The Slope of the BATSE Number-Flux Distribution
David M. Caditz · The Astrophysical Journal · 1995
The use of data smoothing for astronomical survey data is discussed with particular attention being paid to the calculation of differential as opposed to cumulative distribution functions. Smoothing is shown, in principle, to produce a source distribution that, based upon an integrated mean square error statistic, can give a more accurate global estimate than the traditional cumulative histogram method. Data smoothing is applied, as an example, to the BATSE 2B γ-ray burst catalog, and the slope of the y-ray burst log N-log f distribution is obtained in continuous (i.e., unbinned) form. This slope is found to deviate from the value S = 3/2 below a peak photon flux of f ∼ 10 photons cm-2 s-1 reaching S ∼ 0.7 at f ∼ 0.2 photons cm-2 s-1. At higher fluxes, discreteness effects dominate the BATSE distribution function and obscure a possible 3/2 slope. Because the differential distribution is inherently more sensitive to subtle features in the data than the cumulative log N-log f curve, sensitive comparisons may be made with model halo and cosmological distributions. A cosmological distribution consistent with the BATSE data is derived.