The Nature of Compact Galaxies in the Hubble Deep Field. I. Global Properties

We present 10 m Keck spectroscopy and photometry for a sample of 61 small (r1/2 ≤ 0.″5), faint (I814 ≤ 23.74), high-surface brightness (μI814 < 22.2 mag arcsec-2) galaxies in fields flanking the Hubble Deep Field. The majority of this empirically defined sample of compact galaxies lies at redshifts 0.4 ≲ z ≲ 1 (88% completeness in redshift identifications), ruling out a large component of low-redshift galaxies. The number of such galaxies in the range 1.4 ≲ z ≲ 2.2 is also constrained to ≲10%. The majority of the observed galaxies are emission-line systems, while a significant fraction (23%-34%) appear to be normal ellipticals or otherwise early-type systems. One object is an active galactic nucleus, and two are at high redshift (z > 2). The Keck redshift and photometric data are combined with Hubble Space Telescope images to derive luminosities and physical sizes. We also use emission-line widths, where available, to estimate masses. About two-thirds of the emission-line galaxies, or roughly one-half the sample, are small, low-mass, relatively luminous systems with properties resembling those of local H II galaxies. We compare the properties and numbers of these galaxies to the "bursting dwarf" model of Babul & Ferguson. Our sample includes many galaxies similar to the model galaxies in the redshift range 0.4 ≲ z ≲ 0.7, but the majority of our compact galaxies are more luminous (by up to an order of magnitude) than those of the model. The number of galaxies fitting the model parameters are lower by a factor of 2-3 than predicted. An examination of samples used in analyses of disk surface brightness at redshifts z > 0.5 shows that compact galaxies are likely to contribute to the strong disk luminosity evolution found in some studies. Estimates of comoving volume densities indicate that the population of apparent H II galaxies evolves rapidly from redshifts of z ~ 1 to the present. It appears that not all of these galaxies can be progenitors of present-day spheroidal galaxies, although the numbers of them with sizes and masses comparable to spheroidals is not dissimilar to estimates of the local field spheroidal density. We also present 51 additional redshifts, acquired for other projects during the same observing period, for a total of 105 objects with identified redshifts z < 2 in the Hubble Deep Field and its flanking fields.


INTRODUCTION
The Hubble Space Telescope (HST ) has provided enormous insight into the nature of faint Ðeld galaxies through its high angular resolution. In particular, morphological studies have identiÐed a likely major component of the faint blue galaxy excess (see, e.g., as Kron 1980 ; Tyson 1988) late-type, irregular, and/or peculiar galaxies Wind- (Driver, horst, & Griffiths et al. et 1995a ;Driver 1995b ; have set constraints on 1995 ; Abraham 1996) the evolution of early-type galaxies et al. (Im 1996 ; However, deep HST images also reveal numer-1996a). ous small, high surface brightness, "" compact ÏÏ Ðeld galaxies (see et al. for which little morphological GrifÐths 1994), information can be gleaned from the images alone. Such faint, compact galaxies are candidates for low-luminosity dwarfs at relatively low redshift et al. bursting (Im 1995), dwarfs at redshifts that have faded or disappeared by z [ 1 today Songaila, & Hu & Rees (Cowie, 1991 ;Babul 1992 ;& Ferguson low-luminosity AGNs et Babul 1996), (Tresse al. or smaller premerger components proposed to 1996), explain faint galaxy number counts & Rocca-(Guiderdoni Volmerange Ellis, & Glazebrook 1990 ;Broadhurst, 1992) or as part of hierarchical clustering models et (Kau †mann al. et al. Faint compact galaxies are also 1993 ;Cole 1994). likely to include more examples of the moderate-redshift compact narrow-emission-line galaxies (CNELGs ; Koo et al. et al. Because of their small 1994Guzma n 1996). angular sizes, the nature of these faint compact galaxies is best revealed through spectroscopy, which provides redshifts (and hence luminosities and physical sizes), stellar population information, internal kinematics, conditions of the ISM, and star formation rates.
In this pair of papers, we present spectroscopy and photometry of a sample of compact galaxies in the Ñanking Ðelds of the Hubble Deep Field (HDF ;et al. Williams 1996). We deÐne "" compact ÏÏ on purely empirical groundsÈthe objects have small angular size (half-light radius r 1@2 ¹ 0A .5) and relatively high surface brightness (¹22.2 mag arcsec~1 I-band). The present paper discusses the global properties -.4 of these galaxies : redshift distribution, luminosities, sizes, and masses. The sample selection, observations, and many of the analysis techniques are discussed in The proper-°2. ties of the sample are described in discusses°3. Section 4 how these galaxies compare to other observations and the predictions of models. Notes on individual objects, as well as a summary table of redshifts for 51 additional HDF galaxies not part of the compact sample, are included in the Appendix. et al. hereafter discuss spectral Guzma n (1997a, Paper II) line diagnostics, star formation rates, and the signiÐcance of these galaxies to the evolution of the general galaxy population.
This work is part of the DEEP project We . adopt km s~1 Mpc~1 and throughout, H 0 \ 50 q 0 \ 0.05 unless otherwise stated. All magnitudes are on the Vegabased system.

