| Abstract
| - Context. Detailed oscillation spectra comprising individual frequencies for numerous solar-type stars and red giants are either currently available, e.g. courtesy of the CoRoT, Kepler, and K2 missions, or will become available with the upcoming NASA TESS and ESA PLATO 2.0 missions. The data can lead to a precise characterisation of these stars thereby improving our understanding of stellar evolution, exoplanetary systems, and the history of our galaxy. Aims. Our goal is to test and compare different methods for obtaining stellar properties from oscillation frequencies and spectroscopic constraints. Specifically, we would like to evaluate the accuracy of the results and reliability of the associated error bars, and to see where there is room for improvement. Methods. In the context of the SpaceInn network, we carried out a hare-and-hounds exercise in which one group, the hares, simulated observations of oscillation spectra for a set of ten artificial solar-type stars, and a number of hounds applied various methods for characterising these stars based on the data produced by the hares. Most of the hounds fell into two main groups. The first group used forward modelling (i.e. applied various search/optimisation algorithms in a stellar parameter space) whereas the second group relied on acoustic glitch signatures. Results. Results based on the forward modelling approach were accurate to 1.5% (radius), 3.9% (mass), 23% (age), 1.5% (surface gravity), and 1.8% (mean density), as based on the root mean square difference. Individual hounds reached different degrees of accuracy, some of which were substantially better than the above average values. For the two 1M⊙ stellar targets, the accuracy on the age is better than 10% thereby satisfying the requirements for the PLATO 2.0 mission. High stellar masses and atomic diffusion (which in our models does not include the effects of radiative accelerations) proved to be sources of difficulty. The average accuracies for the acoustic radii of the base of the convection zone, the He II ionisation, and the Γ 1 peak located between the two He ionisation zones were 17%, 2.4%, and 1.9%, respectively. The results from the forward modelling were on average more accurate than those from the glitch fitting analysis as the latter seemed to be affected by aliasing problems for some of the targets. Conclusions. Our study indicates that forward modelling is the most accurate way of interpreting the pulsation spectra of solar-type stars. However, given its model-dependent nature, this method needs to be complemented by model-independent results from, e.g. glitch analysis. Furthermore, our results indicate that global rather than local optimisation algorithms should be used in order to obtain robust error bars.
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