© ESO, 2012

1. Introduction

More than 15 years after the discovery of the first extrasolar planets and brown dwarfs (see, for example, Mayor & Queloz 1995; Rebolo et al. 1995), a number of questions remain open regarding the relation between these two types of objects. Principal among these questions is the problem of distinguishing members of one class from members of the other. As discussed by, for example, Basri & Brown (2006), the criteria used to classify these objects can concern their physical characteristics, and their origin, among other things.

The common idea that brown dwarfs are “failed” stars that only fusion deuterium, and that are unable to sustain a constant luminosity throughout their lifetimes (e.g. Burrows et al. 1997; Baraffe et al. 2003), while planets are objects that are simply too light to fusion deuterium seems to imply that a definition based on physical characteristics would be the best. Traditionally, the deuterium-burning mass was taken to be 13 M_Jup (Burrows et al. 2001), but there is an important uncertainty related to the equation of state used in these computations. Additionally, more recent models by Spiegel et al. (2011) show that the deuterium-burning mass limit depends on the helium abundance, the initial deuterium abundance, and the metallicity of the model, among other things. Therefore, the authors find that the deuterium-burning mass can range from 11 M_Jup up to 16 M_Jup. Choosing a single mass as the limit between both categories may therefore lead to an oversimplification of the scenario. Additionally, because the minimum mass needed to start gravitational collapse, either in a disk or in a molecular cloud, is probably around a few Jupiter masses (Whitworth & Stamatellos 2006), and because the core-accretion models predict objects with masses as high as a few tens of Jupiter masses (Mordasini et al. 2009), there surely is an important overlap in mass for objects of different origins. For example, Kirkpatrick et al. (2006) have reported the discovery of an L-type brown dwarf with a mass that could be as small as 6 M_Jup. This might make the distinction by mass not completely satisfactory.

On the other hand, a criterion based on formation history would stand on the fact that brown dwarfs are thought to form as stars (see the reviews by Luhman et al. 2007; Whitworth et al. 2007), i.e. by gravitational collapse of molecular cloud cores on dynamical timescales, while planets are widely believed to form from accretion of a solid core in a protoplanetary disk, a process believed to be much slower (Pollack et al. 1996; Alibert et al. 2005). This could in principle allow us to distinguish one type from the other, but this is not without a few drawbacks. First of all, it is practically impossible to unambiguously trace the history of an object back to its origins. Additionally, there is no complete consensus about the mechanisms that rule the formation processes, either for brown dwarfs, or for massive planets. For example, massive planets are also proposed to be able to form by disk collapse (Boss 1997) or by protostellar cloud fragmentation followed by inward migration by disk capture (Font-Ribera et al. 2009). A definition based on formation history might then prove provisional.

To produce a consistent picture of brown dwarfs and extrasolar planets, a solid observational base for formation and evolution models is crucial. Constraining the multiplicity properties of these objects, such as frequency, separation and mass ratio distributions, should permit us to distinguish between different formation models.

Most of the known extrasolar planets have been discovered by high-precision radial velocity (RV) surveys (see exoplanet.eu, and Schneider et al. 2011). Owing to the large reflex motion they induce in the stars they monitor, these surveys should easily discover brown dwarf companions and properly characterise their orbital elements and frequency. However, the brown dwarf desert (Marcy & Butler 2000; Grether & Lineweaver 2006), i.e. the paucity of massive sub-stellar companions to solar-type stars in close orbits, has hindered this endeavour, resulting in only a few tens of these objects known to date (Sozzetti & Desidera 2010; Sahlmann et al. 2011b). Indeed, the frequency of close brown dwarf companions around sun-like stars has been recently determined to be below 0.6% (Sahlmann et al. 2011b). Additionally, the RV method provides a lower limit for the mass only, which means that a fraction of the brown dwarf candidates detected by RV surveys are actually low-mass stars in low-inclination orbits. As a consequence, studies of massive planets and brown dwarf properties are faced with a small and uncertain sample of objects, and therefore all efforts to either increase the number of these objects or to determine their true mass accurately will prove valuable.

Different authors have attempted to measure the true mass of RV candidates using astrometric measurements (Halbwachs et al. 2000; Zucker & Mazeh 2001; Sahlmann et al. 2011b; Reffert & Quirrenbach 2011). Although most of these analyses fail to yield direct measurements of the mass and are limited by the precision of their measurements to upper limits of the mass, they have proven efficient in discarding relatively massive stellar companions in low-inclination orbits.

In this paper, we report the detection of seven new objects with minimum masses between 10 and 90 M_Jup, orbiting main-sequence stars of spectral types F, G, and K. The detections are based on precise radial velocity measurements obtained as part of the sub-progamme 2 of the SOPHIE search for northern extrasolar planets (Bouchy et al. 2009a). We have already announced three of these objects, albeit with preliminary parameters (Díaz et al. 2011). Additionally, we improve on the orbital parameters of an already known brown dwarf, HD 137510 b. Finally, our attempts to measure the true mass of these candidates are described as well.

In Sect. 2 we describe the observations and the data reduction, in Sect. 3 we describe the methods used to analyse the data, fit the orbits, and estimate the stellar parameters of the primaries. We also describe the techniques employed to constrain the true nature of the companions, including the analysis of astrometric data from the Hipparcos mission. In Sect. 4 we report the results obtained for each object, which are roughly classified using the mass-based criterion described above into planetary candidates, brown dwarf candidates and stellar-mass objects. The results are then discussed in Sect. 5. Finally, in Sect. 6 we summarise the results and present our conclusions.

2. SOPHIE radial velocities

2.1. Observations

Radial velocity measurements were performed with SOPHIE, a high-resolution echelle spectrograph that is fiber-fed from the Cassegrain focus of the 1.93-m telescope at the Haute-Provence Observatory (OHP). It is installed in a temperature-stabilised environment and the dispersive elements are kept at constant pressure in order to provide high-precision radial velocities (Perruchot et al. 2008). SOPHIE spectra cover most of the visible wavelength range in 39 spectral orders.

Observations were performed in high-resolution mode, which produces spectra with resolving power of λ/Δλ ~ 75   000 at 550 nm. Two optical fibers are used in this mode: one of them records the stellar spectrum while the other can be used to simultaneously calibrate the spectrum with a thorium argon lamp (thosimult mode) or to record the background sky spectrum during the observations (objAB mode). Most of the observations reported here were obtained in the objAB mode, since the stability of the instrument is sufficient to allow the calibrations to be obtained every approximately 2 h without degrading the desired velocity precision¹. The observations performed in thosimult mode date from the first season of observations with SOPHIE when its stability had not yet been confirmed. Moreover, in objAB mode, the sky fiber can be used to correct for scattered light that contaminates the star fiber (e.g. Barge et al. 2008; Pollacco et al. 2008; Santerne et al. 2011).

The targets reported in this paper are listed in Table 1. We include the date of the first and last observation of each target, the time span of observations and the number of measurements obtained. In the last column of Table 1 we indicate the section in which the results of each target are presented. The exposure time was varied to reach a signal-to-noise ratio (S/N) of 50 per resolving element under varying weather conditions. The exposure time and S/N of each individual observation are reported in Table 2.

2.2. Data reduction

The spectra were reduced and extracted using the SOPHIE pipeline (Bouchy et al. 2009a), which performs all steps from the raw images to the wavelength-calibrated 2D spectra. These are then correlated using numerical binary masks corresponding to different spectral types (G2, K5 and M4). The cross-correlation function (CCF) averaged over all 39 spectral orders is then fitted with a Gaussian function to obtain the RV, the full-width at half-maximum (FWHM), and contrast relative to the baseline. Additionally, the bisector velocity span of the CCF is computed in the way described by Queloz et al. (2001) for the subsequent analysis, and the radial velocity is computed considering only the blue or red halves of each spectral order, which we call RV_blue, and RV_red, respectively (see Sect. 3.4.1). For reference we report in Table 3 the numerical mask closest to the measured spectral type for all targets studied in this paper (Sect. 3.1), and the median values of the CCFs parameters: RV, FWHM and contrast. The errorbars reported correspond to the standard deviation of each magnitude.