Sample Selection and Size Measurements
The original targets were selected on the basis of high surface brightness within the half-light radius. For the initial selection of targets, photometry of all the HDF Ñanking Ðelds was performed with automated algorithms, measuring the light in a series of circular apertures ¹3A diameter, to derive total magnitudes and half-light radii. The e †ects of neighboring objects were identiÐed by slope changes in the curve of growth, and corrections were applied. Objects brighter than (978 in total) I 814 \ 23.74 and with surface brightness above 22.24 mag arcsec~2 (388 objects) were retained as possible compact targets.
These targets represent galaxies in the upper D37% in surface brightness. Fifty-three objects which followed an obvious stellar sequence were removed from (r 1@2 \ 0A .16) the target pool. Objects that appeared on target lists for other programs (54, consisting mostly of galaxy candidates and highly inclined disks) were also removed from the pool ; we will consider the e †ects of this exclusion below. Targets were selected for spectroscopy from this remaining pool with a slight preference given to objects with the ( Fig. 1a), highest surface brightness. There was no preference based on magnitude.
Following the observations, the HST images I 814 -band of observed objects were reanalyzed in more detail than was feasible to do for the entire catalog (see below). We°2.3 found a few instances where, on the basis of the automated photometry, we had selected features such as bars within large spirals which completely Ðlled the 3A aperture, and highly inclined disk galaxies of fairly large major-axis extent. These galaxies are easy to identify morphologically as elliptical or disk galaxies and are not "" compact ÏÏ in the sense of small angular size. In fact, we found that objects with major-axis radii could be readily identiÐed a 1@2 [ 0A .5 morphologically in the HST images. We therefore added an upper angular size limit of to deÐne the Ðnal a 1@2 \ 0A .5 sample of 63 observed compact objects shown in Figure 1b. The surface brightness has been calculated using the semimajor axis radius, following The correspond-Kent (1985). ing number of potential targets following the Ðnal size cut is estimated to be D245. The corresponding number of galaxies in the catalog meeting the Ðnal size cri-I 814 ¹ 23.74 teria, but of any surface brightness, is D560.
Within our other scientiÐc projects from this run, we observed nine objectsÈmostly elliptical galaxy candidatesÈthat Ðt our compact galaxy criteria. These observations will be presented in detail elsewhere, but the galaxies are included in this paper for purposes of statistical analysis (see We also searched the HDF redshift data°3.1). published by et al. for other compact galaxies, Cohen (1996) Ðnding eight additional galaxies that pass our Ðnal criteria. We have included these galaxies in our discussion whenever possible. However, as we do not know the selection criteria  magnitude for the observed sample of compact targets. These are independent measurements I 814 made following the observations, using isophotal elliptical apertures and masking out neighboring objects. We use the half-light semimajor axis, as a a 1@2 , more stringent criterion for compactness, since highly inclined disks may have a small circular half-light radius and yet are easily identiÐed morphologically. Note that the two smallest objects have been identiÐed spectroscopically as stars (S). The objects identiÐed as early-type galaxies are marked with (E or redshift detection rate for these galaxies, they must be excluded from any statistical analysis. LRIS is a multiobject spectrograph which uses 1995). slitmasks to provide nearly 8@ of available slit length on the sky ; for these observations, we covered 30È40 objects with a single slit mask. Primary science goals targeted objects in the HDF itself, leaving much of the slit mask space in the Ñanking Ðelds available for observations of compact objects. For each slit mask, we obtained a pair of 1500 s exposures with each of the 600 line millimeter~1 red and 600 line millimeter~1 blue gratings, providing continuous spectral coverage from about 4000È8500 at 1.26 A A pixel~1. The e †ective resolution, which depends on the slit width object size, and Keck seeing was about (1A .1), (D0A .9), 3.1 FWHM for stars (see below). Most compact A °3.5 galaxies were observed through only one slit mask, for a total exposure time of 3000 s. The length of each slitlet was greater than 8A in almost all cases, providing adequate room for sky subtraction after accounting for seeing and object size.

Spectroscopic and Photometric Observations
The Ñanking Ðelds were imaged by HST through only the F814W Ðlter We also obtained two 300 s V -band ("" I 814 ÏÏ). exposures with LRIS in direct imaging mode, in order to provide some color information for the compact galaxies. 2.3. HST Image Analysis Using the STSDAS ISOPHOTE package, we Ðtted a series of isophotal ellipses to each image out to 8A and constructed a curve of growth for Ñuxes within those elliptical apertures. This was used to derive an asymptotic "" total ÏÏ magni-I 814 tude and a major-axis half-light radius. During this process, images of neighboring galaxies were masked out. We also attempted to characterize the major-axis proÐle as exponential or r1@4-law, but in many cases the spatial resolution was too poor to do this convincingly.
Comparison of the original photometry used for sample selection and the Ðnal photometry showed good agreement (0.02^0.12 mag rms) in the derived total magnitudes. A slight o †set was seen in the half-light radii, with the semimajor axis radii larger than the preliminary circular by r 1@2 a median amount of 17%, consistent with a median ellipticity of D0.28. A few larger noncompact objects showed signiÐcant deviations, mostly because they were too large for the 3A diameter aperture used in the original photometry.
2.4. E †ects of W FPC2 PSF on Half-L ight Radii Since the objects in this study are so small in angular size, the WFPC2 Point Spread Function (PSF) may have a systematic e †ect on the measurement of half-light radii. In order to test this, we constructed several model galaxies of standard forms (de Vaucouleurs ellipticals and exponential disks) using the IRAF ARTDATA package. The models, of galaxy sizes relevant to this study, were constructed at a pixel scale of pixel~1 and rebinned to the Wide Field 0A .025 Camera scale, pixel~1. We measured these using the 0A .1 same methods as for our sample galaxies and compared the input models and measured half-light radii, as shown in The good agreement between the model input Figure 2a. and the measured radii veriÐes the image analysis technique used above. We then convolved the model galaxy images with a model PSF constructed using TinyTim v4.0 (see the convolution was performed before rebin-Krist 1993) ; ning to avoid undersampling the PSF. These images were then scaled to intensities typical for the Ñanking Ðeld images and appropriate noise was added. The Ðnal images were analyzed and the half-light radii compared At (Fig. 2b). radii larger than e †ects of the PSF on size measure-D0A .4, ments are small (\10%), but at smaller radii the measurements become systematically too large. In particular, the three point sources have measured half-light radii of 0A .14 We Ðnd that, to Ðrst order, the measured half-light 0A .02. radii can be restored to the input values by subtracting 0A .15 in quadrature. The measured radii thus "" corrected ÏÏ are shown in This correction has been adopted in Figure 2c. our subsequent analysis.
These tests also provide a check on the accuracy of our method of photometry. The model galaxies all have the FIG. 2.ÈMeasured half-light radii compared to input radii in model galaxy images, before and after degradation with a WFPC2 PSF and noise (a and b, respectively). Symbols denote r1@4-law proÐles ( Ðlled circles), exponential disks ( Ðlled triangles) and point sources ( Ðve-pointed stars). In (b), the systematic trend toward measurements which are too large at small radii is attributed to the e †ects of the PSF. This trend can be corrected to Ðrst order by subtracting a small constant, in quadrature, as shown in (c The seven objects for which no redshifts could be identi-Ðed all have reasonably strong continua. Four of the seven have ground-based V photometry (the others fell outside the direct image Ðelds). Two of these show relatively red colors consistent only with early-type galaxies (V 606 [ I 814 ) at z D 1, and the other two show colors consistent with an intermediate stellar population at a similar redshift (although the colors are not unique in this latter case). An alternative, that the unidentiÐed objects are halo dwarf stars, is ruled out for all but one object by their extended images. The one possible stellar object, in fact, has a spectral shape rather similar to high-redshift objects, showing what appears to be a Lya break at z D 3.5, but we have been unable to make a convincing match to speciÐc spectral features, nor is its color particularly sug-(V 606 [ I 814 \ 1.16) gestive of such high redshift (see et al. Lowenthal 1997). The total compact object sample is listed in Table 1, along with basic measurements (coordinates, redshift, I 814 magnitude, color and half-light radius), derived V 606 ÈI 814 rest frame parameters (B-band luminosity, size), and velocity width. For the eight compact galaxies observed by others, we have photometry, size measurements, and redshifts but no other spectral information. Notes on selected objects with unusual spectra are provided in the Appendix.

