Abstract We present results on two related topics: 1) A discussion of high redshift candidates (z > 4.5) and 2) A study of very small galaxies at intermediate redshifts, both sets being detected in the region of the northern Hubble Deep Field covered by the deep NICMOS elizabethcarroll@example.net and 1.1 microns. The high redshift candidates are just those with redshift z > 4.5 as given in the recent catalog of Thompson, Weymann and Storrie-Lombardi, while the "small galaxy" sample is defined to be those objects with isophotal area ≤ 0.2 2 ′′ and with photometric redshifts 1 ≤ z ≤ 4.5. Abstract Of the 19 possible high redshift candidates listed in the Thompson et al. catalog, 11 have (nominal) photometric redshifts less than 5.0. Of these, however, only 4 are "robust" in the sense of yielding high redshifts when the fluxes are randomly perturbed with errors comparable to the estimated measuring error in each wave band. For the 8 other objects with nominal photometric redshifts greater than 5.0, one (WFPC2 4-473) has a published spectroscopic redshift. Of the remaining 7, 4 are robust in the sense indicated above. Two of these form 1 Based on observations obtained with the Near-Infrared Camera and Multi-Object Spectrometer and the Wide Field and Planetary Camera 2 on the NASA/ESA Hubble Space Telescope which is operated by AURA Inc., under contract with NASA. Abstract -2 -a close pair (NIC 586 and NIC 107). The redshift of the object having formally the highest redshift, at 6.56 (NIC118 = WFPC2 4-601), is problematic, since F606W and F814W flux are clearly present, and the nature of this object poses a dilemma. Abstract Previous work by Colley et al. has suggested that compact sources in the WFPC2 HDF images are subgalactic components at redshifts z > 0.5 since they are correlated on scales less than 1", corresponding to physical scales of less than 8 kpc (H 0 = 65 km s −1 Mpc −1 , q 0 = 0.125). We confirm these correlations in the WFPC2 data. However, we do not detect the correlation of close pairs of galaxies on small scales in the ∼ 0.65 2 ′ region of the HDF that we surveyed with NICMOS. The smaller area surveyed and lower resolution will make any real correlation more difficult to measure in these data. We have examined averaged images of these faint (V 606 ∼ 27-29), compact objects to search for extended, surrounding flux from older, fainter populations of stars. We find no evidence from the averaged images that isolated, compact objects in the Hubble Deep Field are embedded in fainter, more extended galaxies. For three different assumptions about possible star formation histories in these objects we set limits on the total amount of stars which could have been formed in an annulus corresponding to radii between ∼ 6 to 10 kpc, which is typically a few times 10 8 M ⊙ . We suggest that some of these objects may be protogalactic fragments. Introduction The redshifts, number counts, sizes, morphologies, and colors of galaxies are used to determine their evolutionary history and constrain cosmological models. It is therefore crucial to understand what we are counting and measuring as we peer deeper into the history of the Universe where objects appear fainter, smaller, and commonly measured features in rest frame optical wavebands move into the near-infrared and beyond. The optical images of the Hubble Deep Field (HDF; Williams et al. 1996) showed us an exquisitely detailed view of some high redshift galaxies, though the view is inherently distorted (Ferguson 1998) due to the effects of cosmological surface brightness dimming, the effects of dust on galaxy colors, and the fact that we view higher redshift galaxies at progressively bluer rest wavelengths. Introduction NICMOS observations of the Hubble Deep Field provide us with two additional redder wavebands to help disentangle some of these effects. In Thompson, Weymann, & Storrie-Lombardi (2001; hereafter TWS) we presented a comprehensive table of objects detected in these six wavebands, together with estimates for their redshifts, starformation rates and internal extinction, and estimated the global star formation rate as a function of redshift based on these results. We also commented briefly on some objects of special interest. Introduction In the present paper, we discuss in more detail two different, but related subsets of objects relevant to the early formation of galaxies: 1) A set of 19 objects which are candidates for being high redshift 1 galaxies according to Table 1 of TWS, regardless of their morphological properties. 2) A set of objects with estimated redshifts at intermediate values, and which are characterized by being very small, some of which may be protogalactic objects which will eventually be assembled into normal galaxies. 2 The motivation for examining the high redshift candidates is obvious: We would like to understand the epoch and manner in which the earliest episodes of star formation took place. 2 The motivation for our study of the set of intermediate redshift, very small objects stems from a paper by (O'Connell & Marcum 1997) . For these objects, the combination of the brighter, clumpier star-forming regions moving into the optical filters, and surface brightness dimming will make these intermediate redshift, compact, UV-bright objects more prominent than lower surface brightness objects at the same redshift. (Colley et al. 1996) discussed how this is evident in the Hubble Deep Field by measuring the two-point correlation function of galaxies detected in the WFPC2 fields. They found a positive signal in the correlation function for scales ≤ 1 arcseconds for small objects. At cosmological distances this corresponds to subgalactic scales, e.g., 1 arcsecond ≈ 8 kpc for redshifts z > 1 (H 0 = 65 km s −1 Mpc −1 , q 0 = 0.125). This led them to suggest that many of the 'galaxies' detected by source counting algorithms are probably sub-galactic components. Alternatively, some of these very compact objects could well be small protogalaxies undergoing their first episodes of star formation even though they are at somewhat lower redshifts than the high redshift candidates mentioned above. In this case, some models of galaxy formation suggest that one might not expect a strong signal in the two-point correlation on such small scales (Rauch, Haehnelt & Steinmetz 1997 [see pages 603,622] ; Steinmetz 1998) . Understanding this issue is obviously relevant in how we interpret number counts. The two NICMOS bands enhance our ability to detect fainter, older stellar populations that might be connected with brighter starforming regions seen at bluer wavelengths, as well as galaxies whose radiation is attenuated by dust at optical wavelengths. 