Rates and redshift distributions of high-z supernovae

Using observed star formation rates at redshifts up to z similar to 5, we c alculate cosmic supernova rates for core collapse and Type Ia supernovae. T ogether with supernova statistics and detailed light curves, we estimate th e number of supernovae, and their distribution in redshift, that should be detectable in different filters with various instruments, including both ex isting and future telescopes, in particular the NGST We find that the NGST should detect several tens of core collapse supernova e in a single frame. Most of these will be core collapse supernovae with 1 less than or similar to z less than or similar to 2, but about one third wi ll have z greater than or similar to 2. Rates at z greater than or similar to 5 are highly uncertain. For ground based 8-10 m class telescopes we pred ict similar to 0.1 supernova per square arcmin to I-AB = 27, with about twi ce as many core collapse SNe as Type Ia's. The typical redshift will be z s imilar to 1, with an extended tail up to z similar to 2. Detectability of h igh redshift supernovae from ground is highly sensitive to the rest frame U V flux of the supernova, where line blanketing may decrease the rates sever ely in filters below 1 mu m. In addition to the standard 'Madau' star formation rate, we discuss alterna tive models with flat star formation rate at high redshifts. Especially for supernovae at z greater than or similar to 2 the rates of these models dif fer considerably, when seen as a function of redshift. An advantage of usin g SNe to study the instantaneous star formation rate is that the SN rest fr ame optical to NIR is less affected by dust extinction than the UV-light. H owever, if a large fraction of the star formation occurs in galaxies with a very large extinction the observed SN rate will be strongly affected. An a dditional advantage of using SNe is that these are not sensitive to selecti on effects caused by low surface brightness. Different aspects of the search strategy is discussed, and it is especially pointed out that unless the time interval between the observations spans a t least 100 days for ground based searches, and one year for NGST, a large fraction of the Type IIP supernovae will be lost. Because of the time delay between the formation of the progenitor star and the explosion, observatio ns of z greater than or similar to 1 Type Ia supernovae may distinguish dif ferent progenitor scenarios. A major problem is the determination of the redshift of these faint superno vae, and various alternatives are discussed, including photometric redshift s. In practice a reliable classification based on either spectroscopy or li ght curves requires the SNe to be similar to 2 magnitudes above the detecti on limit. The uncertainties in the estimates are discussed extensively. We also discuss how the estimated rates depend on cosmology. Finally, some com ments on effects of metallicity are included.