General Spectral Properties
Fifty-one of the 54 compact galaxies with redshift identiÐcations lie at redshifts z \ 2 and display no spectral evidence for AGNs. These galaxies, which make up D95% of  a Also shows emission system at z \ 0.912. our identiÐed galaxy sample, are the focus of our investigation into the nature of compact galaxies. Examination of the spectra reveals four objects with no detectable emission lines but generally strong Ca II H ] K breaks typical of elliptical galaxies. Five more have relatively weak emission lines and again have relatively strong (W j 3727 \ 20 A ) H ] K breaks. These spectra are typical of local spiral galaxies of Hubble types SBc and earlier (Kennicutt 1992), including many elliptical galaxies. We will refer to these continuum-dominated spectra as "" early type.ÏÏ It is not surprising to Ðnd a number of elliptical or bulgedominated galaxies among the compact galaxies ; these galaxies are strongly concentrated in their central regions so that the average surface brightness within the half-light radius is quite high (see, e.g., Furthermore, Kent 1985). surface brightness increases with decreasing e †ective radius among luminous ellipticals so that the (Kormendy 1985), ellipticals most likely to satisfy the surface-brightness cuto † will also be the smallest. In fact, about 25 galaxies were removed from the target pool of compact galaxies based on their elliptical appearance had these been included, (°2.1) ; we might have expected 25 ] (63/245)^6 to fall in our sample. Among the nine galaxies actually observed from this excluded sample for other science programs, seven proved to be early-type, one was a small inclined disk, and one was a strong emission-line object at z \ 0.136.
As noted above, some or all of the seven unidentiÐed galaxies in our compact sample may be early-type absorption or weak emission line systems. Therefore, between nine and 16, or 15%È26%, of the observed sample of 61 galaxies appear to be normal early-type systems. Since the majority of the excluded galaxies were thought to be ellipticals, we need to make a correction to this percentage. To Ðrst order, we may do this by adding the nine galaxies from that sample which were actually observed (comparable to the six we might have expected to observe if these galaxies had not been excluded). Adding these galaxies, the number of earlytype galaxies becomes 16 to 23 out of 70, or 23%È33%.
Most of the remaining galaxies have strong emission lines consistent with later type, star-forming (W j 3727 ? 20 A ), galaxies The spectral properties and star (Kennicutt 1992). formation rates of these objects are discussed in Paper II.

Redshifts
The redshift distribution of the sample, compared with all HDF redshifts to date, is shown in Sources for the Figure 4. total sample are et al. Zepf, & Cohen (1996) 4.ÈDistribution of redshifts of the compact galaxies compared to other galaxies in the HDF, compiled from several sources (see text). The scarcity of compact objects at low redshift is probably caused by our cuto † in angular half-light radius, whereas at z [ 2 we expect few a 1@2 ¹ 0A .5, galaxies to meet our surface-brightness criteria because cosmological dimming becomes severe. Otherwise, the compact galaxies show a generally similar redshift distribution to the other galaxies, although with somewhat less concentration in redshift "" spikes.ÏÏ since target selection varied from group to group and often focused on preselected groups of galaxies, such as the colorselected z [ 2 candidates et al. et (Steidel 1996 ;Lowenthal al. Furthermore, some galaxies in the HDF itself may 1997). Ðt our criteria for compact galaxies (however, none of the 12 objects in from the Lowenthal et al. sample Ðt our Fig. 4 speciÐc criteria).
The sample of compact galaxies appears deÐcient in both low-redshift (z \ 0.4) and high-redshift (z [ 2) galaxies compared to the total HDF sample. Some of this is because of bias in the total sample (e.g., an emphasis on preselected z [ 2 targets), and some is because of our selection criteria. For example, at z \ 0.2, our maximum size of a 1@2 \ 0A .5 eliminates all galaxies larger than kpc from our R e \ 1 compact sample. On the other hand, cosmological dimming quickly becomes severe at redshifts above z D 1, which means our surface brightness cuto † will tend to exclude high-z objects.
Within the range we Ðnd the redshift dis-0.4 [ z [ 1.2, tribution of the compact objects follows the peaks and valleys of the total sample fairly well. There is a suggestion that the compact galaxies are less likely than other galaxies to fall in redshift "" spikes,ÏÏ such as those at, e.g., z \ 0.475 and 0.559 et al. Cohen et al. Ðnd 54 out of 140 (Cohen 1996). HDF galaxies, or D39%, in six such peaks ; statistically, we might expect 18 of our galaxies to lie in the same structures. In fact, we observe only eight, a di †erence signiÐcant at a greater than 99% conÐdence level.
To further quantify these points, we ran a double-sided K-S test on the distributions of the compact galaxies versus the remaining sample (excluding the z [ 2 objects), which we refer to as the "" noncompact ÏÏ sample. The probability that the two samples are not drawn from the same population is 88%. However, restricting both samples to z º 0.4 (where our compact sample will not su †er strong biases) and reducing by one-half the number of galaxies in each redshift spike of et al. brings this likelihood to only Cohen (1996) 3%Èthat is, there is a 97% probability that the compact sample could have come from the same parent population as the noncompact galaxies, were it not for clumping in redshift spikes in the noncompact galaxies. This demonstrates both the general similarity of the redshift distributions for redshifts z º 0.4 and the di †erence of concentration in redshift structures between the compact and noncompact galaxy samples.
We do see a fairly sharp drop in the number of compact galaxies above z D 1, which may seem important in testing the "" bursting dwarf ÏÏ hypothesis (see below), but the°4 drop appears reÑected in the noncompact sample as well and is almost certainly caused by selection biases in our redshift identiÐcations. For example, we are largely insensitive to redshifts where the [O II] j3727 line falls z Z 1.4, beyond the observed spectral range, and thus any identiÐcations must be made using relatively weak UV absorption features of Mg II and Fe II (in fact, we have no secure redshifts in this range). For redshifts beyond z \ 0.95, j3727 enters the wavelength region of intense night-sky emission, so that weak [O II] may easily be missed. It is similarly difficult to make identiÐcations of absorption-line spectra at when the 4000 break enters the night sky forest. z Z 0.85, A For star-forming galaxies, we recover some sensitivity beyond when Lya enters our range of spectra. z Z 2.2, However, there cannot be a large population of sample galaxies in the range since only seven objects 1.4 [ z [ 2.2, out of 63 (11%) remain unidentiÐed.