2 The paper is organized as follows. In § 2 we examine in more detail the list of high redshift galaxies listed in Table 1 of TWS and discuss some of the ambiguities that arise in the interpretation of some of these objects. In § 3 we discuss how the sample of small, intermediate redshift galaxies was selected and the redshift estimates for this sample. In § 4 we discuss averaging the images of fainter galaxies in this sample in order to place limits on the extended flux. In § 5 we discuss the expected extended flux from compact galaxies at intermediate redshifts, based upon moving observed lower redshift star-forming galaxies to higher representative redshifts. In § 6 we examine the two-point autocorrelation function of the optically selected galaxies with high redshift colors and the small galaxies selected in the NICMOS field. In § 7 we summarize and discuss our main conclusions. High Redshift Candidates Examination of Table 1 of TWS reveals that there are 19 objects whose photometric redshifts exceed 4.5 (Note that because of the lookup table in TWS all the photometric redshifts are quantized in steps of 0.08) In Table 1 we reproduce selected columns of those rows from Table 1 of TWS containing these 19 objects, but now sorted according to the photometric redshifts published in TWS. High Redshift Candidates Column 1 contains the NICMOS ID number, and, when identification with an object in the Williams et al. (1996) catalog has been made according to the precepts given in TWS, column 2 contains the WFPC2 identification. Columns 3,4 contain the total and 0.6 arcsec aperture F160W magnitudes. Columns 5 and 6 are the J2000 coordinates (12h 36m is to be added to the RA; +62 degrees is to be added to the Dec.). Column 7 gives the photometric redshift published in TWS. The remaining columns are explained below. In Figure 1 we show, for these 19 objects, the run of χ 2 vs. redshift for the particular extinction and population template selected by our photometric redshift code. By definition, the lowest value occurs at redshifts above 4.5. However, in some cases it is apparent that there are other minima almost as deep at lower redshifts. The absolute value of the minimum χ 2 fit is not a good indicator of the robustness of the high redshift nature of these candidates, since (cf TWS equation (1)), very faint objects will tend to have smaller values of χ 2 than brighter ones for comparable percentage errors in the fitted and observed fluxes. The relative depth of the primary minimum compared to other minima give some indication of the robustness of the photometric redshift. However, as in TWS, a somewhat better indication of the robustness of the photometric redshifts can be obtained by randomly perturbing the fluxes according to the estimates for the distribution of the photometric errors in each of the 6 wave bands of interest-F300W, F450W, F606W, F814W, F110W and F160W, though none of these objects have any measurable flux in the F450W or F300W bands. However, in contrast to the "typical" galaxy in TWS, most of these 19 objects are extremely faint, and the photometric errors relatively large. Consequently, the perturbed fluxes yield photometric redshifts which are far less robust than brighter objects. The distribution of these perturbed photometric redshifts is not remotely Gaussian, or even symmetrical about the median value, but typically will have a very low redshift ( 0 to ∼1) tail in the distribution of the perturbed photometric redshifts, with a discontinuous jump to high values (typically to z > 4.0). For each of the 19 objects in the table, 100 randomly perturbed fluxes were generated and run through exactly the same photometric redshift estimation algorithm described in TWS. For a given object, when these redshifts are ordered, their ranks can thus be crudely regarded as confidence estimates for the redshift. In columns 9 and 10 we give the redshifts at which ∼ 5% of the perturbed set have a lower value, and for which ∼ 10% of the perturbed set have a higher value. In view of the comment above about the discontinuous nature of these redshift distributions, another indicator of robustness is the rank at which the redshift is above 4.0, and this rank is given in column 11. In the discussion below we consider that if this rank is 5 or less (ie, less than 5% of the perturbed redshifts fell below 4.0) then the classification of the object as a high redshift galaxy is "robust". In column 8 the symbol R is used for the robust objects and NR for the non-robust objects. We now give a very brief description of the morphology and run of the χ 2 fit with redshift for each of the robust objects, and, because of its peculiar nature the object with the highest nominal photometric redshift in the TWS list, NIC118.0. NIC131.0: There is a well-defined minimum at the published photometric redshift; all the other secondary minima are much poorer fits. It is a very faint smudge on the F606W image, distinctly brighter and resolved on the F814W image with an indication of a brighter nucleus. Both the F110W and F160W images are slightly resolved and readily visible, though the lower resolution of the NICMOS images prevents detailed comparison between the F110W and F160W images and the WFPC2 F606W and F814W images, a comment that applies to all subsequent objects and will not be repeated. NIC274.0: While there is a