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5.1. Models

We have considered three models for the central surface brightness distributions of disk galaxies in order to explore the possible contributions from LSB galaxies. These models are taken from Ferguson & McGaugh 1995 (FM95) and can be generally described as follows: a standard passive evolution model in which all galaxies have central surface brightnesses in the range 21 < µ0(BJ) < 22 mag arcsec-2 (Model PE); an LSB-rich model (Model A), in which galaxies of all luminosities have 21.5 < µ0(BJ) < 25 mag arcsec-2; and a more conservative LSB model (Model B), in which µ0 is monotonically decreasing for galaxies fainter than L/L * < 1 and 21 < µ0(BJ) < 22 mag arcsec-2 otherwise (see Figure 15). We include passive luminosity evolution in all three models, as the no-evolution models have been clearly ruled out by both number counts and our own EBL results. As Model A (Model PE) has a broader (narrower) surface brightness distribution than is found by recent LSB surveys (Sprayberry et al. 1997, Dalcanton et al. 1997, O'Neil & Bothun 2000), these models are taken as illustrative limits on the fraction of low surface brightness galaxies in the local universe. Recent determinations of the number density of galaxies as a function of both luminosity and surface brightness (c.f. Blanton et al. 2001 and Cross et al. 2001) are well bracketed by these models: Model A allows for too many low surface brightness galaxies, while the PE model clearly allows for too few (see Figure 15).

Figure 15

Figure 15. The dark hatched regions in the three panels show the surface brightness distribution as a function of luminosity for the models adopted here (Model A, Model B, and PE). For comparison, the light hatched region shows the surface brightness distribution as a function of luminosity (relative to L*) as found by Blanton et al. (2001).

As described in Table 2 of FM95, each surface brightness distribution model has been paired with a tuned luminosity function, so that each model matches the observed morphological distributions and luminosity functions recovered by local redshift surveys. The models include identical distributions in the relative number of galaxies of different Hubble types (E/S0, S0, Sab, Sbc, and Sdm), which are described by bulge-to-disk flux ratios of 1.0, 0.4, 0.3, 0.15, and 0.0, with small scatter. The bulge components for all galaxies have E-type SEDs, and S0 to Sdm galaxies have disk components with E, Sa, Sb, and Sc-type SEDs, for which we have used the Poggianti (1997) models. Bulges were given r1/4-law light profiles with central surface brightnesses drawn from the empirical relationship found by Sandage & Perelmuter (1990), µ0 = - 0.48MBT + 11.02. For disk components, we adopted exponential light profiles, with surface brightnesses drawn from the 3 model distributions for disk galaxies listed above.

We have calculated passive evolution and K-corrections from the population synthesis models and SEDs of Poggianti (1997), shown in Figures 12 and 13, and we have assumed uniform comoving density as a function of redshift in all cases. All models were run with H0 = 50 and 70 km s-1 Mpc-1 and (OmegaM = 0.2, OmegaLambda = 0), (1,0), and (0.2, 0.8). Different values of H0 have little effect (< 10%) on the integrated counts or background. The total background increases for models with larger volume - (1,0), (0.2,0), and (0.2,0.8), in order of increasing volume - but the fractional flux as a function of redshift changes by less than 10% with cosmological model.

All three models under-predict the number counts and integrated flux in observed sources, as expected, and will clearly under-predict the total EBL as illustrated in the passive evolution model discussed in Section 4.2.

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