (see Paper II for details). This has the disadvantage, that the spatial resolution (i.e. the minimum separation of objects neighboring each other) is limited by the data with the worst seeing. However, it is not clear whether the obvious alternative -- deconvolution techniques -- can be optimized such that the systematic errors can be kept below a few percent for a wide variety of objects.

The performance of the MEV estimator depends critically on the assumption that not only the color indices but also their errors are determined correctly. For the survey strategy this implies, that an optimization of the photon noise errors under the expense that an accurate estimation of these errors is no longer possible may lead to worse performance than slightly larger errors which are known accurately.

5.3 Ongoing applications and their scientific goals

In this section, we want to mention examples for survey applications using this method and comment on the usefulness of our classification approach. A number of multi-color surveys have been conducted, where filters and exposure times were chosen to match some primary survey strategy. Although, none of these might have been optimal choices in terms of a general classification, we used or intend to use our approach to extract class and redshift data on the objects contained. These surveys are in chronological order of their beginning:

1.

The Calar Alto Deep Imaging Survey (CADIS): Three broad-band and twelve medium-band filters have mostly been chosen to match the needs of the emission line survey in CADIS, while some of them fill in gaps in the spectral coverage. The multi-color part of CADIS has been used to study the evolution of the galaxy luminosity function at , to search for quasars at all visible redshifts and to use the observed faint stellar population to check models of the Galactic structure and the stellar luminosity function (Meisenheimer et al. 1998; Wolf et al. 1999; Fried et al. 2000; Phleps et al. 2000; Paper II);

2.

A lensing study of the galaxy cluster Abell 1689: Two broad-band and seven medium-band filters have been chosen to separate well between the cluster galaxies at $z \approx 0.19$ and the background population. The galaxy luminosity function in the background of the cluster is compared to a control field taken from CADIS, and the cluster mass is estimated from weak lensing effects on the apparent luminosities (Dye et al. 2000);

3.

A widefield survey for Classifying Objects by Medium-Band Observations in 17 filters (COMBO-17): the filters (setup A from Sect.4.1) are chosen to provide a selection function and a redshift accuracy for quasars and galaxies, which is as independent of redshift as feasible. The data will be used to study the faint end of the quasar luminosity function at all accessible redshifts and galaxy-quasar correlation at , as well as weak lensing effects in the cluster group Abell 901/2 and in the open galaxy field (Wolf et al. 2000);

4.

The Sloan Digital Sky Survey (SDSS): five broad filters have been chosen, which span the entire range of presently available CCD sensitivity. We intend to apply our classification to search for quasars and to separate stars from compact galaxies, where morphology data are not sufficient.

From simulations of the classification scheme presented in this paper, we expect in all these projects, that we should be able to classify virtually all objects above some magnitude limit purely by color, and that especially the medium-band surveys should have selection functions which are not very dependent of redshift. This way, we can omit morphological criteria for defining catalogs of the stellar vs. galaxy vs. quasar population. This conclusion leads to a number of advantages for our method, we like to state explicitely here:

• The star-galaxy separation reaches deeper and avoids confusion better than if based on morphology. Accordingly, studies of the stellar population and of the galaxy population can be extended to much fainter magnitude;
• Quasars can be found at all accessible redshifts, especially in the medium-band surveys, where the overlap with the stellar sequence at redshifts of is much reduced in the color space;
• Quasars do not need to be selected from a subcatalog of point sources only, allowing for objects with resolved host galaxies to be found, including high-redshift Seyfert I galaxies;
• We also believe that the multi-color redshifts from the medium-band surveys are accurate enough so that the applications listed above do not require follow-up spectroscopy. E.g., the evolution of the galaxy luminosity function can be analysed with the multi-color redshifts, as long as no trends in a redshift intervall $\Delta z < 0.1$ are searched for.