5. FLUX FROM SOURCES BELOW THE SURFACE BRIGHTNESS DETECTION LIMIT

The fractional EBL23 flux which comes from detected sources is simply the ratio of the flux in detected sources (measured by "ensemble photometry") to the detected EBL23 (± 2 limits). The maximum fractional EBL23 flux coming from undetected sources is what remains: 0-65% at U₃₀₀, 0-80% at V₅₅₅, and 0-80% at I₈₁₄. Although these limits include the possibility of no additional contribution from undetected sources, it is worthwhile to note that if the progenitor of a normal disk galaxy at z = 0.1 (central surface brightness µ₀(V) ~ 21.3 mag arcsec^-2 and V ~ 22 mag) existed at z ~ 2, then the z ~ 2 progenitor would have a core surface brightness (within 0.2 × 0.2 arcsec²) of ~ 26 mag arcsec^-2 for standard K-corrections and passively evolving stellar populations (e.g. Poggianti 1997), which is roughly the detection limit for the HDF. In particular, regardless of the exact evolutionary or k-corrections, dimming due to cosmological effects alone (redshift and angular resolution) produce ~ 5 mag of surface brightness dimming. This effect is independent of wavelength, so that dimming at other bandpasses is similar, modulo differences in the evolutionary and K-corrections (shown in Figures 12, 13 and 14). At I, for example, the drop in surface brightness for a disk galaxy at z ~ 2 relative to z ~ 0 is ~ 0.5 mag greater than for V. The progenitor of a typical disk galaxy at z = 0.1, which has V - I ~ 0.9 and µ₀(I) ~ 20.3 mag arcsec^-2 (de Jong & Lacey 2000), will have V - I ~ 0.5 at z ~ 2 and µ₀(I) ~ 25.5. Thus the typical disk galaxy at z ~ 2 is close to the HDF detection limit in I as well as V. Irrespective of the color evolution with redshift, the point is that cosmological surface brightness dimming alone suggests that a significant fraction of the EBL23 may come from normal galaxies at redshifts z < 4 which are undetectable in the HDF. Furthermore, recent redshift surveys for low surface brightness (LSB) galaxies now suggest that the distribution of galaxies in µ₀ is nearly flat for µ₀ > 22.0B mag arcsec^-2 at some luminosities (Sprayberry et al. 1997, Dalcanton et al. 1997, O'Neil & Bothun 2000, Blanton et al. 2001, Cross et al. 2001). If such populations exist at high redshift, they may contribute significant flux to the EBL as presently undetectable sources.

Figure 12. K-corrections for various filters as a function of redshift calculated using Poggianti (1997) SEDs for present day E, Sa, and Sc galaxies. Bandpasses are standard Johnson/Cousins filters and the corresponding WFPC2 filters, shown with solid and dotted lines, respectively.

Figure 13. Evolutionary corrections for various filters as a function of redshift calculated using Poggianti (1997) SEDs for E, Sa, and Sc galaxies evolving passively with redshift. Bandpasses are standard Johnson/Cousins filters and the corresponding WFPC2 filters, shown with solid and dotted lines, respectively.

Figure 14. The sum of the evolutionary and K-corrections for Johnson/Cousins (solid lines) and WFPC2 filters (dotted lines) shown in Figures 12 and 13.

In this section, we explore the possible contributions to the EBL23 from galaxies at all redshifts which escape detection in the HDF because of low apparent surface brightness. To do so, we have simulated galaxy populations at redshifts 0 < z < 10 as the passively evolving counterparts of local galaxy populations and then "observed" the simulated galaxies through the Gaussian 0.1" FWHM point spread function of WFPC2. We define the surface brightness detection threshold to be consistent with the 5 detection limits of the HDF images (see Table 3), which correspond to roughly the turn-over magnitude in the number counts. This exercise is not meant to approximate realistic galaxy populations at high redshift; the evolution of galaxy populations in surface brightness, luminosity, and number density is so poorly constrained at present that more specific modeling is unwarranted. The models discussed here simply address the question: how much of the total flux from a local-type galaxy population at a redshift z can be resolved into individual sources?