Astron. Astrophys. 363, 851-862 (2000)

4. Sensitivity of faint counts to cosmological parameters

We emphasise that our purpose here is not to determine values of h, or , but rather to answer the following question: what is the net effect of changing the cosmological parameters on faint galaxy counts from the UV to the submm. We explore the set of cosmological parameters displayed in Table 1. All the astrophysical parameters are fixed at the "natural values" of the "quiescent" mode of star formation based on the local universe.

On Fig. 1 and Fig. 2, we show multi-wavelength counts obtained for the SCDM, CDM, and OCDM cosmologies defined in Table 1. From these figures, one clearly sees that, in agreement with Heyl et al. (1995) and Somerville & Primack (1999), the UV to NIR counts are relatively insensitive to changes in the cosmological parameters. This relatively "stable" behaviour extends to the FIR range. In sharp contrast, the differences between the predictions of the various cosmological models are spectacular in the submm range : at 850 µm and for the flux level of 10 mJy, the model predicts times more sources (or times brighter sources) in the OCDM cosmology than in the SCDM. An interesting trend also comes out of these figures: with the quiescent model, any low matter-density universe does a better job at matching the ISOPHOT counts at 175 µm and the SCUBA counts at 850 µm than a critical one. Our OCDM is even able to fit the submm counts "naturally", without any additional ingredient.

Fig. 1. Influence of the different cosmologies on the UV/near-IR faint counts. Dots stand for CDM, dashes for OCDM, and solid lines for SCDM. Data are from Hogg et al. (1997) (U band), Williams et al. (1996) (, B & I bands), Arnouts et al. (1997) (B band), Bertin & Dennefeld (1997) (B band), Gardner et al. (1996) (B, I & K bands), Metcalfe et al. (1996) (B band), Weir et al. (1995) (B band), Smail et al. (1995) (I band), Le Fèvre et al. (1995) (I band), Moustakas et al. (1997) (K band), and Djogorvski et al. (1995) (K band).

Fig. 2. Influence of the different cosmologies on the mid-IR/FIR/submm counts. Data are from Elbaz et al. (1999) (15 µm), Kawara et al. (1998) and Puget et al. (1999) (175 µm), Smail et al. (1997), Eales et al. (1999) and Barger et al. (1999a) (850µm). Coding for the lines is the same as in Fig. 1.

The influence of cosmology on the faint counts is produced by the complicated combination of several effects. For instance, for lower values of the density parameter , either with zero cosmological constant, or with zero curvature, we have the following changes:

1. For halos of a given mass, the collapse occurs earlier on an average (see Fig. A.1);

2. The halo number density is lower (see Fig. A.1);

3. With a fixed value of , the baryon fraction is higher, so that there is, on an average, more fuel for star formation per halo of a given mass;

4. Volume elements are larger;

5. Luminosity distances are larger;

6. The time versus redshift relationship changes, and the amount of evolution undergone by the sources at any redshift with respect to is larger.

These six effects act in different ways. If they are taken separately, points 3, 4, and 6 increase the slope of the counts whereas points 1, 2, and 5 decrease the slope. In addition to this, there is the effect of the k-correction. In the optical, and NIR, the k-correction is positive, and cancels out partly what is occurring at high redshift in such a way that the faint counts are weakly sensitive to cosmology. At optical wavelengths, the net effect is that faint counts in low matter-density universes are below those in the SCDM. This conclusion is opposite to the predictions of phenomenological models based on backward evolution of the local luminosity function, under the assumption of monolithic collapse and pure luminosity evolution (see e.g. Guiderdoni & Rocca-Volmerange 1990). The latter models predict that the OCDM is over the SCDM. The origin of this discrepancy is that the phenomenological models do not take points 1, 2 and 3 into account.

This weak sensitivity extends to the mid-IR and FIR, but the behaviour of the submm counts is very different. In contrast with the optical, NIR, mid-IR and FIR, the k-correction is negative at submm wavelengths (see Fig. 17 of Paper I for an illustration), and enhances the effects of cosmology and evolution at high redshift. The dominant effects are the earlier collapse (see Fig. A.1) and larger volume available at high redshift in low matter-density universes.

Such an effect is particularly marked on the redshift distribution of the sources given in Fig. 3. These predictions are compared with the faintest redshift survey in the I band (the CFRS, Lilly et al. 1995; Crampton et al. 1995), with , and the North Ecliptic Pole Region (NEPR) survey from IRAS at 60 µm, with mJy (Ashby et al. 1996). The CFRS survey is correctly reproduced by the quiescent model, whatever the cosmology, though all quiescent models seem to overpredict low-luminosity objects and produce a peak at too low a redshift with respect to the data ( instead of ). This is clearly due to the overproduction of low-luminosity objects in the luminosity function. There is not much sensitivity to cosmology. At 60 µm, the various cosmologies predict different redshift distributions. The SDCM peaks at low redshift, without any high-redshift tail, as anticipated by GHBM. The CDM and the OCDM peak at higher redshift, with broader distributions. The OCDM already seems to overpredict high-z galaxies in the NEPR at 60 µm. Finally, the sensitivity of the redshift distributions to cosmology is spectacular in the submm range. The wavelengths 175 µm and 850 µm and the flux cuts at 100 and 2 mJy respectively correspond to on-going redshift surveys of the ISOPHOT and SCUBA sources. There are no firm results for these surveys because of identification problems (Downes et al. 1999; Smail et al. 1999), and we prefer not to plot data.

Fig. 3. Influence of the different cosmologies on multi-wavelength redshift distributions of galaxies. Coding for the lines is the same as in Fig. 1. Data are from Crampton et al. (1995) (Canada-France Redshift Survey), and Ashby et al. (1996) (North Ecliptic Pole region). The predicted curves in the I band and at 60 µm have been renormalised to the total number of galaxies in the data.

However, our quiescent models do not contain mergers and therefore do not account for the massive ULIRGs seen by ISOPHOT and SCUBA. This has to be taken into account in the model, though a low matter-density universe lessens noticeably the importance of the contribution of ULIRGs to the cosmic FIR luminosity. We now try to assess the impact of such mechanisms on our results phenomenologically.

© European Southern Observatory (ESO) 2000

Online publication: December 5, 2000
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