3. THE BRIGHTNESS OF THE NIGHT SKY

The contribution of known galaxies to the optical EBL can be calculated directly by integrating the emitted flux times the differential number counts down to the detection threshold. The results for 0.35 2.2 µm are listed in Table 1, along with the magnitude range of integration and the estimated 1 error bars, which arise mostly from field-to-field variations in the numbers of relatively bright galaxies.

Table 1. Integrated Galaxy Light

(Å)	AB (range)	I	+	-
3600	18.0-28.0	2.87	0.58	0.42
4500	15.0-29.0	4.57	0.73	0.47
6700	15.0-30.5	6.74	1.25	0.94
8100	12.0-29.0	8.04	1.62	0.92
11000	10.0-29.0	9.71	3.00	1.90
16000	10.0-29.0	9.02	2.62	1.68
22000	12.0-25.5	7.92	2.04	1.21

In all seven bands, the slope of the differential number-magnitude relation is flatter than 0.4 above m_AB ~ 20 (25) at near-IR (optical) wavelengths, and this flattening appears to be more pronounced at the shorter wavelengths. ⁽¹⁾ The leveling off of the counts is clearly seen in Figure 1, where the function i = 10^{-0.4(m_AB+48.6)} N(m) is plotted against apparent magnitude in all bands. While counts having a logarithmic slope d log N/dm_AB = 0.40 continue to add to the EBL at the faintest magnitudes, it appears that the HDF survey has achieved the sensitivity to capture the bulk of the near-ultraviolet, optical, and near-IR extragalactic light from discrete sources. The flattening at faint apparent magnitudes cannot be due to the reddening of distant sources as their Lyman break gets redshifted into the blue passband, since the fraction of Lyman-break galaxies at (say) B 25 is small (Steidel et al. 1996; Pozzetti et al. 1998). Moreover, an absorption-induced loss of sources cannot explain the similar change of slope of the galaxy counts observed in the V,I,J,H, and K bands. While this suggests that the surface density of optically luminous galaxies is leveling off beyond z ~ 1.5, we are worried that a significant amount of light may actually be missed at faint magnitudes because of systematic errors.

The spectrum of the optical EBL is shown in Figure 2, together with the recent results from COBE. The value derived by integrating the galaxy counts down to very faint magnitude levels (because of the flattening of the number-magnitude relation most of the contribution to the optical EBL comes from relatively bright galaxies) implies a lower limit to the EBL intensity in the 0.2-2.2 µm interval of I_opt 15 n W m^-2sr^-1. Including the tentative detection at 3.5 µm by Dwek & Arendt (1999) would boost I_opt to 19 n W m^-2sr^-1. Recent direct measurements of the optical EBL at 3000, 5500, and 8000 Å from absolute surface photometry by Bernstein et al. (1999) lie between a factor of 2.5 to 3 higher than the integrated light from galaxy counts, with an uncertainty that is largely due to systematic rather than statistical error. Applying this correction factor to the range 3000-8000 Å gives a total optical EBL intensity in the range 25-30 n W m^-2sr^-1. This could become ~ 45 n W m^-2sr^-1 if the same correction holds also in the near-IR. The COBE / FIRAS (Fixsen et al. 1998) measurements yield I_FIR 14 n W m^-2sr^-1 in the 125-2000 µm range. When combined with the DIRBE (Hauser et al. 1998; Schlegel et al. 1998) points at 140 and 240 µm, one gets a far-IR background intensity of I_FIR (140-2000 µm) 20 n W m^-2sr^-1. The residual emission in the 3.5 to 140 µm region is poorly known, but it is likely to exceed 10 n W m^-2sr^-1 (Dwek et al. 1998). Additional constraints - provided by statistical analyses of the source-subtracted sky - on the EBL have been discussed by, e.g. Martin & Bowyer (1989), Kashlinsky et al. (1996), and Vogeley (1997).

Figure 2. Spectrum of the optical extragalactic background light from resolved sources as derived from a compilation of ground-based and space-based galaxy counts in the UBVIJHK bands (filled dots), together with the FIRAS 125-5000 µm (dashed line) and DIRBE 140 and 240 µm (filled squares) detections (Hauser et al. 1998; Fixsen et al. 1998). The empty squares show the DIRBE points after correction for WIM dust emission (Lagache et al. 1999). Also plotted (filled triangle) is a FOCA-UV point at 2000 Å from Armand et al. (1994), and a tentative detection at 3.5 µm (empty dot) from COBE / DIRBE observations (Dwek & Arendt 1999). The empty pentagons at 3000, 5500, and 8000 Å are Bernstein et al. (1999) measurements of the EBL from resolved and unresolved galaxies fainter than V = 23 mag (the error bars showing 2 statistical errors). Upper limits are from Hauser et al. (1998), the lower limit from Elbaz et al. (1999). The solid curve shows the synthetic EBL produced by a WD-progenitor dominated IMF with = 4 and (zF, X, XWD) = (36, 0.5, 0.1), in the case of zero dust reddening.