8. SUMMARY AND CONCLUSIONS

Based on surface photometry from HST/WFPC2 and simultaneous ground-based surface spectrophotometry from Las Campanas Observatory, we find mean values for the flux of the EBL23 (the background light from sources fainter than V = 23 A B mag) as follows: I_F300W = 4.0 ± 2.5, I_F555W = 2.7 ± 1.4, and I_F814W = 2.2 ± 1.0 in units of where uncertainties quoted are 1 combined statistical and systematic errors. These results are presented in detail in Paper I and are summarized in Section 3. Adding in the flux from sources brighter than V = 23 A B mag (see Table 2), we find the total EBL flux is I_F300W = 4.3 ± 2.6, I_F555W = 3.2 ± 1.5, and I_F814W = 2.9 ± 1.1 cgs.

In the context of these measurements of the EBL, we have discussed constraints on the slope of number counts, the luminosity density as a function of redshift, the fraction of galaxies which lie below current surface brightness detection limits, and the history of stellar nucleosynthesis and metal production in the universe. We reach the following principle conclusions:

(1) We find that the corrected number counts at V and I magnitudes fainter than 23 A B mag obey the relation N 10^m with = 0.33 ± 0.01, and = 0.34 ± 0.01, respectively, which is consistent with the slope found at brighter magnitudes (e.g. Smail et al. 1995, Tyson 1988). This is significantly steeper than the slope of the raw HDF number counts (~ 0.24 ± 0.1 at V > 23 A B mag, and ~ 0.22 ± 0.1 at I > 23 A B mag). In contrast with the raw counts, the corrected counts show no decrease in slope to the detection limit. If we integrate the corrected number counts down to an apparent magnitude corresponding roughly to a dwarf galaxy (M_V ~ - 10 mag) at z ~ 3, V ~ 38 A B mag, we obtain a total flux of 1.2 × 10^-9 cgs in both V and I. This is 1.2 below the mean EBL23 flux we estimate at V₆₀₆ (I₈₁₄), suggesting that number counts would need to be steeper over some range in apparent magnitude fainter than the current detection limits in order to obtain the mean EBL flux we detect, or that the value of EBL23 is roughly ~ 1 below our mean detections at V and I.

(2) Based on a local luminosity density consistent with Loveday et al. (1992), passive evolution in the luminosity density of galaxies under-predicts the EBL by factors of roughly 3, 2, and 2 at U₃₀₀, V₅₅₅, and I₈₁₄, respectively. Note, however, that if the local luminosity density is a factor of two higher than the Loveday et al. values we have adopted here, as found by Blanton et al. (2001), then passive evolution agrees with the flux in resolved galaxies (minEBL23) and with our mean EBL detections to within 1. The mean detected EBL therefore requires stronger evolution in the luminosity density than passive evolution will produce, however, the exact form of that evolution is not well constrained by our results.

Adopting the local luminosity density assumed by Lilly et al. (1996, CFRS), the 1 upper limits of the cumulative flux measured by Lilly et al. from redshifts 0 < z < 1 is smaller than the flux in resolved sources by more than a factor of 2: this fact alone demonstrates that significant flux must be contributed by galaxies at redshifts z > 1. If we adopt (, z) (1 + z)⁽⁾ for the luminosity density at 0 < z < 1 based on the Lilly et al. results, then constant luminosity density at z > 1, such as suggested by Steidel et al. (1999) is consistent with the detected flux in sources at V₅₅₅ and I₈₁₄, and with the detected EBL at U₃₀₀. At the upper limit of the EBL detections, we find that the luminosity density can continue to rise as a power law to z ~ 2.5 without over-predicting the EBL.

(3) We have modeled the effects of cosmological K-corrections, passive evolution, and (1 + z)⁴ cosmological surface brightness dimming on the detectability of local-type galaxy populations as a function of redshift. For these models, we have adopted the spatial resolution and surface brightness limits of the HDF. For models which bracket the observed surface brightness distribution of galaxies in the local universe, we find that roughly 10-40% of the EBL from galaxies fainter than V ~ 23 (i.e. those sampled in an HDF-sized image), comes from galaxies which are, at present, individually undetectable at wavelengths > 4500Å, and roughly 20-70% comes from individually undetected galaxies at < 4500Å. Most of the flux from a local-type galaxy population located at z = 3 would come from sources that would not be individually detected in the HDF. Our models indicate that the true EBL is likely to be between the mean detected EBL23 values and the 1 lower limits of those detections at V and I, and within ± 1 at U.

(4) Scaling the model of the bolometric EBL derived by Dwek et al. (1998), which is based on a combined UV-optical estimate of the star formation rate and a model for dust obscuration and re-emission based on the spectrum of IRAS sources, we find that the optical EBL we detect corresponds to a total bolometric EBL (0.1 to 1000µm) of 100 ± 20 nW m^-2sr^-1.

(5) From this estimate of the total bolometric EBL, we estimate that the total baryonic mass processed through stars is _* = 0.0062(± 0.0012) h^-2 = 0.33(± 0.07)_B, and that the mean metal mass density in the universe is _Z = 0.0040(± 0.0022)h^-2 Z = 0.24(± 0.13) Z _B, for _B = 0.019(± 0.001)h^-2 (Burles & Tytler 1998). These estimates are consistent with limits from other observational constraints.

We would like to thank the referee, M. Bershady, for detailed and helpful comments. We also thank R. Carlberg, J. Dalcanton, E. Dwek, P. Madau, R. Marzke, J. X. Prochaska, T. Small, and I. Smail for helpful discussions. This work was supported by NASA through grants NAG LTSA 5-3254 and GO-05968.01-94A to WLF, and by NASA through Hubble Fellowship grant # HF-01088.01-97A awarded by STScI to RAB.