Colors and L uminosities
The compact galaxies span a range in color, 0.32 ¹ V 606 shows the colors plotted against [ I 814 ¹ 2.05. Figure 5 redshift. The reddest galaxies have z D 0.8, whereas the bluest span the entire range of observed redshift. Most of the galaxies form a broad band at nearly constant while those with early-type spectra form V 606 [ I 814 D 0.9, a reasonably tight red sequence.
In order to show the expected color behavior for galaxies of di †erent types, we have taken three representative spectral energy distributions (SEDs) and calculated V 606 [ I 814 as the spectra are shifted through our photometric passcolor as a function of redshift. The tracks of local FIG. 5.ÈV 606 [ I 814 elliptical, SBc, and starburst (NGC 4449) galaxies are based on observed SEDs (no color evolution). Most of our galaxies lie in the region occupied by local star-forming galaxies, with a signiÐcant fraction having similar colors to NGC 4449. The continuum-dominated systems (E), not unexpectedly, fall near the track of the local elliptical SED. Symbols are as in horizontal bars mark the colors of the four sample galaxies with Fig. 1 Ellis & A. G. Bruzual 1983, private communication). The resulting tracks are overlaid in the Ðgure. The bulk of the compacts lie on or just redward of the starburst curve, agreeing with the spectroscopic identiÐcation of actively star-forming galaxies based on the presence of strong emission lines (also see Thus, the Paper II). majority of the compact galaxies belong to the "" faint blue galaxy ÏÏ population. The spectroscopically identiÐed earlytype galaxies lie between the SBc and elliptical tracks, with an upper envelope just blueward of the elliptical track, as expected for a passively evolving stellar population.
Redshifts allow us to estimate luminosities from apparent magnitude, adopting k corrections based on measured V 606 colors. For this purpose, we used the 11 model [ I 814 SEDs of & Koo see also Gronwall (1995 ;Gronwall 1996), which provide a Ðner sampling of the color-redshift space than the three SEDs above. No evolution with redshift is included in these SEDs. Since most of the compact galaxies lie in the redshift range where the B-band corresponds to the observed V through range the k I 814 (0.25 [ z [ 0.85), corrections should be well constrained. The distribution of luminosities as a function of redshift is shown in Figure 6. The selection cuto † of is shown for the reddest I 814 \ 23.74 and bluest SEDs. The galaxies span a range of nearly 7 mag in with luminosity and redshift strongly correlated M B , because of the magnitude selection criterion. We might expect that the compact galaxies at z D 1, which tend to be L * galaxies, would have little in common with those at z D 0.5 (typically and even less with those at M B * ] 2) z [ 0.2 but this will be shown to be only partially (M B * ] 5), true. The early-type galaxies tend to lie in the upper ranges of luminosity at a given redshift, but this is certainly (at least in part) attributable to a selection biasÈabsorption features are more difficult to identify in less luminous galaxies, particularly at higher redshifts where the strongest features (Ca II H ] K, G band, etc.) can coincide with intense nightsky emission lines.
FIG. 6.ÈDerived B luminosities as a function of redshift. Our e †ective limit of is indicated for two extreme model SEDs. Our sample I 814 [ 23.74 of compact galaxies spans a wide range in luminosity, indicating that we are probably not dealing with a homogeneous group of galaxies.
3.4. Size versus L uminosity Physical properties of galaxies (size, mass, luminosity) tend to follow certain scaling relationships, and we can use these to probe the nature of the compact galaxies. In Figure  we plot B luminosity against the half-light radius in kilo-7, parsecs. These physical radii are based on the major-axis angular radii, corrected for PSF e †ects as discussed in a 1@2 , above. Also plotted are representative values for local°2. We see immediately that the compact galaxies generally fall in the same region of this diagram as the local H II galaxies. For a given luminosity, they are much smaller than Magellanic irregulars. Of course, this is largely a selection e †ect ; the sharp lower bound of the compact galaxies results mainly from the cuto † in surface brightness. Given a reasonable redshift distribution, our selection criteria guarantee that the compact galaxies fall where they do in this diagram.
Also plotted in are the "" compact narrow These are small but luminous H II Guzma n (1996). galaxies, which lie at redshifts A handful of 0.1 [ z [ 0.7. our galaxies reach the extreme small sizes of the CNELGs for a given luminosity, but most are somewhat larger (i.e., less compact).
Except for the early-type systems, the compact galaxies generally lie well o † the sequence deÐned by the luminous spirals and ellipticals. It is reassuring that the early-type systems fall in the expected region. The largest galaxies in FIG. 7.ÈRest frame half-light radii and blue luminosities of our compact galaxies and representative samples of local galaxies of di †erent morphological types. In general, our compact emission line galaxies fall in the same region as local H II galaxies ; a few have the extreme compactness of so-called compact narrow emission line galaxies (CNELGs). Some of the larger compact galaxies, including all of the early-type systems, fall near the sequence deÐned by luminous ellipticals and spirals. our sample are not necessarily the most luminous, but rather fall in the same region as the early-type systems, consistent with being normal galaxies (disks and bulges) of higher than average surface brightness. The similarity among the compact galaxies, local H II galaxies, and CNELGs is shown even more clearly in where luminosity is plotted against rest frame Figure 8, average surface brightness. In this Ðgure, the H II galaxies form a broad band o †set toward higher surface brightness from the spirals and Magellanic irregulars, with the CNELGs deÐning the extreme high surface brightness edge. Again, the compacts fall in the H II galaxy regime, spanning the range from the CNELGs to the spirals with the highest highest surface brightness. Note that the upper envelope of the compacts is set primarily by the upper size cuto †, and so again results from our selection criteria. a 1@2 ¹ 0A .5, 3.5. Emission-L ine W idths Widths of emission lines can provide valuable information about the internal kinematics of galaxies. Our spectra allow us to measure line widths as small as D1 corre-A , sponding to D40 km s~1 at (e.g., Measuring emission-line widths for these galaxies is complicated, however, by many factors such as seeing, slit width, and small galaxy size, all of which have similar scales for distant galaxies. These problems are discussed in some detail in et al. Ðtted by a pair of Gaussian proÐles whose spacing was Ðxed at (1 ] z) ] 2.75 Ó.
Finally, we needed to determine an instrumental proÐle for the LRIS spectra. This is a complicated task, since the slit is resolved, the seeing disk is typically smaller than or comparable to the slit width, and LRIS is slightly undersampled. As an empirical test of the instrumental resolution, we measured narrow absorption features in the spectra of bright stars, which indicated a value of 3.1 FWHM. Also, A we compared model slit proÐles to observed night-sky line proÐles, Ðnding that the instrumental FWHM of the LRIS camera (including the anamorphic factor) must be D1.7 pixels. We used this to model an emission line for a galaxy with and zero internal velocity, following the pror 1@2 \ 0A .3 cedure in Vogt et al.
This model indicated an (1996,1997). e †ective resolution of 3.4 in good agreement with that A , measured empirically. We have adopted the empirically determined value of 3.1 Note that a larger value for the A . instrumental resolution would have the e †ect of making line widths, and thus velocities and masses, smaller. All measured line widths were adjusted by subtracting the instrumental resolution in quadrature and then converted to velocities. Where more than one emission line was available, we calculated a weighted average based on the quality of the individual measurements (see Paper II).
The results are shown in plotted against the Figure 9, physical half-light radius of each galaxy. Since these are all emission-line galaxies, we have split our sample into lower (z \ 0.7) and higher redshift groups to look for any systematic trend. Again, we show the representative sample of local galaxies and CNELGs for comparison.
In the underlying tracks for galaxy masses (in Figure 9, units of assume the virial mass estimation used by M _ ) et al.
This estimate is Guzma n (1996). M^3c 2 /Gp2R e , where is a geometry-dependent factor et al. c 2 (Bender 1992) FIG. 8.ÈRest frame surface brightness and blue luminosities. The surface brightness is averaged within the half-light radius. For clarity, we have plotted separately (a) a local comparison sample (see text) and (b) the compact galaxies of the present sample, distant compact narrow emission line galaxies (CNELGs), and local H II galaxies. Dotted lines indicate the general regions occupied by di †erent classes of local galaxies ; the arrow in (b) represents the direction of simple fading. The compact galaxies form a sequence that crosses the locus of elliptical galaxies and parallels the CNELGs (see text). The galaxies match the locus of local H II galaxies reasonably well. and with compact objects at z [ 0.7 marked with Z. The bulk of the 7 8, compact galaxies at z \ 0.7 fall in the same region as the CNELGs (triangles) and local H II galaxies (crosses). Those at higher redshift tend to be more massive on the average, but only a few approach the region of normal spirals. and is the half-mass radius, which we equate with the R e half-light radius. Exponential proÐles of dwarf systems can be reasonably Ðtted by a King model with a ratio of tidal to core radii of & Cameron For log(r t /r c ) \ 1.2 (Binggeli 1991 shows that the compact emission-line galaxies in Figure 9 our sample span an apparent mass range from about M D 3 ] 109 to 2 ] 1010 extending from the region M _ , occupied by low-mass H II galaxies and irregulars to that of low-mass spirals. Again, many compact galaxies overlap the locus of the CNELGs. Compact galaxies at tend to z Z 0.7 be more massive on the whole, but there is considerable overlap between higher and lower redshift objects. Figure 9 supports the conclusion that the majority (two-thirds) of the emission-line galaxies in our sample are similar to local H II galaxies, with the others likely to be small disk systems.
Note that the position of a point in this diagram is independent of the mass-to-light ratio of the stellar population, provided the star formation has a distribution similar to any underlying population ; only evolution in size and/or mass would a †ect the location of a galaxy in this Ðgure. However, underlying populations are usually larger than regions of intense star formation in starburst and H II galaxies, so fading may produce an increase in (see if the currently observed starburst is 1996) centrally concentrated.
Finally, we present a mass-to-light diagram for the emission-line galaxies in Masses have been esti- Figure 10. mated as discussed above, assuming that velocity widths are indicative of the galaxy mass (see et al. et Guzma n 1996 ;Rix al. However, the validity of this assumption 1997 ; Paper II). does not a †ect comparisons between di †erent classes of galaxies, since all have been treated with the same mass estimation methods.
conÐrms what we would expect Figure 10 from Figures and viz., that the mass to light ratios of 7 9, our galaxies are generally similar to those of local H II galaxies, with a few in the extreme range populated by CNELGs. If we interpret this latter group (M/L^0.1) as CNELGs, we see that our sample extends the population of CNELGs to masses of 1010 Once again, about one-M _ . third of our galaxies appear to be less extreme than the local FIG. 10.ÈDerived masses and mass to luminosity ratios for the same sample galaxies as in Our galaxies span the range in Fig. 9. solar units (dashed lines). Symbols are as in including H II galaxies Fig. 9, (crosses), CNELGs (triangles), HDF compact galaxy ( Ðlled circles ; those at z [ 0.7 also marked with Z). The compact galaxies with M/L comparable to the CNELGs reach masses and luminosities about 3 times higher than previously observed in the CNELGs. show all of our galaxies with measurable 9 10 emission lines, including four weak-lined galaxies classed above as early-type. Three of these four fall in the more massive, M/L D 1 region, and the other lies quite near the M/L D 0.1 line. This latter case (sw3 -1378 -0453) shows a reasonably high ellipticity, 0.32, so its small velocity width almost certainly indicates low mass rather than a projection e †ect. Its major-axis proÐle is clearly exponential, and its color is bluer than that of any of the other early-V 606 ÈI 814 type galaxies. The relative weakness of the emission lines may be due to a poststarburst nature.

