ARlogo Annu. Rev. Astron. Astrophys. 2000. 38: 761-814
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4.1.1. Source Counts: Evidence for Strong Evolution

Figure 14 (from Serjeant, private communication; Elbaz et al 1999a) gives the integrated and differential source counts derived from these surveys. Given the difficulties of reliable faint source detection and photometry mentioned previously, it is reassuring that the counts of the different surveys agree quite well. Starting with IRAS and going to fainter flux densities, the number counts initially lie on a linear (log-log plot) extrapolation of the IRAS counts and do not require strong evolution. However, from > 10 mJy down to 0.4 mJy the counts increase rapidly, with a slope in the integrated counts of alpha = -3. This is significantly steeper than expected in a Euclidean model without luminosity/density evolution (alpha = -2.5). Below 0.4 mJy down to the faintest flux densities sampled, the slope is flatter (alpha = -1.6) and the counts appear to converge. In the differential source counts (right inset of Figure 14; Elbaz et al 1999a, 2000) this leads to a prominent hump peaking at ~ 0.4 mJy. At the peak of the hump the observed source counts are an order of magnitude above non-evolution models, obtained by extrapolating the local IRAS 12 µm luminosity function (Rush et al 1993, Fang et al 1998). The mid-infrared source counts require strong cosmic evolution of the mid-infared emission of galaxies (Oliver et al 1997, Roche & Eales 1999, Clements et al 1999, Elbaz et al 1999a, b, Serjeant et al 1999).

Figure 14

Figure 14. Top left: Summary of integrated 15 µm source counts from the different ISO surveys (from Serjeant, private communication; Elbaz et al 1999a; normalizing downward by a factor 1.5 the counts of Serjeant et al 1999), compared to non-evolution models (continuous) matching the IRAS counts (the Rush et al 1993 counts were renormalized downward by a factor of 2). Top right: Differential 15 µm counts with the shaded area marking the counts predicted with non-evolution models (from Elbaz et al 1999a). The counts are normalized to a Euclidean distribution of non-evolving sources, which would have a slope of index -2.5 in such a universe. Data points: A2390 (open stars; Altieri et al 1999, Metcalfe et al 1999), HDF(N) (open circles; Aussel et al 1999a), HDF(S) (filled circles; Elbaz et al 1999a), Marano (open squares, crosses, stars; Elbaz et al 1999a), Lockman hole (open and filled triangles; Elbaz et al 1999a).

The 15 µm integral number counts agree with model predictions over more than five orders of magnitude in flux density (Franceschini et al 1994, 2000, Pearson & Rowan-Robinson 1996, Guiderdoni et al 1997, 1998, Xu et al 1998, Roche & Eales 1999). Common to all these models is the assumption of strong luminosity and/or density evolution of dusty star formation in bright normal spirals and starburst galaxies, with varying contributions from AGNs. We now discuss in more detail the models by Xu et al (1998), since they are based on the most recent ISO SWS-ISOPHOT-S spectra of template galaxies to determine accurate, mid-IR k-corrections. These are important because of the structure caused by UIB features in the 6-13 µm spectra of most galaxies. The models of Pearson, Rowan-Robinson, Franceschini, Roche & Eales, and Guiderdoni et al lead to similar results. Xu et al constructed a local luminosity function from IRAS observations (Shupe et al 1998) and assigned to each of these galaxies a mid-IR spectrum composed of three categories (cirrus/PDR, starburst, AGN, or a mixture). They then extrapolated the local luminosity function to higher redshift by applying the appropriate k-corrections and evolution. The predicted differential, Euclidean, normalized source counts for the LW3 ISOCAM filter show distinct differences between luminosity evolution [L(z) propto (1 + z)3] and density evolution [rho(z) propto (1 + z)4]. For pure density evolution the predicted source counts are fairly flat, from 1 Jy to 100 µJy. For luminosity evolution, however, a characteristic bump is predicted at around 300 µJy, with a sharp fall-off of the counts at fainter flux densities. This is similar to what is actually observed by Elbaz et al (1999a; Figure 14), although the amplitude of the hump in the differential source counts requires an even steeper evolution than considered by Xu et al [e.g. in aqn Einstein-de Sitter universe combination of (1 + z)3 luminosity evolution and (1 + z)6 density evolution, for the starburst component only, at z < 0.8-0.9; Franceschini et al 2000]. The interpretation of the bump is that with luminosity evolution and flat or even "negative" k-correction (between z = 0.5 and 1; Elbaz et al 1999b) the number counts increase initially, with decreasing flux density much faster than Euclidean. The unfavorable k-correction and the decreasing slope of the available comoving volume cause the number counts to drop rapidly with increasing z for z geq 1. For sources near the bump, the luminosity evolution model predicts a broad redshift distribution, with a median at z ~ 0.9 but extending with significant probability to redshifts > 2. In contrast, the pure density evolution model predicts a much smaller median redshift (~ 0.5) and essentially no sources with z > 1. When the mid-infrared counts are compared to K-band counts at the same energy (nu Snu), the mid-infrared sources contribute only about 10% of the energy at the bright end, but more than 50% at S15µm ~ a few hundred µJy (Elbaz et al 1999a). Thus, the ISOCAM sources must represent an important subclass of the optical/near-IR galaxies that are dusty and infrared active.

The situation is less clear at 6.75 µm (Goldschmidt et al 1997, Taniguchi et al 1997a, Aussel et al 1999a, b, Sato et al 1999, Serjeant et al 1999, Flores et al 1999a). The stellar contamination is larger. The local luminosity function and template spectra appropriate for the galaxies are less well known than at 15 µm. The number of confidently detected sources is also much smaller. They are (more) compatible with a non-evolution (i.e. passive evolution) model with a significant contribution of ellipticals/S0s (E/SOs; Roche & Eales 1999). They are also consistent with the Pearson & Rowan-Robinson (1996) luminosity evolution model, but not with that of Franceschini et al (1994) (Serjeant et al 1999).

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