© ESO, 2014

1. Introduction

Radial-velocity surveys have continuously provided new extrasolar planetary candidates since 1995 (Mayor & Queloz 1995). The observing strategy, consisting of multiple observations of single stars, is time-consuming and requires long-term programs on quasi-dedicated telescopes. These observations are necessary, however, to achieve a complete picture of the exoplanet population, especially towards the most populated long-period or/and low-mass ends. Statistical analyses were recently published by Mayor et al. (2011), Howard et al. (2010), and Wright et al. (2012), indicating the frequency of stars that harbour close-in massive planets – also called hot Jupiters: Mayor et al. (2011) reported a value of 0.89 ± 0.36% for the occurrence of planets more massive than 50 M_⊕ that have periods shorter than 11 days, Howard et al. (2010) found an occurrence of 1.2   ±    0.2% for planets more massive than 100 M_⊕ with periods shorter than 12 days and Wright et al. (2012) estimated 1.2 ± 0.38% for planets more massive than 30 M_⊕ with periods shorter than 10 days. In the Kepler survey, which has a different target sample, 0.43% of stars are found to harbour giant planets with radii between 6 and 22 Earth radii and periods shorter than 10 days (Howard et al. 2012; Fressin et al. 2013). The frequency of planets then increases towards lower masses, to reach more than 50% of the stars (Mayor et al. 2011) within the current detection limits of the available instruments. Hot Jupiters are thus extremely rare objects, although they have been at the heart of exoplanetary science for more than fifteen years, particularly for detailed characterizations, such as atmospheric studies and observations.

In this paper, we report the discovery of three new planets with orbital periods shorter than 20 days and projected masses of about one Jupiter mass. Interestingly, they are the inner planets in a multiple system, with a more massive second companion in the external part of the system. These discoveries were made in the context of a large program with SOPHIE, the high-precision radial-velocity spectrograph at the Observatoire de Haute-Provence. The survey for giant planets occupies about 12% of the telescope time since 2006 and has already allowed the discovery of twelve companions in the planet or brown dwarf range (da Silva et al. 2007; Santos et al. 2008; Bouchy et al. 2009; Hébrard et al. 2010; Boisse et al. 2010; Díaz et al. 2012). In Sect. 2, we describe the observations and analyses, in Sect. 3 we report the stellar properties, and in Sect. 4 we show and analyse the radial-velocity observations. In Sect. 5, we discuss the results and conclude.

2. Spectroscopic observations

The spectroscopic observations were obtained with the SOPHIE spectrograph at the Observatoire de Haute-Provence with the 1.93 m telescope in the framework of the large program (PNP.CONS) led by the SOPHIE Exoplanet Consortium, presented in detail by Bouchy et al. (2009). The SOPHIE instrument (Perruchot et al. 2011) is a fiber-fed environmentally stabilized echelle spectrograph covering the visible range from 387 to 694 nm. The spectral resolving power is 75 000 in high-resolution mode.

The radial velocities (RV) are obtained by cross-correlating the extracted spectra with a numerical mask based on stellar spectra, following the method developed by Baranne et al. (1996) and Pepe et al. (2002). For all three stars the numerical mask corresponding to a G2 spectral type was used because it provides the smallest individual error bars and residual scatter compared with the other available F0 and K5 masks.

The spectrograph has been upgraded in two steps (Bouchy et al. 2013), resulting in a slight zero-point motion at dates JD-2 400 000 = 55 730 and 56 274. The first update corresponds to the installation of a section of octagonal fibers upstream of the double scrambler, the second one to another section of octagonal fibers downstream; SOPHIE+ labels the measurements obtained after the updates. When applicable, the data sets should thus be taken as independent, with a free offset to be adjusted together with the Keplerian solution. The velocity offset between SOPHIE and SOPHIE+ is 11 ± 10 m s^-1 for HD 13908 and 37 ± 12m/s for HD 159243. They agree at 1.2σ, converging into a 24 ± 12 m s^-1 velocity shift for solar-like stars. The error on this offset propagates into the parameters of the orbits, with the largest impact on the errors on the mass and period of the outer planets.