Summary of Properties
The major points from the preceding sections are the following : 1. Approximately 15% of our observed compact galaxies are normal early-type galaxies at 0.4 \ z \ 0.9. Correcting for the bias against bright ellipticals in our sample raises the fraction to D23%. It is likely that the true fraction is somewhat larger, up to D33%, if we account for the unidentiÐed objects.
2. Approximately 70% are emission-line galaxies. Of these, about two-thirds appear to be relatively low-mass H II galaxies ; the others are consistent with being small, high surface brightness disk galaxies. Correcting for the excluded elliptical sample, the fraction is reduced to D64%.
4. Only two of our galaxies (D3%) are low-luminosity systems with M B º M* ] 3. 5. Only three galaxies (D5%) fall in the range z [ 0.4. 6. Galaxies in the range cannot account for 1.4 [ z [ 2.2 more than D10% of our observed compact sample.

Fraction of L ow-Redshift Compact Galaxies
The basic properties of the compact galaxies rule out a large fraction of low-luminosity, highÈsurface brightness galaxies at low redshift. This is not surprising, since our cuto † in angular size corresponds to a very small physical size at low redshift ; however, such small, low-z objects would su †er little cosmological dimming and so would be biased toward inclusion in our sample if they existed. Recall that the original observed sample included objects of r 1@2 [ but only two out of the 11 of these we observed were at 0A .5, low z (0.070 and 0.137). We conclude that if a large population of low-z, low-luminosity galaxies exists at these magnitudes, most of these cannot have high intrinsic surface brightness. This Ðnding is in keeping with most locally dwarf-rich models, which generally argue that low-z dwarfs are missed in surveys because they have low surface brightness and thus faint isophotal magnitudes (see, e.g., [ I 814 from our pool of compact objects. The objects with spectroscopic identiÐcations are indicated with Ðlled symbols ; all are conÐrmed to be stars. We also plot the two stars which were found in our compact sample ( Ðlled triangles) and the location of the one AGN observed in our sample (cross). We would expect AGNs to appear among the bluest objects in this plot. It is unlikely that we rejected a large number of AGNs or compact galaxies by excluding starlike objects from our sample.