well-defined minimum at z = 4.64, a secondary minimum at a redshift of 0.80 is almost as deep, and is fit by a hot unreddened population, whereas the elizabethcarroll@example.net requires some reddening of a hot population. Thus, while this is formally robust against flux perturbations, its reality as a high redshift object is less convincing than for NIC131.0. The F606W image appears compact, while the F814W image appears to have a small extension. The F110W image is bright with no obvious structure, while the F160W image shows a small nearby companion. NIC267.0: A well-defined minimum occurs at z = 4.80, and there is no other reasonable fit. All four images are compact and show no structure. NIC150.0: As in NIC267, the χ 2 plot against redshift shows only a deep minimum at a redshift of 4.80 and no other reasonable fit. There is no WFPC identification and no object is visible on the F606W image. However there are two small slightly amorphous objects clearly visible on the F814W image, one of which agrees well with the nominal F160W and F110W coordinates. However both the F110W and F160W images show the same two small objects with possibly a more diffuse fainter chain-like structure underlying them. NIC277.212: The primary minimum at a redshift of 5.04 is deep, but rather broad. There is also a well defined secondary minimum at a redshift of 0.8, though not nearly as good a fit as the high redshift minimum. The F160W image does not separate this object from a nearby larger and brighter galaxy, but the F110W image shows it as an apparently well-separated object. The WFPC2 images are curious, in that the F814W image is quite bright, but there is no convincing evidence at all of the object in the F606W image, which, given the brightness in the F814W image and the nominal redshift is surprising. Thus, the nature and redshift of this object is somewhat suspect. NIC184.0 = WFPC2 4-473.0: This object has a spectroscopically determined redshift of 5.60 and was the subject of a separate publication ), and will not be discussed further here. NIC645.0: A well-defined minimum exists at a redshift of 5.52, and there is no reasonable secondary minimum. This is an extremely faint object, barely discernible in both F110W and F160W and somewhat diffuse in F110W. The F814W image is readily apparent and slightly elongated, (and hence has a WFPC2 identification), although there is no convincing evidence for flux in the F606W image. In this respect this object is somewhat similar to NIC184.0, (which has the same photometric redshift). NIC586.0 and NIC107.0: We consider these two objects together since they are separated by only about 1.0 arcsec. Both objects are extremely faint. The deepest minimum for NIC586.0 yields the photometric redshift of 5.68, but the minimum is not very well defined nor is the fit very good. The same remarks apply to the χ 2 curve vs. redshift for NIC107.0, whose deepest minimum yields a photometric redshift of 5.92. The F160W image of this pair shows one compact and one slightly diffuse object in a field with several other nearby objects. There appears to be no doubt about the reality of these two objects on the basis of the F160W image. However, the flatfield properties of the F110W image in this area of the chip are rather grainy and noisy and it is difficult to compare the morphology of the two images, and the F110W photometry is quite uncertain. There is a barely discernible very compact object in the F814W image at the appropriate position for NIC586.0, but nothing visible for NIC107.0. No convincing evidence for either object appears in the V image. NIC586.0 and NIC107.0: NIC118.0 = WFPC2 4-601.0: This object was discussed in TWS. It is not a robust object in the sense described above, but we discuss it because it has the highest photometric redshift in the TWS table and because its interpretation is not at all clear. NIC586.0 and NIC107.0: Our measured 0.6" AB magnitudes for the F160W, F110W, F814W, and F606W wavebands are 27.79, 27.68, 30.41 and 30.44 . In a qualitative way, this might be thought consistent with a high redshift, and our formal fit has a fairly well defined minimum at the photometric redshift of 6.56. However at the photometric redshift given in TWS, it is difficult to understand how there could be any flux whatsoever in the F606W band. The significance of the V 606 and I 814 detections in our convolved images is only about 1σ but in the original WFPC2 images this object is detected with a 5.75σ significance. Visual inspection of the images makes it almost certain that there are positive detections in the V 606 and I 814 wavebands and that the V 606 flux is not substantially less than the I 814 flux (see discussion and figure in the appendix). NIC586.0 and NIC107.0: Alternatively, the object might be a lower redshift, but highly reddened object. A second alternative involves the chance superposition of two objects of quite different redshifts. None of these interpretations is at all satisfactory, as discussed in some detail in the Appendix. NIC586.0 and NIC107.0: We close the discussion on high redshift candidates by comparing our photometric redshifts of the 19 objects with redshifts ≥ 4.5 with the only other extensive compilation which extends to high redshifts in our field, namely the catalog of Fernandez-Soto et al. (1999) , hereafter FLY. These authors provide a list of 170 photometric redshifts which fall in our deep NICMOS field on chip 4, which is to be compared with the list of 282 in TWS. FLY based their photometric redshift estimates on the 4 WFPC2 bands augmented by ground-based observations in the standard J, H, and K bandpasses. These ground-based observations have, of course, much lower spatial resolution than the NICMOS images, and the J and H observations do not go nearly as deep as the F110W and F160W NICMOS fluxes. Consequently, for the very faint objects on our list, these ground based observations generally do not yield statistically significant detections. Nevertheless it is of interest to compare the