The complete radial velocity datasets obtained with the mask closest to the spectral type of each target are reported in Table 2, where the uncertainties include the photon noise error, estimated with the method by Bouchy et al. (2001), the error in the wavelength calibration (~2 m s^-1), and an additional systematic error of 3 m s^-1, which was added quadratically to the other sources of uncertainty. The systematic errors arise from imperfect guiding, the so-called seeing effect (Boisse et al. 2011a, see also Sect. 3.4.1 of the present paper), uncorrected velocity drifts of the spectrograph, and other still unidentified sources.

In April 2007, SOPHIE was upgraded with a bandpass filter to reduce the contamination of the stellar spectra by argon lines caused by the ThAr lamp during observations in thosimult mode. For three stars of our sample some observations were performed in thosimult before the upgrade: HD 14651, HD 22781, and HD 30246. These observations are identified in Table 2, and they exhibit a clear contamination in the red part of the spectra. To mitigate the effects of this contamination, the six reddest spectral orders were not considered for the computation of the average CCF and the radial velocity. To maintain the uniformity of the reduction, the remaining spectra of each star were also reduced in the same way. The resulting velocities are slightly different from those obtained using all spectral orders for these same spectra, but there is no systematic shift between both observation modes. The orbital fits performed using the corrected velocities exhibit a reduced scatter. The remaining observations were performed in objAB mode.

3. Data analysis

3.1. Stellar parameters

The CCF obtained (Sect. 2.1) has been used to obtain an estimate of the stellar metallicity ([Fe/H]) and the projected stellar rotational velocity (v   sinI, where I is the inclination of the rotation axis of the star with respect to the line of sight) using the calibrations described in detail by Boisse et al. (2010). The estimated uncertainty of these calibrations is 1 km   s^-1 on v   sinI and about 0.09 dex on [Fe/H]. Additionally, a more detailed spectral analysis was carried out using the SOPHIE spectra obtained in objAB mode that were not contaminated by moonlight. The method (Santos et al. 2004) provides the effective temperature T_eff, the surface gravity log    g and the metallicity [Fe/H] of the observed stars. To obtain the stellar masses, we interpolated the isochrones by Girardi et al. (2000), using the method described by da Silva et al. (2006). The values derived from this analysis are reported in Table 4. The uncertainties for the stellar masses range from 2.6% to 5.8%. However, these are the formal uncertainties, which do not take into account the systematic uncertainties in the models, and we therefore decided to adopt a conservative uncertainty of 10% on the stellar mass. The spectral types reported in Table 1 are obtained from interpolating the tables from Cox (2000) to the values of T_eff obtained. We note that in all cases the spectroscopic determination of the metallicity agrees with the method based on the CCF (Boisse et al. 2010) to within 1-σ.

3.2. Stellar activiy

We computed the activity index (Noyes et al. 1984) on each spectrum of each target using the method described by Boisse et al. (2010). In Table 4 we report the median value of the index for each target and its standard deviation², computed using the spectra obtained in objAB mode only, since the contamination by the ThAr lamp present in the rest of the spectra is expected to change the depth of the spectral lines. The obtained values were used to estimate the age of the host stars using the relation by Mamajek & Hillenbrand (2008). We report the results in Table 4. The activity-determined ages agree with the values obtained from isochrone fitting, except for HD 137510 and HD 167215. These stars are the two least active stars in the sample, and their are either at the limit of, or outside the range of applicability of the Mamajek & Hillenbrand (2008) formula, which is valid only for .

It is known that stellar activity is a source of uncertainty in the RV measurements (e.g. Queloz et al. 2001; Boisse et al. 2011b). In some cases (Boisse et al. 2010; Melo et al. 2007), the RV jitter produced by stellar activity was corrected, with the result of improved determinations of the orbital and planetary parameters. This was performed by decorrelating the residuals of the orbital fit with the bisector velocity span. We checked for all our sample stars if the residuals of the best-fit Keplerian orbit exhibited any dependence with the measured bisector span. We found no correlation with a significance above 2σ. In the case of HD 30246, the most active star in our sample (), a slight hint of a negative correlation is seen, with a fit slope of b =  −0.13  ±  0.08. On the other hand, HD 16702 has a similar activity level (), but the residuals do not exhibit any correlation with activity index . However, as will be discussed in Sect. 4.3, the companion to HD 16702 is most likely a low-mass star, which might contaminate the determination of . We note that the stars studied by Boisse et al. (2010) (HD 189733) and Melo et al. (2007) (HD 102195) exhibit activity levels similar to that of HD 30246 and HD 16702, but their data are much more precise, which might permit detecting subtler trends.

3.3. Moon contamination

Whenever present, moonlight scattered in the Earth’s atmosphere can pollute the observed stellar spectrum. If the Moon’s RV is close to the velocity of the observed star, moonlight can bias the measurement of the velocity. Prior to performing a Keplerian fit to the data, we verified that none of the RV measurements were biased by this effect. For an observation to be polluted, two conditions must be fulfilled: in the first place, the scattered moonlight must contribute significantly to the light entering the spectrograph’s fiber. For the observations in objAB mode, this can be addressed using fiber B. We considered conservatively that the moonlight level is sufficient to pollute a stellar spectrum if the S/N in fiber B was higher than 3 and if the contrast of the corresponding CCF was higher than 1%, i.e. if the CCF peak of the Moon is detected in the sky fiber, even if marginally. The second condition is that the Moon RV must be close to the stellar velocity. To study this, we considered the baricentric Earth radial velocity (BERV) on the day of the observation, and in the direction of the target, which is within  ~1 km s^-1 of the Moon radial velocity. The Moon RV was considered to be close to the measured RV if the BERV was less than  ~7σ away from the measured stellar peak, where σ is the width of the the CCF. For those cases in which the second fiber was dedicated to obtain the spectrum of a ThAr lamp simultaneously, for which no sky monitoring is possible, the presence of the Moon was assumed whenever its illuminated portion was larger than 40%. Besides this, the same criterion based on the BERV was applied.

With these criteria, none of the reported velocities is polluted, mainly because the targets are bright. However, to confirm for limiting cases that the effect of moonlight pollution was negligible, we performed the Moon correction as is described Barge et al. (2008) and Pollacco et al. (2008) for SOPHIE and by Bonomo et al. (2010) for HARPS. We found that the corrected velocities excellently agreed in all cases with the uncorrected measurements, which were therefore retained.

3.4. Keplerian orbits

The radial velocity measurements of all targets exhibit variations greatly in excess of the measurement precisiont. Therefore, no periodogram analysis was needed to detect the presence of a signal in the data. The RVs were fitted using a single Keplerian orbit model. A genetic algorithm was employed to pick up the starting point for the Levenberg-Marquardt method. The best-fit parameters are reported in Table 6 together with the 68% confidence interval, obtained from 5000 Monte Carlo simulations. In most cases, the histograms of the obtained parameters have a single peak and Gaussian-like appearance, and therefore the errors reported can be taken as the 1-σ intervals. In a few cases, however, double-peaked or highly asymmetric distributions were found. These cases are studied in detail for each object in Sect. 4. In Fig. 1 we plot the RV curves for all stars observed together with the best-fit model and the residuals, after correction of the seeing effect (see below).

3.4.1. Correction of the seeing effect

Radial velocities obtained with SOPHIE exhibit a systematic effect thought to be caused by an incomplete radial scrambling in the optical fiber coupled with aberrations in the optical system, which lead to a variation in the illumination of the spectrograph’s pupil. The consequence of this effect is an artificial variation in the measured velocity when the point spread function changes, as a consequence of seeing variations, focus variations, etc. This effect induces RV variations with an amplitude of about 20 m s^-1 and constituted the main limitation on the spectrograph’s precision until very recently³.

Boisse et al. (2011a) present a detailed description of this effect and provide a way to diagnose and correct it. We followed the method described by these authors, but using a different variable to decorrelate the data. Since simulations of the optical path of SOPHIE have shown that variations in the pupil’s illumination produce a differential effect between the red and blue parts of each order (Boisse et al. 2011a), we have used the difference between the velocities measured in each half of the CCD (see Sect. 2.1) as an indicator of this effect. We define the pupil’s illumination proxy δ_RV as where RV_blue and RV_red indicate the velocities measured using the blue and red part of the orders, respectively.

