3.3. Faint blue sub-galactic clumps
Fig. 5a shows the size distribution for the z 2.39 candidates from both the Cycle 5 (shaded, P96b) and Cycle 6 (open, P97) fields in F410M. Most z 2.4 candidates are very compact, with half-light radii rhl 0".1-0".3 or 0.5-1.5 kpc at z 2.4. Their typical rhl 0".2 is smaller than the typical WFPC2 galaxy scale-lengths at these faint magnitudes ( 0".3-0".4 at B 27; see Fig. 1 & O96). Several of the Cycle 6 z 2.4 candidates fall into the rhl = 0".3-0".35 bin, likely due to the lower signal-to-noise of these images and the corresponding tendency to overestimate their true sizes. The z 2.4 candidates, whose cores are in many cases barely resolved by the HST, are typically detected at least 3-4 scale lengths out in the deeper Cycle 5 images, suggesting that here the scale-length measurements are more robust (see Fig. 6a, which also shows a typical stellar profile for comparison). Due to the compactness of these objects, they do not suffer the full cosmological (1 + z)4 SB dimming as truly extended objects do. (Their wings of course do, which is why any disks may have disappeared into the background noise of the WFPC2 CCD; cf. Fruchter et al. 1997, this volume; see also P96b and Section 4.3 below). To derive a mean intensity profile with the greatest dynamic range, intensity-weighted composite images of 14 compact and isolated candidates were produced in each filter, assuming that the candidates are to first order all similar in shape and size at z 2.39 (cf. G96). The total effective exposure times of the image stacks are 14 x 5.7 hours in F606W and F814W and 14 x 16 hours in F450W, and have the best SB sensitivity. To measure the scale-length of the mean observed profile in Fig. 6a, model profiles were convolved with an empirical PSF taken from a star in the images. The B450 and F410M data were almost properly sampled, owing to 0.5 pixel substeps between individual exposure sequences, and the measurements were done on interleaved mosaics on 0.5-pixel centers. In each filter, the profiles are better fitted by an r1/4-law than by a disk-like exponential over a range of almost five magnitudes in SB. The continuum scale-lengths of the candidates have a mean value of 0".11 ( 0.5 kpc at z 2.39) and are very similar in BVI, showing no dependency on restframe wavelength below ~ 4000 Å.
The question arises as to whether or not one is seeing the full extent of these z 2.4 candidates. The K-correction for young spectral-energy distributions at z 2.39 could have compensated for at least some of the cosmological (1 + z)4 SB dimming (W91). Unlike the initial burst of star formation that may take place in ellipticals and the bulges of spirals, disk star formation rates can be almost constant with time (K89). Disks can, therefore, actually brighten toward decreasing redshift for a significant time, eventually reaching an approximately steady level until gas exhaustion. However, with the exception of 53W002 itself, which already has at z 2.39 a r1/4-like profile with a relatively large scale-length (Figs. 5a & 6b), suggesting a massive early-type galaxy (W92, W98), and was by selection included in this WFPC2 field, none of the other candidates are yet fully assembled massive ellipticals or spirals. Their scale-lengths are quite comparable to those of bulges in local spirals, which range from 0.2-4 kpc with a type-dependent median close to 1 kpc for S0-Sbc's. Given that the average value of the bulge-to-disk scale-length ratio of nearby late-type galaxies is ~ 0.07 ± 0.04 (Co96), these z 2.39 candidates may be subgalactic-sized (compact) and young (blue) spheroids, possibly representing the bulges of young galaxies that have not (yet) developed significant disks around them, and/or disks that are reduced in brightness in the HST images by the severe SB-dimming (Section 4.3).
Figure 5. (a) [Top] Histogram of WFPC2 continuum scale-lengths for the significant Ly emitting z 2.4 candidates in Cycle 5 (shaded, P96b) and Cycle 6 (white, P97). The scale-lengths were averaged over BVI and are typically 0".1-0".3; (b) [Bottom] Histogram of WFPC2 V606 luminosities for the significant Ly emitting z 2.4 candidates in both the Cycle 5 & 6 fields. The upper axis indicates their absolute magnitude distribution. The (evolving) L* value is indicated by the upward arrow. AGN contributions were subtracted in a few cases as indicated (cf. W92, P96b). The labeled boxes represent the five spectroscopically confirmed z 2.4 candidates of P96b, with Seyfert, Quasar, Galaxy-like objects indicated.
Fig. 5b shows the luminosity distribution of all significant F410M z 2.4 candidates from Cycles 5 (shaded, P96b) and 6 (open, P97). The implied luminosities at z 2.39 for all candidates range typically from MV -23 to -18 mag, based on the stellar population models, age estimates, and K-corrections from W91. With BVI photometry, the K-corrections are straightforward, provided that redshifts are known to be at z 2.39 either from spectroscopy or from the (F410M-B450) colors. Subtraction of any contributions from an AGN was done following W92. The (evolving) absolute magnitude of an L* galaxy at z 2.4 is MV -23 mag, assuming that there would have been ~ 2 mag of luminosity evolution since z 2.39 for a typical starburst ~ (0.3-0.5) x 109 years earlier, as the candidates' unreddened blue colors suggest (Fig. 4 & P96b).
Figure 6. (a) [Top] Average light profiles vs. radius (in r1/4 units) of the 14 z 2.39 candidates without neighbors in BVI (see P96b). The profiles are reliable for radii between the two vertical dotted lines, but are affected by the WFPC2 PSF etc. at smaller radii, and by sky-errors at larger radii. The stellar PSF is plotted in B450 (short dashes) to illustrate that these compact clumps are indeed barely resolved by HST. Solid lines indicate best-fit r1/4 model profiles; (b) [Bottom] Light profiles in BVI for the extended component of the radio galaxy 53W002 at z = 2.390 in the quadrant that is relatively free of the blue clouds (Section 4.2 & W98). The central AGN and blue clouds were subtracted in each filter, using a faint star as PSF (W98). Short dashes represent the 25% AGN component in B, which affects the profile for r1/4 0.5 (r 0".06). The horizontal dotted lines indicate the 2 sky-subtraction errors, which affect the profiles for r1/4 0.8 (r 0".4). For 0.5 r1/4 0.8 (0".06 r 0".4), 53W002's profile is consistent with an r1/4-law, but at large radii it is affected by the blue clouds (Section 4.3.4).
The z 2.4 sample is not complete for V606 25.5 mag (MV -20 mag), as shown by the downwards arrows, which indicates the shallower completeness limit of the underexposed F410M images, compared to B450 or V606. Given this completeness limit, the true luminosity distribution of the z 2.4 candidates thus likely continues for MV -20 mag, and the initial (luminous) mass spectrum of this group of z 2.4 candidates could be quite steep. The Cycle 5 and Cycle 6 F410M data sets contain mostly z 2.4 candidates with MV -20.5 to -21.5 mag. Assuming that most significant F410M emitters are at z 2.4 and given the K-corrections discussed above, these are sub-L* luminosities. Therefore, if indeed their stellar populations are young, most of the z 2.4 candidates have luminosities of 0.1-1 L*, and so possibly had only ~ 109-1010 M processed into stars at z 2.39. For these parameters, the free-fall time expected for these clumps is ~ (2-4) x 108 years, long enough that the original population of short-lived O and early B stars are gone, but comparable to the age of the dominant stellar population (late B and early A stars). Hence, there was indeed enough time for their mass distributions to settle into regular r1/4-like light profiles.