In the context of the program where HD 13908, HD 159243, and HIP 91258 were observed, the objective was to obtain multiple measurements on a large sample of stars at a moderate RV precision. A signal-to-noise ratio of 50 only is aimed at, which gives an average noise level of 5 m s^-1 for individual measurements.

The radial velocity measurements of the three stars are given in Tables 5–7.

3. Stellar properties

The SOPHIE spectra were used to spectroscopically determine stellar parameters. The method described in Santos et al. (2004) and Sousa et al. (2008) was used on the mean high-signal-to-noise-ratio spectrum obtained for each star. We derived the effective temperature T_eff , gravity log g , and the iron content of the stellar atmospheres of HD 13908, HD 159243, and HIP 91258 using equivalent width measurements of the Fe I and Fe II weak lines by imposing excitation and ionization equilibrium assuming local thermal equilibrium. Errors were obtained by quadratically adding respectively 60 K, 0.1, and 0.04 dex to the internal errors on T_eff , log g , and [Fe/H].

The new reduction of the Hipparcos data (van Leeuwen 2007) was used to obtain the stellar parallaxes and derive the stellar luminosities after including the bolometric corrections proposed by Flower (1996) for the given effective temperatures. Then, the stellar mass, radius, and ages were derived using the evolutionary tracks and Bayesian estimation of da Silva et al. (2006). To take into account systematic effects, we adopted conservative uncertainties of 10% on the stellar mass.

The results are summarized in Table 1. All three stars are solar-like dwarfs. HD 13908 and HD 159243 have solar metallicity, while HIP 91258 has a significant excess of metal compared with the Sun, with [Fe/H]  = 0.23 ± 0.05.

Fig. 1 Variations with time of the $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ activity index for HD 13908 (top), HD 159243 (middle), and HIP 91258 (bottom).

Fig. 2 SOPHIE radial velocities and Keplerian model of the HD 13908  system: (top) as a function of time, with the residuals; (middle) as a function of phase for the inner planet; (bottom) as a function of phase for the outer planet. The blue points correspond to SOPHIE data obtained before June 2011, the red points correspond to more recent measurements after the SOPHIE+ upgrade.

Fig. 3 Periodogram of the radial velocity measurements of HD 13908 with both signals (top), with the outer-planet signal removed (middle), and periodogram of the bisector span (bottom).

Fig. 4 Bisector variations as a function of radial-velocity residuals from HD 13908 SOPHIE measurements, (top) without the outer planet signal, (middle) without the inner planet signal, and (bottom) without both planet signals.

The cross-correlation function allows various stellar indicators to be estimated: the bisector span (tracer of activity and blended stellar systems) and the projected rotational velocity (using calibrations developed in Boisse et al. 2010). In addition, the activity level of the stellar chromosphere was estimated from the calcium H and K equivalent widths. The average value of the $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ parameter is also given in Table 1. While HD 13908 is not active ($\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$= −4.9 dex), HD 159243 and HIP 91258 have a relatively high activity level ($\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$= −4.65 dex for both). The variations of the $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ value with time were systematically checked (Fig. 1) to verify whether the slow radial-velocity modulation is due to the long-term cycles of the star (Dumusque et al. 2011). Then, the bisector variations were inspected to determine whether they correlate with the radial-velocity signal at each detected period. A negative correlation between the bisector spans and the radial velocities usually indicates that the distortion of stellar lines due to spot activity produces radial-velocity jitter (Queloz et al. 2001; Boisse et al. 2012), and the planet interpretation may be compromised. The expected jitter due to activity is of the order of 9, 12, and 12 m s^-1 for HD 13908, HD 159243, and HIP 91258, respectively, using calibrations described in Santos et al. (2000). Finally, ranges for the rotation periods can be estimated from the B − V and $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ values. We found ranges of 5–9, 3–16, and 17–30 days, using the equations in Noyes et al. (1984) and a 3-σ error range on $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ .

4. Radial-velocity analysis

4.1. HD 13908

Seventy-seven SOPHIE measurements have been collected on the star HD 13908 during more than four years between October 2008 and January 2013. The average noise of individual measurements is 7.9 m s^-1 using SOPHIE, and 5.2 m s^-1 using SOPHIE+ (Fig. 2). The radial-velocity fluctuations have a standard deviation of 74 m s^-1, with a short-term component and a longer-term component. Because the measurements were secured in both the SOPHIE and SOPHIE+ configurations (Table 5), we split the data set into two parts (delimited by the horizontal line in the table).