Not all stars in our sample exhibit a clear correlation between the residuals and δ_RV. This is also the case when the estimator from Boisse et al. (2011a) is used, but the reasons for this differential behaviour are currently under study. For the moment, we have decided to perform the correction only on the stars for which the Pearson’s correlation coefficient between δ_RV and the fit residuals is greater than 0.5. In this case the residuals were decorrelated and added back to the fit curve. The resulting data set was then used to find a new solution to the 1-Keplerian fit, which is shown in Fig. 1. The data of only three stars fulfil this criterion: HD 16702, HD 92320 and HD 137510, for which the correlations between residuals and δ_RV are shown in Fig. 6. The correlation is not significant for the rest of the sample and the data reported do not include any correction.

3.5. Resolving the nature of the companions

The high minimum mass of most of the reported companions imply a non-negligible probability that the objects are actually low-mass stars in low-inclination orbits. To narrow down this possibility and, when possible, conclude on the nature of the detected objects, we have carried out a series of tests and simulations using the available RV data and astrometric observations from the Hipparcos satellite (Perryman et al. 1997).

3.5.1. Bisector analysis and CCF simulations

If the companion object is relatively luminous, we expect it to pollute the peak of primary star in the CCF, and to produce a variable distortion of its shape, which results in a variation of its bisector velocity span throughout the object’s orbit. We have searched for significant variations in the bisector velocity span, as well as correlations between the bisector velocity span and RV measurements. The detection of a correlation indicates that the velocity signal is the product – at least in part – of a deformation of the stellar CCF. This can either mean that the velocity signal is in fact a product of stellar activity – which would be unprecedented for the large RV amplitudes observed in these targets, and which could easily be identified using other diagnostics such as the correlation between RV and the  index –, or that the companion is contributing non-negligibly to the observed CCF. For all stars of our sample, except for HD 16702 (see Sect. 4 below), the bisector velocity span observations have negligible variability and do not exhibit any significant correlation with radial velocity measurements.

In the context of this paper, the lack of correlation between the bisector velocity span and the radial velocities can be used to constrain the mass of the companion by means of CCF simulations. To exploit this possibility, we assumed that both the host and the companion objects are dwarf stars, and that each contributes its own peak to the observed CCF. We modelled each CCF as a Gaussian function. The parameters of the primary CCF were set to the median values of the observed quantities. The area and FWHM of the secondary peak were varied according to the modelled mass ratio and rotational velocity, assuming the same metallicity as the primary star, and using the calibrations from Boisse et al. (2010). For each observed orbital phase the primary and secondary CCF were simulated at the expected position in RV space and were added after normalisation using the flux ratio of the stars. Here we assumed that the measured RV corresponds approximately well to the RV of the primary star, which holds for small mass ratios. For each simulated orbital phase, the RV, bisector velocity span, FWHM and contrast of the joint CCF were computed similarly to the real data, and the results were compared to the observations. The value of the χ² statistics was computed over a grid of masses and rotational broadening values for the secondary, and confidence regions were obtained from intersecting the χ² surface with constant planes. In general, we found that the bisector velocity span provides strong constrains on the mass of the secondary, resulting in many cases in lower upper limits than those issued from astrometric measurements. The results from these simulations are reported on a target basis in Sect. 4.

3.5.2. Mask effect

Similar to the bisector analysis, the dependence of the amplitude of the RV variations with the numerical mask used to measure them can reveal the contribution of a secondary stellar object to the flux entering the spectrograph (Bouchy et al. 2009b; Santos et al. 2002).

When analysing our data in search of this effect, we proceeded in the following way: first, we computed the best Keplerian fit as described in Sect. 3.4, using the best-matching numerical mask (Table 3). Then we adjusted the RV measurements obtained with other masks, fixing all orbital parameters, except for the semi-amplitude K and the centre-of-mass velocity γ, which is expected to change from mask to mask. Because the fit is linear on these two parameters, the errors were obtained directly from the covariance matrix. For all our targets, except for HD 16702 (see Sect. 4.3), the amplitudes obtained in all three masks are compatible.

3.5.3. Analysis of the Hipparcos astrometry

All stars listed in Table 1 were catalogued by the Hipparcos astrometry satellite (Perryman et al. 1997). We used the new Hipparcos reduction (van Leeuwen 2007) to search for signatures of orbital motion in the intermediate astrometric data (IAD). The analysis was performed as described in Sahlmann et al. (2011b), where a detailed description of the method can be found. Using the orbital parameters given by the RV analysis (Table 6), the IAD was fitted with a seven-parameter model, where the free parameters are the inclination i, the longitude of the ascending node Ω, the parallax ϖ, and offsets to the coordinates (Δα^⋆, Δδ) and proper motions (Δμ_α^⋆, Δμ_δ). A two-dimensional grid in i and Ω was searched for its global χ²-minimum with a standard nonlinear minimisation procedure. The statistical significance of the derived astrometric orbit was determined with a permutation test employing 1000 pseudo orbits. Uncertainties in the solution parameters were derived by Monte Carlo simulations. This method has proven to be reliable in detecting orbital signatures in the Hipparcos IAD (Sahlmann et al. 2011b,a). Where the astrometric signal was not detected in the data, i.e. the derived significance is low, the Hipparcos observations were used to set an upper limit to the companion mass following the method described by Sahlmann et al. (2011b,a).

Table 5 lists the target identifiers and the basic parameters of the Hipparcos observations relevant for the astrometric analysis. The solution type indicates the astrometric model adopted by the new reduction. For the standard five-parameter solution it is “5”, whereas it is “7” when the model included proper-motion derivatives of first order to obtain a reasonable fit, which is the case for HD 167215. The parameter N_Orb represents the number of orbital periods covered by the Hipparcos observation timespan and N_Hip is the number of astrometric measurements with a median precision of σ_Λ. Outliers in the IAD had to be removed because they can substantially alter the outcome of the astrometric analysis. We eliminated one outlier for HD 30246 and HD 92320 and two outliers for HD 156279.

An orbit signature is detected for HD 16702, with a 2.5-σ significance, which provides a measurement of the real mass of the companions and places it in the stellar-mass range (see Sect. 4.3). For the rest of the targets, no significant orbit is detected, but upper mass limits are derived. These are reported on a target basis in Sect. 4. The only exception is HD 30246, for which not even an upper limit can be reliably derived from Hipparcos data (see Sect. 4.2).

Fig. 1 Radial velocity measurements obtained with SOPHIE for all objects studied in this paper. In the left column, the measurements are plot as a function of time, while on the right column, they have been folded to the orbital phase. The solid curve represents the best fit to the data and the lower panels on the left column show the residuals to the fit.

Fig. 1 continued. For HD 137510, the red, green and blue points correspond to data from McDonald, TLS, and Lick, respectively.

4. Results

In this section we discuss the results for each target. We have classified the reported companions roughly according to their minimum mass and evidence for or against them being stellar companions.

4.1. Planetary candidates

HD 22781

HD 22781 (HIP 17187) is a V = 8.8 mag K0 star located at d = 33 parsec from the Sun, with a stellar mass M_s = 0.75   M_⊙. The RV measurements obtained with SOPHIE (Fig. 1) reveal the presence of a sub-stellar companion with minimum mass M_csini = 14 M_Jup in a highly eccentric (e = 0.82), 528-day period orbit. Owing to the effective temperature of the target, the velocities used to obtained the Keplerian fit are those obtained using the K5 mask.

