Slicing Through Multicolor Space: Galaxy Redshifts from Broadband Photometry

As a means of better understanding the evolution of optically selected galaxies we consider the distribution of galaxies within the multicolor space $U$, $B_J$, $R_F$ and $I_N$. We find that they form an almost planar distribution out to $B_J =22.5$ and $z<0.3$. The position of a galaxy within this plane is dependent on its redshift, luminosity and spectral type. While in the original $U$, $B_J$, $R_F$ and $I_N$ space these properties are highly correlated we can define an optimal rotation of the photometric axes that makes much of this information orthogonal. Fitting the observed spectroscopic redshifts with a quadratic function of the four magnitudes we show that redshifts for galaxies can be estimated to an accuracy better than $\Delta z =0.05$. This dispersion is due to the photometric uncertainties within the photographic data. Assuming no galaxy evolution we derive a set of simulated galaxy fluxes in the U, J, F and N passbands. Using these data we investigate how the redshift is encoded within the broadband magnitudes and the intrinsic dispersion of the photometric-redshift relation. We find that the signal that defines a galaxy's photometric redshift is not related to specific absorption or emission lines but comes from the break in the overall shape of the galaxy continuum at around 4000 \AA. Using high signal-to-noise photometric data we estimate that it is possible to achieve an intrinsic dispersion of less than $\Delta z =0.02$.Comment: 20 Pages, 6 figures; uuencoded, compressed, postscript files. Accepted for publication in AJ. Figure 1 (color JPEG file) and paper are available on http://tarkus.pha.jhu.edu/~ajc