Oscillation mode lifetimes in $\xi\,$Hydrae: will strong mode damping limit asteroseismology of red giant stars?

We introduce a new method to measure frequency separations and mode lifetimes of stochastically excited and damped oscillations, so-called solar-like oscillations. Our method shows that velocity data of the red giant star ξ Hya (Frandsen et al. 2002) support a large frequency separation between modes of roughly 7 µ Hz. We also conclude that the data are consistent with a mode lifetime of 2 days, which is so short relative to its pulsation period that none of the observed frequencies are unambiguous. Hence, we argue that the maximum asteroseismic output that can be obtained from these data is an average large frequency separation, the oscillation amplitude and the average mode lifetime. However, the significant discrepancy between the theoretical calculations of the mode lifetime (Houdek & Gough 2002) and our result based on the observations of ξ Hya, implies that red giant stars can help us better understand the damping and driving mechanisms of solar-like p-modes by convection.