Annu. Rev. Astron. Astrophys. 1992. 30: 613-52
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2.3 Colors

Colors of field galaxies provide the data needed to categorize the mixture of stellar populations and to measure star formation rates. By adding passbands, one can rapidly increase the number of dimensions for analysis of spectral energy distributions. Although higher precision (typically < 0.1 mag in the color) is needed, such data can be efficiently gathered with broad-band filters for faint galaxies. With three or more passbands, multicolor photometry measures independently the intrinsic colors and crude redshifts of faint galaxies (Baum 1962; Koo 1985; Loh and Spillar 1986), especially if multiple medium-wide passbands are employed (Couch et al. 1983). Extending this technique to large numbers of narrow bands may be practical (Gibson and Hickson 1991).

Measurements of color for galaxies brighter than the B < 15.5 limit of the Zwicky catalogue are surprisingly few, even for galaxies with measured redshifts. This imbalance is due to the same difficulties encountered by counts of bright galaxies, namely the need for coverage of a large solid angle; the saturation of bright galaxies on photographic plates; and the more complex procedures required to handle contamination by the relatively high surface density of stars.

In the last decade, near-infrared photometry has provided a large extension of the spectal range useful for observations of faint galaxies. The first such study was a B = 21.5 sample of 47 field galaxies by Ellis and Allen (1983). This was followed by the larger but brighter sample by Mobasher et al. (1986) which was limited at B = 17. A K-limited sample can be derived that is complete to about K < 12.5 (89 galaxies in this sub-sample). With the advent of near-infrared arrays, K-band fluxes have been measured for faint field galaxies (Elston, Rieke, and Rieke 1990; Bershady et al. 1990), even to surface densities similar to those achieved in the optical band (Cowie et al. 1990; Cowie et al. 1992).

There are additional technical complications from combining two or more magnitudes together. Colors may be measured within a smaller aperture than used for the magnitudes (sometimes within a fixed aperture size) to improve the signal-to-noise ratio. The implicit assumption is that radial color gradients in galaxies are small. Some workers have even combined fluxes measured through different effective apertures, but this is likely to introduce dangerous systematic color variations as a function of magnitude and true color. There is also the complication of deciding how to choose the detection limits in the various bands. Images in each passband may be combined before the photometric procedures are applied to improve the depth of the survey or to provide simultaneous measurement of the magnitudes and colors (Ciardullo 1987). For photometry at very faint levels, fluxes in some bands may even be measured as negative, due to expected sky-subtraction fluctuations. Moreover, unless the photometric errors are very small, color errors are usually asymmetrical and can exhibit complicated shapes in different regions of multicolor diagrams (see Figures 9a or 9c of Koo 1986). Having different incompleteness limits for each passband further complicates the interpretation of such plots.

Many passbands have been used for faint-galaxy work; since published photometry in Kron's (1980a) blue and red bands spans a large range in magnitude, we will adopt this as a common system for this review. For the blue, bJ is defined by the combination of Eastman IIIa-J emulsion and GG385 filter. For galaxies at z ~ 0.5 and with colors typical of spirals, a rough approximation is bJ = B - 0.3. For the red, rF is defined by the Eastman IIIa-F emulsion and GG495 filter, and is photometrically intermediate between V and R.

2.3.1 PHOTOGRAPHIC COLORS 15 < B < 20 The color distribution of nearby galaxies can be determined from a number of relatively bright surveys. Kirshner, Oemler, and Schechter (1978) measured asymptotic or ``total'' magnitudes and colors on photographic plates for a sample of 807 field galaxies brighter than B ~ 16 in eight fields towards the Galactic caps. A fainter, red-limited sample (to their F ~ 17) was subsequently published by Kirshner et al. (1983). The results of these two surveys, plus an extension to B ~ 19 for field galaxies, have been tabulated in convenient form by Butcher and Oemler (1985) as part of their study of the colors of nearby rich clusters of galaxies (Figure 2). A similar study was made by Couch and Newell (1984), who compiled a large sample of field galaxy colors as a function of R magnitude.

Figure 2. bJ - rF color histogram for specified bJ magnitudes in bins of 0.1 mag. Numbers give sample size. Left-hand plots are all photographic data, as follows: Butcher and Oemler (1985), the two plots brighter than 19; Kron (1980a), as slightly modified by Koo (1986), for the next three panels. The dotted histogram in the 20-21 panel is Jones et al. (1991), plotted for comparison with the transformation of Metcalfe et al. (1991). Right-hand plots are CCD data, with the exception of the dotted histogram in the top panel which extends Kron (1980a) and Koo (1986) another magnitude. From 22 to 24, Metcalfe et al. (1991); fainter data are from Guhathakurta (1991) with the BJ - R passbands of Tyson (1988) (no transformation applied). Guhathakurta's data are also shown in the 23 - 24 panel as a dotted histogram, for comparison. In the faintest panel, non-detections in the R band contribute to the linear drop of the blue tail (P. Guhathakurta, private communication).