results from the two catalogs. NIC586.0 and NIC107.0: As explained in TWS we cannot make unique associations in all cases with objects from the two lists because of differences in the weight given to different bandpasses in composing the detection images, and in the parameters used by SExtractor in breaking up significant pixels into separate objects. Nevertheless, if we examine the histogram formed by looking at the distance between each object in the list of each of the 170 objects in FLY to the nearest object in the TWS catalog, there is a large cluster of objects with agreement in coordinates less than 0.15" whose median value is about 0.05". There are 155 such objects. Of the remaining 15, all but one are either so near the boundary that we rejected it from our list of 282 objects, or else they fall within the boundaries of a clump of pixels which, for our SExtractor parameters applied to our images, are treated as part of a nearby object. Evidently there are 127 objects in the TWS list which have no clear association with an object for which FLY give a photometric redshift, though in many cases the objects are obviously present but apparently too faint, given the data available to FLY, to derive photometric redshifts. NIC586.0 and NIC107.0: If we confine ourselves to objects in any one of these three lists with redshift of 4.5 or greater, then of the list of 15 FLY objects which have no TWS unambiguous identification, there is one object (FLY #393) which has a photometric redshift of 4.56. On the F160W image it appears as an appendage on the very large low redshift galaxy NIC 26.100 and was not separated with our SExtractor parameters. However, on the V and I images it appears cleanly separated and is almost certainly a separate object. In the list of 127 objects in the TWS catalog not appearing in the FLY catalog there are 13 out of our high redshift list of 19, so there is no basis for comparison among these objects: NIC #s 108, 1075, 150, 92, 693, 562, 96, 1040, 645, 586, 248, 107, and unfortunately, 118 = WFPC2 4-601 the object discussed at length in the Appendix. Finally, among the 155 objects which can be unambiguously associated in both catalogs, there are two in the FLY catalog which do not appear in our list of 19 high redshift candidates: NIC 103 (WFPC2 4-625.1) and NIC 1062.0 (WFPC2 4-600.0 = FLY 471), however in both cases the TWS redshift is just below our cutoff with photometric redshifts of 4.48, compared to 4.52 given in FLY for NIC 103 and 6.52 for NIC 1062.0. We return to NIC 1062.0 below. NIC586.0 and NIC107.0: Our high redshift list contains two objects for one of which the discrepancy between FLY and TWS is mild (NIC 131 = WFPC2 4-530 where TWS obtain z = 4.56 and FLY obtain z = 4.32) and one serious discrepancy (the non-Robust object NIC 287 = WFPC2 4-148.0 where TWS obtain 4.64 and FLY obtain 1.24). NIC586.0 and NIC107.0: In the case of NIC 287 = WFPC2 4-148.0 = FLY#305, our fluxes give a much better fit at z = 4.64 elizabethcarroll@example.net in all three colors (V-I), (I-J), and (J-H). NIC586.0 and NIC107.0: The image of NIC 1062 = WFPC2 4-600 is very curious. It lies about 0.7 arcsec from a much brighter object, NIC61. It is most prominent in the F814W image, where it appears as a somewhat diffuse object with only moderate central concentration. The F606W image is very much weaker and the SNR is much lower than in the F814W image, and its flux will depend upon exactly which pixels are included in the measurement. FLY used the F814W profile as a template for the aperture in which all the other bands were measured, and obtained an AB V-I color of about 2.77-this is presumably what drove their very high redshift value of 6.52 NIC586.0 and NIC107.0: The NICMOS F160W and F110W images are unexpectedly weak, and the contamination from NIC61 appears to be more severe than in the F606W and F814W bands. This makes the flux measurements in the two NICMOS bands problematic. While in principle we might attempt to deblend the NIC1062 and NIC61 images, the SNR of NIC1062 is not high enough in the two NICMOS bands to make this practical. There were 12 pixels in the original "detection map" used in TWS for the NIC1062 fluxes. In an attempt to minimize the contamination from NIC61, we dropped three pixels between NIC61 and NIC1062 and remeasured the fluxes with SExtractor. For these measurements we used only the flux contained within a 3x3 pixel square centered on the coordinates of NIC1062 in the F814W image rather than the 0.6" aperture fluxes of TWS. Even in this case however, the F160W flux and especially the F110W flux may suffer from significant contamination by NIC61. NIC586.0 and NIC107.0: Nevertheless, taking at face value these new flux measurements we still obtain virtually the same redshift for NIC1062 (4.64) compared with that given in TWS (4.48). The fit obtained predicts a flux in the F110W band which is about twice that observed, but the SNR in this band is only about one so the discrepancy is not necessarily indicative of a failure in the template. NIC586.0 and NIC107.0: On the other hand, the very high redshift of order 6.5 obtained by FLY seems very unlikely: Our best fit at this redshift to the fluxes measured in the 3x3 patch predicts an F814W flux which is nearly 7 sigma lower than the observed value. The situation is even worse if, as suggested above, we have overestimated the F160W and F110W fluxes because of the contamination from NIC61. NIC586.0 and NIC107.0: In summary, the detection of 9 robust high redshift candidates with five candidates at redshifts greater than 5 in an area of less than 1.0 2 ′ indicates that adding the near infrared bands to the deep optical images is an excellent way to identify high redshift objects. The flux measurements in the F160W band essentially double the range of identification of high redshift galaxies via the strong Lyman break. It is clear from Fig. 4 of TWS that these galaxies are at or near L * luminosities, indicating that such luminosities exist at high redshifts where the