A Statistical Analysis of the Detection Limits in Fast Photometry

Abstract

This work investigates the statistical limits for the detection of stellar variability using ground based fast photometry. We show that when sky transparency variations are very low or have been efficiently removed from the raw light curve, the overall noise is of a Mixed Poisson (MP) nature (photon noise mixed by scintillation). As a consequence, three regimes appear for the detection of photometric variations depending on the star's brightness (scintillation, scintillation and photon noise, photon noise and sky background). The proposed analysis is mainly applied to the Indian sites of Manora Peak (existing 104 cm telescope) and Devasthal (future 1 m automated telescope, and 3 m telescope project). As shown by some examples, it can be applied to any site with the corresponding parameters. For 1 m class telescopes at an altitude of about 2000 m, the frontier magnitudes between the different detection regimes are about 10 mag and 15 mag. By analysing the corresponding statistics of the MP noise periodogram, the minimum amplitude variation that one can detect with a given confidence level is evaluated for each observational setting. For example, with a 3 m telescope at about 2500 m, ≈120 µmag variations would be detected in 2 h with a 99% confidence level for stars brighter than magnitude 12. For a star of 15th magnitude, ≈400 µmag oscillations would still be detected at that level. These detection limits are discussed in the light of observations obtained in Manora peak, and compared to results obtained at different astronomical sites.