Several solutions were tried and compared by estimating the standard deviation of the residuals: single-planet model, single-planet model with linear and quadratic trend, two-planet model, two-planet model with trends, and three-planet models. The best solution was found with a two-Keplerian model with respective semi-amplitudes of 55.3 ± 1.2 and 90.9 ± 3.0 m s^-1 (Fig. 2). The periodograms of the RV measurements are shown in Fig. 3. The peak corresponding to the outer companion is shown in the top plot; when the long-period signal is removed from the data, the inner-planet peak becomes proeminent (middle plot). The residuals of the two-planet model have an rms of 9.6 m s^-1 for the first data set, and 5.3 m s^-1 for the second data set after the spectrograph’s upgrade. These residual values are close to the one predicted from the activity jitter of 9 m s^-1 in Santos et al. (2000) and may be attributed to the stellar photospheric activity.

We searched in vain for periodicity in the time series of the bisector span (Fig. 3 bottom) and the chromospheric index $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$, therefore it seems unlikely that the short-period signal is generated by the rotation period of the star or that the long-period signal is related to the activity cycle of HD 13908 (Dumusque et al. 2011). The bisector spans do not vary with the radial velocity for any of the detected signals, which rules out that the photospheric activity is the main source of the variations (Fig. 4). The origin of the two signals is most likely the Doppler shift of the stellar spectrum that is caused by the orbital motion of the planets around the star and not by the deformation of the stellar profile due to photospheric activity. Note that the scatter of the bisector and $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ activity indices are 13 m s^-1 and 0.15 dex.

Because activity is discarded as a possible source of the radial-velocity variations, the system around HD 13908 is very likely composed of a Jupiter-like planet in a 19.4 day orbit and a massive giant planet in a 2.5 year long orbit. Parameters obtained with Monte Carlo Markov Chain simulations in yorbit, using 500 000 iterations, are given in Table 2. Although the eccentricity of the inner planet is not significantly different from zero, we kept it as a free parameter to include the associated error in the general modeling of the system.

The short-period planet has a transit probability of 3%. Photometric observations were attempted. No transit was detected because we missed the transit window, as we realized later from the refined ephemeris. Additional observations are therefore encouraged at the transit times given by JD =   2   455   756.032 + N × 19.382.

Finally, we searched the Hipparcos astrometry data for the signature of the outer companion with the method presented in Sahlmann et al. (2011). Since five orbital elements are determined by spectroscopy (P,e,T₀, ω, K), the intermediate-astrometry data (van Leeuwen 2007) can constrain the two remaining orbital parameters, in particular the orbit inclination i that yields the companion’s mass. No astrometric signature corresponding to the spectroscopic orbit was detected, which can be translated into a limit on i and an upper limit of 0.15 M_⊙ for the mass of HD 13908 c. This constraint is compatible with the non-detection of a secondary signal in the cross-correlation function.

4.2. HD 159243

We secured fifty-three SOPHIE radial-velocity measurements of HD 159243  during 767 days, from March 2011 to April 2013. Thirty-two measurements were obtained after the SOPHIE+ upgrade. The total data set features individual error bars with an average of 5.2 m s^-1 (Fig. 5). The standard deviation of the time series is 71 m s^-1. In the same way as for HD 13908, we compared several models with sets of 1, 2, or 3 planets and trends. The best-fit model was obtained with two Keplerian orbits, although it gives a residual noise of 12.4 and 9.4 m s^-1 for the two data sets.