2.3.2 PHOTOGRAPHIC COLORS B > 20 There is extensive multicolor photometry fainter than B ~ 20, mostly from prime-focus plates taken with 4-m class telescopes. These plates cover 0.3 to 0.5 deg2 and typically yield 10,000 galaxies or more per exposure to B = 24, with useful colors brighter than B ~ 23.

Kron (1980a) showed that the bJ - rF colors of fainter galaxies become significantly bluer beyond B ~ 22. Many faint galaxies were actually bluer than an actively star-forming galaxy like the Large Magellanic Cloud, unless placed at redshifts beyond z ~ 1. Shanks et al. (1984), Infante, Pritchet, and Quintana (1986), and Tyson (1984) confirmed these results. By adding U and I bands, Koo (1986) was able to add two more dimensions to the color analysis and thus resolve the ambiguity between redshifts and intrinsic colors. One new and somewhat unexpected finding was evidence for a substantial increase of intrinsically blue galaxies at redshifts between z = 0.4 and 1. This was, however, a model-dependent conclusion that needed spectroscopic redshift confirmation. The colors of some galaxies fainter than bJ = 23 are consistent with substantially higher redshifts (see Koo 1990). Koo also found that the slope of the counts depends on the bandpass, such that the slope progressively becomes flatter from the super-Euclidian rise (DeltalogA / Deltam > 0.6) from U = 20 to 22, to shallower values for the redder bands. The photographic work of Jones et al. (1991) has largely confirmed these slope changes.

2.3.3 CCD COLORS B > 20 With the high sensitivity of CCD's, much fainter limits have become feasible, albeit with only 0.003 to 0.07 deg2 per frame. Hall and Mackay (1984) published the first such survey, covering a total of 50 arcmin2 to a surface density of 150,000 objects deg-2. They pioneered a scanning technique to achieve excellent flat-fields, and reported that the mean of the R - I colors of their galaxies was essentially constant over their magnitude range, and that the red counts had a relatively flat slope of DeltalogA / Deltam = 0.4, confirming the results of the earlier photographic work.

This was followed by the well-known survey of Tyson and Seitzer (1988) and Tyson (1988), who used three passbands (BJRI) that reached even fainter limits (using a shift-and-add technique that they developed), approaching 500,000 galaxies deg-2. The difference in the slope between the blue and red counts was again seen. Tyson (1988) also noted an ``extreme blueing trend in BJ - R color with R magnitude,'' by more than a magnitude in color over a two-magnitude range in R (his Fig. 17). A similar sharp change in the B - I color with increasing I magnitude was reported by Cowie and Lilly (1990), but subsequent work (Lilly, Cowie, and Gardner 1991) shows instead a more gradual trend to bluer colors. Lilly, Cowie, and Gardner (1991) also found mean colors redder than Tyson by ~ 0.8 mag at the faint end. Moreover, the UBJ RI survey of Guhathakurta, Tyson, and Majewski (1990a) found very little change in B - R from R = 23 to beyond R = 26. The sample of Metcalfe et al. (1991) shows blueing of only a few tenths of a magnitude in B - R over a range of 2 magnitudes (R = 22 to R = 24), but does not reach as faint as these other surveys.

Loh and Spillar (1986) obtained six-band photometry of galaxies in five 0.02 deg2 fields, complete to m8000 = 22. They attempted to estimate a redshift for each galaxy based on its apparent low-resolution spectrum, and the derived redshift distribution (Loh, private communication) is at least qualitatively consistent with the redshift distributions derived spectroscopically, discussed in Section 2.4.

Cowie (1988) suggested the presence of a large fraction of faint galaxies with z > 2.8 based on the observed flux at 3400 Å being very faint, presumed to be due to the Lyman-continuum break at 912 Å entering the U band. However, the deep U-band CCD surveys reported by Majewski (1988, 1989), Guhathakurta, Tyson, and Majewski (1990a), and Lilly, Cowie, and Gardner (1991) do not find an unusual proportion of galaxies with red U - B colors.

In summary, one of the relatively well-established phenomena of faint galaxy photometry is the gradual trend to bluer mean colors at fainter magnitudes. This is seen in colors comprising a blue band like U - B, B - V, and B - I (Kron 1980a; Koo 1986; Guhathakurta, Tyson, and Majewski 1990a; Lilly, Cowie, and Gardner 1991; Metcalfe et al. 1991), but is not so evident in redder colors like R - I or R - K (Hall and Mackay 1984; Koo 1986; Tyson 1988; Hintzen, Romanishin, and Valdes 1991; Elston, Rieke, and Rieke 1990). A possible interpretation is that the proportion of intrinsically blue galaxies fainter than B = 22 increases, but the blue galaxy population does not itself become much bluer (Figure 2). However, it is worth recalling that qualitatively, the trend to bluer colors fainter than approximately B = 22 is expected even in the absence of evolutionary effects because the K-correction selects against the intrinsically redder and more luminous galaxies and because the color-absolute magnitude relation progressively favors the nearer, bluer galaxies.

