Deriving the radial-velocity variations induced by stellar activity from high-precision photometry

Abstract

Context. Stellar activity induces apparent radial velocity (RV) variations in late-type main-sequence stars that may hamper the detection of low-mass planets and the measurement of their mass. Aims. We use simultaneous measurements of the active planet host star HD 189733 with high-precision optical photometry by the MOST satellite and high-resolution spectra by SOPHIE. We apply on this unique dataset a spot model to predict the activity-induced RV variations and compare them with the observed ones. Methods. The model is based on the rotational modulation of the stellar flux. A maximum entropy regularization is applied to find a unique and stable solution for the distribution of the active regions versus stellar longitude. The RV variations are synthesized considering the effects on the line profiles of the brightness perturbations due to dark spots and bright faculae and the reduction of the convective blueshifts in the active regions. Results. The synthesized RV time series shows a remarkably good agreement with the observed one although variations on timescales shorter than 4-5 days cannot be reproduced by our model. Persistent active longitudes are revealed by the spot modelling. They rotate with slightly different periods yielding a minimum relative amplitude of the differential rotation of ΔΩ/Ω = 0.23 ± 0.10. Moreover, several active regions with an evolution timescale of 2-5 days and an area of 0.1-0.3 percent of the stellar disc are detected. Conclusions. The method proves capable of reducing the power of the activity-induced RV variations by a factor from 2 to 10 at the rotation frequency and its harmonics up to the third. Thanks to the high-precision space-borne photometry delivered by CoRoT, Kepler, or later PLATO, it is possible to map the longitudinal distribution of active regions in late-type stars and apply the method presented in this paper to reduce remarkably the impact of stellar activity on their RV jitter allowing us to confirm the detection of low-mass planets or refine the measurement of their mass.

A Decade of Hα Transits for HD 189733 b: Stellar Activity versus Absorption in the Extended Atmosphere

“…On the other hand, Shapiro et al (2015) (see also Foukal 1998; Lockwood et al 2007) find that photometric variations for more active stars are spot-dominated and that the ratio of facular/plage coverage to spot coverage decreases with increasing activity level. Lanza et al (2011) find that RV modulations in HD 189733's spectrum are best modeled with values of Q = A f ac /A spot ∼0, i.e., they find no evidence of facular/plage effects on the measured RV values. Furthermore, Lanza et al (2011) find spot filling factors of ∼1% are able to reproduce HD 189733's photometric variations across ∼4 weeks of nightly observations.…”

“…We ignore all small-scale velocity effects in the spectra, such as photospheric convective blue shifts, since we are only concerned with the overall contrast between the different regions. The contrast is weakly affected by these velocity shifts, which are of the order ∼200-300 m s −1 (e.g., Lanza et al 2011). …”

Magnetic activity of F stars observed byKepler

“…This has also been seen in stars with a nearby companion (e.g. Lanza et al 2011) whose interaction would generate a stable spot on the surface of the star. However, no signature of such a companion has been detected for these two stars.…”

Starspot activity and rotation of the planet-hosting star Kepler-17

“…However, this lower value of Q is typical of sun-like stars that are more active than the Sun (cf. Lanza et al 2009aLanza et al , 2010Lanza et al , 2011a and suggests an increasing weight of the dark spots in the photometric variations as a star becomes more active, as indicated by the results of, e.g., Radick et al (1998) and Lockwood et al (2007).…”