A Brief Review of Photometric Redshifts
The concept of photometric redshifts is not new. This page will outline
a brief history of the photometric redshifts. The list of papers reviewed here
is not exhaustive; however, it does cover most of the development of the
1. Direct shift measurement
Baum (1962) was the first to develop a technique for measuring redshifts photometrically. He used a photoelectric photometer and 9 bandpasses spanning
the spectrum from 3730Å to 9875Å. With this system he observed the spectral energy distribution (SED) of 6 bright elliptical galaxies in the Virgo cluster. He then observed 3 elliptical galaxies in another cluster (Cl0925+2044,
also known as Abell 0801). By plotting the average SED of the Virgo galaxies
and the average SED of the Cl0925 galaxies on the same graph using a logarithmic wavelength scale, he was able to measure the displacement between
the two energy distributions, and hence the redshift of the second cluster.
His redshift value of z=0.19 agreed closely with the known spectroscopic
value of z=0.192, so he extended his technique to a handful of clusters of
then unknown redshifts out to maximum redshift of z=0.46. He then derived
a very rough value of Omega_0. Baum's technique was fairly accurate, but because
of its dependence on a large 4000Å break spectral feature, it could only work
on elliptical galaxies.
2. Color-color diagrams
Koo (1985) followed a different approach. First, he used photographic plates
instead of a photometer, making it possible to measure photometric redshifts
for a large number of galaxies simultaneously. Second, instead of using 9 filters he used only 4: UJFN (photographic U, B_J, R_F and I_N). Third, instead of using an empirical spectral
energy distribution, he used the theoretical Bruzual (1983, among others)
no-evolution models for all galaxy types.
The most important difference, however, was the way the colours were
used. Instead of converting the photometric colours into a kind of low resolution spectrum, he converted the Bruzual templates into colours, and plotted
lines of constant redshift and varying spectral type, known as iso-z lines, on a
colour-colour diagram. Finding that the most normal colour-colour diagrams
(e.g. U-J versus J-F and J-F versus F-N) were degenerate in
a range of redshifts, he invented what he called colour-shape diagrams. The
shape measured whether the SED turned up or down at both ends, that is,
whether the spectrum was bowl shaped or humped. Another way to put it is
that the colour measured the first derivative with respect to wavelength of the
spectrum and the shape measured the second derivative. For colour he used
either 2U-2F or U +J-F-N , both of which span a large wavelength
range. For shape, he used either U+2J-F or -U+J+F-N .
Following this method to measure the redshift of a galaxy, Koo calculated
the colour and the shape from the UJFN magnitudes and plotted them
on the colour-shape diagram. The redshift of the galaxy was then found by
finding the iso-z line closest to the point representing the galaxy. Koo tested
this method on a sample of 100 galaxies with known spectroscopic redshifts
ranging from z=0.025 to z=0.700.
This method is similar to that used by Pello et al. (1996) and Miralles,
Pello & Le Borgne (1996). They used the colours of galaxies to determine
"permitted redshifts" in the following manner: The colors of galaxies are
plotted as a function of redshift from the Bruzual & Charlot (1993) models.
Each available color (with its associated uncertainty) of a galaxy defines a
"permitted" redshift range on the corresponding color-redshift diagram. The
intersection of the permitted redshift ranges for all the colours determines
the redshift. This method was used by Pello et al. (1996) to discover a cluster
of galaxies at z>0.75 by looking for an excess in the redshift distribution in
the field of a gravitationally lensed quasar. Miralles et al. (1996) used the
method to determine the redshift distribtion of the Hubble Deep Field.
The "ultra-violet dropout" techniques of Steidel et al. (1996) and Madau
et al. (1996) are similar if simpler. All galaxy spectra have a large Lyman
break; shortward of 912Å, the continuum drops dramatically. When this
break is redshifted into and past the U filter, the U flux is greatly reduced
or non-existant, resulting in very red ultra-violet colours.
In the ultra-violet dropout techniques, an exact redshift of a galaxy is
not determined. Rather, the redshift is determined to be in the redshift
range where the Lyman break is in or just past the U filter. Since U filters
typically have a central wavelength of 3000Å, this works out to a redshift
of z > 2.25. In practical terms, redshifted template galaxy spectra are used
to determine a locus on a colour-colour plot where most galaxies lie in a
particular redshift range. Those galaxies whose measured colours lie within
the locus are deemed to be in that redshift range. Clearly, this method is a
lot simpler than that of Pello et al. (1996) as only two colours are considered.
It is also a lot less precise as the redshift is not very constrained. For both
these reasons it is ideally suited for pre-selecting galaxies at high redshift
for spectroscopic confirmation. Steidel et al. (1996) did exactly this using
the UGR filters. Madau et al. (1996) applied this technique to the
Hubble Deep Field using the F300W, F450W, F606W and F814W filters.
The technique was extended by using F450W dropouts to find galaxies of
3. Template Fitting
The template fitting technique developped by Loh & Spillar (1986b) more
closely resembles that of Baum (1962) than that of Koo (1985).
