The Total Errors In Measuring Epeak for Gamma-Ray Bursts

TL;DR

This paper thoroughly examines the various sources of error in measuring Epeak for gamma-ray bursts, revealing that systematic uncertainties are significant and impact the accuracy of individual and collective burst analyses.

Contribution

It quantifies the total measurement uncertainties of Epeak, highlighting the dominant sources of error and emphasizing the need for standardized definitions in the community.

Findings

Analyst choices contribute 28% uncertainty in Epeak measurements.

Detector response uncertainties are negligible.

Total one-sigma uncertainty for burst collections is approximately 55%.

Abstract

While Epeak has been extensively used in the past, for example with luminosity indicators, it has not been thoroughly examined for possible sources of scatter. In the literature, the reported error bars for Epeak are the simple Poisson statistical errors. Additional uncertainties arise due to the choices made by analysts in determining Epeak (e.g., the start and stop times of integration), imperfect knowledge of the response of the detector, different energy ranges for various detectors, and differences in models used to fit the spectra. We examine the size of these individual sources of scatter by comparing many independent pairs of published Epeak values for the same bursts. Indeed, the observed scatter in multiple reports of the same burst (often with the same data) is greatly larger than the published statistical error bars. We measure that the one-sigma uncertainty associated with the analyst's choices is 28%, i.e., 0.12 in Log10(Epeak), with the resultant errors always being present. The errors associated with the detector response are negligibly small. The variations caused by commonly-used alternative definitions of Epeak (such as present in all papers and in all compiled burst lists) is typically 23%-46%, although this varies substantially with the application. The implications of this are: (1) Even the very best measured Epeak values will have systematic uncertainties of 28%. (2) Thus, GRBs have a limitation in accuracy for a single event, with this being reducible by averaging many bursts. (3) The typical one-sigma total uncertainty for collections of bursts is 55%. (4) We also find that the width of the distribution for Epeak in the burst frame must be near zero, implying that some mechanism must exist to thermostat GRBs. (5) Our community can only improve on this situation by using collections of bursts which all have identical definitions for the Epeak calculation.