3 A long period planet around HD213240

3.1 Stellar characteristics

HD213240 (HIP 111143, CD-5013701A) is a high proper-motion 6.8 magnitude G0 dwarf in the southern constellation Grus (the Crane). Its colour index (B-V) is 0.60 - from the Hipparcos catalogue (ESA 1997) - and from the parallax measurements its distance is $\sim$40parsec ( $\pi=24.54\pm0.81$mas) implying an absolute visual magnitude M_v=3.76. The basic stellar parameters for HD213240 are summarized in Table1.

From a high S/N CORALIE spectrum we have derived the stellar atmospheric parameters for HD213240. The technique used is well described in Santos et al. (2000b, 2001). The obtained $T_{{\rm eff}}$, surface gravity, microturbulence parameter and iron abundance ([Fe/H]) are 5975K, 4.32dex, 1.29 and +0.16, respectively. The derived effective temperature is about 200K higher than the value of 5770K obtained from ubvy-photometry of Olsen (1994) and the calibrations in Schuster & Nissen (1989), and 100K above the value of 5880K derived from the calibration of $T_{{\rm eff}}$ vs. B-V presented by Flower (1996). As for the [Fe/H], the result determined from the ubvy-photometry calibration (-0.16) is not compatible with the +0.16 obtained from our fully spectroscopic analysis. Finally, using the Hipparcos parallax we derive a surface gravity $\log{g}=4.10$ for HD213240 (e.g. Allende-Prieto et al. 1999), quite lower than the 4.32dex obtained from our analysis. We do not completely discard, however, that the star may be already a bit evolved, given that the surface gravities derived from our spectroscopic analysis have usually higher values that the ones computed using e.g. Hipparcos parallaxes.

Using $T_{{\rm eff}}=5975$K and $\rm [Fe/H]=+0.16$ from the more precise spectroscopic analysis, and the luminosity derived from the calibration of Flower (1996), we obtain an age of $4.6\pm0.2$Gyr and a stellar mass of $1.22\pm0.01\,M_{\odot}$ (from the Geneva evolutionary tracks - Schaerer et al. 1993).

  

Table 2: CORALIE best Keplerian orbital solutions derived for HD28185 and HD213240 and inferred planetary parameters.

$$\begin{tabular}{l@{}lr@{\hspace{0.05cm}$\pm$\hspace{0.05cm}}l... ...multicolumn{2}{c}{180--300$\dag\dag $} \\ \hline \end{tabular}$$

$\dag$ In this paper we have used the albedo of Jupiter ($\sim$0.35) - Guillot et al. (1996) - since there are big uncertainties in the current models of exoplanet atmospheric structure, and that there are no direct measurements of the albedo for these objects (e.g. Burrows et al. 2001). The values for $T_{{\rm eq}}$ should consequently just be regarded as an approximation.
$\dag$$\dag$ Range of $T_{{\rm eq}}$ corresponding to periastron and apoastron distances from the central star.

From CORALIE spectra we can compute a chromospheric activity index $S_{{\rm cor}}$ (Santos et al. 2000a), similar to the one derived at Mount-Wilson (Vaughan et al. 1978). We have obtained $S_{{\rm cor}}=0.176\pm0.017$ (where the error indicates the rms around the mean of the 5 measurements, covering more than 1 year), corresponding to $S_{{\rm MW}}=0.19$; this value is compatible with the one obtained by Henry et al. (1996) of $S_{{\rm MW}}=0.16$ (in one measurement). Using $S_{{\rm MW}}=0.19$, we obtain $\log{R'_{\rm HK}}=-4.80$, a value typical for a non-active dwarf, and an age of 2.7Gyr (Henry et al. 1996; Donahue 1993).

3.2 Planetary signature of HD213240

Using CORALIE measurements, a clear long period radial-velocity variation was found. The 72 high-precision radial-velocity measurements, spanning about two years, allow us to derive an orbital solution (see Table2). In Fig. 2 we can see a phase-folded and a "temporal'' radial-velocity diagram of the measurements. The best Keplerian fit holds a period of 951days, an amplitude of 91ms^-1 and an eccentricity of 0.45. This corresponds to the expected radial-velocity signature of a planet with a minimum mass of $\sim$4.5 $M_{{\rm Jup}}$ orbiting at about 2.03AU from the star. No long term significant drifts are evident in either the CORALIE and/or the CORAVEL data.

Non-identified long term drifts could in fact affect the estimation of the orbital eccentricity of the companion around HD213240. This may be particularly true in this case, since the measurements still do not cover a complete orbital period. In order to test if the presence of a trend is responsible for the computed high-eccentricity, we have corrected the radial-velocities for the small drift present in the CORAVEL+CORALIE data (about $0.01\pm0.01$ms^-1day^-1, and non-significant) and computed a new orbit. The result shows that the orbital parameters, and in particular the eccentricity and the residuals (O-C), remain unchanged. The same is true if we vary the slope of the linear correction within the uncertainties. We thus conclude that the "high''-eccentricity obtained for the planet orbiting HD213240 does not seem to be explained by any unidentified short amplitude long term drift.

The projected rotational velocity of the star is $v\,\sin{i}=3.97\,\pm\,0.61$kms^-1 (from CORAVEL measurements - Benz & Mayor 1984). From the chromospheric activity level, using the calibration of Noyes et al. (1984), we obtain a rotational period of 15days. Given the temperature and luminosity of the star, we derive a stellar radius of $\sim$1.5 times the radius of the Sun. This radius and rotational period correspond to $V_{\rm rot}=5.1$kms^-1, and the derived $\sin{i}$ is thus $\sim$0.78, corresponding to an angle of about $\sim$50 degrees. This would mean that the mass of the planet is about 1.3 times higher than the measured minimum mass, if we assume that the orbital plane is perpendicular to the rotation axis of the star.

In any case, and as for HD28185, we note that the probability that the companion has a minimum mass in the Brown-Dwarf regime is quite low (around 5% in this case), and thus the planetary explanation seems the most credible.

Hipparcos photometry (ESA 1997) show that the star is stable up to a precision of 8mmag (158 measurements), a typical value for a dwarf of its magnitude. The rms around the radial-velocity orbital solution is 11ms^-1, with an average photon-noise error of 6.5ms^-1 for the individual measurements. Subtracting quadratically, this gives a "jitter'' of 9ms^-1, as expected from Eq. (3) of Santos et al. (2000a). A Fourier-Transform of the residuals does not show any significant signature of a shorter period companion.

Pannunzio et al. (1992) have classified HD213240 as the A component of a double system, where the B component (CD-5013701B) is a faint 12 magnitude star located about 20 arcsec away. At the distance of HD213240, 20arcsec correspond to a projected minimum distance of about 800AU, and if the stars constitute a bound binary system, significant perturbations in the orbit of the planetary companion might be expected, at least if the orbit of the fainter (and less massive) stellar companion is eccentric (Rasio & Ford 1996). The presence of a longer period companion could indeed help to explain the eccentricity of the planetary orbit (see e.g. "similar'' case of 16CygA and 16CygB - Cochran et al. 1997; Mazeh et al. 1997). There are, however, no indications from the available radial-velocity data that the objects are related, and the B component might just be a background star. In the Hipparcos catalogue HD213240 is classified as a single star.

A search for an astrometric signature using Hipparcos data (F. Arenou, private communication) did not reveal any trace of a companion, confirming the low mass of the object orbiting HD213240. Furthermore, no cross-correlation function bisector changes were found correlated with the radial-velocity. As for HD28185, the presence of a planetary companion represents the only reasonable explanation to the observed radial-velocity variations.