The SNR of a Transit

Abstract

Accurate quantification of the signal-to-noise ratio (SNR) of a given observational phenomenon is central to associated calculations of sensitivity, yield, completeness and occurrence rate. Within the field of exoplanets, the SNR of a transit has been widely assumed to be the formula that one would obtain by assuming a boxcar light curve, yielding an SNR of the form $(\delta /{\sigma }_0)\sqrt{D}$. In this work, a general framework is outlined for calculating the SNR of any analytic function and it is applied to the specific case of a trapezoidal transit as a demonstration. By refining the approximation from boxcar to trapezoid, an improved SNR equation is obtained that takes the form $(\delta /{\sigma }_0)\sqrt{(T_{14}+2T_{23})/3}$. A solution is also derived for the case of a trapezoid convolved with a top-hat, corresponding to observations with finite integration time, where it is proved that SNR is a monotonically decreasing function of integration time. As a rule of thumb, integration times exceeding $T_{14}/3$ lead to a 10% loss in SNR. This work establishes that the boxcar transit is approximate and it is argued that efforts to calculate accurate completeness maps or occurrence rate statistics should either use the refined expression, or even better numerically solve for the SNR of a more physically complete transit model.

arXiv commentAccepted to MNRAS

References in corpus (33)

• The Transiting Exoplanet Survey Satellite
• Analytic Lightcurves for Planetary Transit Searches
• The PLATO 2.0 Mission
• Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler
• The false positive rate of Kepler and the occurrence of planets
• A box-fitting algorithm in the search for periodic transits
• Prevalence of Earth-size planets orbiting Sun-like stars
• The Occurrence Rate of Small Planets around Small Stars
• The Transiting Exoplanet Survey Satellite: Simulations of planet detections and astrophysical false positives
• Terrestrial Planet Occurrence Rates for the Kepler GK Dwarf Sample
• Binning is sinning: morphological light-curve distortions due to finite integration time
• A Revised Exoplanet Yield from the Transiting Exoplanet Survey Satellite (TESS)
• Transit Least Squares: Optimized transit detection algorithm to search for periodic transits of small planets
• Occurrence Rates of Planets orbiting FGK Stars: Combining Kepler DR25, Gaia DR2 and Bayesian Inference
• Dos and don'ts of reduced chi-squared
• Analytic Approximations for Transit Light Curve Observables, Uncertainties, and Covariances
• A Giant Planet Candidate Transiting a White Dwarf
• Kepler Planet Occurrence Rates for Mid-Type M Dwarfs as a Function of Spectral Type
• Observational biases in determining extrasolar planet eccentricities in single-planet systems
• Measuring Transit Signal Recovery in the Kepler Pipeline I: Individual Events
• Empirical Constraints on the Oblateness of an Exoplanet
• Nightside Pollution of Exoplanet Transit Depths
• Predicting the Yields of Photometric Surveys for Transiting Extrasolar Planets
• The occurrence of planets and other substellar bodies around white dwarfs using K2
• Giant planet occurrence within 0.2 AU of low-luminosity red giant branch stars with K2
• Transit Light Curves with Finite Integration Time: Fisher Information Analysis
• Observational biases for transiting planets
• A Cloaking Device for Transiting Planets
• Binning is Sinning (Supernova Version): The Impact of Self-Calibration in Cosmological Analyses with Type Ia Supernovae
• On the detectability of transiting planets orbiting white dwarfs using LSST
• Spin-Orbit Misalignment and Precession in the Kepler-13Ab Planetary System
• Precovery of TESS Single Transits with KELT
• Is binning always sinning? The impact of time-averaging for exoplanet phase curves

Cited by in corpus (2)

• Adaptation of the Phase Distance Correlation Periodogram to Account for Measurement Uncertainties
• Validating the Orbital Periods of the Coolest TESS Exoplanet Candidates