A New Window on Galaxy Formation and Evolution

Sensitive sub-mm observations present the first opportunity to detect dust in normal galaxies at high redshift. At wavelengths around 100 microns, the bulk of the luminosity of normal, star-forming galaxies is reprocessed star-light from dust and so observations in the sub-mm band can provide robust estimates of both the dust mass and total star-formation rate in a galaxy. Furthermore, the negative K-correction at wavelengths longer than 400 microns means that sub-mm observations select star-forming galaxies at z > 1 in an almost distance-independent manner, providing an efficient method for the serendipitous detection of star-forming galaxies at very large redshifts, z < 10 (Blain & Longair 1993). The potential power and sensitivity of sub-mm observations for investigating galaxy evolution has provoked considerable theoretical interest (Blain & Longair 1993, 1996 - BL96; Blain 1996, 1997; Guiderdoni et al. 1997; Franceschini et al. 1997a, 1997b; Eales & Edmunds 1997). Realistic simulations including instrumental sensitivities and the assumed spectral properties of the sub-mm populations indicate that such surveys have the best chance of success at 850 microns with SCUBA (BL96; Franceschini et al. 1997a).

Most published sub-mm studies of distant galaxies have targeted atypical galaxies (e.g. radio loud galaxies, Ivison et al. 1997). We report here the first deep sub-mm survey to probe the nature of normal galaxies at moderate and high redshift, z = 0.5 - 5. In this study we have attempted to maximise the available sample of distant galaxies by concentrating on fields in moderate-redshift clusters. While the dominant spheroidal populations of these clusters are expected to be quiescent in the sub-mm band, the in-fall of field galaxies associated with the growth of the clusters (Smail et al. 1997) means that these fields may contain over-densities of moderate-redshift field galaxies, as compared with `blank' field surveys.

The main attraction of the clusters observed here, however, is that they are strong gravitational lenses, magnifying any sub-mm source lying behind them (Blain 1997). Given the expected steep rise in the sub-mm counts (BL96), this amplification bias could increase the source counts in these fields by a substantial factor (Blain 1997). Thus these two effects are expected to increase the sub-mm counts in cluster fields above those predicted in typical blank fields, and so the counts in these fields provide upper limits to those in blank fields. The gravitational amplification by the cluster lens alone indicates a maximum surface density of < 10 sources per SCUBA field down to 1 mJy at 850 microns (c.f. Blain 1997). Moreover, by targeting those clusters which contain giant arcs, images of distant field galaxies that are magnified by factors of 10 - 20, we can also obtain otherwise unachievable sensitivity (< 0.1 mJy at 850 microns) on the dust properties of a few serendipitously-positioned normal galaxies at high redshift.

We have started a program to map the core regions of moderate redshift clusters in order to probe the sub-mm properties of intermediate and high redshift field galaxies, including the large population of background galaxies amplified by the cluster lenses. The angular scales of the region where highly magnified high-redshift galaxies are likely to be found is well-matched to the SCUBA field-of-view. In the following sections we give details of the observations and their reduction, and discuss the results within the framework of current theoretical models of galaxy formation and evolution. We adopt H_o = 50 km/s/Mpc and q_o = 0.5.

The maps, linearly interpolated onto an astrometric grid using an approximately Nyquist sampling, of 2 and 4 arcsec/pixel at 450 and 850 microns respectively, are presented in Fig. 1. These maps have been smoothed to the instrumental resolution and have had their boundaries apodized for the purposes of display. Even without including a factor to account for the lensing amplification, the data shown in Fig. 1 are the deepest sub-mm maps ever published, and illustrate the cosmetically clean and flat maps achievable with SCUBA in long integrations.

Fig. 1. The 450 and 850 microns maps of the two fields: a) A370, 850 microns; b) Cl2244-02, 850 microns; c) A370, 450 microns; d) Cl2244-02, 450 microns. The maps are smoothed to the instrumental resolution at each wavelength and are displayed as a grayscale from -4 sigma to 4 sigma, the contours are positive and show 3, 4, 5, 10, 15 sigma for each field. The major tick marks are 20 arcsec in all panels.

Source catalogs from our fields were constructed using the Sextractor package (Bertin & Arnouts 1996). The detection algorithm uses the criterion that the surface brightness in 4 contiguous pixels exceeds a threshold, after subtracting a smooth background signal and convolving the map with a 4 x 4 pixel top-hat filter. Our observations are far from being confusion limited at the current depth (60 beams per source).

First, to assess the contribution of noise to our catalogs we re-ran the detection algorithm on the negative fluctuations in the map. This gives a simple estimate of the number of false-positive detections that may arise from the noise, assuming that the noise properties of the map are Gaussian. We estimate that there are no false detections in our catalogs, and so we conclude that all the detections are real. The presence of the brightest source in the reference beams (60 arcsec to the East and West in the 850 microns map of A370) was disregarded. This detection, however, does confirm the reality of positive features at this faint level, while the absence of any other negative detections limits the number of luminous sources which can lie in the regions covered by the reference beams.

