Transit and Radial Velocity Survey Efficiency Comparison for a Habitable Zone Earth

Transit and radial velocity searches are two techniques for identifying nearby extrasolar planets to Earth that transit bright stars. Identifying a robust sample of these exoplanets around bright stars for detailed atmospheric characterization is a major observational undertaking. In this study we describe a framework that answers the question of whether a transit or radial velocity survey is more efficient at finding transiting exoplanets given the same amount of observing time. Within the framework we show that a transit survey's window function can be approximated using the hypergeometric probability distribution. We estimate the observing time required for a transit survey to find a transiting Earth-sized exoplanet in the HZ with an emphasis on late type stars. We also estimate the radial velocity precision necessary to detect the equivalent HZ Earth-mass exoplanet that also transits when using an equal amount of observing time as the transit survey. We find that a radial velocity survey with sig_rv~0.6 m/s precision has comparable efficiency in terms of observing time to a transit survey with the requisite photometric precision sig_phot~300 ppm to find a transiting Earth-sized exoplanet in the HZ of late M~dwarfs. For Super-Earths, a sig_rv~2.0 m/s precision radial velocity survey has comparable efficiency to a transit survey with sig_phot~2300 ppm.