The amplitude of this jitter is compatible with the expected jitter of 12 m s^-1 (see Sect. 3). It is therefore probably caused by activity, since the average $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ is –4.65 dex, indicative of an active star. During the period of observations, however, the stars showed almost no variation of its bisector span (rms = 15 m s^-1) and chromospheric activity (Fig. 1). The $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ parameter has an rms of 0.08 dex, and its variation is not correlated with the radial velocity signal. The radial-velocity variations are only weakly correlated with the bisector span for the two signals at 12.6 and 248 days (Fig. 6). The estimated rotation period of ≃10 days (see Sect. 3) and the marginally correlated behaviour of the bisector span without the outer planet signal (Fig. 6 middle), however, might cast some doubt on the inner planet. With an amplitude of 91 m s^-1, it is nevertheless unlikely that the signal is entirely generated by spot activity. With an activity-induced scatter amplitude of the order of 12 m s^-1, spot-related activity could explain the residual noise level, but not the 12 day period or the 91 m s^-1 amplitude signal. Dedicated activity simulations are needed to estimate the required correction, as in Boisse et al. (2012). In Fig. 7, we compare the periodogram of the radial-velocity measurements with the periodogram of the bisector spans. While the former (top plot) exhibits a strong peak at 12.6 days, the latter (bottom plot) shows faint peaks at 7.8 and 10.9 days. In this paper, we neglected the contribution of the activity to the inner-planet signal.

The best two-Keplerian model shows that the system of HD 159243  is composed of a 12.6 day Jupiter-like planet (minimum mass of 1.13 ± 0.05M_Jup) with a second giant planet with a minimum mass of 1.9 ± 0.13M_Jup in a 248 day period. The outer planet, despite its lower amplitude, is clearly detected in the periodogram of the radial-velocity measurements without the inner-planet signal (Fig. 7, middle plot). The two planetary companions have circular orbits. Table 3 gives the parameters of the planets obtained after 500 000 MCMC iterations. The non-detection of an astrometric signal with Hipparcos sets an upper limit of 0.52 M_⊙ for the outer companion HD 159243 c, a weak constraint that can also be established independently by the non-detection of a secondary signal in the spectra.

Fig. 5 SOPHIE radial velocities and Keplerian model of the HD 159243  system. The display is the same as in Fig. 2, i.e. the middle and bottom panels correspond to the inner and outer planets, respectively.

Fig. 6 Bisector variations as a function of radial-velocity residuals for HD 159243. Same plots as in Fig. 4.

Fig. 7 Periodogram of the radial-velocity measurements of HD 159243 with both signals (top), without the inner-planet signal (middle), and the periodogram of the bisector span (bottom).

Fig. 8 Relative flux of HD 159243 phased with the orbital period and time of transit of companion b. The dotted line shows the 1-σ uncertainty in the transit ephemeris. The thick line shows the transit duration and expected transit depth for the nominal ephemeris. There is no evidence of a transit, although it cannot be ruled out in the whole range.

A transit search was carried out with several telescopes despite the relatively low transit probability of 4%. Observations were carried out on 30 July 2012 at the Oversky Observatory¹ (La Palma, Spain) with a 14-inch telescope. The instrument includes a CCD SBIG STL-1001e camera and a Sloan r′ filter. Photometric observations were reduced using the software Muniwin 2.0. The sequence lasted 4.3 h and the normalized flux reached a scatter of 0.7%. A second series of observations was secured on 9 April 2013 at Saint-Michel l’Observatoire. It was obtained with a 20 cm telescope at f/5.5 equipped with an SBIG ST8XME camera during 2.2 h; a standard deviation of the normalized flux 0.46% was measured. Two additional sequences on 4 May and 10 June 2013 made use of the ROTAT² 60 cm telescope at the Haute-Provence Observatory, equipped with an SBIG STL11000 camera at the Newton focus reduced at f/3.2. Images of all sequences were processed with Muniwin 2.0 and relative photometry was extracted using one or several comparison stars. The first sequence of 4.1 h duration has a scatter of 0.5% in relative flux; the second sequence lasted 3.9 h and the flux has an rms of 0.6%. Together the photometric observations cover 75% of the transit window as allowed at the latest date of observations (June 2013). The transit ephemeris error (~9 h) is now much larger than the transit duration (expected 1.8 h). Recovering a more accurate transit ephemeris would require a new intensive radial-velocity campaign over several weeks. The standard deviation of the full photometric time series is 0.7%, and no transit is detected with a limiting depth of about 0.5%. Figure 8 shows the relative flux of HD 159243  and the expected ephemeris, duration, and depth of a potential transit, with a tolerance of 9 h corresponding to the propagated error in mid-2013. More data are needed to conclude.

