Theoretical detection limits and error reduction for radial velocity observations of an Earth-like exoplanet

Abstract

The intent of this project was to determine the relationship between the number of radial velocity observations of an Earth-twin exoplanet and the error in the mass calculated from the detected signal. If the planet's period is known through prior transit observations, the mass may be measured by radial velocity more accurately; this project tested and measured the conditions for this error reduction. Simulated sets of radial velocity data taken by HARPS (accurate to 1 m/s) for an Earth-mass planet in a circular, edge-on, 1 AU orbit around a Sun-like star were used with a least-squares fit to measure the amplitude of the sinusoidal radial velocity curve. The three conditions in which the mass fit was compared were: evenly-spaced observations with the period unknown; evenly-spaced observations with the period known; and an unevenly-spaced observation method in which observation times are chosen to be very frequent and clustered around the peaks of the radial velocity curve. For evenly-spaced observations, knowledge of the period did not reduce the error in the mass measurement compared to the period-unknown case, though it did allow for the elimination of the false-negative detection case. When observations were evenly spaced, the percent error in the detected mass had a power law relationship with the number of observations of [sigma]%error 1250=N -⁰.⁵. However, when using the knowledge of the period from transits to choose clustered observation times near the peaks of the curve, the error in the mass was reduced by about 20% for the same number of total observations, and was thus approximated by the power law [sigma]%error = 1030N-⁰.⁵. This indicates that if the period of a low-mass planet is known through transits, the use of clustered observations allows its mass to be measured more accurately with the same number of radial velocity observations than if the period were unknown.