3 Radial-velocity analysis and orbital solution

On the 24th of April 2001, we had in hand a total of 61 radial-velocity measurements for analysis: 6 from HIRES and 55 from ELODIE. The mean uncertainty on the velocities are of the order of 14 m s$^{\rm -1}$ (systematic error + photon noise) for both instruments. The HIRES velocities have an arbitrary zero point. From contemporaneous observations, we applied a preliminary shift to these velocitites to bring them to the ELODIE system: $\Delta RV=+3.807$ km s$^{\rm -1}$. To account for possible errors in this zero-order shift, the orbital solution presented in Table 2 includes the residual velocity offset $\Delta {RV}_{\rm H-E}$ between HIRES and ELODIE as an additional free parameter. The obtained $\Delta {RV}_{\rm H-E}$ is consistent with zero. Figure 1a shows the temporal velocities for HD 80606. The phase-folded velocities are displayed in Fig 1c. The fitted orbital eccentricity is extremely high - $e=0.927\pm0.012$. Assuming a mass of $1.1~{M_{\odot}}$ for HD 80606, a typical value for a very metal-rich star with a solar effective temperature, the planetary companion minimum mass is $m_{\rm 2}=3.90\pm0.09~M_{\rm Jup}$. The semimajor axis is 0.469 AU and the orbital separation ranges from 0.034 AU (periastron) to 0.905 AU (apastron).

  

Table 2: Fitted orbital elements to the radial-velocity measurements for HD 80606. The velocities obtained with the HIRES spectrograph (H) have been set into the ELODIE (E) system.

$$\begin{tabular}{llr@{ ~$\pm$~ }l} \hline $P$ & days & 111.81 ... ...ulticolumn{2}{c}{17.7 (E:16.3, H:29.9)}\\ \hline \end{tabular}$$

The residuals to the fitted orbit cannot be explained by our measurement errors. The computed $\chi^2$ probability for the full set of data is lower than 10^-3 ($\chi^2$ = 102.45, $\nu$ = number of degrees of freedom = N-7 free parameters = 54). Our measurement errors are correctly estimated for both instruments (see e.g. the low residuals value obtained for HD 178911 B, Zucker et al., in prep.). The very low $P(\chi^{\rm 2})$ value found for HD 80606 can therefore not result from an underestimation of our measurement errors. Using our HIRES high-signal spectrum, no chromospheric emission is detected for HD 80606 so the expected stellar jitter is low (a few m s^-1, see e.g. Santos et al. 2000b; Saar et al. 1998). Activity related processes are therefore probably not responsible for the observed residuals. The later could be explained by the presence of another planet around HD 80606 on a longer period orbit perturbating the stellar radial-velocity signal induced by the inner companion. No clear velocity trend was detected from the residuals curve (see Fig. 1b). Future measurements should help to solve the question.