The residuals of a single-Keplerian fit exhibit a scatter of around 12 m s^-1, much higher than the typical measurement error, and too high to be explained by the effect of stellar jitter, estimated to be about 1 m s^-1 (  =   −5.0). Furthermore, the residuals seem to exhibit a trend with a maximum around BJD = 2 455 100 and a subsequent decrease (see Fig. 2). In view of this, the RV measurements were also fitted using a Keplerian orbit plus a quadratic drift. The best-fit parameters of this solution are reported in Table 6. We note that the parameters corresponding to the Keplerian orbit are consistent at the 1-σ level with those derived from a single-Keplerian fit. Concerning the parabolic drift, we can obtain a rough estimate of the possible body that produces this drift by assuming that its orbital period and the RV semi-amplitude correspond roughly to twice the time between the zeros of the parabola, and to its maximum, respectively. In this way the fit coefficients imply a companion with minimum mass around 1.0 M_Jup in a 9.2-year orbit. A two-Keplerian fit, on the other hand, produces a fit with half this period and a slightly smaller minimum mass (0.8 M_Jup) mass for the second companion, and reduces the scatter in the residuals to about 7 m s^-1, which is comparable to the scatter level of the other targets. However, the fit semi-amplitude has a significance below 2-σ. We therefore decided to keep the solution with a quadratic drift, and note that this system warrants additional observations in order to confirm the presence of a second orbiting body. We therefore warn the reader that the orbital elements reported in Table 6 should be taken as preliminary.

The bisector velocity span of these observations is compatible with a constant (reduced χ² smaller than unity) and a linear regression of the bisector as a function of RV yields a flat slope (b < 0.012, at 3-σ confidence level). These results hold for all spectroscopic masks employed, which reinforces the case for a sub-stellar companion. Additionally, no significant difference is observed in the semi-amplitudes obtained using different masks. The astrometric orbit derived from Hipparcos data has a low significance of 22%, but we can set an upper limit of 0.31   M_⊙ for the mass of the companion, which is increased by the low number of 69 Hipparcos measurements with moderate precision and the high eccentricity of the system. If the secondary is a slow-rotating star, this constraint can be slightly improved by means of the CCF simulations described in Sect. 3.5.1, which give an upper limit of 0.23 M_⊙. The upper limit is similar to that from astrometry for a fast rotating star.

We conclude that the companion to HD 22781 is most likely a sub-stellar object that could have formed either by core-accretion (Mordasini et al. 2009) or by gravitational collapse. The term “superplanet” used by Udry et al. (2002) for objects of similiar mass seems adequate (see Sect. 5). The detection of a potential second companion – albeit with low significance – also points to the planetary nature of HD 22781 b, although it is known that circumbinary planets exist Doyle et al. (2011). The dynamical stability of this scenario could be promptly tested by numerical simulations, but this is outside the scope of this paper. In any case, this system warrants additional RV observations over a longer time period.

Fig. 2 Residuals of a single-Keplerian fit to the radial velocities of HD 22781, without any additional drift.

Fig. 3 Confidence regions for the mass of the secondary and the FWHM of its CCF, issued from numerical simulations of HD 156279. The dashed line is the upper limit derived from the astrometric analysis of Hipparcos data. At the 3-σ level the mass of the secondary is constrained by these simulations to  ≲ 0.35   M⊙. Astrometric data discard the high-mass family with FWHM  ~  7 km s-1 permitted by the bisector data.

HD 156279

HD 156279 (HIP 84171) is a G6 dwarf star with a mass of 0.93 M_⊙. It is located 35 pc away from the Sun and has a V-band magnitude of 8.08. The RV variations observed with SOPHIE imply the presence of a planetary-mass companion (M_csini = 9.71 ± 0.66 M_Jup) in a 130-day eccentric orbit. The best-fit orbit is shown in Fig. 1 and the parameters are reported in Table 6.

Bisector velocity span measurements for this star do not exhibit any significant variation in time, nor any dependence with RV, and present a scatter of 6.5 m s^-1. The CCF simulations (Fig. 3) put an upper limit of roughly 0.35 M_⊙, although solutions with higher mass are possible for rotational velocities around the resolution limit of SOPHIE (FWHM  ≈  6−7 km s^-1, depending on spectral type). However, this family of solutions is discarded by Hipparcos measurements, for which the derived upper mass is 0.41   M_⊙. Additionally, no mask effect is detected at a significant level, which also supports the hypothesis of a sub-stellar object orbiting HD 156279.

HD 156279 b is the least massive object reported in this paper, and may have been formed as a planet. Its minimum mass is below the lowest deuterium-burning mass determinations (Spiegel et al. 2011). HD 156279 b is therefore established as a planetary candidate.

4.2. Brown dwarf candidates

HD 14651

HD 14651 (HIP 11028) is a V = 8.3 mag star with a mass M_s = 0.955 M_⊙, measured as described in Sect. 3.1. The Keplerian fit to the RV measurements obtained with SOPHIE (Fig. 1) indicates that this star possesses a companion of minimum mass M_csini = 47   M_Jup in a 79.4-day orbit, with an eccentricity e = 0.48.

Evidence that the companion is indeed a sub-stellar object comes from the fact that the amplitude of the orbital fit does not depend on the numerical mask used to compute the CCF, and from the bisector analysis, which is compatible with a constant (reduced χ² = 0.6), and does not exhibit any correlation with the RV measurements. Indeed, the Pearson and Spearman correlation coefficients between the RV and the bisector velocity span are  −0.11 and  −0.14, respectively, and the slope obtained by linear regression is consistent with zero at the 1-σ level. Additionally, we do not detect an orbital signature in the Hipparcos astrometry, the significance being 17%. We can set an upper limit of 0.72 M_⊙ for the mass of the companion, which is high partly because of the low number of Hipparcos measurements (N_Hip = 59) with moderate precision and the considerable eccentricity of the system. On the other hand, the CCF simulations constrain the mass of the secondary to be smaller than 0.4 M_⊙ if the star is rotating with projected velocity vsinI ≈ 10 km s^-1, and smaller than 0.28 M_⊙ if vsinI < 3 km s^-1.

We conclude that the companion to HD 14651 is a bona fide brown dwarf candidate that requires further observations to pinpoint its true nature. For example, astrometric observations from the future GAIA mission, or near-infrared spectroscopy that could detect the peak of the companion, and therefore measure the mass ratio between primary and secondary (see Sect. 5).

HD 30246

HD 30246 (HIP 22203) is a V = 8.3 mag G1 star located at 51 parsec from the Sun, with a measured mass M_s = 1.047   M_⊙. The RV measurements obtained with SOPHIE exhibit a peak-to-peak variation of 2 km s^-1 that can be explained by the presence of a M_csini = 56   M_Jup companion in a 990-day orbit, with an eccentricity e = 0.85. HD 30246 belongs to the Hyades cluster (Griffin et al. 1988) and has been the object of several studies, discussed in part below. It is also the most active star in the sample, compatible with its probably young age (Holmberg et al. 2009).

For this target, observations do not cover one of the extrema of the RV curve (see Fig. 1). As a consequence, the Monte Carlo distribution of the minimum mass of the companion has a long high-mass tail, and a slightly bimodal behaviour, allowing for a family of solutions corresponding to a low-mass star (Fig. 4). The distributions of the semi-amplitude K and the orbital eccentricity e exhibit a similar feature, with the high-mass solutions corresponding to high-eccentricity orbits. Because the value of the χ² statistics is not systematically higher for any value of the eccentricity or the semi-amplitude K, the identification of the correct solution is hindered. We note, however, that less than 14% out of the 5000 Monte Carlo realisations of the data produce an orbital solution with minimum mass above 80 M_Jup. The best-fit orbital solution is shown in Fig. 1, and the obtained parameters obtained using mask G2 are reported in Table 6.

Fig. 4 Left: minimum mass distribution for HD 30246 obtained from 5000 Monte Carlo simulations. The bimodal behaviour is clearly seen and allows for stellar-mass solutions. Right: correlation between orbital eccentricity and RV semi-amplitude from the same Monte Carlo simulations, showing that high-mass solutions correspond to very eccentric orbits.

