The Total Errors In Measuring Epeak for Gamma-Ray Bursts
  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.
