3 A Saturn-mass planet in eccentric orbit around HD 108147

3.1 Stellar characteristics of HD 108147

HD 108147 (HIP 60644) is a F8/G0 dwarf in the Crux constellation. Its magnitude is V = 6.99 while the HIPPARCOS catalogue (ESA 1997) lists a color index B-V = 0.537. The precise astrometric parallax is $\pi=25.95\pm 0.69$ mas corresponding to a distance of about 38.57 pc from the Sun. The derived absolute magnitude, M_V = 4.06, is typical for a G0 dwarf.

Stellar parameters such as effective temperature $T_{\rm eff}=6265$ K, surface gravity $\log g=4.59$, as well as [Fe/H] = +0.2 have been derived in the detailed LTE spectroscopic analysis carried out by Santos et al. (2001). The obtained metallicity is slightly higher than the average value for stars of the CORALIE sample, like most of the stars with giant planets, and is very close to the mean value of [Fe/H] of stars with planets (Santos et al. 2001). Using the evolutionary tracks of the Geneva models given by Schaerer et al. (1993), Santos et al. (2001) compute a stellar mass M=1.27 $M_{\odot}$. The stellar mass is higher than the "typical'' mass of G0 dwarfs and can be explained by the high metallicity of the star.

Figure 2: $\lambda 3968.5$ Å Ca II H absorption line region of the summed CORALIE spectra. Upper panel: HD 108147. Lower Panel: HD 168746. Both objects show low chromospheric activity. Strong activity would result in an emission peak in the center of the absorption line.

Figure 2 shows the Ca II H absorption line region of the CORALIE spectrum at $\lambda 3968.5$ Å. The emission flux in the core of the Ca II H line corrected for the photospheric flux provides us with the chromospheric activity index $S_{\rm Cor}$ (Santos et al. 2000) from which we derive the activity indicator $\log{(R^{\prime}_{\rm HK})}=-4.72$. This value is typical for stars with a low chromospheric activity level (Henry et al. 1996). Using the calibration given by Donahue (1993) and quoted in Henry et al. (1996) we compute for this star an age of approximately 2 Gyrs, while the rotational period resulting from the calibration given by Noyes et al. (1984) is of 8.7 days. The star is not seen as photometrically variable in the HIPPARCOS data, confirming again the low activity level. We have estimated the projected rotational velocity of the star to be $v\sin i = 5.3$ km s^-1 by means of the CORALIE cross-correlation function (CCF) (Queloz et al. 1998). The relatively high stellar rotation could cause a small jitter on the radial-velocity data, which are however expected to be in the order of only few m s^-1 (Saar & Donahue 1997; Santos et al. 2001). The observed and inferred stellar parameters are summarized in Table 1.

  

Table 1: Observed and inferred stellar parameters for HD 108147 and HD 168746. Photometric and astrometric data have been extracted from the HIPPARCOS catalogue (ESA 1997) while spectroscopic data are from Santos et al. (2001).

$$\begin{tabular}{l@{}lcc} \hline\hline \multicolumn{2}{l}{\bf... ...\rm HK}$) & [Gyr] & 2.17 & --/old star \\ \hline \end{tabular}$$

3.2 CORALIE orbital solution for HD 108147

The precise radial velocity data of HD 108147 have been collected by our group during the period of time from March 1999 to February 2002. The result of this campaign is a set of 118 data points having a mean photon-noise error on the individual measurements of $\langle \varepsilon_i \rangle$ = 7.8 m s^-1. A periodic variation of the radial velocity could be detected on this data, which clearly indicates the presence of a planetary companion. The measured variation cannot be produced by stellar activity: the Geneva photometry data show very low dispersion of 1 mmag and no CCF-bisector variation (Queloz et al. 2001b) has been measured at the m s^-1 level. Therefore the planetary explanation seems to be the most likely.

The best-fit Keplerian orbit to the data is shown in Fig. 3. It yields a precisely-determined orbital period P of $10.901\pm 0.001$ days and a large eccentricity $e=0.50\pm 0.03$. The semi-amplitude of the radial-velocity variation is $K=36\pm 1$ m s^-1. The weighted rms of the data to the Keplerian fit is 9.2 m s^-1. The complete set of orbital elements with their uncertainties are given in Table 2.

Using the best-fit orbital parameters and the mass of HD 108147 given above we derive for the companion a minimum mass $m_2~\sin{i}=0.40$  $M_{\rm Jup}$ (which is about only 1.34 times the mass of Saturn). Because of the many data points and the long observation period the orbit is determined very accurately. This allows us to determine the minimum mass of the companion with accuracy of better than 4%, provided that we do not consider the major error source, namely the uncertainty on the mass of the primary. From the orbital parameters and the star mass we get also the separation of the companion to its parent star which is a=0.104 AU. The surface equilibrium temperature of the planet at such a distance is estimated to be about 890 K, following Guillot et al. (1996).

HD 108147 b belongs to the so-called hot Jupiter (or better: hot Saturn!) category of extra-solar planets. The close location to its parent star makes the planet a good candidate for a photometric transit search. The photometric monitoring described in a forthcoming paper (Olsen et al., in prep.) did unfortunately not show any indication for a transit.

