4 First interpretation

In order to study the nature of the oscillations detected in $\xi$ Hya, it is necessary to compare the observed frequency spectrum with model predictions, taking into account the constraints on the three observational stellar parameters  $T_{\rm eff}$, L and Z. We have redetermined the atmospheric parameters and use $T_{\rm eff} = 5000\pm100\$K, $L = 61.1\pm6.2$ $L_{\odot}$, $\log g = 2.85$, [M/H] = $0.06\pm0.07$ ( $Z = 0.019\pm0.006$) and $v \sin i = 1.8\pm1.0\$ . Details of how these values were obtained will be reported in a subsequent paper.

Using the evolution code of Christensen-Dalsgaard (1982), evolutionary tracks were produced, spanning the error box defined by the uncertainties of  $T_{\rm eff}$, L and Z. The model tracks were computed using the EFF equation of state (Eggleton et al. 1973), OPAL opacities (Iglesias et al. 1992), Bahcall & Pinsonneault (1992) nuclear cross sections, and the mixing-length formalism (MLT) for convection.

The evolutionary track passing through the observed ( $T_{\rm eff}$, L) corresponds to a mass of $3.07~M_\odot$ for Z = 0.019(Fig. 4). Oscillation frequencies were calculated for the model in that track closest to the observed location of $\xi$ Hya in the HR diagram. The average separation between radial modes in the range 50-100 $\mu$Hz is $\Delta \nu_{\rm theo} = 7.2$ $\mu$Hz in agreement with the observational value. The model frequencies fit a linear relation for orders 5 < n < 17 or $50 < \nu < 125~\mu$Hz given by  $\nu = 7.15 + 7.14~n$with absolute values only 1-2 $\mu$Hz from the observed frequencies. The maximum deviation of the model frequencies from the line is $\sim$$0.5~\mu$Hz.

Radial modes are expected to dominate the spectrum for giant stars (cf. Dziembowski et al. 2001, Fig. 2). Further analysis of the spectrum is beyond the scope of the current discovery paper and will be done in a forthcoming paper, dealing in detail with the issue of modelling and considering also the possibility that $\xi$ Hya could be a core helium burning star with a smaller mass.

Figure 4: Hertzsprung-Russell diagram with evolutionary tracks for Z = 0.019 for masses $3.07~M_\odot$ (solid line), 2.93 and $3.15~M_\odot$ (lower and upper dashed lines, respectively). The location of $\xi$ Hya in the diagram is given by the error box.