Statistics – Computation
Scientific paper
Jan 2012
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012aas...21914206c&link_type=abstract
American Astronomical Society, AAS Meeting #219, #142.06
Statistics
Computation
Scientific paper
High-energy photon data from the Fermi LAT provides an excellent source for constraining Lorentz invariance and limiting photon dispersion across the Universe. Photon groupings at the super-GeV level in Fermi gamma-ray bursts suggest upper limits on the time scales for dispersion over cosmological distances. A computational Monte Carlo approach allows us to find conservative limits on dispersion time scales at various levels of significance. By generating many random sets of "photons" with the same conditions as a chosen LAT data set, any number of small time scales can be tested and compared between the random bursts and the actual burst to observe the uniqueness of this burst within a desired tolerance or significance level. Similarly, applying a method of gap multiplication to both actual and Monte Carlo cases provides another quantitative evaluation of the overall bunching reminiscent of entropy. We have developed such algorithms using GRB 090510A as a focused case due to the presence of heavily bunched structure at energies above 1 GeV. Bunching time scales in GRB 090510A were calculated at a 3-sigma significance level with both numerical approaches and the resulting limits on dispersion and variance in photon travel speeds are the strongest to date. The application of such algorithms to many GRBs - above 1 GeV or otherwise - not only allows for a broader overview of photon dispersion time scales but also easily singles out unique cases with significant bunching at higher energies.
Connolly Ryan
Holmes Justin
Nemiroff Robert J.
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