2.3.4 ``FLAT-SPECTRUM'' GALAXIES Some very blue galaxies have spectra that are approximately constant in fnu over at least a modest range in frequency - these are the so-called flat-spectrum galaxies. They are of interest because of their high rates of massive star formation, whatever their redshifts (Cowie et al. 1988). Lilly, Cowie, and Gardner (1991) actually adopt (B - I)AB leq 0.7 as a criterion for very blue galaxies, which corresponds to fnu ~ nu alpha where alpha ~ -1. The criterion alpha > -1 for very blue galaxies is useful because common subdwarf stars rarely have colors bluer than this. Thus the colors of such stars measured in the same field can then serve as an internal calibration and a check on the size of systematic errors in the photometry. Note that the K-correction for a power-law spectral energy distribution is K(z) = -2.5(1 + alpha)log(1 + z), and alpha = -1 conveniently corresponds to zero K-correction.

The alpha = -1 point on a U - B, B - V diagram such as that of Huchra (1977; see Matthews and Sandage 1963) shows that few nearby galaxies are as blue as this (and essentially none are as blue as alpha = 0). Therefore, if such galaxies are seen to appear in the faint (and presumably distant) samples, at face value it would indicate that the redshifts are large enough to bring the expected rise in the rest-frame ultraviolet into the visible band (Code and Welch 1982). Such a claim, however, must be balanced by consideration of the sizes of random and systematic errors in the colors.

The actual colors to be associated with a particular spectral index are not well known, mostly because the stars used to define the photometric system have spectra that are very different from power-laws. In attempting to determine the color of alpha = -1 in a particular photometric system, we found that different techniques yielded different values by up to 0.15 mag. Hence, the following quoted fractions of blue galaxies are only rough estimates.

The (B - I)AB versus IAB diagram of Lilly, Cowie, and Gardner (1991) shows that only about 20% of the galaxies in the faintest complete magnitude interval, 23.5 < IAB < 24.5, are bluer than (B - I)AB = 0.7. Unfortunately the number of stars in their small area is too few to allow comparison with the colors of the bluest subdwarfs.

The R - I versus R diagram of Hintzen, Romanishin, and Valdes (1991) contains many more objects, but is complete to only R = 24. There is a well-defined blue limit to the stars at about R - I = 0.25, bluer than which there are fewer than 10% of the galaxies within any magnitude interval. The alpha = -1 color is expected to correspond to about R - I = 0.43, and roughly 20% of the galaxies are bluer than this limit.

Similarly, Metcalfe et al. (1991) displayed the color distribution of the objects classified as stars, and in this case the blue edge of the stellar distribution does match closely with the B - R color expected for alpha = -1, namely B - R = 0.70. The fraction of blue galaxies is at most 15% for the faintest B-selected sample, and much less for the R-selected sample.

We estimate that alpha = -1 corresponds very roughly to BJ - R = 0.6 in Tyson's system, which is consistent with the colors of the bluest stars in his survey. His Figure 9 shows BJ - R versus BJ, and approximately half of the galaxies qualify as blue, alpha > -1. The same is apparent in BJ - R versus R (see also Guhathakurta, Tyson, and Majewski 1990a). Earlier we remarked on the sharp trend to bluer colors in Tyson's survey; evidently this trend manifests itself as a population of galaxies that is both bluer and more numerous at a given color than found in the surveys mentioned above.

Color versus near-infrared magnitude diagrams have been presented for K-band selected samples by Elston, Rieke, and Rieke (1990) and by Cowie et al. (1992). The former paper shows R - K versus K, and there appears to be a trend to redder colors in the range 14 < K < 18. Part of this trend is attributable to galaxies at K > 17, R - K > 5, which the authors suggest are luminous, intrinsically red galaxies with an unusually high space density at z ~ 1. The latter paper shows I - K versus K, for which there is no obvious trend of median color with magnitude over the range 16 < K < 22. The baseline in the colors R - K and I - K is so long that in general there is significant curvature over the sampled spectral range, and the adopted criterion a > -1 for blue galaxies is less meaningful.

In summary, the population of faint galaxies with alpha > -1 (or bJ - rF < 0.6 in Figure 2), measured in the visible spectral range, gradually increases and is of order 20% at B ~ 24; these are the blue galaxies to which Kron (1980a) originally called attention. Fainter than B = 24 the fraction may increase to roughly 50%, but this result needs independent confirmation (cf. Lilly et al. 1991). The galaxies with alpha = 0 (i.e. the bona fide flat-spectrum objects) comprise a much smaller fraction, especially once reasonable allowance is made for random errors in the color measurements.

If the rate of star formation in galaxies was generally substantially higher in galaxies at z ~ 0.5, then such an evolutionary effect would be expected to produce a shift toward bluer apparent colors with increasing magnitude. However, there is no strong evidence that these galaxies have especially peculiar luminosities, intrinsic colors, or space densities: In the spectroscopic surveys discussed below, the bluest galaxies at B > 21 have been found to have moderate redshifts (Colless et al. 1990, Cowie et al. 1991). Moreover, because of the color-luminosity relation for field galaxies, the shift to bluer colors is expected even without evolution. The interpretation of the field galaxy color distribution must allow for this effect.

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