Frequency of AGNs
Only one galaxy dominated by an AGN was detected in our sample, implying that such galaxies are not common. Our sample could be biased against strong AGNs : if the AGN were several times more luminous than the host galaxy, we might have mistaken it for a star and excluded it during the selection process. Some insight into this comes from the colors of the rejected stellar objects, shown in along with the two conÐrmed stars and the AGN Figure 11 in our sample. Eleven of these rejected stellar objects were observed by et al. and L. L. Cowie (1996, Cohen (1996 private communication) (nine of which have colors measured by us), and all turned out to be stars. We would expect AGNs to have relatively blue colors (see, e.g., et Hall al. so it appears likely that only a few of the presumed 1996), stars could actually be In only four AGNs6. Figure 11, unconÐrmed "" stars ÏÏ lie in the blue region where we might expect missed AGNs to be found ; this means that, at most, 4 ] (63/245)^1 AGN could be missing from our sample.
Using emission-line diagnostics, et al. found Tresse (1996) that at least 8% of galaxies at z \ 0.3 in the Canada-France Redshift Survey (CFRS) display evidence of "" activity, ÏÏ that is, evidence for an ionizing source other than young stars. While analysis of line ratios is deferred to the Paper II, identiÐcation of only one AGN (based on broad Mg II 6 The same question could be asked about extremely compact galaxies being rejected as stars. Some galaxies in our sample have V 606 [ I 814 colors up to D2 mag, and some presumed stars have colors this red. However, our angular size cuto † for exclusion of stars must have been fairly conservative, as no galaxies have yet been found among the excluded starlike sample, whereas two Ðeld stars were found among our selected galaxy sample. emission) in our higher redshift sample does not support a rate of º8%, which would mean at least four such objects out of the 52 galaxies at z \ 2. These numbers are clearly subject to small number Ñuctuations, however. We also note that two galaxies in our sample show weak, narrow Mg II in emission (see Appendix) ; this might be indicative of AGN-like activity, although an examination of UV spectra of various galaxy classes et al. fails to yield a (Kinney 1993) consistent picture as to what kind of galaxies display such emission.
4.3. T he "" Bursting Dwarf ÏÏ Hypothesis Our sample may provide observational evidence for the model of & Ferguson who propose a mixture Babul (1996), of "" normal ÏÏ galaxies (which passively evolve into the local observed galaxy population) and a population of "" bursting dwarfs ÏÏ as hypothesized by & Rees The Babul (1992). Babul & Rees dwarfs arise in "" minihaloes ÏÏ of mass D109 where gas is gravitationally bound but star formation M _ , is delayed until When star formation does take place, z [ 1. a single burst (107 yr) is followed by the expulsion of the remaining gas by supernovae, and the galaxy fades. These bursting dwarfs may explain the excess of faint blue galaxies (see, e.g., Because these bursting Kron 1980 ; Tyson 1988). dwarfs are physically small kpc) but luminous, they (R e D 1 should be well represented in our sample. Do we observe such galaxies ? & Ferguson Babul (1996) give these plausible characteristics for the bursting dwarfs : and 0.47 mag at z \ 1, placing a few more objects into the speciÐed range.) However, most of our objectsÈeven most of the emission line galaxiesÈfall outside the burstingdwarf range, being in general too large and luminous.
shows that all the objects at redshifts are Figure 6 z Z 0.8 more luminous than the model dwarfs, and many of those at lower redshifts also exceed the upper luminosity.
From Figure 10 of & Ferguson we may Babul (1996), estimate the expected fraction of bursting dwarfs in a representative sample whose magnitude distribu-I 814 \ 23.74 tion matched that of our sample. This fraction is found to bê 15% of all galaxies (irrespective of angular size). Working in 0.5 mag bins, we estimate that, if the bursting dwarfs all belonged to our compact galaxy pool, we should see 32 such dwarfs. (On the other hand, if the surface brightness distribution of the bursting dwarfs were the same as that of our total catalog, we should see six.) The I 814 \ 23.74 number of galaxies with the size and luminosity of bursting dwarfs that we actually observe is 11È14, a number too low by a factor of 2È3. This number may be consistent with the & Ferguson model if the pool of compact Babul (1996) galaxies is biased to include a large percentage, but not all, of the bursting dwarfs. On the other hand, it is likely that Babul & Ferguson have somewhat overestimated the number of dwarfs needed by adopting a nonevolving population for the rest of the galaxies, whereas some evolution in that population is both expected from evolution models and observed in late-type galaxies (see, e.g., Driver et al. 1995aDriver et al. , et al. et al. 1995bGlazebrook 1995 ;Abraham 1996). It is interesting to consider those compact galaxies that are too luminous to Ðt the bursting dwarf model. In Figure  we have shown the standard relationship adopted by 12, & Ferguson for the dwarfs, namely, Babul (1996) R e P M1@3 P L 1@3 , and calibrated to their galaxies at peak luminosity. This relationship Ðts our compact galaxies quite well. The majority of our compact galaxies are therefore consistent with starbursting galaxies, but with masses and luminosities an order of magnitude greater than those allowed by the Babul & Ferguson model. We also note that the CNELGs and many of our galaxies lie above the line, demonstrating that galaxies such as CNELGs have even higher surface brightness (i.e., more intense global starburst) than the proposed bursting dwarfs. The origin of such objectsÈwhat triggered the burstsÈremains an interesting question. & Ferguson list a number of critical tests for Babul (1996) their model. The only one we might be able to test is the redshift distribution. The major prediction of the model is a sharp increase in faint blue galaxies at where condiz [ 1, tions Ðrst permit the collapse of gas in the minihalos and bursts can occur. The model also predicts a peak at z [ 0.1 that consists of faded dwarfs, but these will all be lowÈ surface brightness objects and thus missing from our sample. At Ðrst glance, the sharp cuto † in redshift at z^0.95 might be interpreted as supporting the (Fig. 4) model. As noted above, shows that we are not Figure 6 sensitive to Babul & Ferguson dwarfs, whose peak luminosities are beyond z D 0.8 ; that is, we are not M B D [19.3, sampling the relevant redshift range to see the sharp turn-on of bursting dwarfs. Therefore, the redshift distribution of the compact galaxy sample does not test the speciÐc & Ferguson model. Since the apparent drop in Babul (1996) the redshift distribution at is seen among all z Z 0.95 galaxies, not just the compacts, it is likely caused by selection biases in redshift identiÐcation, as discussed in°3.2.
In summary, we Ðnd evidence for a population of bursting dwarfs similar to those discussed by & Ferguson Babul but we Ðnd that the number of them in our sample is (1996), too low by a factor of 2È3 to strictly support the Babul & Ferguson model. We are unable to test the redshift distribution of the model with the current sample.

