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Correlations between the arrival time and the energy of photons emitted inoutbursts of astrophysical objects are predicted in quantum and classicalgravity scenarios and can appear as well as a result of complex accelerationmechanisms responsible for the photon emission at the source. This paperpresents a robust method to study such correlations that overcomes somelimitations encountered in previous analysis, and is based on a Likelihoodfunction built from the physical picture assumed for the emission, propagationand detection of the photons. The results of the application of this method toa flare of Markarian 501 observed by the MAGIC telescope are presented. Themethod is also applied to a simulated dataset based on the flare of PKS2155-304 recorded by the H.E.S.S. observatory to proof its applicability tocomplex photon arrival time distributions.

A new method to study energy-dependent arrival delays on photons from astrophysical sources