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Astron. Astrophys. 350, 349-367 (1999)

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4. Alternative star formation scenarios

4.1. High extinction models

There are several claims that an extinction [FORMULA]=0.1, as estimated by Madau (1998) and used here, is too low. Meurer et al. (1997) use the ratio between the far-IR and UV fluxes as a probe of the dust extinction in a galaxy, and find that the high redshift UV dropout galaxies may have a UV absorption of 2-3 mag. Using ISO observations of the HDF, Rowan-Robinson et al. (1997) estimate that only a third of the star formation is revealed by the UV-luminosity, with the rest shrouded by dust. Observations with SCUBA at 850 µm (Hughes et al. 1998; Smail et al. 1997) also indicate that a large fraction of the early star formation is hidden by dust. Several other estimates, based on observations of high-z galaxies (eg. Sawicki & Yee 1998; Ellingson et al. 1996; Soifer et al. 1998), support a higher extinction of [FORMULA] 0.3. Observations of the far-infrared extragalactic background (Burigana et al. 1997) also seem consistent with a higher extinction.

With an extinction of [FORMULA] 0.3 it is likely that the observed peak in the SFR derived from UV-luminosities is illusive, and that the star formation history is compatible with a more constant rate, as in a monolithic collapse scenario (e.g., Larson 1974; Ortolani et al. 1995). In this model galaxy formation is thought to have occurred during a relatively short epoch at high redshift, [FORMULA] 5. This yields a SFR that increases from z = 0 to [FORMULA] 1.5 and then stays almost constant up to [FORMULA] 5. A SFR of this form may be compatible also with a hierarchical model, as shown in a recent paper by Somerville & Primack (1998).

It should be noted that although there is much in favor for models with a flat SFR to [FORMULA] 5, they tend to over-predict the metallicity in the region [FORMULA] 2-3, compared to estimates from damped Lyman-[FORMULA] systems (Blain et al. 1999; Madau et al. 1998b; Pei et al. 1998). These models also seem to over-predict the local K-band luminosity (Madau et al. 1998b).

We have calculated the SFR and the resulting SNRs for this high dust scenario by adjusting the observed UV luminosities of Lilly et al. (1996) and Madau (1998) to an extinction [FORMULA]=0.3. We also increase the local SFR in this model so that the observed B band luminosity density of Ellis et al. (1996) is reproduced. The onset of star formation is set to [FORMULA] = 5, while at even higher redshifts the SFR declines quickly. In Sect. 4.3 we comment on how higher values of [FORMULA] affect the estimated rates. For the normalization of the type Ia's at z = 0, we assume that the increase in the intrinsic local B-band luminosity density should lead to an increase in the Type Ia rate by approximately the same amount. In Fig. 7 we show this SFR and the intrinsic SNR for both core collapse SNe and Type Ia SNe, assuming [FORMULA] = 1 Gyr (dashed lines).

[FIGURE] Fig. 7. Intrinsic SNRs for the three different models. Solid lines show the hierarchical model with [FORMULA] = 0.1, dashed lines show the high dust model with [FORMULA] = 0.3 and flat SFR at high z, and dotted lines show the model with [FORMULA] = 0.1 and a flat SFR at high z. Upper lines show the rates of core collapse SNe. These scale directly with the SFR, given on the right axis. Lower lines show the rate of Type Ia, for [FORMULA] = 1.0 Gyr model for each of the SFR models.

4.2. Low extinction models

The model above combines a high star formation at high redshifts with a high extinction in order to match the same observed luminosity densities. Another alternative scenario is an increased SFR at high z, but a low extinction, as in the original hierarchical model. Evidence for such a scenario come from Pascarelle et al. (1998), who calculate the evolution of the UV luminosity density up to [FORMULA] 6 from [FORMULA] 1000 galaxies with photometric redshifts in the HDF. Taking the effects of cosmological surface brightness dimming into account and using a limiting surface brightness independent of redshift, they argue that the claimed UV luminosity density decrease at [FORMULA] is mainly caused by a selection effect. Further, Hu et al. (1998) show that an increasing fraction of the total SFR at high redshift takes place in Ly[FORMULA] emitters, and find that the fraction at [FORMULA] 3 may be comparable to that derived from the dropout galaxies. Most of these objects would not show up in a survey such as the HDF, due to their low surface brightness. There is, however, no reason why SNe in these galaxies should not be detectable, especially since the authors argue that the extinction in these objects should be low.

To mimic this scenario we have constructed a SFR with low extinction, [FORMULA]=0.1, that increases like the hierarchical model up to [FORMULA] 1.5, but stays flat at higher redshifts up to a formation redshift, [FORMULA] = 5. The normalization of the Type Ia's at z = 0 is the same as in the hierarchical model. This SFR and corresponding SNRs are shown in Fig. 7 as the dotted line.

4.3. Results for alternative dust and star formation models

We have repeated our calculations in Sect. 3 for the two additional scenarios described above. In the optical filters (probing rest-frame UV to optical), the increased SFR in the high dust model is mostly compensated for by higher extinction, resulting in observed rates that are only [FORMULA] 10% above those in the hierarchical scenario. The NIR filters (probing rest-frame optical to NIR) are less affected by extinction, which leads to a factor [FORMULA] 2 higher rates in the high dust model, compared to the hierarchical model. The estimates differ even more when comparing high redshift subsamples, i.e. when [FORMULA] 2 is observed. This illustrates that the observed SNR may serve as an independent probe for the instantaneous SFR that is not subject to the same high uncertainty due to the unknown amount of dust extinction as the UV-luminosity is.