hierarchical models expect very few high mass galaxies. However, since these galaxies have SEDs that are dominated by very high mass, extremely luminous stars, high luminosity does not necessarily imply high mass. In the next section we examine the question of small galaxies at intermediate redshifts. Selecting Compact, Intermediate Redshift Galaxies As noted in the introduction, an exact one-to-one correspondence does not exist between the list of objects presented in this section and that which would result from a similarly selected subset of objects in Table 1 of TWS. As explained in TWS the selection of objects for inclusion in that paper was based upon a "χ 2 " map following the prescription of Szalay, Connolly, and Szokoly (1999) . There, since we had a particular interest in identifying objects to the highest possible redshift, we used only the equally weighted F814W, F110W, and F160W wavebands in composing the χ 2 map. For the present purpose, at the low end of the intermediate redshift regime in which we are interested, there will be important information in both the F450W and F606W WFPC2 images, and hence we used a χ 2 map based upon equal weights for the F450W, F606W, F814W, F110W, and F160W wavebands. However, we used the same significance level to define "significant pixels" (2.3) and the same required minimum number of contiguous pixels (3) in the SExtractor algorithm (Bertin & Arnouts 1996) as used in TWS. Since most of these very small objects are at the very edge of our detection threshold, we elected to measure "isophotal" fluxes (or, more precisely, the flux contained in all the "significant" pixels as defined in the χ 2 map) rather than fluxes measured through an 0.6 arcsecond aperture, in order to keep sky noise to a minimum. Otherwise, the methodology for selection, flux measurement, flux error estimation, the estimates for the photometric redshift, template type and internal extinction as well as their attendant errors, are exactly as described in TWS. The higher resolution images were convolved to match the F160W images. The goal was to select galaxies that are centrally concentrated as well as those where we are only detecting a bright knot measured above our detection threshold. Selecting Compact, Intermediate Redshift Galaxies For our sample of compact objects, we then selected a subset of the objects detected by SExtractor with the parameters described above, using the following criteria: Selecting Compact, Intermediate Redshift Galaxies • The "isophotal" area, as measured by SExtractor on the χ 2 map, is ≤ 0.2 2 ′′ . Selecting Compact, Intermediate Redshift Galaxies • The photometric redshift is 1.0 ≤ z ≤ 4.5. Selecting Compact, Intermediate Redshift Galaxies • The SExtractor parameter FLAGS=0 was required, so we only select objects that are not blended/overlapping with others and are not on the edge of the image. Selecting Compact, Intermediate Redshift Galaxies This resulted in 93 selected galaxies. Selecting Compact, Intermediate Redshift Galaxies As in TWS we tested the robustness of the photometric redshifts determined for this sample by perturbing the fluxes in each of the 6 wavebands, and then running the perturbed fluxes through the photometric redshift estimator. Selecting Compact, Intermediate Redshift Galaxies This set of small compact objects tends to be at least as faint as the high redshift candidates in the previous section, so that once again the photometric errors are large and the resultant uncertainties in the estimated photometric redshifts are very large. In fact, of the 93 galaxies in our sample, only 11 have percentile values z 10 and z 90 within ∆z = 0.5 of the value determined from the unperturbed fluxes. Averaging Images to Place Limits on Extended Flux The 11 robust galaxies identified in the previous section may be separated into three groups: (i) Those with detectable F300W flux with photometric redshifts less than ∼ 2.0, of which there are two. (ii) Those with detectable F450W flux but little or no detectable F300W flux, whose photometric redshifts cluster around z ∼ 2.7, of which there are six. (iii) Three additional objects with little or no detectable flux in either F300W or F450W whose redshifts are around z ∼ 3.9. Groups (ii) and (iii) we refer to as "F300W dropouts" and "F450W dropouts". Averaging Images to Place Limits on Extended Flux For the remaining 82 galaxies, the photometric uncertainties are too large at these faint flux levels to obtain individual reliable photometric redshift estimates. Instead, we simply visually inspected the images in all six wavebands and placed them into one of the three categories above. Even though these are faint objects the quality of the HST images and the availability of six wavebands makes grouping them into categories with and without F300W/F450W flux very straightforward. While this procedure certainly does not provide an accurate redshift discriminant it should provide a rough guide to the redshift range appropriate for these three groups. Averaging Images to Place Limits on Extended Flux From the two groups of F300W and F450W dropout galaxies thus assembled we next selected those which appeared to be "truly small". This was done by visual inspection of the images, keeping only those which have no close companions and show no obvious extended flux. Averaging Images to Place Limits on Extended Flux The objection might be raised that this is a circular procedure, in which by selecting objects showing no extended flux we find objects with no extended flux! But our objective is to discover whether there is any subset of the small galaxies which show no extended flux. This procedure resulted in 14 "isolated F450W dropouts" and 23 "isolated F300W drop" galaxies. Only two of the galaxies with robust photometric redshifts are included in this subsample. We then averaged together each waveband at the galaxy positions and used the fluxes measured from these images to obtain a 'mean' photometric redshift for each 'averaged' F300W drop and F450W dropout galaxy. The