Fig. 9 SOPHIE radial velocities and Keplerian model of the system orbiting HIP 91258: (top) as a function of time, with the residuals to the model including a quadratic long-term trend, and (bottom) as a function of phase for the inner planet.

Fig. 10 Periodogram of the radial-velocity measurements of HIP 91258 (top) and of the bisector span (bottom).

Fig. 11 Bisector variations as a function of radial-velocity residuals for HIP 91258. (top) without the 5.05 day period planet signal, and (bottom) without both the planet signal and the quadratic trend.

4.3. HIP 91258

The star HIP 91258 was observed with SOPHIE+ only after its major upgrade in June 2011. Twenty-seven measurements were secured on this target. The average uncertainty of this data set is 3.4 m s^-1. The periodogram of the RV series shows a peak at 5 days and its harmonics and aliases, as seen in Fig. 10. When modelled with a single Keplerian, we derive a standard deviation of the residuals of 45 m s^-1, indicating that another signal is present. The residuals drop to 13 m s^-1 when a linear trend is added, then to 6 m s^-1 when the trend is quadratic. Adding a second planet to the fit does not improve the residuals. The simplest and best fit is thus obtained with a quadratic trend and a short-period planet. The star does not show strong signs of activity, with a flat bisector span as a function of the radial velocity (Fig. 11) and an rms of 8 m s^-1. The periodogram of the bisector spans shows only noise (Fig. 10 bottom). The $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ value varies very little and shows no cyclic behaviour (Fig. 1), with a standard deviation of 0.03 dex during the period of observations. When the Keplerian+quadratric trend model is removed from the data, the periodogram shows a peak near 29 days that could be caused by activity, since the estimated stellar rotation period from the average $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ index is 24 ± 7 days.

The main detected signal is attributed to a planet with a minimum mass of 1.09 M_Jup  in a 5.05 day circular orbit with a semi-amplitude of 130.9 ± 1.7 m s^-1. The full set of parameters is given in Table 4. When a model with two Keplerian orbits is adjusted to the data, the best solution favours an outer body with a 5 yr period and a mass slightly above the hydrogen-burning limit. The time span of observations is, however, insufficient to precisely characterize this distant body in the system of HIP 91258, and we defer its identification to future studies based on several-years long additional observations. If adjusted to the shortest possible period of 150 days and using a null eccentricity and an RV amplitude of 100 m s^-1 as observed, the lowest possible mass of the outer companion is 2.5 M_Jup. A regular RV monitoring with five to ten measurements per year over two years would provide a sufficient constraint to determine whether the outer companion is in the planet, brown dwarf or star domain. Adaptive-optics imaging or future space astrometry with GAIA of this target would also allow constraining a possible stellar companion.

The HIP 91258 b planet has a transit probability of 12%. Nine series of observations were carried out on 15 and 30 August 2012 and in May to July 2013 with the Oversky, ROTAT, BROA and Crow facilities. BROA uses a 20 cm Celestron C8 with a KAF402XME camera and an R_c filter. The Crow observatory uses a 30 cm aperture Meade LX200, an I_c filter, and an SBIG ST8XME camera. Combining the 47 h of observations of this target (Table 8), we can exclude that a transit occurred between –9 and +6 h around the expected times for the transit center. Figure 12 shows the merged photometric light curve obtained at the expected time of transit. The rms of the measurements is 2 mmag. A transit with 0.4% depth would have been detected, while a depth of ~1% is expected for a Jupiter-sized planet passing accross a solar-like disk.

Fig. 12 Relative flux of HIP 91258 phased with the orbital period and time of transit of companion b. The dotted line shows the 1-σ uncertainty in the transit ephemeris. The thick line shows the expected transit duration and depth for the nominal ephemeris. Transits are ruled out to a depth of ~0.4%.

5. Discussion

The stars HD 13908, HD 159243, and HIP 91258  host multiple-planet systems with at least two companions. The inner companion is a hot/warm-Jupiter-like planet and the outer companion is more massive. Each planet in the three systems thus represents one of the two main populations of giant planets: hot/warm Jupiters, and distant giant planets. Planets HD 13908 c and HD 159243 c are located inside the ice line of their respective host star. For the system around HIP 91258, the outer companion is not yet characterized, since only part of the orbit is observed, although we were able to estimate that its mass is larger than 2.5 M_Jup. Because the ratio of periods (inner/outer) is lower than 0.2, the three systems can be considered as stable hierarchical systems. Their dynamical evolution is not subject to mean-motion resonance interactions but rather to secular perturbations (Beaugé et al. 2012).

