3 Results

We fit the $E_{\rm pk}-\mathcal{E}$ relation to our 41 clean pulses using FITEXY (Press et al. 1992). From the $\chi^{2}$ and the number of fluence bins for each decay fit, we calculated the probability Q of randomly getting a higher $\chi^{2}$ by chance. If $E_{\rm pk}$ does indeed cool linearly with $\mathcal{E}$in all pulses selected for fitting, then when plotting the cumulative distribution of Q values, we would expect 10% of the pulses to have a Q less that 0.1, 20% of the pulses to have a Q less than 0.2, and so on. Figure 2 shows the cumulative distribution of Q values for our pulses with acceptable fits. An excess of pulses with very high Q values would suggest a biased pulse selection process. The Kolmogorov-Smirnov test gives a probability P = 0.18 that this distribution is drawn from the unit distribution. From this, we conclude that our $E_{\rm pk}-\mathcal{E}$function (Eq. (3)) adequately describes the pulses in this subset. We discuss this work and its implications in more detail elsewhere (Crider et al. 1999).

  

Figure 2: Cumulative distribution of Q values for 41 pulses. In this plot, N is the fraction of pulses that have a Q value less than that of a certain pulse. If all of these GRB pulses cooled linearly as a function of energy fluence, one would expect the cumulative Q distribution to match the unit distribution (N=Q)

Acknowledgements

AC thanks NASA-MSFC for his GSRP fellowship and the Rome GRB Conference Committee for waiving his conference fees. AC also wishes to acknowledge useful discussions with Charles Dermer and Andrew Lemanski that greatly influenced this paper. This work is supported by NASA grant NAG5-3824.