5 Conclusions

The main conclusions of this study are as follows. Solar-like oscillations have been firmly discovered in the bright G7III star $\xi$ Hya. The amplitudes of the strongest modes are somewhat below  $2\ensuremath{~\rm {m~s}^{-1}}$. The observed frequency distribution of the modes detected (Table 1) is in agreement with theoretically calculated frequencies both in terms of the spacing and the absolute values. The modes with the largest amplitudes can be well matched with radial modes that have an almost equidistant separation around 7.1 $\mu$Hz.

A most important and exciting result of our study is the confirmation of the possibility, suggested by the results reported on $\alpha$ UMa and Arcturus, to observe solar-like oscillations in stars on the red giant branch. This opens the red part of the HR diagram for detailed seismic studies. The latter require an accuracy within the range of current and future ground-based instruments. Such future studies will only be successful if an extremely high stability of the instrument is achieved and if one performs multisite observing campaigns covering several months in order to resolve the frequency spectrum of the oscillations and to eliminate the aliasing problems.

Acknowledgements

CA and TM acknowledge the Fund for Scientific Research of Flanders under project G.0178.02 for its financial support of the Leuven contribution to the CORALIE observations of $\xi$ Hya and of the Ph.D. position of TM. Part of this work was supported financially by the Swiss National Science Foundation. Support was received as well from the Danish National Science Foundation through the establishment of the Theoretical Astrophysics Center, from Aarhus University and from the Danish Natural Science Research Council. TCT is supported by research grant SFRH/BPD/3545/2000 of the Fundação para a Ciência e a Tecnologia, Portugal.