F300W dropout mean redshift is in fact z = 2.7 and the F450W dropout mean redshift is z = 3.9. In both cases the hottest galaxy template (a 50 Myr starburst; template #6 in TWS) with a small amount of reddening is preferred. Images for all six HST wavebands for the (averaged) F300W and F450W dropouts are shown in Figure 2 . Averaging Images to Place Limits on Extended Flux Overplotted are 1.0 arcsecond diameter apertures. The galaxies still appear compact in the averaged images. The galaxies in the averaged samples have similar fluxes but we were concerned that the brightest galaxies might dominate the average. We did experiments removing the brightest one or two galaxies from the stack but this didn't change the results. Averaging Images to Place Limits on Extended Flux Since we expect any older stellar population surrounding the small nucleus to be redder than the population comprising the nucleus itself, one check for the existence of such an older population is to measure the colors of the galaxies in successively larger apertures. Within the uncertainties they are constant (Table 2 ). It is difficult to get accurate photometry at these faint magnitudes so we measured the colors with both the SExtractor and IRAF photometry routines. These give consistent results. The errors calculated for the photometry are of order ± 0.1. It can be seen from the table that the uncertainties are at least this large as the 2.5" aperture gives a slightly fainter magnitude than the 1.5" aperture for the F160W filter. Averaging Images to Place Limits on Extended Flux There is no evidence for diffuse, redder flux outside of the core. The F160W images for these "averaged" galaxies were remeasured with SExtractor and yield isophotal diameters of ∼ 0.5", which corresponds to ∼ 4kpc (H 0 = 65 km s −1 Mpc −1 , q 0 = 0.125). If we measure the 3σ limiting depth in the blank elizabethcarroll@example.net microns in a 1.5" − 2.5" diameter annulus we obtain an F160W AB magnitude of 29.3 for the F300W dropout and 29.4 for the F450W dropout. Limits on the amount of previous star formation that we can we infer from these limits are discussed in § 5.2. The Expected Extended Flux from Compact Galaxies In § 4 we set approximate empirical limits on the count rate in the F160W band through an annulus with inner diameter 1.5" and outer diameter of 2.5" associated with the mean of the isolated F300W and F450W dropout galaxies described above. Our failure to detect such extended flux may be interpreted in at least two ways: The Expected Extended Flux from Compact Galaxies 1. They are either the bright nuclei or star-forming knots in galaxies with significantly lower average surface brightness made up of an older, cooler population (we make no attempt to distinguish between these two possibilities). The Expected Extended Flux from Compact Galaxies 2. They are young protogalaxy fragments which are not embedded in an older stellar population. Colley et al. (1996) argue for the former of these two possibilities on the basis of the twopoint correlation function, but our sample from the NICMOS field contains too few objects to make this a decisive test (see § 6). The Expected Extended Flux from Compact Galaxies When we repeat the Colley et al. analysis on the HDF north WFPC2 chips 2,3 and 4 optical data set (see § 6)we also find a significant signal in the autocorrelation function on small scales, but visual inspection of the images shows that the galaxy pairs responsible for the signal are often obviously two pieces of the same galaxy. Clearly, in such cases, the Colley et al. interpretation of compact "galaxies" is the correct one. Simulating Extended, Old Stellar Populations Alternatively, we can ask whether surrounding lower surface brightness material from a putative older population would be expected to be detectable or not if it were placed at either of the two representative redshifts (z = 2.7 and z = 3.9) inferred for the F300W and F450W dropout subsamples described above, and what the limits are for the stellar mass of an extended older population. For illustrative purposes, and to stay as close as possible to the data set we are analyzing, we selected a relatively bright galaxy from the HDF, WFPC2 4-378 (Williams et al. 1996) , with a photometric redshift of z = 1.20 (NIC 124.000 and 1022.00, TWS; the redshift has since been measured spectroscopically at z=1.225 by Cohen et al. 2000.) This object provides a good example of a galaxy with bright star-forming regions surrounded by an older population or less actively star-forming regions. To test the robustness of the photometric redshift estimate with respect to where in this galaxy the flux is measured we selected 4 different aperture positions: 1=bright F160W nucleus, 2=bright F814W off-nuclear knot, 3=dim F814W off-nuclear region, and 4=the whole galaxy. The flux was measured in 0.6" diameter apertures for positions 1 through 3 and a 2.6" aperture for position 4. These are marked on the F606W+F814W image shown in figure 3. It has been scaled and rotated to match the NICMOS orientation and resolution and the image stretch has been set to emphasize the lumpy nature of the morphology. The F606W−F160W colors range from 1.91 for position 1 to 0.86 for position 4. The photometric redshifts for each of these apertures were z = 1.20 or z = 1.25. Simulating Extended, Old Stellar Populations We then measured the flux in an 0.6-1.5 arcsecond annulus centered on the bright nucleus. This is the region we would hope to detect at higher redshift if the compact galaxies in our sample are embedded in a comparable extended source. The best least squares fit between the observed broadband annular fluxes and those calculated on a grid of models in redshift-reddening-population type space for this galaxy is very good and constrains the spectral energy distribution over the range covered from the F300W band to the F160W band fairly tightly (even though there is ambiguity between, e.g., a very hot, but internally reddened population and a somewhat cooler but