Sectoral r modes and periodic radial velocity variations of Sun-like stars

¹ INAF-Osservatorio Astrofisico di Catania, Via S. Sofia, 78 – 95123 Catania, Italy
e-mail: antonino.lanza@inaf.it
² Max-Planck-Institut für Sonnensystemforschung, Justus-von-Liebig-Weg 3, 37077 Göttingen, Germany
e-mail: gizon@mps.mpg.de
³ Georg-August-Universität, Institut für Astrophysik, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
⁴ Center for Space Science, NYUAD Institute, New York University Abu Dhabi, PO Box 129188, Abu Dhabi, UAE
⁵ Space Research Institute, Austrian Academy of Sciences, Schmiedlstraße 6, 8042 Graz, Austria
e-mail: Teimuraz.Zaqarashvili@oeaw.ac.at
⁶ Abastumani Astrophysical Observatory at Ilia State University, 3/5 Cholokashvili Avenue, 0162 Tbilisi, Georgia
⁷ IGAM-Kanzelhöhe Observatory, Institute of Physics, University of Graz, Universitätsplatz 5, 8010 Graz, Austria

Received: 23 November 2018
Accepted: 24 January 2019

Abstract

Context. Radial velocity (RV) measurements are used to search for planets orbiting late-type main-sequence stars and to confirm the transiting planets.

Aims. The most advanced spectrometers are now approaching a precision of ~10 cm s⁻¹, which 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. These r modes are toroidal modes of oscillation whose restoring force is the Coriolis force; they propagate in the retrograde direction in a frame that co-rotates with the star. The solar r modes with azimuthal orders 3 ≤ m ≲ 15 were identified unambiguously because of their dispersion relation and their long e-folding lifetimes of hundreds of days.

Methods. In this paper, we simulate the RV oscillations produced by sectoral r modes with 2 ≤ m ≤ 5 by assuming a stellar rotation period of 25.54 days and a maximum amplitude of the surface velocity of each mode of 2 m s⁻¹. This amplitude is representative of the solar measurements except for the m = 2 mode, which has not yet been observed on the Sun.

Results. Sectoral r modes with azimuthal orders m = 2 and 3 would produce RV oscillations with amplitudes of 76.4 and 19.6 cm s⁻¹ and periods of 19.16 and 10.22 days, respectively, for a star with an inclination of the rotation axis to the line of sight i = 60°. Therefore, they may produce rather sharp peaks in the Fourier spectrum of the radial velocity time series that could lead to spurious planetary detections.

Conclusions. 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 constraints on the amplitude of the m = 2 mode on the Sun.