Introduction
Extra-solar planets can be detected by monitoring a star's radial velocity (RV) – the speed with which a star moves away or towards us along our line-of-sight from Earth. A planet orbiting a star exerts a gravitational pull on its host, which can lead to detectable RV variations as the star and planet orbit their common centre of mass. These variations can be detected by measuring the Doppler shift of the light emitted by the star, using a spectrograph.
With extremely stable spectrographs such as High Accuracy Radial Velocity Planetary Search (HARPS)(Mayor et al. Reference Mayor2003) and HARPS-North (Pepe Reference Pepe2010), it is now possible to detect signals corresponding to low-mass planets such as super-Earths and even Earth-mass planets such as the recently discovered alpha Centauri Bb (Dumusque et al. Reference Dumusque2012). However, RV signals induced by these low-mass planets are entangled with the noise arising from the star's magnetic activity, and this had led to much controversy in planetary systems such as alpha Centauri B (Hatzes Reference Hatzes2013) and CoRoT-7 (Leger et al. Reference Leger2009; Queloz et al. Reference Queloz2009; Hatzes et al. Reference Hatzes2010, Reference Hatzes2011; Lanza et al. Reference Lanza2010; Pont et al. Reference Pont, Aigrain and Zucker2010 and others).
The magnetic activity of a star leads to the emergence of various features on the stellar surface (the photosphere). In stars like the Sun, the photosphere sits on top of a convection zone in which hot fluid cells are carried upwards due to buoyancy. When they reach the surface, they cool and eventually the fluid sinks back between the large convection cells. The pattern formed on the photosphere is known as granulation.
Granulation is inhibited in regions of strong magnetic fields; in these areas hot fluid is prevented from rising to the surface, so the photosphere is cooler and therefore appears darker. These dark regions are known as starspots (or sunspots in the case of the Sun). Strong magnetic fields can also lead to small bright pores, known as faculae. They are found around starspots and also inhibit the convection process.
The presence of these features can lead to RV variations of several m s−1 in Sun-like stars (Saar & Donahue Reference Saar and Donahue1997; Hatzes Reference Hatzes2002; Meunier et al. Reference Meunier, Desort and Lagrange2010a, Reference Meunier, Lagrange and Desortb). Considering that the RV induced by the motion of an Earth-mass planet orbiting at 1 AU from its parent star is of the order of 0.1 m s−1 (Mordasini et al. Reference Mordasini2009), it is essential to find ways to model activity-induced RV variations in order to be able to detect such planets with confidence.
Data
We study the case of CoRoT-7. This Sun-like star was first observed in 2009 and was found to host a transiting super-Earth with the smallest measured planetary radius at the time (Leger et al. Reference Leger2009). This discovery was followed by an intensive RV campaign with HARPS to measure its mass and investigate on the possible presence of other planets (Queloz et al. Reference Queloz2009). Since then, several analyses were made but all yielded different results due to the star's strong magnetic activity.
In 2012, CoRoT-7 was re-observed with the CoRoT satellite and the HARPS spectrometer, at the same time. These simultaneous photometric and RV data allow us to perform a new analysis.
Method
The lightcurve of a star, after all planet transits have been removed, only contains information about the star's magnetic activity. It is modulated by the presence of starspots on the stellar disk.
We can use the information contained in the simultaneous lightcurve to model the RV variations produced by those spots. This is done according to a model developed by Aigrain et al. (Reference Aigrain, Pont and Zucker2011).
The activity model is incorporated into a total RV model accounting for stellar activity and the orbit of several planets. The best model is found through an Monte Carlo Markov Chain (MCMC) analysis.
Results and conclusions
Figure 1 shows the RV data (top panel), the best fit models obtained for the two stellar activity basis functions (second panel), the Keplerian models found for each planet (three subsequent panels) and the total fit (second to last panel) with the residuals of the fit (last panel). The residuals appear to contain some correlated noise which is likely to be due to incomplete modelling of stellar induced RV variations. This is discussed in depth in Haywood et al. (submitted to MNRAS).
Fig. 1. Time series of the various parts of the total RV solution. All RVs are in m s−1. Second panel: model for suppression of convective blueshift (orange/light shade) and for stellar rotation (purple/dark shade). Second to last panel: the total model (red) is the sum of activity and planet RVs. Subtracting it from the original data yields the residuals plotted in the bottom panel. The error bars on the residuals represent the original errors of the data (smaller bars), and the errors after the extra noise term have been added (larger bars) for comparison.
We confirm the presence of three planets in the system: CoRoT-7b, with a mass of 3.38±0.86 Earth masses, and two sub-Neptune mass planets, CoRoT-7c (13.31±1.27 Earth masses) and CoRoT-7d (11.92±2.11 Earth masses), at orbital periods of 3.68±0.03 and 8.54±0.24 days, respectively. More details are given in Haywood et al. (submitted to MNRAS).
We find that the RV variations induced by stellar activity are dominant contributors to the total RV of the CoRoT-7 system. We conclude that modelling the activity-induced RV is essential in the search for super-Earths and Earth-mass planets around moderately active Sun-like stars.
