Testing the intrinsic scatter of the asteroseismic scaling relations with Kepler red giants

Asteroseismic scaling relations are often used to derive stellar masses and radii, particulaly for stellar, exoplanet, and Galactic studies. It is therefore important that their precisions are known. Here we measure the intrinsic scatter of the underlying seismic scaling relations for $\Delta\nu$ and $\nu_{\rm max}$, using two sharp features that are formed in the H--R diagram (or related diagrams) by the red giant populations. These features are the edge near the zero-age core-helium-burning phase, and the strong clustering of stars at the so-called red giant branch bump. The broadening of those features is determined by factors including the intrinsic scatter of the scaling relations themselves, and therefore it is capable of imposing constraints on them. We modelled Kepler stars with a Galaxia synthetic population, upon which we applied the intrinsic scatter of the scaling relations to match the degree of sharpness seen in the observation. We found that the random errors from measuring $\Delta\nu$ and $\nu_{\rm max}$ provide the dominating scatter that blurs the features. As a consequence, we conclude that the scaling relations have intrinsic scatter of $\sim0.5\%$ ($\Delta\nu$), $\sim1.1\%$ ($\nu_{\rm max}$), $\sim1.7\%$ ($M$) and $\sim0.4\%$ ($R$), for the SYD pipeline measured $\Delta\nu$ and $\nu_{\rm max}$. This confirms that the scaling relations are very powerful tools. In addition, we show that standard evolution models fail to predict some of the structures in the observed population of both the HeB and RGB stars. Further stellar model improvements are needed to reproduce the exact distributions.