For comparatively bright limiting magnitudes, that do not probe SNe above the proposed peak in the hierarchical scenario, the two models with [FORMULA]=0.1 give, by construction, the same result. Observations must reach SNe at [FORMULA] 2 before the rates start to differ.

Except for the rare Type IIn's, a SN at peak magnitude at [FORMULA] 2 has [FORMULA], making NGST necessary for this type of observations. As an illustration, Table 3 shows to what extent rates of core collapse SNe are useful to constrain the SFR at high redshifts. For core collapse SNe with [FORMULA] 2, NGST should detect [FORMULA] 3 and [FORMULA] 2 times higher rates for the high-dust-flat-SFR model and the low-dust-flat-SFR model, respectively, compared to the hierarchical model. At [FORMULA] 4 these factors are [FORMULA] 5 and [FORMULA] 4.


Table 3. Estimated number of core collapse SNe per sq. arcmin in the M´ and K´ band for different SFR and dust models. N(tot) gives the total number of SNe, while the other columns gives the number of SNe with a redshift above different specified values. The two models with flat SFR at high z has a formation redshift [FORMULA] = 5, except in the two rightmost columns where the formation redshift is set to [FORMULA] = 7 and [FORMULA] = 10, respectively.

Due to the short time interval between formation and explosion in the case of core collapse SNe the choice of formation redshift enters only for observations that are deep enough to actually probe [FORMULA]. Table 3 shows the variation of the estimated number of core collapse SNe with [FORMULA] 5 in the two models with flat SFR as [FORMULA] is changed from [FORMULA] = 5 to [FORMULA] = 7 and [FORMULA] = 10. Note that more than 10% of the SNe in the M´ band have a redshift [FORMULA] 5 in these models, compared to [FORMULA] 2% in the hierarchical model.

Our calculations show a modest increase in the number of Type Ia's for the high dust scenario, compared to the hierarchical scenario, at magnitudes brighter than [FORMULA] 25. At magnitudes corresponding to [FORMULA] 1, the differences are considerably larger. This is also true for the scenario with flat high-z SFR and low extinction, but the increase is modest, and it does not start before [FORMULA] 1.5 As an illustration, Fig. 8 shows for the [FORMULA] = 1 Gyr model that for [FORMULA], the number of Type Ia SNe increases by a factor [FORMULA] 2 for the two models with flat SFR at high z, compared to the hierarchical model. Including the full range of [FORMULA] and different star formation scenarios, the NGST should detect between 5-25 Type Ia SNe per field in the K´ band. For the ground based limit, IAB = 27, the number of Type Ia SNe increases by a factor 1.4-1.9 for the high dust scenario, and a factor 1.0-1.8 for the low dust scenario with flat SFR (smaller increase for lower values of [FORMULA]).

[FIGURE] Fig. 8. Redshift distribution for core collapse and Type Ia SNe observed to [FORMULA]=31 for the three different SFR models. Results for core collapse SNe are shown in the left panel, while the right panel shows the results for Type Ia SNe with [FORMULA]=1.0 Gyr. Note the different scales on the y-axis.

If [FORMULA] is long, stars formed at early cosmological epochs may survive until low redshifts before ending as Type Ia SNe. Therefore, the increased star formation at high redshifts in the two constant SFR models makes the rate of Type Ia SNe sensitive to the assumed formation redshift, [FORMULA]. The choice of [FORMULA] affects the SNR down to a redshift z, corresponding to a time [FORMULA]. Increasing [FORMULA] to [FORMULA] 5 increases the rates at [FORMULA] 2.7, [FORMULA] 2.0 and [FORMULA] 1.0 for [FORMULA] = 0.3, 1 and 3 Gyr, respectively. For example, with [FORMULA] = 1 Gyr the high-z cutoff in the Type Ia rate occurs at [FORMULA] 2.5 for the two models with flat SFR and [FORMULA] = 5 (see Fig. 7). With [FORMULA] = 7 and [FORMULA] = 10 the cutoff in the rates moves to [FORMULA] 3.0 and [FORMULA] 3.4, respectively. This effect is larger for smaller values of [FORMULA].

As earlier mentioned, a further possibility that may increase the predicted counts of core collapse SNe is if the first SNe and their progenitors sweep away the dust, making the extinction lower for a large fraction of the SNe relative to the stars that produce the UV luminosity. We have studied this scenario by simply neglecting the extinction of the SNe in the two models with [FORMULA] = 0.1 (not included in Table 3). The main difference occurs for the optical bands, where the effect of a lower extinction is largest. In the I band the counts increase by a factor [FORMULA] 2, whereas the counts increase by a factor [FORMULA] 1.4 in the K´ band for limits [FORMULA]. At fainter K´ limits, i.e. reaching beyond the peak region, the differences decrease because a majority of all SNe is detected in both models, despite the different amount of absorption. For [FORMULA] = 31.4 the increase is therefore only [FORMULA] 10%.

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999