The Statistics of the Prompt-to-Afterglow GRB Flux Ratios and the Supercritical Pile GRB Model

We present the statistics of the ratio, ${\mathrm R}$, between the prompt and afterglow "plateau" fluxes of GRB. This we define as the ratio between the mean prompt energy flux in the {\em Swift} BAT and the {\em Swift} XRT, immediately following the steep transition between these two states and the beginning of the afterglow stage referred to as the "plateau". Like the distribution of other GRB observables, the histogram of ${\mathrm R}$ is close to log-normal, with maximum at ${\mathrm R = R}_{\rm m} \simeq 2,000$, FWHM of about 2 decades and with the entire distribution spanning about 6 decades in the value of ${\mathrm R}$. We note that the peak of the distribution is close to the proton-to-electron mass ratio $({\mathrm R}_{\rm m} \simeq m_p/m_e = 1836)$, as proposed by us earlier, on the basis of a specific model for the conversion of the GRB blast wave kinetic energy into radiation, before any similar analysis were made. It therefore appears that, in addition to the values of the energy of peak luminosity ${E_{\rm pk}\sim m_{e} c^2}$, GRB present us with one more quantity with an apparently characteristic value. The fact that the values of both these quantities (i.e. $E_{\rm pk}$ and ${\mathrm R}$) comply with those implied by the same specific model devised to account for an altogether different issue, namely the efficient conversion of the GRB blast wave kinetic energy into radiation, argues favorably for its underlying assumptions.