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

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1. Introduction

The cosmic star formation rate (SFR) has now been estimated up to redshifts [FORMULA] 5. By combining the evolution of the 2800 Å luminosity density calculated from CFRS-galaxies (Lilly et al. 1996) at redshifts [FORMULA] 1, and the 1500 Å luminosity density calculated from high redshift galaxies ([FORMULA] 2) in the HDF found by the Lyman dropout techniques, Madau et al. (1996) argue that the SFR should peak at 1 [FORMULA] 2. Complementary to these, Connolly et al. (1997) have used HDF photometric measurements, together with ground based near-IR photometry, to derive the 2800 Å luminosity density at redshifts 0.5 [FORMULA] 2. These results are in good agreement in the region overlapping with the CFRS, supporting the case of a peak in the SFR. This conclusion is, however, sensitive to the fact that the rest frame light may have been strongly attenuated by dust. Absorption by dust is especially severe for the UV-light, and since shorter rest frame wavelengths are sampled at higher z, this uncertainty increases with redshift.

The evolution of the SFR is reflected in the cosmic supernova rate (SNR). It should therefore, in principle, be possible to use supernova (from now on SN) observations to distinguish between various star formation scenarios. Even more important, core collapse SNe, i.e. Types II and Ib/c, provide a direct probe of the metallicity production with cosmic epoch. In reality these relations are non-trivial to establish. When it comes to core collapse SNe, the observational constraints at high redshifts are nearly non-existent. Even at low redshift the statistics are severely affected by selection effects. A main problem comes from the fact that core collapse SNe observationally show a large diversity, both in terms of luminosities and types, and with uncertain distributions. In addition, dust absorption, as well as background contamination, affect the statistics. Nevertheless, because of their importance for the nucleosynthesis, as well as galaxy formation, direct observations of the rate of core collapse SNe are of high interest. It is therefore hardly surprising that this is one of the main goals for the Next Generation Space Telescope (NGST) (Stockman 1997).

For Type Ia SNe, the unknown time delay between formation and explosion of the progenitors unties the link to the SFR, making predictions more model dependent. Observations of the Type Ia rate at high redshift therefore provides a possibility to distinguish different progenitor scenarios.

In this paper we present estimates for the expected number of observable SNe for the NGST, as well as for ground based instruments, and discuss various complications entering the analysis. Previous studies include Madau et al. (1998a), Ruiz-Lapuente & Canal (1998), Jorgensen et al. (1997), Miralda-Escudé & Rees (1997), Sadat et al. (1998), Yungelson & Livio (1998). With respect to most of these, our work differs in that we include information about the light curve, as well as spectral evolution, which allow us to predict the simultaneously observable number of SNe. That this is important is obvious from the fact that a nearby SN seen at the tail of the light curve is indistinguishable from a more distant object at the peak. We divide the SNe into different types with maximum absolute magnitudes and spectral distributions that varies with time and type. This also introduces a large dispersion in magnitudes at a given redshift. Neglect of these effects introduces a severe Malmquist bias. We calculate the counts for different broad band filters, and include information about the expected redshift distribution of the detected SNe. Some preliminary results were given in Dahlén & Fransson (1998).

Sect. 2 describes our model. Results are presented in Sect. 3. In Sect. 4 we discuss alternative star formation scenarios. In Sect. 5 we discuss how other cosmologies affect out results. The effects of gravitational lensing are discussed in Sect. 6. Problems concerning redshift determination are discussed in Sect. 7. A general discussion follows in Sect. 8, and conclusions are given in Sect. 9. Throughout most of the paper we assume a flat cosmology with [FORMULA] and [FORMULA] = 1, unless otherwise stated.

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© European Southern Observatory (ESO) 1999

Online publication: October 4, 1999