Secondly, to determine the completeness of our sample we added a template faint source to the maps repeatedly, re-ran our detection algorithm and estimated the efficiency of detecting this source as a function of its flux density. This should provide a reliable estimate of the visibility of a faint compact source in the maps. The template source was a scaled version of our calibration source, Uranus. The incompleteness limits are relatively bright for the 450 microns maps because a large proportion of the flux density (about 40%) is found in the low surface brightness wings of the point spread function. The simulations also indicate that the measured 850 microns flux densities are unbiased and are typically accurate to 10% at 25 mJy and 30% at 4 mJy.

We will discuss the detailed properties of the sources in another paper (Ivison, Smail & Blain 1997), where we also place limits on the dust masses of the numerous strongly-lensed distant galaxies covered by our maps. However, we note that, based on their weak or non-detection at 450 microns, all of the 850 microns sources in our sample appear to have the sub-mm spectral characteristics of distant (z > 1) star-forming galaxies and are thus unlikely to be associated with the clusters.

Converting the observed number of sources into a surface density and correcting for incompleteness, we determine a cumulative number density across our two fields of 2400 +/- 1000 per square degree down to a 50% completeness limit of 4 mJy at 850 microns (all errors include only Poisson contributions). At 450 microns, the single source we detect places only weak limits on the likely surface density: 1000 +/- 1000 per square degree brighter than 80 mJy. These surface densities should be upper limits to those in a typical blank field because of both a possible excess of star-forming cluster galaxies and also the amplification of background sources by the cluster lens.

We now estimate the likely lens amplification factors, and so place tighter limits on the typical blank-field counts. Because the distances to the detected sources are unknown, this estimate will, by necessity, be crude and so we have not attempted a detailed analysis. The cluster potentials are modelled as isothermal spheres with masses and centers determined from the redshifts and observed shapes of the giant arc in each cluster (Kneib et al. 1993; Smail et al. 1996). In these models the mean amplification factors for background sources (z > 1) are about 2 and 1.3 in the regions covered by our maps of A370 and Cl2244-02 respectively, while the observed area of the maps (5.4 square arcmin at 850 microns) corresponds to 1.8 and 4.0 square arcmin in the respective source planes. Correcting the flux densities of our sources to take account of the probable lens amplifications, but not correcting for incompleteness, we predict the source counts presented in Fig. 2. These indicate integrated number densities in blank fields of 2500 +/- 1400 and 3600 +/- 1600 per square degree to flux limits of 4 and 3 mJy respectively at 850 microns.

Fig. 2. Models of the integral number counts of sources at 850 microns in a parametric model of galaxy evolution, adapted from BL96 and from a simple model based on the limits on strongly star-forming systems in optical surveys of distant galaxies. The observations are represented by filled circles, with error bars showing the Poisson errors on the integrated counts, note that the errors are not independent on the various points. The observations have been corrected for the effects of lens amplification using simple models for the cluster lenses, but no corrections for incompleteness have been applied. The solid curves represent, in order of increasing predicted counts, models that include: no evolution; (1+z)^3 evolution with z_max = 2 and z_0 = 5 (Model A); and (1+z)^3 evolution with z_max = 2.6 and z_0 = 7 (Model B). The dashed lines represent models where we fill the Universe across z = 0 - 10 with a constant density 0.6E-4 per cubic Mpc) of star-forming galaxies with fixed star-formation rates. In order of increasing predicted counts the dashed lines represent star-formation rates for the population of: M = 20, 50 and 150 M_solar/year, where we have assumed a dust temperature of 60 K. Clearly only models including high densities of strongly star-forming galaxies are compatible with the observed surface density of sources.

From the flux densities associated with the resolved sources in the fields we calculate lower limits to the background radiation intensities of 2.6E-10 and 2.4E-10 W/m^2/sr at wavelengths of 450 microns and 850 microns respectively, averaged over both fields. By extrapolating the 850 microns counts using our best-fit model (Fig. 2) to faint flux densities, we estimate total intensities of diffuse extragalactic background radiation of about 26E-10 - 28E-10 and 4.4E-10 - 6.7E-10 W/m^2/sr at wavelengths of 450 and 850 microns respectively. These background radiation intensities are broadly consistent with the tentative detection of an isotropic component of the background radiation in the sub-mm by Puget et al. (1996). If we assume that all of the background radiation intensity we infer is due to the formation of massive stars, then we expect that a density parameter of heavy elements of < 6E-4 will have accumulated in the Universe by the present epoch. This density corresponds to about 1.1% of the density parameter in baryons Omega_b if Omega_b = 0.05, and so it is fully consistent with present limits. We reiterate, however, that these are tentative estimates, the accuracy of which depends on the models assumed for both the lens and the form of the counts of distant galaxies.

