Sectoral r modes and periodic RV variations of Sun-like stars

Abstract

Radial velocity (RV) measurements are used to search for planets orbiting late-type main-sequence stars and confirm the transiting planets. The most advanced spectrometers are approaching a precision of $\sim 10$ cm/s that implies the need to identify and correct for all possible sources of RV oscillations intrinsic to the star down to this level and possibly beyond. The recent discovery of global-scale equatorial Rossby waves in the Sun, also called r modes, prompted us to investigate their possible signature in stellar RV measurements. R modes are toroidal modes of oscillation whose restoring force is the Coriolis force and propagate in the retrograde direction in a frame that corotates with the star. The solar r modes with azimuthal orders $3 \leq m \lesssim 15$ were identified unambiguously because of their dispersion relation and their long e-folding lifetimes of hundreds of days. Here we simulate the RV oscillations produced by sectoral r modes with $2 \leq m \leq 5$ assuming a stellar rotation period of 25.54 days and a maximum amplitude of the surface velocity of each mode of 2 m/s. This amplitude is representative of the solar measurements, except for the $m=2$ mode which has not yet been observed. Sectoral r modes with azimuthal orders $m=2$ and $3$ would produce RV oscillations with amplitudes of 76.4 and 19.6 cm/s and periods of 19.16 and 10.22 days, respectively, for a star with an inclination of the rotation axis $i=60^{\circ}$. Therefore, they may produce rather sharp peaks in the Fourier spectrum of the radial velocity time series that could lead to spurious planetary detections. Sectoral r~modes may represent a source of confusion in the case of slowly rotating inactive stars that are preferential targets for RV planet search. The main limitation of the present investigation is the lack of observational constraint on the amplitude of the $m=2$ mode on the Sun.