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Getting Redshifts the Imaging Way (1Sep95)
(from NOAO HIGHLIGHTS!, NOAO Newsletter No. 43, September 1995)

It's easy to find distant galaxies by taking deep images, but getting
to know them well requires redshifts---and the daunting task of
faint-object spectroscopy---if you are keen to look back to
cosmologically interesting times. Andy Connolly, Robert Brunner, Alex
Szalay (all at Johns Hopkins), and Matt Bershady (Penn State), however,
are asking if the use of multicolor images alone to obtain "photometric
redshifts" can be improved so that useful galaxy properties and
distances can be measured without burning the time needed for deep
spectra. To answer their question, they are using the KPNO 4-m to
obtain deep multicolor CCD photometry of a sample of faint (B <  25)
galaxies. The photometry will be reduced to obtain luminosities,
spectral properties, and redshifts of galaxies within the slice of the
universe probed by their survey.

                          [Figures not included]

     Deep U (left) and I (right) survey images taken with
     the Prime Focus camera on the 4-m at KPNO.

The position of a galaxy within the four color space of U, B, R and I
is defined by its redshift, luminosity and spectral type. A study of
the colors of galaxies using the photographic data of David Koo and
Richard Kron shows that the distribution of galaxy colors (in their
restframe) lies on a tight locus within this four-space. Adding the
luminosity of a galaxy as a further dimension stretches this line into
a thin plane (see Figure 1).  The principal axes of this plane are the
luminosity and spectral type of a galaxy. As galaxies are redshifted,
their magnitudes dim and their colors change. The "slab" in the
color-space comprising the multicolor magnitudes of a complete galaxy
sample at a given redshift is thus displaced from its orginal location
as the redshift increases. The result is a shifted stack of slabs (each
with its own constant redshift) passing through the multicolor
distribution. This effect is illustrated in Figure 1 where planes of
constant redshift are seen to project through the multicolor space.
Because the constant-redshift slabs separate out in multicolor space,
the location of a galaxy within the slab still contains sepctral
information independent of redshift.

One consequence of this is that galaxies at different redshifts
separate out within multicolor space. By fitting a second order
relation to the data, a photometric-redshift relation can be derived.
Figure 2 shows a comparison of the photometric and spectroscopic
redshifts. The dispersion about this relation is delta z <  0.05, for
galaxies out to a redshift of 0.6 (details to be published in AJ).
While estimated redshifts accurate to 0.05 provide an opportunity to
study the evolution of galaxies (from luminosity functions to
correlation functions) the observed dispersion is already limited by
uncertainties in the photographic data (simulations have shown that
delta z <  0.03 is attainable).

To determine the intrinsic dispersion in the photometric-redshift
relation and to extend the analysis to include estimates of luminosity
and spectral type, Connolly, Brunner, Bershady and Szalay, in
collaboration with David Koo, have undertaken a program to observe the
deep redshift surveys of Koo and Kron using the 2048 x 2048 Prime Focus
CCD on the KPNO 4-m in the U, B, R and I passbands.  The cover figures
show two CCD images taken with the TK2B CCD in the U and I passbands.
Integration times of 7200s in U and 1200s in I result in a point source
5s limit of approximately 25.9 and 24.3 magnitudes respectively. All
observations utilize the scan table, which substantially improves the
flatness of the images and reduces small scale fringing present in the
I band. These photometric data will be combined with existing redshift
catalogs and follow up spectroscopic observations undertaken on the
WIYN and Keck telescopes to derive a sample of galaxies with redshifts
at the limit of the photometric data.

The ability to estimate the redshift, spectral type and luminosity of a
galaxy from its broadband colors will allow large statistical studies
of galaxy evolution tobe undertaken (i.e.  where spectroscopic
redshifts would require orders of magnitude more observing time).  With
the advent of new multicolor photometric surveys, such as the Sloan
Digital Sky Survey, these techniques may open a new dimension in
studies of the distribution of galaxies.

                         [Figures not included]

     Figure 1. Galaxies occupy a small fraction of the
     available multicolor parameter space. This figure shows
     a schematic of how galaxies separate out in color
     space. In their restframe, galaxies lie on a plane
     (with principal axes of luminosity and spectral type).
     Redshifting the galaxies moves these planes in the flux
     and color directions, separating them in multicolor
     space. The total effect of the redshift is the vector
     sum of the K correction and dimming vectors.

     Figure 2. A comparison of redshifts derived from
     broadband multicolor photometry and those observed
     spectroscopicly. The dispersion about the one-to-one
     correlation is 0.05 in redshift.

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