Comparison with Other Studies
There have been several recent studies of kinematics in faint Ðeld galaxies, mostly dealing with galaxies that are spatially well resolved, at least on HST images. Vogt et al.
sampled emission-line widths in disk galaxies at (1996) similar redshifts. Both of these studies found evidence for only modest increases in luminosity for given rotation velocities compared to local galaxies. On the other hand, Simard & Pritchet found evidence for luminosity (1997) increases of D1.5È2.0 mag in a strong-[O II]Èselected sample for which they could spatially resolve emission lines with the Canada-France-Hawaii Telescope (CFHT). Their galaxies had redshifts of z D 0.35 and had velocities comparable to those of local sub-L * galaxies. However, none of these studies included compact galaxies as we have deÐned them. Three of the Simard & Pritchet galaxies might have been included in our sample if they had been at z \ 0.7 ; two of these show signiÐcantly high luminosities for their velocities compared to local galaxies, and the other shows signiÐcantly low luminosity. The remaining galaxies actually show a somewhat higher o †set to greater luminosities than the potential compact galaxies.
The most relevant kinematical study is that of et al. Rix who measured [O II] line widths in a sample of blue (1997), sub-L * galaxies at z D 0.25. They concluded that the galaxies in their sample exhibit a D1.5 mag increase in blue luminosity relative to comparable local galaxies. It is interesting that our sample galaxies have surface brightnesses roughly 1.7^0.9 mag brighter than spirals and Magellanic irregulars of comparable luminosity Since Rix et al. (Fig. 8). selected their sample on photometric criteria only, we might speculate that their sample contained a signiÐcant fraction of compact galaxies, which are also predominately blue and have a low M/L ratio. While this remains a possibility, a limited number of HST images of a similarly selected sample show mostly well-resolved disk galaxies (P. Guhathakurta 1997, private communication).
Other evidence for brightening of galaxy disks at earlier epochs has been found by Schade et al. (1995Schade et al. ( , 1996bSchade et al. ( , 1996c. The half-light radii of the Schade et al. disks are generally, but not exclusively, larger than those of the compact galaxies. Since reliable measurements are difficult to make for compact galaxies from ground-based observations, we limit our detailed comparison to the galaxies observed with HST Schade et al. Two of the 15 disk-dominated gal-by (1995). axies in that sample Ðt our selection criteria, assuming the usual ratio of exponential scale length to half-light radius. These two galaxies are the two most deviant points with respect to the local size-luminosity relationship and contribute D0.3 mag to the increase in surface brightness found Schade et al. by (1995). Ground-based studies described in Schade et al. (1996a, are consistent with this pictureÈa large number of 1996b) their galaxies (D20%È30% of the total et al. Schade 1996c z [ 0.5 sample) would fall under our compact galaxy classi-Ðcation, and these are the objects showing the greatest deviation from the local relation. If such galaxies are removed from the sample, the amount of brightening is signiÐcantly reduced, although not quite enough to be consistent with the modest levels found by et al. and Vogt et Forbes (1996) al. et al. point out the increase (1996. Schade (1996c) in volume density of luminous small disks at higher redshift, and the data of Schade et al. suggest that the (1996bSchade et al. suggest that the ( , 1996c strongest increase in surface brightness occurs with the smallest disks (also see & Pritchet We associ-Simard 1997). ate these small disks with galaxies in our sample, which we also associate with H II galaxies.
In summary, we have explored a hypothesis that compact galaxies could account for some of the di †erences found in luminosity evolution in several recent studies. There remains no evidence that kinematical studies et al. (Rix & Pritchet have been biased by the 1997 ; Simard 1997) inclusion of compact galaxies in the samples, although it remains a possibility. On the other hand, it appears compact galaxies are present and exert a signiÐcant inÑuence in the samples of Ðeld galaxies studied by Schade et al. (1995Schade et al. ( , 1996bSchade et al. ( , 1996c. 4.5. Evolution of Compact Galaxies The compact objects in our sample are not a homogeneous group. In general, the early-type systems will not evolve strongly but instead will fade and redden slightly. On the other hand, about half of our sample are emission-line objects that appear to be similar to local H II galaxies, and we would expect these galaxies to evolve rapidly. Star formation could terminate in these galaxies, with the galaxies then fading and reddening signiÐcantly as the stellar population ages. If, instead, vigorous star formation continues instead, older stellar populations would accumulate and become increasingly prominent as the galaxies evolve. In either case, these galaxies will not retain the properties of compact galaxies as we have described them. We will focus on the fate of these galaxies.
Continuing the discussion above, et al.

Schade
(1996c) Ðnd comoving volume densities for the smallest luminous disks at to be the same as those for disks D1.5 z median D 0.73 mag fainter at Therefore, one possibility is z median D 0.28. that star formation rates in compacts decline, and they then fade to become small but "" normal ÏÏ disk galaxies. This hypothesis is not well supported by Figures  and  7 8, however. Fading by somewhat more than 1.5 mag would bring the compacts to the edge of the region of the smallest local Magellanic irregulars, but the correspondence is not striking. It is not possible for most of these galaxies to become normal spirals through passive evolution, as seen most clearly in where the location of objects is Figure 9 insensitive to fading.
If compact galaxies are somewhat less extreme examples of CNELGs, they could be the progenitors of spheroidal7 galaxies, as argued by et al. and et al. Koo (1994) Guzma n for the CNELGs. This idea is somewhat supported (1996) by Figures and at least for the lower redshift objects, 7, 8, 9, but most of the higher redshift objects appear to be too large to evolve into the spheroidals seen today.
We can easily derive rough comoving volume densities for the galaxies in our sample, and comparison to local volume densities can shed some light on the nature of these objects. However, we caution that these comparisons are highly uncertain because of the small number of objects involved and sometimes rather questionable assumptions. Furthermore, our selection criteria are difficult to apply to local samples for a proper comparison.
There Finally, if we adopt a relatively conservative "" lifetime ÏÏ of D108 yr, then these numbers should be increased by at least a factor of 20, corresponding to the age width for each redshift interval. This gives a total space density of 1.8 ] 10~2 and 8.1 ] 10~2 Mpc~3 for the descendents of the lower and higher redshift populations, respectively. These densities point to a rapidly evolving population, as the numbers fall a factor of 4 between the two redshift intervals. Note the implicit assumption that the galaxies in each group are the same class of object.
For comparison, the local population of H II galaxies has a volume density of D1.7 ] 10~4 Mpc~3 for M B \ [18 This can be compared directly to the observed (Salzer 1989). low-redshift (z D 0.55) compact galaxy density, 3.2 ] 10~3 Mpc~3, and a density of 1.4 ] 10~2 Mpc~3 for the highredshift (z D 0.85) galaxies extrapolated to the same luminosity. All of these densities have errors D30% from small number statistics alone, and we are assuming that all of the local H II galaxies would meet our compactness criteria at the appropriate redshift. These cautions aside, and assuming again that we are dealing with a single class of galaxies, there is a sharp decline in the density of H II-like galaxies toward lower redshift.
The density of Ðeld spheroidals in the local universe can be crudely estimated as follows : within a D50 Mpc3 volume in the Virgo cluster, Sandage, & Binggeli, Tammann Ðnd 225 spheroidals brighter than (1985) M B \ [13.7, roughly the level of fading we would expect for the compacts undergoing a single burst of star for-M B D [19 mation. Assuming that Virgo has an overdensity of D600 with respect to the Ðeld Binggeli, & Tammann (Sandage, and that the ratio of spheroidals to all galaxies is 0.39 1985), in the Ðeld and 0.60 in Virgo Tarenghi, & (Binggeli, Sandage this gives a Ðeld density of D5 ] 10~3 1990), Mpc~3Èabout 20 times less than that expected for the descendents of the compacts in our sample. This would appear to rule out the majority of our sample galaxies as progenitors of present-day spheroidals. However, we have already noted that most higher redshift compacts are too large to evolve into spheroidals, and yet these higher ( Fig. 9) redshift objects dominate the total space density we have derived. These larger galaxies may have a signiÐcantly different evolutionary path than the ones of size and mass similar to the spheroidals. The volume density of the smaller compact galaxies is within a factor of 4 of the estimate for the local Ðeld population of spheroidals. Given the large uncertainties in our estimates, we cannot rule out the hypothesis that at least some of the compact galaxies in our sample evolve into spheroidals.
Perhaps the most interesting objects in our sample are the relatively massive galaxies that have (M Z 109.7 M _ ) low M/L D 0.1 similar to local H II galaxies The (Fig. 10). low M/L values suggest very high star formation rates per unit mass ; this is conÐrmed in The evolution of Paper II. these galaxies is unclearÈthey are somewhat too large to fade into spheroidals, and apparently neither massive nor large enough to become typical spirals. One possibility is that they are disks forming from the center outward, and so the radius of the luminous material and enclosed mass are small compared to present-day spirals, but this explanation is highly speculative and we have no supporting evidence. This class of compact galaxy remains enigmatic.

