Selection Effects in Periodic X-Ray Data from Maximizing Detection Statistics

Abstract

Abstract The Neutron Star Interior Composition Explorer (NICER) records exceptional data on pulsars’ energy-dependent X-ray pulse profiles. However, in searching for evidence of pulsations, Guillot et al. (2019) introduce a procedure to select an ordered subset of data that maximizes a detection statistic (the H-test). I show that this can degrade subsequent analyses using an idealized model with stationary expected count rates from both noise and signal. Specifically, the data-selection procedure biases the inferred mean count rate to be too low and the inferred pulsation amplitude to be too high, and the size of these biases scales strongly with the amount of data that is rejected and the true signal amplitude. The procedure also alters the H-test’s null distribution, rendering nominal significance estimates overly optimistic. While the idealized model does not capture all the complexities of real NICER data, it suggests that these biases could be important for NICER’s observations of J0740+6620 and other faint pulsars (observations of J0030+0451 are likely less affected). I estimate that these effects may introduce a bias of  ( 10 % ) on average in the inferred modulation depth of lightcurves like J0740+6620's, and may be as large as  ( 50 % ) for fainter pulsars. However, the change for a single data set like J0740+6620 is expected to be a shift between −5% and +20%. This could imply that the lower limit on J0740+6620's radius is slightly larger than it should be, although preliminary investigations suggest the radius constraints shift to larger radii by  ( 1 % ) with the same overall statistical precision using real J0740+6620 data.