All gamma-ray telescopes suffer from source confusion due to their inability
to focus incident high-energy radiation, and the resulting background
contamination can obscure the periodic emission from faint pulsars. In the
context of the Fermi Large Area Telescope, we outline enhanced statistical
tests for pulsation in which each photon is weighted by its probability to have
originated from the candidate pulsar. The probabilities are calculated using
the instrument response function and a full spectral model, enabling powerful
background rejection. With Monte Carlo methods, we demonstrate that the new
tests increase the sensitivity to pulsars by more than 50% under a wide range
of conditions. This improvement may appreciably increase the completeness of
the sample of radio-loud gamma-ray pulsars. Finally, we derive the asymptotic
null distribution for the H-test, expanding its domain of validity to
arbitrarily complex light curves.Comment: 10 pages, 11 figures, published by ApJ; v2 fixes an error in Eq.