Cosmic γ-Ray Bursts as a Probe of Star Formation History

The cosmic γ-ray burst (GRB) formation rate, as derived from the variabilityluminosity relation for long-duration GRBs, is compared with the cosmic star formation rate. If GRBs are related to the collapse of massive stars, one expects the GRB rate to be approximately proportional to the star formation rate. We found that these two rates have similar slopes at low redshift. This suggests that GRBs do indeed track the star formation rate of the Universe, which in turn implies that the formation rate of massive stars that produce GRBs is proportional to the total star formation rate. It also implies that we might be able to use GRBs as a probe of the cosmic star formation rate at high redshift. We find that the cosmic star formation rate inferred from the variability-luminosity relation increases steeply with redshift at z > 3.0. This is in apparent contrast to what is derived from measurements of the cosmic star formation rate at high redshift from optical observations of field galaxies, suggesting that much high-z star formation is being missed in the optical surveys, even after corrections for dust extinction have been made. THE COSMIC STAR FORMATION RATE The variation of the total cosmic star formation rate with redshift z − the SFR plot − is conventionally determined by measurements of the Hα luminosity of galaxies at z < 0.2 and of UV luminosities at z > 0.2 (Madau et al. 1996). Two major complications in constructing the SFR plot at any z are (i) the need to correct UV luminosities for dust extinction, and (ii) the need to assume a stellar IMF. However, both of these seem to have been addressed with considerable success: (i) by adopting the corrections of Calzetti (1997), which when applied to the CFRS data of Lilly et al. (1996) produce a SFR plot similar to that generated from infrared ISO observations (Flores et al. 1999), which are sensitive to the absorbed and reradiated UV flux, and (ii) by using an IMF that flattens below 1 M⊙ e.g. that of Kroupa et al. 1993, which seems to be universal (Gilmore & Howell 1998). The SFR plot constructed with both of these assumptions, when integrated over cosmic time, reproduces the correct local stellar density of Ω∗ ∼ 0.005 that we derive from a number of methods. We can therefore have considerable confidence in current determinations of the SFR plot at z < 3 (Somerville et al. 2000). At z > 3, there are additional, potentially more serious, complications. The only types of high-z galaxies whose contributions to the SFR plot have been unambiguously determined are the Lyman-break galaxies (LBGs; Steidel et al. 1999). Lyman-α (Lyα) emitters may contribute too, but current indications are that their contribution is small (10 M⊙ yr −1 Mpc compared to 10 M⊙ yr −1 Mpc for the LBGs; Hu et al. 1998). However, these Lyα-emitters and other galaxies which might exist but cannot be found by the selection techniques used to find either Ly-break or Lyα galaxies, could have their contributions systematically underestimated. Such galaxies might be lost due to (1 + z) surface-brightness dimming (Lanzetta et al. 2000), or the detectability of a small fraction of the members of a population might be enhanced by supernovae that happened to go off in those members causing us to miss the bulk of the sources representing that population (the supernovae are not dimmed by (1 + z) and can affect detectability if 10 log(1 + z) > magSN −maggal). Therefore, indirect constraints are important at such high z. The constraint from Ω∗ is weak since the contribution to the total integral of the SFR plot is small at high z since dt/dz is small there. Another constraint is that all the star formation at z > 3 must produce enough metals to enrich the Lyα forest at z = 3 (Cowie & Songaila 1998), but this is also of limited use here, since it is unclear what fraction of metals escape from the galaxies in which the stars form. A potentially more powerful probe is given by the γ-ray burst (GRB) formation rate plot, which must track the SFR plot closely if the majority of GRBs originate from the collapse of massive stars. This is what we investigate here. THE γ-RAY BURST RATE GRBs are detectable out to the farthest reaches of the observable Universe, and provide information about processes occurring at all cosmic epochs. Recent observations suggest that the long-duration GRBs and their afterglows are produced by highly relativistic jets emitted in core-collapse supernova explosions. Hence the redshift distributions of GRBs should track the cosmic star formation rate of massive stars accurately (Lamb & Reichart 2000; Blain & Natarajan 2000). At present, however, there are too few redshift measurements with which to estimate the global GRB formation rate. Nonetheless, these few measured redshifts can be used to calibrate properties of GRBs that might let them serve as standard candles. Fenimore & Ramirez-Ruiz (2000) have suggested that the spikiness of the burst time structure is correlated with luminosity, with smooth bursts being intrinsically less luminous. In principle, the measured spikiness combined with the observed flux can be used to obtain distances much like Cepheid observations give distance estimates from the pulsation period. Using a sample of 220 bright BATSE bursts for which high-resolution light curves were available, Fenimore & RamirezRuiz (2000) estimated the evolution of the GRB formation rate from parameters measured solely at γ-ray energies. FIGURE 1. A summary of the current state of knowledge of the star formation history of the Universe. The data points plotted are described in Somerville et al. (2000). The open stars are the GRB formation rate obtained by Fenimore & Ramirez-Ruiz (2000) normalized to the SFR at z=1 (ΩΛ = 0.7, Ωm = 0.3, Ho = 65 km s −1 Mpc). The error bars represent the systematic uncertainty in the burst formation rate calculated from the uncertainty in the variability-luminosity relationship, and are clearly larger than the statistical uncertainty on each