Due to the negative K-corrections expected for distant galaxies, sub-mm observations provide a good estimate of the volume density of luminous star-forming galaxies at z > 1. In the absence of redshifts for all the sources, the evolution of this population can be understood by comparing parameterised models to the counts (BL96). The BL96 models are based on the 60-micron luminosity function of IRAS galaxies (Saunders et al. 1990) and assume that the luminosities evolve as (1+z)^3 out to a redshift, z_max, and then maintain the enhanced luminosity out to a cutoff redshift, z_0. The form of this evolution is motivated by the observations of similar behaviour in both the radio galaxy and QSO number counts (Dunlop & Peacock 1991) as well as the luminosity density of field galaxies at z < 1 (Lilly et al. 1996). BL96 also give predicted counts for a non-evolving model using the same luminosity function. The adopted parameters for the models described in that paper give source counts which roughly span the range predicted by other similar works (e.g. Guiderdoni et al. 1997). In Fig. 2, we plot both the no-evolution case and two other parametric models based on BL96: model A - Model 2 in BL96 - with values of z_max = 2 and z_0 = 5; and model B, has z_max = 2.6 and z_0 = 7, although most combinations of z_max 2.2 - 2.9 and z_0 > 5 give comparable results.

From Fig. 2 it can be seen that the no evolution predictions fall short by 2 - 3 orders of magnitude of the observations. Thus, this first analysis of a deep sub-mm survey indicates that the number density of strongly star-forming galaxies and hence the mean star-formation rate in the distant Universe is considerably larger than that seen locally. To estimate the extent of this evolution we assume that all the detected sources lie beyond the clusters. We then require strong evolution, of the form given in model B, out to z > 2 to fit the 850 microns counts. For consistency, we check the predictions from model B for the observed counts at 450 microns; 0.7 sources are expected in the two fields, in agreement with the single detection.

We conclude from the 850 microns counts that the integrated star-formation rate in the Universe, as traced by the number density of the most luminous sources, must continue to rise out to z > 2, extending the trend observed at z < 1 (Lilly et al. 1996). The inferred form of evolution corresponds to an increase in the sub-mm luminosity density by a factor of > 10 - 40 at z > 1. At z > 1, the typical luminosity of the star-forming sources we detect is L(FIR) = 0.5E13 - 1.0E13 L_solar, with a star-formation rate of M > 100 - 300 M_solar/yr. Using the observed surface density of these objects and assuming a constant space density of sources between z = 1 - 5, we estimate a number density of strongly star-forming galaxies of: N(M > 150 M_solar/yr) = 1.2E-4 per cubic Mpc, at z > 1.

Limits on the number density of strongly star-forming galaxies at z = 2 - 3.5 have recently been published by Madau et al. (1996) on the basis of Lyman-dropout surveys. Their limit is N(M > 20 M_solar/yr) < 0.6E-4 per cubic Mpc. We plot in Fig. 2 three models using this limit on the number density of sources to uniformly populate the volume from z = 0 - 10, but allowing the corresponding star-formation rate to vary. The star-formation rates used in the three models are: 20, 50 and 150 M_solar/yr, representing the maximum star-formation rate allowed by Madau et al. for this number density, the Madau et al. star-formation limit corrected for dust extinction by the factor of 3 suggested by Pettini et al. (1997) on the basis of the rest-frame UV colors of the distant population, and a mean star-formation rate closer to that needed to fit our observations. From Fig. 2 we see that a galaxy population which complies with the limits from the optical survey of Madau et al. predicts a source density 3 orders of magnitude less than are observed. Even including modest dust extinction proposed by Pettini et al. still under-predicts the observed surface densities (unless the dust in this population is very cold, 40 K, and they have extremely large dust masses). To match the observed surface density of 850 microns sources we must significantly increase the mean star-formation, either by further increasing the star-formation rate associated with the optically-selected samples or more probably by introducing a population of strongly star-forming, but highly obscured, distant galaxies missed by the Lyman-dropout surveys. The number density of these sources is comparable to that of L* ellipticals at the present day if these formed in a short period of time, < 1 Gyr. Moreover, the star-formation rates implied for such a population are similar to the limits we derive. We suggest that the highly obscured, but strongly star-forming population represents the formation phase of luminous elliptical galaxies. Forthcoming deep sub-mm surveys (BL96; Pearson & Rowan-Robinson 1996) are thus necessary to provide the unbiased view of star-formation in the distant Universe needed to understand galaxy formation.

In conclusion then:

We have presented the first sub-mm survey of the distant Universe, deep enough that we should detect the evolving galaxies predicted by current theoretical models, while at the same time covering a sufficiently large area to be statistically reliable. We derive cumulative source counts of 2400 +/- 1000 per square degree down to 4 mJy at 850 microns.

The surface density of faint sources in the sub-mm far exceeds a simple non-evolving model using the locally observed 60-micron galaxy luminosity function. Thus our observations require a substantial increase in the number density of strongly star-forming galaxies at z > 1.

Comparison of our observations with the predictions of simple parametric models indicates that the luminosity density of the brightest sub-mm sources must increase out to at least z = 2. This conclusion appears to contradict the recent claims of a deficit of very strongly star-forming galaxies in optically-selected samples of distant galaxies (Madau et al. 1996). We suggest that such samples may be missing a considerable population of strongly star-forming, dust-obscured galaxies at these epochs.

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Ian Smail (Durham), Rob Ivison (IfA, Edinburgh), Andrew Blain (MRAO, Cambridge)