Sensitivity of the radial-velocity technique in detecting outer planets

The technique of measuring radial velocity (RV) has produced spectacular discoveries of short-period Jovian mass objects around a fraction (5%-10%) of nearby G stars. Although we expect Jovian planets to be located in long-period orbits of decades or longer (if our solar system is any guide), detecting such planets with the RV technique is difficult because of the smaller velocity amplitudes and the limited temporal baseline (5-10 yr) of current searches relative to the expected orbital periods. This paper develops an analytical understanding of the sensitivity of the RV technique in the regime in which the orbital period is larger than the total baseline of the survey. Moreover, we focus on the importance of the orbital phase in this "long-period" regime and develop a least-squares detection technique based on the amplitude and phase of the fitted signal. To illustrate the benefits of this amplitude-phase analysis, we compare it with existing techniques. Previous authors, such as Nelson and Angel in 1998, have explored the sensitivity of an amplitude-only analysis using Monte Carlo simulations. Others have supplemented this by using the slope of the linear component of the fitted sinusoid in addition (e.g., Walker and colleagues in 1995 and Cumming and colleagues in 1999). In this paper, we illustrate the benefits of the least-squares technique over periodogram analysis and demonstrate the superiority of an amplitude-phase technique over previous analyses.