The statistics of BAT-to-XRT flux ratio in GRBs: Evidence for a characteristic value and its implications

We present the statistics of the ratio, $R$, between the prompt and afterglow "plateau" fluxes of gamma-ray bursts (GRBs). We define this as the ratio of the mean prompt energy flux in Swift BAT and the Swift XRT one, 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 many other GRB observables, the histogram of $R$ is log-normal with maximum at a value $R_m\simeq 2000$, FWHM of about two decades, and with the entire distribution spanning about five decades in the value of $R$. We note that the peak of the distribution is close to the proton-to-electron mass ratio $(R_m\simeq m_p/m_e=1836)$, as proposed to be the case in an earlier publication, on the basis of a specific model of the GRB dissipation process. It therefore appears that, in addition to the values of the energy of peak luminosity $E_{pk}\sim m_e{c}^2$, GRBs present us with one more quantity with an apparent characteristic value. The fact that the values of both these quantities ($E_{pk}$ and $R$) are consistent with the same specific model invoked to account for the efficient conversion of their relativistic proton energies to electrons argues favorably for its underlying assumptions.