Prospects for the Detection of Earth-Mass Planets

We compare potential state-of-the-art experiments for detecting Earth-mass planets around main-sequence stars using radial velocities, transits, astrometry, and microlensing. For conventionally-discussed signal-to-noise ratio (S/N) thresholds, S/N ~ 8, the last three methods are roughly comparable in terms of both the total number of planets detected and the mass distribution of their host stars. However we argue that S/N ~ 25 is a more conservative and realistic S/N threshold. We show analytically and numerically that the decline in the number of detections as a function of S/N is very steep for radial velocities, transits, and astrometry, such that the number of expected detections at S/N ~ 25 is more than an order-of-magnitude smaller than at conventional S/N thresholds. Indeed, unless Earth-mass planets are very common or are packed much closer to their parent stars than in the solar system, future searches using these methods (as they are currently planned) may not yield any reliable Earth-mass planet detections. On the other hand, microlensing has a much shallower S/N slope than the other techniques and so has much greater sensitivity at realistic S/N thresholds. We show that even if all stars have Earth-mass planets at periods of one year (and adopting other optimistic assumptions as well), the combined yield of all four techniques would be the detection of only about five such planets at S/N ~ 25.