unreddened population, c.f. the discussion in § 6.3 of TWS). With this best fit model, and the observed flux in the bandpasses which most nearly correspond to the 1.6 micron bandpass if the z = 1.225 galaxy were redshifted to z = 2.7 or z = 3.9, we can calculate the expected flux at higher redshift. (In this calculation we ignore the change in proper length with fixed angle, since over this redshift range this change is very small for most cosmological models.) Figure 4 simulates what we would expect to see if our F300W and F450W dropout galaxies were embedded in WFPC2 4-378.0 at a redshift of z = 2.7 or z = 3.9 and were elizabethcarroll@example.net microns. The redshift z = 2.7 case is on the left and the z = 3.9 case is on the right in the figure. The top panels again show the averaged dropout elizabethcarroll@example.net. The center panel shows how WFPC2 4-378.0 would elizabethcarroll@example.net microns when scaled to the expected brightness at z = 2.7 and z = 3.9. The circles overlaid on the images are 1 arcsecond in diameter. To create the simulated higher redshift images we used the photometric redshift SED template that best fit the measured fluxes of the galaxy at z = 1.225 and calculated what we would detect in the F160W bandpass for this galaxy at if it were at z = 2.7 or z = 3.9. We ignored any changes in angular size as the angular size relation is roughly flat for z > 1. We dimmed the F606W+F814W image showin in figure 3 appropriately and added this and added this to blank 'sky' regions from the full NICMOS F160W image that have been averaged together. The bottom panels were created by adding the dimmed versions of 4-378.0 to the dropout galaxies shown in the top panels. Though the full extent of 4-378.0 would not be visible at either z = 2.7 or z = 3.9, comparison of the top and bottom panels makes it obvious that the resulting simulated version of WFPC2 4-378 at these higher redshifts is larger than the isolated galaxies we have detected, and the flux is readily measurable outside of a 0.6" aperture. Simulating Extended, Old Stellar Populations In § 4 we made averaged images that were centered on the compact source in each field. Simulating Extended, Old Stellar Populations If the objects in our sample are truly off-nuclear star-forming knots in an underlying starforming galaxy, then to make a simulation that more accurately mimics what these averaged images might contain, we have again taken the galaxy WFPC2 4-378.0 and randomly rotated the galaxy around 2 different bright knots, marked A and B in figure 5 which shows the same image as figure 3. We then take 20 of the randomly rotated galaxies and average these together in the same way we made the F300W and F450W averaged dropout galaxy images. The result is illustrated in figure 6 . Simulating Extended, Old Stellar Populations Both of these 'averaged' galaxies now show much more diffuse morphology. (Note that though WFPC2 4-378.0 has a bright nucleus in the F160W band, it is not apparent in the F606W and F814W images. Therefore when we make the dimmed, averaged images for z=2.7 and z=3.9 centered on the off-nuclear knots using the HDF optical images, we are not smearing a bright nucleus into appearing as extended flux.) The results from adding these simulated galaxies to the F300W dropout galaxy and F450W dropout galaxy give a result very similar to what we saw in figure 4. Simulating Extended, Old Stellar Populations At z = 2.7 the diffuse flux is easily detected by eye in the images. At z = 3.9 it is much less obvious. However, when the magnitudes are measured in successively larger apertures, the extended flux is definitely measurable. In Table 2 we showed that the F160W magnitudes for the F300W dropout and F450W dropout galaxies didn't change when measured in 0.6", 1.5", and 2.5" apertures. After adding the simulated, extended galaxies to these images, the F300W dropout galaxy (z = 2.7) is ∼0.4 mags brighter in the 1.5" aperture and ∼0.9 mags brighter in the 2.5" aperture in both the knot-A and knot-B cases. The B-drop galaxy (z = 3.9) is ∼0.9 mags brighter in the 1.5" aperture and ∼1.5 mags brighter in the 2.5" aperture. Though faint, the flux from the extended galaxies is detected over an extent of 2 arcseconds. If the compact galaxies we have estimated to be at redshifts z > 1 were embedded in more diffuse, larger galaxies, such as WFPC2 4-378, we would be able to measure this extended flux in the NICMOS images. Limits on The Star Formation History of the F300W and F450W Dropout Galaxies While the foregoing examples suggest that significant star formation occurring outside the nucleus of distant galaxies, similar in character to WFPC2 4-378 would be detectable in our averaged dropout galaxies, we now address the more quantitative question of limits on star forming activity in these dropout galaxies. Limits on The Star Formation History of the F300W and F450W Dropout Galaxies In § 4 we measured the 3σ upper limit on the flux in the F160W filter in an annulus of 1.5" − 2.5" diameter for the averaged F300W dropout and F450W dropout galaxies. These measurements give F160W=29.3 for the F300W dropout and F160W=29.4 for the F450W dropout. This annulus corresponds to an inner and outer radius of about 6 and 10 kpc, respectively-an annulus centered roughly on a strip whose center is comparable to the sun's galactocentric distance. We now investigate what limits on the star formation history in this region the flux limits imply for these two averaged galaxies. Limits on The Star Formation History of the F300W and F450W Dropout Galaxies In the following we consider models for star formation which commenced at about z ≈ 6.0 Although we have referred previously to a possible underlying "old" stellar population, the intervals of time between the epochs corresponding to z ≈ 6.0 and z=2.7 (for the F300W dropouts) and z ≈ 6.0 and z = 3.9 (for the F450W dropouts) are only about 1.4 and 0.6 Gyrs, respectively, so that we would expect an intermediate age, rather than old stellar population to be