How well do we know the scaling relations?

Asteroseismic scaling relations are often used to derive stellar masses and radii, particularly for stellar, exoplanet, and Galactic studies. It is therefore important that their precisions are known. 

Firstly, we tested the intrinsic scatter of the \(\Delta\nu\) and \(\nu_{\rm max}\) scaling relations, using two sharp features that are formed in the H–R diagram by the red giant populations. The scaling relations have intrinsic scatter of ~0.5 (\(\Delta\nu\)), ~1.1 (\(\nu_{\rm max}\)), ~1.7 (M), and ~0.4 per cent (R), which are much smaller than the random errors from measuring \(\Delta\nu\) and \(\nu_{\rm max}\). We pointed out new methods to measure \(\Delta\nu\) and \(\nu_{\rm max}\) in order to further reduce scatter.

Secondly, we focused on the systematic offsets of those relations. We proposed a new revision for the \(\Delta\nu\) scaling relation, using a prescription to correct the surface effect in models. The prescription treats the amount of the surface correction as a smooth and simple function of stellar surface properties, including surface gravity, effective temperature, and metallicity. The values of the correction factor, \(f_{\Delta\nu}\), are 0-2% smaller than those determined without the surface effect considered, suggesting a 0-4% change in the scaling radii and a 0-8% change in the scaling masses. We also tested the \(\nu_{\rm max}\) scaling relation and found no significant departure. Future work is needed to establish the metallicity dependency of this relation.