Issue 
A&A
Volume 571, November 2014



Article Number  A37  
Number of page(s)  36  
Section  Planets and planetary systems  
DOI  https://doi.org/10.1051/00046361/201424158  
Published online  04 November 2014 
Online material
Appendix A: Radial velocity correction from the constant star HD 185144
We present in this Appendix the SOPHIE radial velocities of the constant star HD 185144. During 2012 and 2013, this constant star was observed systematically on the same nights as the Kepler targets. It was observed using the same instrumental mode, i.e. the HighEfficiency mode (HE), but in ThoSimult mode (with the calibration ThoAr lamp observed simultaneously). This star was also observed in HighResolution mode (HR), less systematically, in order to control the performance and stability of the spectrograph to search for lowmass planets (Bouchy et al. 2013). We selected here only the observations that have reached a signaltonoise per pixel in the spectra of at least 50 at 550 nm. The star HD 185144 was observed 137 times in HE during 2012 and 2013. Figure A.1 shows its radial velocity, bisector, and FWHM variations. Those measurements are listed in Table A.6.
Radial velocities of HD 185144 present a rms of 6.9 m s^{1} in HE during both seasons. During 2012 only, this rms was of 8.0 m s^{1} while in 2013 it was of 5.5 m s^{1}. These rms are much smaller than the radial velocity uncertainty of the target KOI1257 (⟨ σ_{RV} ⟩ = 26 m s^{1}). However, even if the rms is relatively small for the required precision of KOI1257, the constant star was observed to vary in HE by a maximum of 34 m s^{1} in 2012 during a timescale of 20 days, and by 24 m s^{1} in 2013 with a timescale of four days. This corresponds to about one third and one fourth of the radial velocity amplitude of the transiting planet (K = 94 ± 21 m s^{1}). Those variations are not well understood but seem to be correlated with the temperature outside the dome. During the summers of 2012 and 2013 at Observatoire de HauteProvence there was a fast drop in the temperature due to a storm after a week of relatively hot days. This fast drop of the local temperature at the observatory is observed for both seasons
Fig. A.1
Radial velocities, bisector, and FWHM variations (from top to bottom) of the constant star HD 185144 observed by SOPHIE in HE during 2012 and 2013. We corrected these measurements by using their median value: about 27.79 km s^{1} for the RVs, about 8.8 km s^{1} for the FWHM, and 3 m s^{1} for the bisector. 

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in HD 185144 data by a radial velocity variation at the level of ~20 m s^{1} with a timespan of about one week. This effect is not observed in the HR mode. Before the implementation of octagonal fibres in June 2011 (Perruchot et al. 2011), the same effect was observed with an amplitude about five times larger (see Hébrard et al. 2013a). s
The bisector of HD 185144 does not show variation within ~4 m s^{1} during 2012 and 2013. We concluded that SOPHIE bisectors are stable and we did not correct the observed bisectors of KOI1257.
The observed FWHM of HD 185144 presents a rms of about 15 m s^{1} for 2012 and 2013. The observed pattern is not well understood, but is correlated with the flux of the ThoAr lamp. The peaktovalley amplitude is of about 60 m s^{1}, which is one order of magnitude less than the variation observed for KOI1257 (at the level of about 600 m s^{1}). Since the observations of KOI1257 were not performed with the simultaneous ThoAr lamp, we decided not to apply a correction to its FWHMs.
Appendix B: Upperlimit constraint in mass from a radial velocity drift
The quadratic radial velocity drift observed in SOPHIE data of KOI1257 was analysed in Sect. 3.8 assuming a circular orbit. The MCMC analysis converged toward a higher probability of having a shortperiod brown dwarf rather than a longperiod solarlike star. However, it is well known that from a radial velocity drift, it is possible to constrain only the lowerlimit in mass of a companion, but not its upperlimit in mass. To understand the result obtained in Sect. 3.8, we performed the following test. We generated synthetic radial velocity data using the SOPHIE observations (the observing times and the radial velocity uncertainty) assuming a pure white noise. We modelled two circular orbits with a period of 3400 days (which corresponds to the mostlikely period of the outer orbit in the KOI1257 system) and a radialvelocity semiamplitude of 1 km s^{1}. The epoch of periastron of the two orbits were chosen in order that the data display either a linear drift or a quadratic drift, the latter being the same as observed in the case of KOI1257. The synthetic data for the linear and quadratic drift are displayed in the top panels of Figs. B.1 and B.2, respectively.
Fig. B.1
Top panel: synthetic radial velocity dataset (black points) superimposed with the circular orbit model (red line) used to generate the data. This model shows only a linear drift during the timespan of the observations. Bottom panel: the 99.7% confidence region of the posterior distribution for the orbital period versus the radial velocity semiamplitude (black line). The modelled orbit is marked with the red circle. The upper limit in the radial velocity amplitude (at 10 km s^{1}) comes from the prior. 

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We analysed both datasets as done in Sect. 3.8 but assuming that the system is only described with a circular orbit. We used exactly the same priors for both analyses, using Jeffreys priors for both the orbital period and the radialvelocity semiamplitude. The other priors were chosen as large and uniform distributions. We show in the bottom panels of Figs. B.1 and B.2 the 99.7% confidence region from the posterior distribution computed through the same MCMC procedure as in Sect. 3.8. The two posterior distributions present a different shape: while the lineardrift dataset (Fig. B.1) provides only a lowerlimit in mass of the companion, the quadraticdrift dataset (Fig. B.2) provides both a lower and an upperlimit in mass. This can be explained easily by considering that it is more likely to observe a significant curvature in the radial velocity data if the orbital period is relatively short. On the other hand, for orbital periods much longer than the timespan of the observations, it is more likely to observe a nearly linear drift. This effect might also be explained by the fact that the secondorder polynomial, needed to describe the radialvelocity data, more accurately constrains the orbit of the companion than a firstorder polynomial. Then, the constraints in period translate into constraints in radialvelocity amplitude (or companion mass) thanks to the assumption of purely circular orbit.
Fig. B.2
Same as Fig. B.1, but for the quadratic drift dataset. 

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The constraints on the uppermass of the companion found in Sect. 3.8 therefore come from the assumption of a perfectly circular orbit and the curvature of the drift observed by SOPHIE.
Appendix C: Addditional tables
Priors used for the analysis of models A, B, C, D, and E.
Results of the analysis for models A, B, C, D, and E.
Priors used in the analysis of the scenarios 0, 1, 2 and 3.
Results of the analysis for the scenarios 0, 1, 2 and 3.
Radial velocity measurements of KOI1257.
SOPHIE HE measurements of the constant star HD 185144.
Groundbased photometric data of KOI1257.
© ESO, 2014
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