2 GRB/OT boxes

The particular analysis method is that originally proposed by Fenimore et al. (1993) as elaborated by Schaefer (1999). In this method, for some assumed peak luminosity, the limit on the apparent magnitude of the host is translated into a fraction ($F_{\min}$) of the faint end of the Schechter luminosity function in which the host must lie. If bursts reside in normal host galaxies, then the average $<F_{\min}\gt$ value should be near a half. With foreground unrelated galaxies and with nondetection thresholds, $<F_{\min}\gt$ can only be larger than half. If bursters do not reside in normal hosts, then the $<F_{\min}\gt$ may be smaller than a half. The analysis procedure is to test a range of assumed peak luminosities to find the values consistent with the presence of normal host galaxies. For the events with measured red shifts, the implied distances have been adopted, except for the GRB 970425 event which is ignored as it must be a special case.

The peak fluxes and limits on the host V magnitudes (corrected for extinction by our Milky Way) have been collected for eight GRBs with small OT boxes (see Table 1).

  

Table 1: Host galaxy Data: GRB/OT boxes

The analysis shows that $<F_{\min}\gt~ = 0.19 \pm 0.07$ for an assumed peak luminosity as given for the no-evolution case. Only when the assumed peak luminosity rises as large as that for the SFR case does $<F_{\min}\gt$ rise to within one-sigma of a half. For $<F_{\min}\gt$to be $\geq 0.5$, the average peak luminosity must be $\geq 6\ 10^{58}$ photon s^-1. The effects of a broad luminosity function on the model $<F_{\min}\gt$ value will be to form an appropriately weighted average over the monoenergetic $F_{\min}$ values, so that the observed $<F_{\min}\gt$ should be compared with the model value for the average peak luminosity. Thus, the result for the eight GRB/OT boxes is that the no-evolution distance scale is rejected, the SFR distance scale is close to being rejected, while the preferred peak luminosity is $\geq 6\ 10^{58}$ photons s^-1 (provided bursters reside in normal galaxies).

This conclusion has some definite weaknesses relating to the lack of knowledge of galaxies at high red shift. In particular, at red shifts of $z \gt \sim 1$, the normal galaxy K corrections are nearly unknown, the luminosity function could be substantially different from the Schechter function, there could be significant unaccounted absorption from dust at early epoch, and even uncertainties in the cosmological parameters start to matter. Given these large potential problems, we should conclude that the SFR model is not rejected. However, the no-evolution model places the bursts at low enough of a red shift that the uncertainties are unlikely to change the conclusion that this distance scale is rejected.