Loh & Spillar (1986b) observed 34 galaxies of known redshift in the
galaxy cluster 0023+1654 through 6 non-standard filters to test their method.
The standard deviation of the redshift differences (z_spec-z_phot ) was 0.12.
They went on to use their technique to measure photometric redshifts for
1000 field galaxies in order to determine a value for the density parameter,
0mega_0 (Loh & Spillar, 1986a).
Gwyn (1995) tested this method using BVRI photometry of the Colless
et al. (Colless et al., 1990; Colless et al., 1993) galaxies. The larger uncertainty in photmetric redshifts thus derived (Delta_z =0.18) was attributed to the
lack of a U filter. Numerous authors (Gwyn and Hartwick, 1996; Lanzetta
et al., 1996; Mobasher et al., 1996; Sawicki et al., 1996; Cowie et al., 1996)
have used this technique to determine redshifts in the Hubble Deep Field.
4. Linear Regression
Prehaps the simplest and certainly the most empirical photometric redshift
technique yet is that of Connolly et al. (1995a). This method requires a
"training set" of a large number of galaxies with multi-color photometry and
spectroscopic redshifts. Redshift, z, is assumed to be a linear or quadratic
function of the magnitudes (M_i) of the galaxies. i.e. if N is the number of
The constants, a_i and a_ij, are found by linear regression. Connolly et al.
(1995a) used a UJFN plus redshift data set extending to z=0.5 of
370 galaxies. They showed that this method could determine redshifts with
uncertainties of sigma_z = 0.057 with a linear fit and sigma_z = 0.047 with a quadratic
fit. There is little or no loss of accuracy if colors (Ci = M_i-M_i+1 ) are used
instead of magnitudes. Using this technique they were able to measure the
luminosity function out to J=24 (SubbaRao et al., 1996).
The advantage of the linear regression technique is its extreme simplicity.
It has a few disadvantages: (1) A substantial collection of spectroscopic redshifts must have been measured before the technique can used. (2) Extension
to fainter magnitudes or deeper redshifts is not possible.
Baum, W. A.: 1962, in G. C. McVittie (ed.), Problems of extra-galactic
research, p. 390, IAU Symposium No. 15
Bruzual, G. A.: 1983, Astrophys. J. 273, 105
Bruzual, G. A. and Charlot, S.: 1993, Astrophys. J. 405, 538
Colless, M. M., Ellis, R. S., Broadhurst, T. J., and Peterson, B. A.: 1993,
M.N.R.A.S. 244, 408
Colless, M. M., Ellis, R. S., Taylor, K., and Hook, R. N.: 1990, M.N.R.A.S.
Connolly, A. J., Csabai, I., Szalay, A. S., Koo, D. C., Kron, R. G., and Munn,
J. A.: 1995a, Astron. J. 110, 2655
Cowie, L. L., Clowe, D., Fulton, E., Cohen, J. G., Hu, E. M., , Songaila,
A., Hogg, D. W., and Hodapp, K. W.: 1996, Redshifts, colors and mor
phologies of the K selected galaxy sample in the Hubble Deep Field, in
Gwyn, S. D. J.: 1995, Master's thesis, University of Victoria
Gwyn, S. D. J. and Hartwick, F. D. A.: 1996, Astrophys. J. Let. 468, L77
Koo, D. C.: 1985, Astron. J. 90, 418
Lanzetta, K. M., Yahil, A., and Fernandez-Soto, A.: 1996, Star-forming
galaxies at very high redshifts, Preprint [astro-ph/9606171]
Loh, E. D. and Spillar, E. J.: 1986a, Astrophys. J. 307, L1
Loh, E. D. and Spillar, E. J.: 1986b, Astrophys. J. 303, 15
Madau, P., Ferguson, H. C., Dickinson, M. E., Giavalisco, M., Steidel, C. C.,
and Fruchter, A. S.: 1996, High redshift galaxies in the Hubble Deep
Field. Color selection and star formation history to z=4, Preprint
Miralles, J.-M., Pello, R., and Le Borgne, J.-F.: 1996, Photometric Analysis
of the Hubble Deep Field, Preprint
Mobasher, B., Rowan-Robinson, M., Georgakakis, A., and Eaton, N.: 1996,
The nature of the faint galaxies in the Hubble Deep Field, Preprint [astro
Pello, R., Miralles, J.-M., Picat, J.-P., Soucail, G., and Bruzual, G. A.: 1996,
Identification of a high redshift cluster in the field of Q2345+007 through
deep BRIJK photometry, Preprint [astro-ph/9603146]
Sawicki, M. J., Lin, H., and Yee, H. K. C.: 1996, Evolution of the Galaxy
Population Based on Photometric Redshifts in the Hubble Deep Field,
Steidel, C. C., Giavalisco, M., Pettini, M., Dickinson, M. E., and Adelberger,
K. L.: 1996, Spectroscopy of Lyman break galaxies in the Hubble Deep
Field, Preprint [astro-ph/9604140]
SubbaRao, M. U., Connolly, A. J., Szalay, A. S., and Koo, D. C.: 1996,
Luminosity Functions from Photometric Redshifts I: Techniques, Preprint
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