The bisector velocity span is compatible with a constant, exhibiting a dispersion of around 16 m s^-1. Also, no relation is detected with the RV above the 1.8-σ level (b =  −0.0059  ±  0.0034), and the amplitudes of the RV variation measured with different masks are in agreement (K_G2 = 1995.1  ±  4.1 m s^-1, K_K5 = 1996.8  ±  4.6 m s^-1, K_M4 = 2005  ±  16 m s^-1). Additionally the large scatter in the fit residuals (around 13 m s^-1) can be partially explained by the stellar jitter of the host star, which is estimated to be around 10 m s^-1, given the median value of activity index   =   − 4.50 (Santos et al. 2000). Furthermore, the analysis of the Hipparcos astrometry provides orbits with low significance (87.6%, or 1.5σ), meaning that the orbital signature is not detected. However, because the orbit is not covered and in addition is highly eccentric (e ~ 0.8), we refrain from deriving an upper limit to the companion mass⁴. On the other hand, the CCF simulations described in Sect. 3.5.1 allow us to set an upper limit at the 3-σ level of 0.28 M_⊙ (respectively, 0.37 M_⊙) for simulations in the slow-rotating (respectively, fast-rotating) extreme of the explored parameter range. Additionally, a possible solution is found for M_c in the interval  [0.42 − 0.51]    M_⊙, with rotational velocity vsinI between 3 km s^-1 and 4.5 km s^-1, at the 3-σ level (see Fig. 5).

Fig. 5 Confidence regions for the mass of the secondary and the FWHM of its CCF, issued from numerical simulations of HD 30246. At the 3-σ level there is a solution with  ~0.45   M⊙ in addition to the upper limit at around 0.33 M⊙.

HD 30246 has been reported to be a spectroscopic binary (Griffin et al. 1988), based on 13 RV measurements with a precision of around 700 m s^-1. Additionally, signs of the spectrum of the secondary were found in 4 infrared spectra obtained with the NASA Infrared Telescope Facility by Bender & Simon (2008). However, according to these authors, the detection of a secondary peak in the CCFs of this target is challenging, and leads to poorly-constrained velocities for the secondary (see Sect. 5.3 and Fig. 4 of their paper). The derived mass ratio q = 0.06  ±  0.04 implies a mass M_p = (66 ± 45)   M_Jup for the companion, when the stellar mass derived in this paper is considered, M_s = 1.05  ±  0.11   M_⊙⁵. This agrees with our determination for the minimum mass of the companion. Additionally, the orbital parameters of HD 30246 b, obtained by Stefanik & Latham and reported by Bender & Simon (2008), agree with the parameters we derived from SOPHIE data. Furthermore, K-band speckle interferometry (Patience et al. 1998) provides a limiting magnitude difference for companions at 0.05′′ from HD 30246 of ΔK = 4.6. Considering the V − K relations for main-sequence stars (Cox 2000) and the mass-luminosity relations from Delfosse et al. (2000), this translates roughly to a maximum mass of 0.19 M_⊙ for companions to HD 30246 at this orbital distance, which is slightly larger than the distance obtained from the Keplerian fit to the data, a = 0.04′′.

We conclude that the initial claim of binarity by Griffin et al. (1988) warrants revision, and that the remaining facts support a sub-stellar candidate companion to HD 30246. The upper limit for the mass is in the stellar regime, however, and therefore more astrometric observations will be needed to decide unambiguously on the nature of this object, as well as a continuing RV monitoring to better constrain the orbital parameters.

Fig. 6 Residuals of the Keplerian orbital fit to the uncorrected data as a function of pupil illumination indicator δRV for the three stars in our sample showing a significant (r > 0.5) correlation. The line is a fit to the data and was used to correct the radial velocities, which leads to a reduced scatter.

HD 92320

HD 92320 (HIP 52278) is a V = 8.38 mag star located at 41 parsec from the Sun. The 16 RV measurements obtained since late 2006 are fitted by a 145-day Keplerian orbit with a semi-amplitude of about 2.6 km s^-1 and an eccentricity of 0.32. The spectral analysis coupled to the comparison with evolutionary models yields a stellar mass of M_s = 0.916   M_⊙ and a companion minimum mass M_csini = 59.5 M_Jup.

The Keplerian fit residuals exhibit a weak correlation with pupil illumination proxy δ_RV (see Sect. 3.4.1), with Pearson and Spearman correlation coefficients  − 0.60 and  − 0.66, respectively. The trend is given mainly by the four points with the highest absolute residuals (see Fig. 6). These measurements do not exhibit unusual S/Ns, CCF contrast or FWHM. We have therefore concluded that the relation is real, and consequently, the detrended measurements were used to obtain the orbital fit plotted in Fig. 1 and the parameters reported in Table 6.

The lack of correlation between bisector velocity span and RV⁶ together with the absence of mask effect argues for a sub-stellar companion as the source of the periodic RV variations. Additionally, we did not detect an orbital signature in the Hipparcos data, but we were able to set an upper limit of 0.34   M_⊙ for the mass of the companion. The CCF simulations described in Sect. 3.5.1 provide a similar upper limit to the mass: at the 99.7% confidence level, the upper limit to the true mass of the companion ranges from 0.26 M_⊙, for slow rotators below the detection limit up to 0.35 M_⊙ for the fastest rotating stars simulated (vsinI = 10 km s^-1). The companion to HD 92320 is therefore established as a brown dwarf candidate that merits additional observations. GAIA measurements should easily detect the reflex motion induced by this object (Sect. 5), and near-infrared spectroscopy might permit detecting the spectrum of the secondary.

HD 137510

HD 137510 (HIP 75535) is a high-metallicity 1.36-M_⊙ sub-giant late-F star, located 42 pc away from the Sun. Its V-band magnitude is 6.26, making it the brightest star in our sample. A brown dwarf companion candidate with a minimum mass of 26 M_Jup was discovered by Endl et al. (2004) based on observations acquired at the McDonald Observatory (McD) in Texas, USA, and at the Thüringer Landessternwarte Tautenburg (TLS) in Germany. Later, Butler et al. (2006) published an independent orbital solution based on 10 RV measurements obtained at Lick Observatory, which led to a slightly less massive object of 22.7 M_Jup, in a mildly less eccentric orbit. Thirteen new measurements of this star were obtained with SOPHIE, which permit improving the system parameters. Indeed, the determination using the combined datasets has reduced uncertainties, particularly in the orbital period and in the eccentricity.

The SOPHIE observations were corrected as described in Sect. 3.4.1 for the seeing effect. The Pearson and Spearman coefficients between the residuals and δ_RV are  − 0.67 and  − 0.70, respectively (Fig. 6). The dispersion of the residuals of the Keplerian fit to the SOPHIE data is improved by this procedure: from around 8.6 m s^-1 for the uncorrected data to 4.6 m s^-1. The fit to the combined data of all four instruments is also improved, albeit less drastically: the scatter of the residuals is reduced from 15.2 m s^-1to 14.4 m s^-1. In Table 6 we report the parameters obtained from the combined fit of all four datasets, and the best-fit curve is shown in Fig. 1.

Concerning the stellar parameters, we find an effective temperature T_eff = 6130  ±  50 K, which agrees well with the value by Lèbre et al. (1999), and about 160 K (3.1-σ) and 230 K (2.8-σ) higher than the value reported by Valenti & Fischer (2005) and Endl et al. (2004), respectively. These discrepancies might be caused by unaccounted systematic errors in the different methods and models used. The metallicity found as described in Sect. 3.1 ([Fe/H] = 0.38  ±  0.13) agrees with previous determinations and also with the metallicity value obtained from the CCF as described in Sect. 3.1.

The scatter in the bisector velocity span measurements is below 16 m s^-1 and is produced mainly by one point, which, if left out, reduces the scatter to around 12 m s^-1, consistent with the typical error of the RV data (~5 m s^-1). Additionally, no correlation with the RV measurements above the 1.5-σ level is present, and there is no significant difference in the RV amplitudes measured through different numerical masks. The results of the CCF simulations are compatible with a sub-stellar object at the 3-σ level, but another solution with M_c ≈ 0.5   M_⊙ is also possible. This last solution is discarded by the astrometric analysis. Indeed, the sub-stellar nature of HD 137510 b has already been established by Sahlmann et al. (2011b) and was later confirmed by Reffert & Quirrenbach (2011). Sahlmann et al. (2011b) derived an upper companion-mass limit of 64.4 M_Jup using Hipparcos astrometry and the spectroscopic elements of Butler et al. (2006). On the basis of the updated RV solution presented here, we find a similar result: the astrometric signature is not detected, but because of the updated orbital elements and the slightly lower stellar mass, we obtain an updated upper limit of 59.5 M_Jup for the mass of the companion, which confirms that HD 137510 b is a brown dwarf companion orbiting an F-star.

