Annu. Rev. Astron. Astrophys. 2000. 38: 667-715
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4.4. Spectroscopic and Photometric Redshifts

The HDF-N and flanking fields have been the focus of some of the most intensive and complete spectroscopic redshift survey work on faint galaxies. Essentially all spectroscopic redshifts in the HDF have come from the W.M. Keck Observatory and LRIS spectrograph [Cohen et al. 1996, Cohen et al. 2000, Lowenthal et al. 1997, Phillips et al. 1997, Steidel et al. 1996, Steidel et al. 1999, Dickinson 1998, Adelberger et al. 1998, Spinrad et al. 1998, Weymann et al. 1998, Waddington et al. 1999, Zepf et al. 1997, Hu et al. 1998]. The most recent compilation is 92% complete for R < 24 in the central HDF-N, and also 92% complete for R < 23 in the flanking fields [Cohen et al. 2000]. The median redshift is z approx 1 at R = 24. Altogether, including unpublished redshifts from the Steidel group, more than 700 spectroscopic redshifts have been measured in the immediate vicinity of the HDF-N, with ~ 150 in the central HDF (WF and PC) alone. This latter corresponds to 30 redshifts per arcmin2, spanning 0.089 < z < 5.60 (and a few stars), a density unmatched by any other field galaxy survey. At the same time, it is sobering to realize that less than 5% of the galaxies from the [Williams et al. 1996] HDF-N catalog have spectroscopic redshifts. The vast majority are fainter than the spectroscopic limit achievable with present-day telescopes. For the HDF-S, the extant spectroscopy is more limited, consisting of about 250 redshifts in an irregular area surrounding the three HST fields [Glazebrook et al. 2000, Dennefeld et al. 2000, Tresse et al. 1999]. Three galaxies at 2.8 < z < 3.5 have been confirmed by the VLT ([Cristiani 1999]). Eleven HDF-S ISO sources have redshift measurements from VLT IR spectroscopy [Rigopoulou et al. 2000].

The estimation of galaxy redshifts using broad-band colors received a tremendous boost from the HDF observations and followup studies. Indeed, the advent of the HDF marked a transition for photometric redshifts, which evolved from an experimental exercise to a widely used technique. This came about for several reasons. Perhaps foremost, as noted above, the WFPC2 HDF data readily detected galaxies as much as 100 times fainter than the practical spectroscopic limits of 10m telescopes. Therefore, in order to interpret the properties of the vast majority of HDF galaxies, non-spectroscopic techniques for estimating redshifts are necessary. Fortunately, the HDF-N WFPC2 data set offered very-high-quality, four-band photometry from 0.3 to 0.8 µm for thousands of faint galaxies, and the extensive followup observations that came later extended this to other wavelengths and wider fields of view. Rapid dissemination of data and source catalogs from the HDF and followup observations made it relatively easy for any investigator to test their photometric redshift method. Indeed, it should be noted that many photometric redshift studies to date have been tested and calibrated solely using the HDF-N.

Several groups ([Steidel et al. 1996, Lowenthal et al. 1997, Clements & Couch 1996, Madau et al. 1996, Madau et al. 1998]) used two-color selection keyed to the passage of the Lyman limit and Lyman alpha forest breaks through the F300W and F450W passbands to identify galaxy candidates at z > 2. Such color-selected objects are variously referred to as Lyman-break galaxies, or UV dropouts. The [Madau et al. 1996, Madau et al. 1998] studies were seminal in combining color-selected HDF samples at z ~ 3 and 4 with previous (spectroscopic, non-HDF) studies at z < 2 to derive a measure of the global history of cosmic star formation, a goal subsequently pursued by many other groups using various kinds of HDF photometric redshifts (see Section 5.5).

More general approaches to photometric redshifts have either fit redshifted spectral templates to the photometric data (e.g., [Gwyn & Hartwick 1996, Mobasher et al. 1996, Lanzetta et al. 1996, Sawicki et al. 1997, Fernandez-Soto et al. 1999, Benítez et al. 1999] for the HDF-N), or have used generalized polynomial fits of redshift vs. multi-band fluxes to a spectroscopic training set (e.g., [Connolly et al. 1997, Wang et al. 1998]). [Cowie & Songaila 1996] and [Connolly et al. 1997] were the first to include IR HDF photometry when deriving photometric redshifts. In principle, this is especially useful in the 1 < z < 2 range where it is difficult to measure redshifts from optical spectroscopy due to the absence of strong, accessible emission or absorption features, and where the strong spectral breaks (e.g. at 4000Å and the 912Å Lyman limit) fall outside the optical passbands. Many other groups have since included IR photometry in their photometric redshift work, using the KPNO 4m JHK images from Dickinson et al. [Fernandez-Soto et al. 1999], or more recently HST NICMOS data [Thompson 1999, Budavari et al. 1999, Yahata et al. 2000].

[Hogg et al. 1998] and [Cohen et al. 2000] have carried out blind tests of the accuracy and reliability of HDF photometric redshifts, comparing photometric predictions by the various groups with spectroscopic redshifts unknown to those groups when the predictions were made. In general, all of the photometric techniques are quite successful at z ltapprox 1.4, where the spectroscopic training sets are extensive, with the best prediction schemes achieving | zphot - zspec| / (1 + zspec) ltapprox 0.05 for gtapprox 90% of the galaxies. At z > 1.9 the results are also generally quite good, with 10 to 15% RMS in Deltaz / (1 + z) after excluding the worst outliers. The intermediate redshift range, where photometric redshifts are particularly interesting, has not yet been tested due to the lack of spectroscopic calibrators.

Photometric redshifts have been used to identify galaxy candidates in both HDFs at z > 5. Two objects noted by [Lanzetta et al. 1996] and [Fernandez-Soto et al. 1999] have been subsequently confirmed by spectroscopy, with z = 5.34 and 5.60 [Spinrad et al. 1998, Weymann et al. 1998]. With the addition of near-infrared data, it becomes possible, in principle, to push to still higher redshifts. Indeed, at z > 6.5, galaxies should have virtually no detectable optical flux. Candidates at these very large redshifts have been identified by [Lanzetta et al. 1998] and [Yahata et al. 2000]. One of these in the HDF-N was readily detected in NICMOS 1.6 µm images by [Dickinson et al. 2000b], but is not significantly detected at J110 or at optical wavelengths. Although this is a plausible candidate for an object at z gtapprox 12, there are also other possible interpretations. It is curious that several of the proposed z > 10 candidates, including this "J-dropout" object in the HDF-N and several of the HDF-S/NICMOS candidates proposed by [Yahata et al. 2000], are surprisingly bright (~ 1 µJy) at 2.2 µm. These would be significantly more luminous than the brightest known Lyman break galaxies at 2 < z < 5. It remains to be seen whether this points to some remarkable epoch of bright objects at z > 10, or whether instead the photometric redshifts for these objects have been overestimated.

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