Figure 3: Phase-folded radial-velocity measurements obtained with CORALIE for HD 108147. The error bars represent photon-noise errors only. On the lower panel the residuals of the measured radial velocities to the fitted orbit are plotted as a function of time. They show a tiny indication for the presence of a long-period, second companion of HD 108147.

  

Table 2: CORALIE best Keplerian orbital solutions derived for HD 108147 and HD 168746, as well as inferred planetary parameters.

$$\begin{tabular}{l@{}lr@{\hspace{0.05cm}$\pm$\hspace{0.05cm}}l... ...n{2}{c}{890} & \multicolumn{2}{c}{900} \\ \hline \end{tabular}$$

3.3 A planetary system around HD 108147?

The weighted rms of the data to the Keplerian fit is 9.2 m s^-1 and the reduced $\chi$ is 1.440, indicating an internal error for the single measurements of 6.4 m s^-1. The residual dispersion is 6.6 m s^-1 and is only partially composed of instrumental errors, which are in the order of 3 m s^-1 (Queloz et al. 2001a). The remaining 6 m s^-1 could be due to stellar jitter, since the star is fairly rapidly rotating. Closer analysis of the residuals (Fig. 3, bottom) might indicate however the presence of a possible second companion with an orbital period P of $587 \pm 34$ days and a minimum mass of $m_2~\sin{i}=0.42$  $M_{\rm Jup}$. A best-fit solution considering a second companion reduces the rms to the Keplerian to 8.0 m s^-1 while the reduced $\chi$ passes from 1.440 to 1.290. In order to confirm or reject this possibility we will continue to collect additional high-precision data during the next observational seasons. We plan to monitor the radial velocity of this object using the CORALIE spectrograph, but also taking advantage of the superior performances of the HARPS spectrograph (Pepe et al. 2000) which is expected to reach a radial-velocity precision of 1 m s^-1.

3.4 Results of the improved cross correlation

As mentioned previously, the radial velocity data have been computed by using the weighted cross correlation and the new numerical mask. For comparison we have nevertheless computed the radial velocity data also using the standard on-line data reduction. The results are summarized in Table 3.

In the error budget of our best single-orbit solution about 6.6 m s^-1 arise from sources other that photon noise. The rms obtained with the standard algorithm was 11.9 m s^-1 and with the weighted cross correlation 10.1 m s^-1. Considered this, the weighted cross correlation reduced the radial velocity dispersion arising from photon noise by a factor 1.31, confirming the simulation results. On the other hand, the rms of 11.9 m s^-1 obtained with the original mask passes to 10.7 m s^-1 with the new clean mask. Thus, we estimate that the telluric lines add a dispersion on the stellar radial velocity of roughly 5 m s^-1.

 

 

Table 3: Comparison of the different data reductions on HD 108147. The rms of the data to the Keplerian fit is reduced from 11.9 to 9.2 m s^-1 if the weighted cross correlation and the clean numerical mask are used.

Cross correlation	Obtained rms [m s-1]
Standard	11.9
Clean mask only	10.7
Weighted only	10.1
Weighted & clean mask	9.2

3.5 The eccentricity of the orbit around HD 108147

Considered the short orbital period, the eccentricity of the orbit around HD 108147 is surprisingly high. According to the commonly believed migration scenario for the formation of hot Jupiters, the giant planets like HD 108147 cannot be formed in situ at a distance of only 0.1 AU from the parent star. On the other hand the orbit of planets having suffered a strong migration are expected to be circularized by the tidal interaction with the accretion disk (Goldreich & Tremaine 1980). Another mechanism must therefore be at the origin of its high eccentricity. One suitable explanation is provided by the gravitational interaction between multiple giant planets in the early stages of the system formation (Weidenschilling & Marzari 1996; Rasio & Ford 1996; Lin & Ida 1997). As a result one planet could have been projected on a short-period orbit with a high eccentricity, leaving different possibilities concerning the destiny of its scattering partner. Eccentric orbits can however also be produced by additional companions on longer-period orbits, which perturb the short-period orbit of the inner companion by tidal forces (Mazeh et al. 1997). The companion can be either planetary or stellar and would be seen in many cases only as a slow drift of the gamma-velocity $\gamma$. Finally, additional scenarios to explain high eccentricities were proposed recently: for example the migration of a single Jupiter-mass planet through a planetesimal disk (Levison et al. 1998), or, the simultaneous formation and migration of two or more planets through the accretion disk, e.g. locked in a resonant system (Murray et al. 2002). The numerical simulations in the latter paper show that a large variety of possible results can be obtained, depending on the initial planetary mass(es), disk properties and time scales.

In summary, various mechanisms can explain short-period eccentric orbits. In almost all of them interaction with planetary or stellar companions plays a fundamental role, and the large eccentricity of the orbit might be an indication for their presence. Therefore it is very likely to find a second, long-period companion around HD 108147. As mentioned above the long-term follow up of this object might confirm or reject this possibility.