4.3. Stellar companions

HD 16702

HD 16702 (HIP 12685) is a V = 8.3 mag G0 star located at 45 parsec from the Sun. The orbital fit to the RV data (Fig. 1) indicates that this star possesses a companion in a 72.8-day orbit with an eccentricity e = 0.14 and minimum mass M_csini = 48.7 M_Jup, given a stellar mass M_s = 0.98   M_⊙.

The residuals of the Keplerian fit exhibit a clear correlation with δ_RV (see Fig. 6), which allowed us to correct the data, as described in Sect. 3.4.1. This reduced the scatter in the fit residuals from 12 m s^-1 to the final value of  ≈ 8 m s^-1. The final fit parameters are listed in Table 6, and the best-fit curve is plotted in Fig. 1.

Fig. 7 Bisector velocity span and radial velocities for HD 16702 (corrected for the seeing effect). The solid line represents the best fit to the data and the dashed lines indicate the 3-σ confidence region. A correlation is detected to 4-σ significance, which hints at the presence of an additional blended star in the fiber of the spectrograph.

Fig. 8 Top: astrometric orbit of HD 16702 projected on the sky. North is up and east is left. The solid red line shows the model orbit, which is orientated counter-clockwise, and open circles mark the individual Hipparcos measurements used for the astrometric fit. Blue filled circles show normal points for each satellite orbit number and are used for display only. Bottom: O − C residuals for the normal points of the orbital solution (filled blue circles) and the five-parameter model without companion (crosses).

Fig. 9 Confidence regions for the mass of the secondary and the FWHM of its CCF, issued from numerical simulations of HD 16702. At the 3-σ level, a strong constraint can be put to the mass of the secondary.

The bisector analysis for this target shows a significant correlation between bisector velocity span and radial velocity, shown in Fig. 7. A linear regression to the data shows that the slope b is significantly different from zero, b =  −5.1  ±  1.3, i.e. a detection at the 4-σ level. Additionally, the amplitude of the RV variations depends on the spectral mask used to compute the CCF. Indeed, we find K_G2 = 2423.7  ±  3.0 m s^-1, K_K5 = 2412.0  ±  5.2 m s^-1, and K_M4 = 2344.0  ±  9.5 m s^-1, which implies an 8-sigma difference between mask G2 and mask M4. This indicates that the companion around HD 16702 might be a star in a low inclination orbit. The spectra obtained would then consist of the addition of the spectrum of the solar-like primary star and the secondary star, probably a low-mass star, moving in anti-phase in velocity space. When correlated with the M4 mask, the relative weight given to the spectrum of the secondary is increased, and the resulting CCF is then skewed towards the velocity of the secondary, which produces a decrease in the measured amplitude of the RV variations.

The astrometric analysis and CCF simulations confirm this scenario. We detect the astrometric signal in the Hipparcos data with a significance of 2.5σ (98.7%) and measure a semimajor axis of 2.9  ±  0.6 mas. We see the system almost face-on with an orbital inclination of  degrees, corresponding to a companion mass of M_c = 0.55  ±  0.14   M_⊙ and we measure the longitude of the ascending node of . The coordinate and proper motion offsets are Δα ^⋆  =  −0.4  ±  0.7 mas, Δδ = 0.0  ±  0.5 mas, Δμ_α ^⋆  =  −1.8  ±  1.2 mas yr^-1, Δμ_δ = 0.6  ±  0.8 mas yr^-1, and the updated parallax is ϖ = 20.9  ±  0.8 mas, which is compatible with the original value. The sky-projected orbit of HD 16702 and the Hipparcos measurements are shown in Fig. 8. The values of 2.5σ for the significance and of 6.5 for the astrometric S/N for this orbit indicate that we are close to the limit of the detection capabilities of Hipparcos. However, our astrometric analysis rules out the possibility of the companion being a sub-stellar object. Indeed, at the 3-σ level, the lower and upper companion mass limits are 0.19   M_⊙ and 1.05   M_⊙, respectively.

Fig. 10 Left: minimum mass distribution for HD 167215 obtained from 5000 Monte Carlo simulations. Only about 25% of the solutions lie below the 80-MJup limit. Right: correlations between the RV variation amplitude and the orbital eccentricity (upper panel) and the orbital period (lower panel).

The CCF simulations permit us to constrain the companion mass even more. In Fig. 9 we show the confidence regions obtained from the χ² surface, as described in Sect. 3.5.1. We deduce that the maximum allowed value, at 99.7% confidence level, ranges from 0.35 M_⊙ to 0.45 M_⊙, depending on the FWHM of the secondary. Interestingly, owing to the significant correlation between bisector and radial velocity shown in Fig. 7, a lower limit of about 0.25 M_⊙ can also be put to the mass of the secondary. On the other hand, no strong constraints can be put on the rotational velocity of the secondary. We note that the best-fit point has χ² = 14.4, comparable with the number of observations (N = 22), which means that the confidence regions are a rigorous way to estimate the mass of the secondary.

HD 16702 is therefore a binary star, with a mass ratio ranging from q ≈ 0.25 to q ≈  [0.35 − 0.46] . See Sect. 5 for a more detailed discussion on this object.

HD 167215

The spectral analysis of HD 167215 (HIP 89270) shows that this object is a low-metallicity 1.15-M_⊙ late-F star. It is located 79 pc away the Sun, and the RV measurements obtained with SOPHIE, although inconclusive because of to their incomplete phase coverage, point at a 600-day period variation with an amplitude of 2 km s^-1.

Fig. 11 Bisector velocity span as a function of RV measurements for HD 167215. The curve is the parabolic fit to the data.

The Monte Carlo distribution of minimum masses (see Fig. 10) exhibits a clear bimodal behaviour, with a lot of power on the stellar-mass range. Indeed, only about 25% of the Monte Carlo realisations of the data are fitted to a minimum mass below 80 M_Jup. Therefore, the orbiting object is most probably a low-mass star. Just as for HD 30246, the high-mass solutions correspond to high-eccentricity orbits. Also, the period is well correlated with the semi-amplitude K (Fig. 10).

The bisector velocity span is presented as a function of RV in Fig. 11. A constant fit to the data gives χ² = 23, for 13 degrees of freedom, and a linear regression gives χ² = 21.6, for 12 degrees of freedom. An F-test and a run test (see Frodesen et al. 1979, Sect. 14.6.2) fail at rejecting the null hypothesis at 5% significance level. Additionally, no evidence of mask effect is detected, which means that no significant amount of light from the putative secondary star enters the spectrograph. Finally, we did not detect an orbital signature in the Hipparcos data, since the derived orbit has a significance of only 56%. We were nevertheless able to set an upper limit of 0.29   M_⊙ for the mass of the companion. When the RV and astrometric analyses are combined with the CCF simulations (Fig. 12), the mass of the secondary is confined to the wedge-like region of Fig. 12 delimited by the upper limit set by astrometry (0.29   M_⊙, shown as a dashed line) and the 99.7% contour level below it. The secondary is likely to have a projected rotational velocity below vsinI ≈ 5.3 km s^-1, which is the value correspoding to FWHM  ≈  10 km s^-1. The χ² of the best fit is 11.3 for 14 observations. Regardless of the low significance of the bisector velocity span variation, the CCF simulations place the mass of the secondary in the stellar domaine, indicating that HD 167215 is likely a stellar binary system with mass ratio between q = 0.17 and 0.25.

5. Discussion

5.1. The SOPHIE objects

The objects reported in this paper span a wide range of minimum masses, from 9.5 M_Jup (HD 156279 b) up to 92 M_Jup (HD 167215B), and are therefore useful to perform a comparative study of the properties of massive planets, brown dwarfs and low-mass stars. In particular, the object orbiting HD 137510 has been established to be a brown dwarf (Endl et al. 2004; Sahlmann et al. 2011b, and this work), and the companions to HD 16702 and HD 167215 have been identified as low-mass stars. Out of the remaining five objects reported here, two have minimum masses below or close to the deuterium-burning limit, and we have labelled them as planet candidates (HD 22781 b and HD 156279 b), while the other three are brown dwarf candidates. Except for HD 92320 b, which has a minimum mass slightly larger, these candidates fall in what has been identified by Grether & Lineweaver (2006) as the driest part of the brown dwarf desert, at  M_Jup. This implies that these candidates are rare and therefore worthy of more observations to pinpoint their true mass. In Table 6 we report the minimum astrometric signal expected for the detected candidates, defined as the semi-amplitude of the periodic motion of the star projected on the plane of the sky, assuming i = 90 degrees. The future space mission GAIA, having an astrometric precision below 1.0  ×  10^-5 arcsec for bright stars such as these (Prusti 2011), should easily detect the orbital signature of all three of these candidates.

