$\begin{figure} \includegraphics[width=8.8cm,clip]{Ef171_f2.eps} \end{figure}$

Figure 2: Power spectrum for $\xi$ Hya. Modes are clearly present in the range 50-130 $\mu$ Hz, corresponding to periods of 2.0-5.5 hours. Panel a) is the power spectrum of the time series using one single spectrum as the reference. Panel b) is for the time series derived using one reference spectrum per night. The insert in Panel b) shows the window function. The frequency scale is made similar to the main plot to facilitate comparison.

The power spectrum of the 433 data points is presented in Fig. 2. In order to show that the excess power in the lower panel in the range 50-130 $\mu$ Hz is not due to elimination of power at low frequencies by the reduction procedure, we show a power spectrum in the upper panel where no correction for drift has been applied. Although more noisy the increase in power between 50 $\mu$ Hz and 130 $\mu$ Hz is also evident in the upper panel. A set of oscillation modes is clearly present, with a power distribution that is remarkably similar to that seen in the Sun and other stars on or near the main sequence, although obviously at much lower frequency. We will show the spectrum displays the characteristic near-uniform spacing of the dominant peaks.

To characterize this pattern we have calculated the autocorrelation of the power spectrum. In order to eliminate the effect of the noise, we have ignored all points with amplitudes below a given threshhold (1.2 $\ensuremath{~\rm {m~s}^{-1}}$ ). In Fig. 3 the alias at 1 c/d stands out clearly, but in addition a spacing $\Delta \nu \sim 6.8\ \mu$ Hz is present in the power spectrum. This is consistent with the visual impression of a regular pattern present in the the power spectrum (Fig. 2).

The expected velocity amplitude for solar-like oscillations scales as L/Maccording to Kjeldsen & Bedding (1995). Using the stellar parameters from Sect. 4 and a mass of 3.0 $M_{\odot}$ (Sect. 4) we find $v_{\rm osc,pred} = 4.6 ~{\rm m}~{\rm s}^{-1}.$ The observed amplitudes in Fig. 2 are only about one third of this prediction. Recent calculations by Houdek & Gough (2002), however, indicate that the simple scaling law of Kjeldsen & Bedding (1995) does indeed not apply. They predict a velocity amplitude $v = 2.1 ~{\rm m}~{\rm s}^{-1}$ , slightly higher than the ones observed by us for $\xi$ Hya.

The stochastic nature of solar-like oscillations implies that a timestring of radial velocities cannot be expected to be a set of coherent oscillations and can therefore not be reproduced perfectly by a sum of sinusoidal terms. As a starting point it is nevertheless a good assumption to try to fit the radial-velocity data of $\xi$ Hya by such a set of functions, as the lifetimes are expected to exceed the length of the observing run (Houdek & Gough 2002). We have performed an iterative fit using different methods, among which Period98 (Sperl 1998) and a procedure by Frandsen et al. (2001). An oscillation with a S/N above 4 is detected at 9 frequencies. When a fit based upon these 9 frequencies is removed from the time series, 5 additional peaks still occur but with a too low S/N to accept them without additional confirmation (hence we do not list them). After removing the 14 frequencies, only a noise spectrum is left. The results for the 9 frequencies are presented in Table 1, where the S/N indicated is calculated from the remaining noise in the amplitude spectrum at the position of each mode. The noise is slightly higher in the range of the modes than at high frequencies, where $\sigma = 0.2~\ensuremath{~\rm {m~s}^{-1}}$ . The frequencies of the modes with amplitudes above $1.5 \ensuremath{~\rm {m~s}^{-1}}$ , i.e., of the five highest-amplitude modes, are unambiguous. Dividing the dataset in two, four out of five modes with S/N > 5.0 are present in each set. For lower S/N the alias problems lead to a risk that false detections are made. Modes with S/N < 5 must be considered with some caution. Confirmation of these frequencies is needed by additional observations. What is stated above has been verified by the analysis of several sets of simulated data assuming a variety of lifetimes in order to check the validity of the identified modes. The details of such simulations will be published in a subsequent paper.

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{Ef171_f3.eps} \end{figure}$

Figure 3: Autocorrelation of the power spectrum for $\xi$ Hya. A ll points with amplitude v < 1.2 $\ensuremath{~\rm {m~s}^{-1}}$ have been set to zero. The dash-dot-dot-dot vertical lines mark the position of the 11.574 $\mu$ Hz daily alias and half of it, and the dash-dot line indicates the peak pointing to a frequency spacing of 6.8 $\mu$ Hz.

**Table 1:** Oscillation frequencies detected in the radial velocities of $\xi$ Hya ordered by amplitude. Formal errors of the fit are given in parenthesis as errors of the last digits. The S/N is calculated by dividing the amplitude by the noise in a 10 $\mu$ Hz bin in the residual spectrum centered on the frequency of the mode. Frequencies in italic indicate modes where the frequency detection methods disagree on the correct alias. The last column gives the difference between the observed frequency and the frequency derived from Eq. (1).
ID	Frequency		Amplitude	S/N	$\Delta \nu$
	c/d	$\mu$ Hz	$\ensuremath{~\rm {m~s}^{-1}}$		$\mu$ Hz
F1	5.1344(26)	59.43	1.85(23)	6.6	0.77
F2	6.8366(27)	79.13	1.84(23)	5.8	-0.86
F3	7.4265(29)	85.96	1.76(23)	5.3	-1.14
F4	8.2318(32)	95.28	1.65(23)	5.1	1.07
F5	9.3507(33)	108.22	1.59(23)	6.0	-0.21
F6	8.7399(36)	101.16	1.36(22)	4.5	-0.16
F7	10.0287(43)	116.07	1.25(23)	5.0	0.53
F8	9.0831(44)	105.13	1.24(24)	4.3
F9	8.5339(40)	98.77	1.23(23)	4.1

The first seven modes can be ordered in a sequence of modes, which fits the straight line

From the present data, we cannot firmly exclude that frequency F8 in Table 1 corresponds to the same mode as F7. The two modes are resolved, but if the damping time is short, they might be different realizations of the same mode.

3 Time-series analysis