CONCLUSIONS
The major conclusions concerning the nature of compact galaxies in the HDF are as follows : 1. Approximately 23% are normal early-type galaxies at 0.4 \ z \ 0.9. It is likely that the true fraction of early-type systems is somewhat larger, up to D33%, if we account for the unidentiÐed objects.
2. Approximately 64% are emission-line galaxies. Among these, about two-thirds appear to be relatively lowmass H II galaxies ; the others are consistent with small, highÈsurface brightness spirals.
3. Approximately 5% are objects at z [ 2 (two) or galaxies dominated by AGNs (one). This fraction could be larger if such objects have a stellar-like appearance, but there is no evidence in our data to support a large population of such objects. 4. Galaxies in the range compose no more 1.4 [ z [ 2.2 than D10% of our observed sample, based on seven objects without redshift identiÐcations.
6. About 25% of the compact galaxies have the physical properties (size and luminosity) of bursting dwarfs as predicted by & Ferguson this number appears Babul (1996) ; too low to be strictly consistent with their model. 7. About 70% of the compact galaxies appear similar to the bursting dwarfs, but with luminosities an order of magnitude higher.
8. Comoving volume densities of those compact galaxies similar to local H II galaxies are very high compared to local values and indicate a strongly evolving population. Their space densities appear too high for all of them to be the progenitors of present-day spheroidal galaxies, but for the smaller compact galaxies, with masses and sizes similar to the spheroidals, the numbers agree to within a factor of a few. However, uncertainties remain too large to draw Ðrm conclusions about compactÈspheroidal connections on the basis of volume densities.
9. Compact galaxies may be responsible for some of the large values of disk luminosity evolution found in recent studies (e.g., Schade et al. This may 1995This may , 1996bThis may , 1996c. help resolve the large discrepancies between these studies and others (e.g., Vogt et al. that examined more 1996, 1997) massive disks.
We thank Caryl Gronwall for helpful discussions and for providing the model SEDs used for k corrections. We are also grateful to Luc Simard for discussions and to the referee for several helpful suggestions. We thank Judy Cohen for help coordinating our selection of HDF targets to avoid overlap. We are grateful, as always, to the sta † of the W. M. Keck Observatory for making these observations possible. Support for this work was provided by NASA through grants AR-06337.08-94A, AR-06337.21-94A, GO-05994.01-94A, AR-5801.01-94A, and AR-6402.01-95A from the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555. We also acknowledge support by NSF grants AST 91-20005 and AST 95-29098. J. G. acknowledges the partial Ðnancial support from Spanish MEC grants PB89È124 and PB93È 456 and a UCM del Amo foundation fellowship. J. D. L. acknowledges support from HF 1048.01-93A.

REDSHIFTS OF ADDITIONAL OBJECTS
The 1996 April Keck observing run of the DEEP project had several science objectives in the HDF besides the study of compact objects. These other projects are described elsewhere et al. et al. et al. (Lowenthal 1997 ;Guzma n 1997b ;Vogt 1997). Redshifts were obtained for a total of 112 targets, as well as for eight additional galaxies that serendipitously fell on slitlets. As an aid to other researchers, we compile in the redshifts of all of the noncompact objects with redshift z \ 2. Combined Table 2 with the redshifts in and the z [ 2 objects presented by et al. these represent all spectral Table 1 Lowenthal (1997), identiÐcations to date by the DEEP group in the HDF and its Ñanking Ðelds.

APPENDIX B NOTES ON UNUSUAL OBJECTS
iw3 -0817 -0556 (z \ 0.960).ÈThis object is identiÐed as an AGN on the basis of broad (FWHM D1800 km s~1) Mg II emission. The spectrum also shows narrow [O II] j5007, [Ne V] j5007, [Ne III] j5007, Hd, and Hc ; presumably there is also a broad component to the Balmer lines, but these fall in the region of intense night-sky lines and the continuum becomes hard to deÐne. There is also a pronounced narrow absorption system at z \ 0.846, showing the Mg II doublet and Fe II at 2344, 2374, 2383, 2587, and 2600 This redshift matches that of the disk galaxy iw3 -0832 -0544, whose center is (18 kpc) from A .
1A .8 the line of sight.
iw2 -0547 -0293 (z \ 2.990).ÈThe Lya line appears asymmetric in emission, with (rest frame) and a strong Lya W j D [4 A absorption trough to the blue. There is also a good match to absorption lines at 1260, 1303, 1335, 1394, 1403, 1527, and 1549È51 The redshift is derived from a cross correlation with the spectrum of a local starburst galaxy, NGC 1741 (see A . et al. Lowenthal 1997). ie2 -0623 -0190 (z \ 2.269).ÈLya does not fall in our observed spectral range, but strong absorption lines at 1527, 1549È51, and 1671 make this identiÐcation secure. There are also good matches with lines at 1260, 1303, 1335, and 1394 The A A . redshifted Fe II lines at 2344, 2374, and 2383 fall in the night sky forest and are plausible but not convincing. As above, the A redshift is from a cross correlation with NGC 1741.
se2 -0021 -0728 (z \ 0.845 and z \ 0.912).ÈThis object has two distinct sets of spectral lines. The principle identiÐcation comes from the semiresolved [O II] emission lines in both cases. The lower redshift system also shows a 4000 break and A probable weak, narrow absorption of Mg II and Fe II in the (rest frame) UV. There is no evidence for a spatial o †set in the [O II] emission. This object is almost certainly a chance superposition of two galaxies widely separated in space but lying along the same line of sight.
oe4 -1223 -1134 (z \ 0.821) and iw4 -1212 -1333 (z \ 0.880).ÈThese two galaxies are unusual because they show narrow Mg II jj2796, 2804 emission. The Ðrst object has clear P Cygni proÐles to the lines ; the second may also have P Cygni proÐles, but the continuum is weaker and we cannot tell with certainty. Both objects have very strong [O II] lines, and strong [Ne III] j3869 lines ; they also show narrow emission lines of Hc and Hd.
hd2 -1747 -0597 \ 12 : 36 : 46.26 ]62 : 14 : 05.7 (J2000) (z \ 0.960).ÈThis object is not part of our compact sample, but we report it here as it is not discussed in any of our other projects. This very red galaxy, whose image shows a sharp core, displays strong Ca II H ] K consistent with a late-type stellar population and an emission system that includes [Ne III] j3869, [Ne IV] j2423, [Ne V] j3426, and (relatively weak) [O II]. The most prominent emission feature is broad, complex Mg II jj2796, 2804, whose poorly deÐned peak corresponds to z D 0.969. Narrow absorption lines of Mg II appear blueward of the peak, at a redshift of z \ 0.958. This object is a reported radio source et al. (Fomalont 1997).