HD 16702 has been identified as a stellar binary system, with a period of 72.8 days and a mass ratio q lying in the interval [0.25 − 0.46] at the 99.7% confidence level. Considering the mass of the companion to be M_c = 0.35   M_⊙, the magnitude differences in the V and K bands imply a contrast of 3  ×  10^-3 and 5.6  ×  10^-2, respectively, using the apparent K-band magnitude from the 2MASS catalogue (Cutri et al. 2003). The measured projected separation for this system is 8.6 mas. It will not be easily resolved with the current adaptive optics facilities. On the other hand, interferometric observations should be able to resolve the system.

For HD 167215, we find a binary system at a period of over 600 days, and a mass ratio in the interval [0.17 − 0.25]. If we consider that the secondary has a mass of 0.25 M_⊙, inversion of the mass-luminosity relations by Delfosse et al. (2000) provide the absolute magnitudes M_V = 12.41 and M_K = 7.28, in the V and K band. The primary star has apparent magnitudes m_V = 8.1 and m_K = 6.69 (Cutri et al. 2003), which give contrasts of 2.8  ×  10^-4 and 8.6  ×  10^-3 in the V- and K-band, respectively. The measured mass for the companion implies that the inclination angle i is roughly 20 degrees, and the projected separation is 26.5 mas. This system will also be difficult to resolve with current adaptive optics instruments, but it might be a suitable target for interferometric observations.

Fig. 12 Confidence regions for the mass of the secondary and the FWHM of its CCF, issued from numerical simulations of HD 167215. When combined with the astrometric analysis, the true mass of the companion is constrained to the region below the astrometric upper limit (dashed line) and the 99.7% contour below it.

The brown dwarf orbiting HD 137510 has been discovered by Endl et al. (2004) and confirmed later by Sahlmann et al. (2011b) and Reffert & Quirrenbach (2011). The minimum mass reported in this paper based on the analysis of all available datasets is compatible with previous determinations, and the analysis of the SOPHIE data alone also produces a compatible result. If we consider that the true mass of the brown dwarf is 30.9 M_Jup, i.e. the expected value assuming random orientation of the system, and including the limit on the inclination provided by the astrometric analysis (sini > 0.4588), then linear interpolation of the model grids by Baraffe et al. (2003) give effective temperatures between 800 K and 870 K for the two limiting values obtained for the age of this system, 3.0 Gyr and 2.3 Gyr. This identifies this object as a T-type dwarf, which should present prominent methane and water features in its near-infrared spectrum (see, for example, Kirkpatrick 2005). However, because it lies about 21 mas from its host star, which outshines it by over 15 mag in the H band, obtaining an spectrum of this object will prove challenging.

HD 22781 exhibits excess variation in the residuals of the single-Keplerian fit, which might indicate the presence of a second companion in the system. A tentative estimation of the mass and period of this object results in a minimum mass of about 1 M_Jup in a nine-year period orbit. Although this would be an unusual system, with the more massive planet in the inner orbit and a lighter companion farther away, this configuration is by no means completely unheard of. For example, HD 20226 (Correia et al. 2005; Udry et al. 2002) presents a similar configuration, with an inner massive planetary candidate in a 255-day orbit, and an outer companion close to the 5:1 resonance. Other examples of systems of this kind are the three-planet system HIP14810 (Wright et al. 2009, 2007), HD 134987 (Jones et al. 2010), and HD 200964 (Johnson et al. 2011).

5.2. Formation and evolution of sub-stellar companions

In this section, we put into context the results obtained by considering similar objects reported in the literature. We do not attempt to perform a complete and thorough statistical analysis of the available data here, which is defered to a future work, but only to present a few relevant characteristics of sub-stellar massive companions that might shed some light on mechanisms involved in their formation and evolution.

Fig. 13 Upper: mass-period diagram for all objects with (minimum) masses between 9 and 90 MJup that orbit solar-type stars with a period shorter than 1  ×  104 days. Lower: eccentricity-period diagram for the same sample of objects. In both panels the objects reported in this paper are shown as red squares. The other coloured symbols represent companions for which the true mass is known either by astrometry (blue circles) or because they transit their host star (green circles). The rest of the objects are candidates detected by RV surveys (white circles), and the plotted mass should be interpreted as a lower limit. Owing to the wide range of objects represented, the error bars for some of them are smaller than the symbol used in the plot.

5.2.1. Orbital period

The SOPHIE objects cover a range of orbital periods from little over 70 days for HD 16702 b up to 990 days for HD 30246 b, or roughly 2 AU. The position of these objects in the mass-period diagram is shown in the upper panel of Fig. 13 together with other similar objects presented in the literature⁷ (Sahlmann et al. 2011b; Sozzetti & Desidera 2010, and references therein). HD 16702B and HD 167215B are not included because their true mass is above the imposed limit of 90 M_Jup. Note that none of our objects have been detected in short-period orbits. Indeed, it seems evident in Fig. 13 that the number of objects with masses above  ~10 M_Jup increases with orbital period, even though RV and transit observations are biased towards discovering objects in short-period orbits. This might be explained by considering that these objects are formed far from the central star by gravitational collapse, reaching the mass needed to open a gap in the disk (Ward 1997) before start to migrate inwards by interactions with the disk. Because then migration will be of type II (Ward 1997), which has longer timescales, these objects might not have time to reach closer orbits before the disk dissipates.

5.2.2. Orbital eccentricity

In the lower panel of Fig. 13 we plot the orbital eccentricity of the SOPHIE candidates as a function of orbital period. It can be seen that all reported objects exhibit a considerable orbital eccentricity. Ribas & Miralda-Escudé (2007) report an increase in the orbital eccentricity of massive planetary objects when compared with less massive objects. These authors argue that this might be indicative of different formation mechanisms, and propose that while low-mass objects form by core accretion in protoplanetary disks, more massive planets might form by gravitational collapse either of a pre-stellar cloud or of a gravitationally unstable circumstellar disk. Because high-mass planets would then need to form far from their stars, the fact that those observed at shorter distances (typically a few AU at most) have higher eccentricities than low-mass planets is, according to these authors, caused by the large radial migration they have undergone. Indeed, numerical simulations (Papaloizou et al. 2001; Nelson et al. 2000) have shown that eccentricity is excited on massive ( ≳ 20 M_Jup) migrating objects by means of interaction with the circumstellar disk, but not so for less massive objects. On the other hand, interactions at disk resonances can damp eccentricity (see Tremaine & Zakamska 2004, and references therein). Therefore, although current data seem to agree with the idea that massive companions have higher eccentricities, it is not clear whether this can be explained by invoking a larger radial migration.

5.2.3. Metallicity

Planetary companions with masses comparable to that of Jupiter are known to occur more frequently around metal-rich stars (Santos et al. 2001; Fischer & Valenti 2005), which is considered strong support for the core-accretion formation scenario (Pollack et al. 1996; Alibert et al. 2005). On the other hand, stellar companions are more common around metal-poor primaries (Grether & Lineweaver 2007; Raghavan et al. 2010), a trend that is more evident for stars with (B − V) > 0.625. Raghavan et al. (2010) interpret this (tentative) result by suggesting that lower-metallicity clouds might be more likely to fragment to form binary stars, as is revealed in numerical simulations. If this is so, and if brown dwarf companions form as stars, then we might expect them to show a similar trend.

