2 The radial-velocity measurements

Figure 1: Radial-velocity measurements of $\xi$ Hya. The dispersion reaches  $4.6~{\rm m}~{\rm s}^{-1}$. a) The whole time string; b) zoom of a small part of the time series.

The $\xi$ Hya observations were made during one full month (2002 February 18 - March 18) with CORALIE, the high-resolution fiber-fed echelle spectrograph (Queloz et al. 2001) mounted on the 1.2-m Swiss telescope at La Silla (ESO, Chile). During the stellar exposures, the spectrum of a thorium lamp carried by a second fiber is simultaneously recorded in order to monitor the spectrograph's stability and thus to obtain high-precision velocity measurements. The spectra were extracted at the telescope, using the INTER-TACOS (INTERpreter for the Treatment, the Analysis and the COrrelation of Spectra) software package developed by D. Queloz and L. Weber at the Geneva Observatory (Baranne et al. 1996). The wavelength coverage of these spectra is 3875-6820 Å, recorded on 68 orders. By taking about 2 measurements every hour, a total of 433 optical spectra was collected. The exposure times were typically 180 s and the S/N ratio for all spectra was in the range of 110-230 at 550 nm.

By the use of the optimum-weight procedure (Bouchy et al. 2001), radial velocities are computed for each night relative to the highest S/N spectrum obtained in the middle of the night. This method requires a Doppler shift that remains small compared to the line-width (smaller than $100 \ensuremath{~\rm {m~s}^{-1}}$) (Bouchy & Carrier 2001). Since the Earth's motion can introduce a Doppler shift larger than $800 \ensuremath{~\rm {m~s}^{-1}}$ during a whole night, each spectrum is first corrected for the Earth's motion before deriving the radial velocities. This is achieved by shifting all spectra with the Earth's velocity at the time of observation and by subsequent rebinning, so that the spectra all have the same wavelength values. From each rebinned spectrum a velocity is derived. The mean radial velocity for each night is then subtracted. The resulting velocities are shown in Fig. 1. The rms scatter of the time series is  $4.6 \ensuremath{~\rm {m~s}^{-1}}$ and is largely due to the oscillations. The mean error on each measurement is  $2.3 \ensuremath{~\rm {m~s}^{-1}}$.