Their configurations are not common, since most multiple systems are composed of low-mass planets. Other hot/warm Jupiter planets (mass greater than 0.5 M_Jup and period shorter than 20 days) with (at least) one known outer companion are: 55 Cnc b, HAT-P-13 b, HAT-P-17 b, HD 187123 b, HD 217107 b, HD 38529 b, HIP 14810 b, and υ And b. All of these systems except HIP 14810 have outer planets more massive than the inner one, like the systems around HD 13908, HD 159243 and HIP 91258 (the mass of HIP 91258 c is still undetermined, but it is larger than the mass of HIP 91258 b).

Including all detection technics, there are currently 146 known multiple-planet systems³, of which 92 have (minimum) mass measurements of all companions through radial-velocity measurements. Ten of these systems have an inner planet of the hot/warm-Jupiter category (with a period shorter than 20 days), which represents 11% of them. This is compatible with the analysis of Steffen et al. (2012) from the Kepler-object-of-interest sample (Batalha et al. 2013), who have shown that planets with periods larger than 6.3 days or with a radius smaller than 0.6 R_Jup have a ≳10% probability to have another transiting or TTV-planet in the system.

We cannot, however, derive reliable occurrence rates of hot/warm Jupiters in systems with respect to single hot-Jupiters from current observations, because the sample of multiple systems is heterogeneous and detection limits vary from one system to the other. In addition, the detection bias of radial-velocity and transit techniques favours the detection of short-period Jupiters, but severely limits the detection of outer planets: the latter requires both long-term observations and an accuracy of a few m s^-1 for the decreasing amplitude; in addition, the transit probability decreases with increasing semi-major axis.

Multiple systems composed of giant planets can serve as important constraints for migration models. The formation of hot Jupiters is not thought to occur in situ, but at large distances from their central star, followed by orbital evolution due to several types of interactions in the system: interaction with the proto-planetary disks (type II migration), dynamical interactions with other planets in the system, or Kozai migration. In early papers after the discovery of 51 Peg b, the formation of a hot-Jupiter planet was shown to result from planet-planet scattering followed by tidal circularization of the inner planet (Rasio & Ford 1996), for certain initial conditions. The formation of giant planets with a massive inclined body at large distances can also result in a decrease of the physical separation between the planet and its host star, until the orbit is circularized by tides (Kozai 1962; Wu et al. 2007). The detection and characterization of systems with a hot/warm Jupiter and another outer body in the system therefore gives practical examples of the potential outcome of these mechanisms. To determine whether type II migration is the most common phenomenon for the formation of hot Jupiters, as was recently discussed by Rice et al. (2012), it would be necessary to have precise observational constraints on all single hot-Jupiter systems, to determine what types of massive outer bodies are allowed by the data. A full picture of planetary system architecture is required to understand the origins of the inner-planet migration. Interestingly, the inner planets HD 13908  b, HD 159243  b, and HIP 91258  b found in the present work do not have periods corresponding to the pile-up of hot Jupiters at a period of about three days (e.g., Udry et al. 2003), but longer periods of 5 to 20 days. This may be a sign that their current distance to their star originates in an evolution induced by other mechanims than friction with the protoplanetary disks, such as planet-planet interactions (for HD 13908  b and HD 159243  b) or planet-star interactions (for HIP 91258  b, whose system may have a planetary or stellar outer companion).

The occurrence of massive planets at about 2 AU, such as HD 13908 c (mass greater than 5 M_Jup) may also be an interesting constraint for the accretion model with migration, beause it was shown by Alexander & Pascucci (2012) that the efficiency of accretion across the gap has a strong influence on the existence of such planets. Moreover, the planet HD 159243 c with about 2 M_Jup at 0.8 AU may correspond to the predicted pile-up of planets caused by photoevaporative clearing of the disk, as predicted in Alexander & Pascucci (2012) and observationally shown by Wright et al. (2009).

