The redshift distribution of distant supernovae and its use in probing reionization

We model the number of detectable supernovae (SNe) as a function of redshift at different flux thresholds, making use of the observed properties of local SNe, such as their light curves, fiducial spectra, and peak magnitude distributions. We assume that the star formation rate (SFR) at high redshift traces the formation rate of dark matter halos. We obtain a rate of 0.4-2.3 SNe arcmin^-2 yr^-1 at z ≳ 5 at the near-infrared (4.5 μm) flux density threshold of 3 nJy (achievable with the James Webb Space Telescope [JWST] in a 10^5 s integration). In a hypothetical 1 yr survey, it should be possible to detect up to several thousand SNe per unit redshift at z ~ 6. We discuss the possible application of such a large sample of distant SNe as a probe of the epoch of reionization. By heating the intergalactic medium (IGM) and raising the cosmological Jeans mass, the process of reionization can suppress star formation in low-mass galaxies. This could have produced a relatively sharp drop in the SN rate around the redshift of reionization (zre). We quantify the detectability of this feature in future surveys of distant SNe by varying the redshift and duration of reionization, as well as its impact on the SFR in low-mass halos, which results in different redshifts, widths, and sizes of the drop in the expected SFR. We find that the drop can be detected out to zre ~ 13, as long as (1) the reionization history contains a relatively rapid feature that is synchronized over different regions to within Δz ≲ 1-3, (2) the star formation efficiency in halos that dominate reionization is epsilon* ~ 10%, and (3) reionization significantly suppresses the star formation in low-mass halos. Depending on the details of (1)-(3), this could be achieved with a survey lasting less than 2 weeks. Detecting this signature would also help elucidate the feedback mechanism that regulates reionization.