Using the Sun to estimate Earth-like planet detection capabilities

Abstract

Context. Radial velocity (RV) time series are strongly impacted by the presence of stellar activity. In a series of papers, we have reconstructed solar RV variations over a full solar cycle from observed solar structures (spots and plages) and studied their impact on the detectability of an Earth-mass planet in the habitable zone of the Sun as seen edge-on from a neighbour star in several typical cases. We found that the convective contribution dominates the RV times series. Aims: The objective of this paper is twofold: to determine detection limits on a Sun-like star seen edge-on with different levels of convection and to estimate the performance of the activity correction using a Ca index. Methods: We apply two methods to compute the detection limits: a correlation-based method and a local power analysis method, which both take into account the temporal structure of the observations. Furthermore, we test two methods using a Ca index to correct for the convective contribution to the RV: a sinusoidal fit to the Ca variations and a linear fit to the RV-Ca relation. In both cases, we use observed Ca and reconstructed Ca to study the various effects and limitations of our estimations. Results: We confirm that an excellent sampling is necessary to have detection limits below 1 MEarth (e.g. 0.2-0.3 MEarth) when there is no convection and a low RV noise. With convection, the detection limit is always above 7 MEarth. The two correction methods perform similarly when the Ca time series are noisy, leading to a significant improvement (down to a few MEarth), which is above the 1 MEarth limit. With a very good Ca noise (signal to noise ratio, S/N, around 130), the sinusoidal method does not get significantly better because it is dominated by the fact that the solar cycle is not sinusoidal, but the RV-Ca method can reach the 1 MEarth for an excellent Ca noise level. Conclusions: For Sun-like conditions and under the simplifying assumptions considered, we first conclude that the detection limit of a few MEarth planet can be reached providing good sampling and Ca noise. The detection of a 1 MEarth may be possible, but only with an excellent temporal sampling and an excellent Ca index noise level: we estimate that a probability larger than 50% to detect a 1 MEarth at 1.2 AU requires more than 1000 well-sampled observations and a Ca S/N larger than 130.