The relatively large semi-major axis of HD 13908 b and HD 159243 b fits the planet-planet scattering models with two initial planets better than those with three or four planets, if the orbital evolution of these systems is due to dynamical interactions between the planets and in the context of the simulations performed and discussed by Beaugé & Nesvorný (2012).

Our study confirmed the interest in extending the observational constraints of the exoplanet sample, in particular by following-up stars with known planets over a time scale of several years, at a precision of a few m s^-1. This allows one, in the long term, to assemble a more general picture of the mass distribution in the system after its dynamical evolution.

Online material

Acknowledgments

We gratefully acknowledge the Programme National de Planétologie (telescope time attribution and financial support), the Swiss National Foundation, and the Agence Nationale de la Recherche (grant ANR-08-JCJC-0102-01) for their support. R.F.D. is supported by the CNES. We warmly thank the OHP staff for their great care in optimising the observations. N.C.S., I.B. and A.S. acknowledge support from the European Research Council/European Community under the FP7 through Starting Grant agreement number 239953. N.C.S., I.B. and A.S. also acknowledge support from Fundacao para a Ciência e a Tecnologia (FCT) through program Ciência 2007 funded by FCT/MCTES (Portugal) and POPH/FSE (EC), and in the form of grants PTDC/CTE-AST/66643/2006, PTDC/CTE-AST/098528/2008, and SFRH/BPD/81084/2011.

References

All Tables

All Figures

	Fig. 1 Variations with time of the $\log {\mathit{R}}_{\mathrm{HK}}^{\mathrm{\prime }}$ activity index for HD 13908 (top), HD 159243 (middle), and HIP 91258 (bottom).
In the text

	Fig. 2 SOPHIE radial velocities and Keplerian model of the HD 13908  system: (top) as a function of time, with the residuals; (middle) as a function of phase for the inner planet; (bottom) as a function of phase for the outer planet. The blue points correspond to SOPHIE data obtained before June 2011, the red points correspond to more recent measurements after the SOPHIE+ upgrade.
In the text

	Fig. 3 Periodogram of the radial velocity measurements of HD 13908 with both signals (top), with the outer-planet signal removed (middle), and periodogram of the bisector span (bottom).
In the text

	Fig. 4 Bisector variations as a function of radial-velocity residuals from HD 13908 SOPHIE measurements, (top) without the outer planet signal, (middle) without the inner planet signal, and (bottom) without both planet signals.
In the text

	Fig. 5 SOPHIE radial velocities and Keplerian model of the HD 159243  system. The display is the same as in Fig. 2, i.e. the middle and bottom panels correspond to the inner and outer planets, respectively.
In the text

	Fig. 6 Bisector variations as a function of radial-velocity residuals for HD 159243. Same plots as in Fig. 4.
In the text

	Fig. 7 Periodogram of the radial-velocity measurements of HD 159243 with both signals (top), without the inner-planet signal (middle), and the periodogram of the bisector span (bottom).
In the text

	Fig. 8 Relative flux of HD 159243 phased with the orbital period and time of transit of companion b. The dotted line shows the 1-σ uncertainty in the transit ephemeris. The thick line shows the transit duration and expected transit depth for the nominal ephemeris. There is no evidence of a transit, although it cannot be ruled out in the whole range.
In the text

	Fig. 9 SOPHIE radial velocities and Keplerian model of the system orbiting HIP 91258: (top) as a function of time, with the residuals to the model including a quadratic long-term trend, and (bottom) as a function of phase for the inner planet.
In the text

	Fig. 10 Periodogram of the radial-velocity measurements of HIP 91258 (top) and of the bisector span (bottom).
In the text

	Fig. 11 Bisector variations as a function of radial-velocity residuals for HIP 91258. (top) without the 5.05 day period planet signal, and (bottom) without both the planet signal and the quadratic trend.
In the text

	Fig. 12 Relative flux of HIP 91258 phased with the orbital period and time of transit of companion b. The dotted line shows the 1-σ uncertainty in the transit ephemeris. The thick line shows the expected transit duration and depth for the nominal ephemeris. Transits are ruled out to a depth of ~0.4%.
In the text