Another trend reported by Ribas & Miralda-Escudé (2007) is that the metallicity of the host star decreases with companion mass. This is interpreted as a hint that two different mechanisms act in the formation of extrasolar planets, as discussed above, and that massive objects form as easily around metal-rich stars as around metal-poor ones. Of course, this statement assumes that the sample of target stars out of which extrasolar planets are detected is uniform in metallicity. However, because massive companions are rare and RV surveys usually have biased samples, the trend observed by Ribas & Miralda-Escudé (2007) might not be real. The actual relevant measurable to study this matter is the occurrence rate of detected objects as a function of the metallicity of their host stars. However, given the small number of detected brown dwarfs around solar-type stars, assessing the reality of any such trend is challenging.

6. Summary and conclusions

We have reported the discovery of seven new sub-stellar candidates that orbit solar-type stars with minimum masses above  ~10 M_Jup. Out of these, we identified two objects as low-mass stellar companions based on astrometric measurements and numerical simulations of their cross-correlation functions. Additionally, the orbital parameters of a known brown dwarf companion, namely HD 137510 b, have been improved upon using radial velocity measurements obtained with SOPHIE. The three confirmed objects are too faint and too close to their host stars to be easily detected by current adaptive optics techniques because they lie within the diffraction limit of the biggest available telescopes. On the other hand, the brown dwarf candidates should be promptly confirmed or rejected with GAIA’s micro-arcsecond astrometry.

Different techniques were employed with the aim of discerning low-mass stars in low-inclination orbits from actual sub-stellar objects. To do this, we employed not only traditional RV diagnostics such as the correlation mask effect and the bisector analysis, but we also analysed astrometric data from the Hipparcos mission, and developed a new technique to fully exploit the information present in the bisector velocity span. This technique has allowed us to set upper limits to the masses of all candidates detected here, even surpassing the possibilities of current astrometric data in some cases, and has allowed the confirmation that one of the candidates is in fact a low-mass star. In some cases, the CCF simulations and the Hipparcos astrometry turn out to be complementary, as for HD 167215. The effectiveness of each technique depends strongly on the orbital parameters, the number of measurements, and the phase coverage, and we have therefore refrained from studying this here (see Santerne et al., in prep.). Improvements of the CCF simulations used in this method are currently under way and will provide additional possibilities for this promising technique, such as validating planetary candidates discovered by transiting surveys that show no variation in their RV or bisector velocity span measurements, as is the case for the recently-announced CoRoT-22 b (Moutou et al. 2011).

Concerning the question of the dividing line between planets and brown dwarfs, if a mass-dependent classification is adopted, motivated by the observed mass distribution, such as the one proposed by Sahlmann et al. (2011b) or Schneider et al. (2011), who set the limit at around 25 M_Jup, then three of the sub-stellar candidates are brown dwarf candidates (HD 14651b, HD 30246b, and HD 92320b), while the remaining two are planetary candidates (HD 22781b and HD 156279b). A more detailed analysis of other possible classifications of the available objects is outside the scope of this paper and will be presented in a future work.

The objects reported here increase the number of similar objects present in the literature by about 12%, contributing to establish solid observational evidence to test and constrain formation and evolution theories. At the time of writing the number of sub-stellar objects or candidates more massive than 10 M_Jup orbiting solar-type stars in relatively short (P < 10⁴ days) orbits amounts to somewhat less than 60 objects. The small size of this sample currently hinders most statistical analyses. Nevertheless, these objects warrant a rigorous statistical study, which might provide new and improved constraints for models and theories. Also, any effort to increase the number of objects in the mass range studied here, as well as all attempts to measure the actual mass of candidates, should be encouraged.

Acknowledgments

We thank the staff of Haute-Provence Observatory for their support at the 1.93-m telescope and on SOPHIE. We thank the “Programme National de Planétologie” (PNP) of CNRS/INSU, the Swiss National Science Foundation, and the French National Research Agency (ANR-08-JCJC-0102-01 and ANR-NT05-4-44463) for their support with our planet-search programs. D.E. is supported by CNES. I.B. and N.C.S. acknowledges the support by the European Research Council/European Community under the FP7 through Starting Grant agreement number 239953, as well as the support from Fundação 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 reference PTDC/CTE-AST/098528/2008 and PTDC/CTE-AST/098604/2008. A.E. is supported by a fellowship for advanced researchers from the Swiss National Science Foundation (grant PA00P2_126150/1).

References

All Tables

All Figures

	Fig. 1 Radial velocity measurements obtained with SOPHIE for all objects studied in this paper. In the left column, the measurements are plot as a function of time, while on the right column, they have been folded to the orbital phase. The solid curve represents the best fit to the data and the lower panels on the left column show the residuals to the fit.
In the text

	Fig. 1 continued. For HD 137510, the red, green and blue points correspond to data from McDonald, TLS, and Lick, respectively.
In the text

	Fig. 2 Residuals of a single-Keplerian fit to the radial velocities of HD 22781, without any additional drift.
In the text

Fig. 3 Confidence regions for the mass of the secondary and the FWHM of its CCF, issued from numerical simulations of HD 156279. The dashed line is the upper limit derived from the astrometric analysis of Hipparcos data. At the 3-σ level the mass of the secondary is constrained by these simulations to  ≲ 0.35   M⊙. Astrometric data discard the high-mass family with FWHM  ~  7 km s-1 permitted by the bisector data.

In the text

	Fig. 4 Left: minimum mass distribution for HD 30246 obtained from 5000 Monte Carlo simulations. The bimodal behaviour is clearly seen and allows for stellar-mass solutions. Right: correlation between orbital eccentricity and RV semi-amplitude from the same Monte Carlo simulations, showing that high-mass solutions correspond to very eccentric orbits.
In the text

	Fig. 5 Confidence regions for the mass of the secondary and the FWHM of its CCF, issued from numerical simulations of HD 30246. At the 3-σ level there is a solution with  ~0.45   M⊙ in addition to the upper limit at around 0.33 M⊙.
In the text

	Fig. 6 Residuals of the Keplerian orbital fit to the uncorrected data as a function of pupil illumination indicator δRV for the three stars in our sample showing a significant (r > 0.5) correlation. The line is a fit to the data and was used to correct the radial velocities, which leads to a reduced scatter.
In the text

	Fig. 7 Bisector velocity span and radial velocities for HD 16702 (corrected for the seeing effect). The solid line represents the best fit to the data and the dashed lines indicate the 3-σ confidence region. A correlation is detected to 4-σ significance, which hints at the presence of an additional blended star in the fiber of the spectrograph.
In the text

Fig. 8 Top: astrometric orbit of HD 16702 projected on the sky. North is up and east is left. The solid red line shows the model orbit, which is orientated counter-clockwise, and open circles mark the individual Hipparcos measurements used for the astrometric fit. Blue filled circles show normal points for each satellite orbit number and are used for display only. Bottom: O − C residuals for the normal points of the orbital solution (filled blue circles) and the five-parameter model without companion (crosses).

In the text

	Fig. 9 Confidence regions for the mass of the secondary and the FWHM of its CCF, issued from numerical simulations of HD 16702. At the 3-σ level, a strong constraint can be put to the mass of the secondary.
In the text

	Fig. 10 Left: minimum mass distribution for HD 167215 obtained from 5000 Monte Carlo simulations. Only about 25% of the solutions lie below the 80-MJup limit. Right: correlations between the RV variation amplitude and the orbital eccentricity (upper panel) and the orbital period (lower panel).
In the text

	Fig. 11 Bisector velocity span as a function of RV measurements for HD 167215. The curve is the parabolic fit to the data.
In the text

	Fig. 12 Confidence regions for the mass of the secondary and the FWHM of its CCF, issued from numerical simulations of HD 167215. When combined with the astrometric analysis, the true mass of the companion is constrained to the region below the astrometric upper limit (dashed line) and the 99.7% contour below it.
In the text

Fig. 13 Upper: mass-period diagram for all objects with (minimum) masses between 9 and 90 MJup that orbit solar-type stars with a period shorter than 1  ×  104 days. Lower: eccentricity-period diagram for the same sample of objects. In both panels the objects reported in this paper are shown as red squares. The other coloured symbols represent companions for which the true mass is known either by astrometry (blue circles) or because they transit their host star (green circles). The rest of the objects are candidates detected by RV surveys (white circles), and the plotted mass should be interpreted as a lower limit. Owing to the wide range of objects represented, the error bars for some of them are smaller than the symbol used in the plot.

In the text