present. Limits on The Star Formation History of the F300W and F450W Dropout Galaxies Out of the infinite number of possible star formation histories, we consider three: Limits on The Star Formation History of the F300W and F450W Dropout Galaxies (i) An initial burst of star formation of duration 50my which began at a redshift slightly less than 6.3 and ended at a redshift of 6.0 (ii) An intermediate case in which star formation began at z = 6.0, decayed exponentially with a time constant of 1 Gyr, but with a constant amount subtracted from this exponentially decaying star formation rate, so that at the epoch of observation the star formation rate had reached zero. (iii) A burst of star formation of duration 50mY which ended just at the epoch of observation. The models include dust extinction using the procedure described in TWS, section 3.2. The best fit includes a small amount of extinction. The results are shown in table 3. The three rows represent cases (i), (ii) and (iii) while columns 2 and 4 give the total mass of stars formed over the observed annulus which would just produce the observed 3σ limit on the F160W flux in the annulus. Columns 3 and 5 give the corresponding instantaneous rates of star formation (in solar masses per year) for case (iii). Limits on The Star Formation History of the F300W and F450W Dropout Galaxies In the rest frame of objects at z = 2.7 and z = 3.9, the center of the F160W band elizabethcarroll@example.net microns occurs at 4324 and 3265Å respectively. The limit for the F300W dropout at z = 2.7 is of course considerably more stringent, simply by virtue of being closer than the F450W dropout. For case (i), which postulates a single initial brief burst of star formation at z = 6.0, occurring anywhere in the outer annulus, the hottest stars have left the main sequence. For the F300W dropout case the F160W band flux samples the region just longward of the Balmer discontinuity and a spectrum would show strong Balmer lines from an intermediate age population. For the intermediate case (ii) the SED is qualitatively similar, but a more extended period of star formation implies that the limit on the total mass of stars formed is significantly less. Case (iii) does not refer to an older population, but merely says that the star formation responsible for the images actually seen in the HDF was confined to a small region, and very little could have occurred in the surrounding annulus. The situation for the F450W dropouts is qualitatively similar, except that in addition to the fainter flux as a consequence of the greater distance, the F160W band for this redshift samples rest wavelengths which are shortward of a strong Balmer discontinuity, though in case (ii), the interval of time between the start of the star formation at a redshift of 6 and the epoch corresponding to the redshift of z = 3.9 is smaller than the decay time, and consequently there is still significant flux from fairly hot stars. Spatial Galaxy Correlations Galaxies Selected from WFPC2 Data We examine here the scale on which the galaxies are correlated in the WFPC2 fields to compare with the results of Colley et al. (1996) . They found a positive signal in the correlation function on scales ≤ 1 arcsecond for high and low redshift color cuts. In particular, they found that for the smallest objects, as well as those with colors that suggest they are at redshifts z > 2.5, there is a strong autocorrelation for scales ≤ 0.5 arcseconds. The color cut used was F300W -F450W > 1.2 + F450W -(F814W + F606W)/2 (Steidel et al. 1996) . Galaxies Selected from WFPC2 Data As an estimator for the two-point angular correlation function, w(r), we used (Efstathiou et al. 1991; Roche et al. 1996) , where N dd is the number of pairs in our data set, N dr is the number of pairs in n r randomly placed objects in our field, and n d is the number of objects in our data set. We calculated w(r) in 0.25 arcsecond bins out to a radius of 5.0 arcseconds with n r = 10,000. Galaxies Selected from WFPC2 Data We extracted galaxies from combined F606W + F814W images of the WFPC2 chips 2, 3, and 4 HDF north fields with SExtractor (2.5σ threshold, 10 pixel minimum area). We next selected a catalog of galaxies matching the above color criterion from 71.0" × 69.2" central regions of the chips that miss the lower signal-to-noise regions near the edges. This results in 273, 215, and 222 galaxies from chips 2, 3, and 4 respectively. The results for the autocorrelation function of this high redshift sample are shown in figure 7 . The data are plotted as stars (WF2), triangles (WF3), and circles (WF4). The ±1σ range for no correlation, determined from 500 realizations of 10000 randomly placed points, is shown as the crosshatched region around w(r) = 0. The high redshift color sample has a strong signal for all three WFPC2 chips on scales less than 0.5", confirming the result found by Colley et al. (1996) . The signal is significant at the 3 − 7σ level, and elizabethcarroll@example.net" − 0.5". No significant autocorrelation is seen at separations > 1". When we examine the pairs on the F606W image, it is clear that SExtractor has counted 2 pieces of what appear to be the same galaxy in many of these cases. Two examples of this are WFPC2 4-603.0 (NIC110.000) and WFPC2 4-555.1 (NIC141.112), also known as the "hot dog". Their respective redshifts are z=2.56 (photometric, TWS) and z=2.803 (spectroscopic, Steidel et al. 1996) . Galaxies Selected from NICMOS Data We ran the same analysis discussed in the previous section on our catalog of 93 small galaxies from the NICMOS data set. To determine the uncertainty we ran the same estimator on 500 sets of 93 randomly placed galaxies. The results are shown in figure 8 . In contrast to the results discussed above for the WFPC2 data, we see no correlation signal in the NICMOS data.
{'paper_id': '5668551', 'title': 'High Redshift Candidates and the Nature of Small Galaxies in the Hubble Deep Field', 's2_url': 'https://api.semanticscholar.org/CorpusID:5668551', 'source': 'S2ORC'}