A Statistical Analysis of the Detection Limits in Fast Photometry

This work investigates the statistical limits for the detection of rapid stellar variations using ground based fast photometry. We show that the noise to be accounted for is of a mixed Poisson (MP) nature (photon noise mixed by scintillation). As a consequence, three regimes appear for the detection depending on the star´s brightness: scintillation; scintillation and photon noise; photon noise and sky background. Both cases of periodic and non periodic signals are investigated. In the case of periodic stellar variations, the minimum amplitude variation that one can detect with a given confidence level is evaluated by analysing the statistics of the MP noise periodogram. The theoretical detection limits are discussed at the light of photometric data obtained on various astronomical sites