On the seismic scaling relations $\Delta \nu - \bar{\rho}$ and $\nu_{\rm max}-\nu_{\rm c}$

TL;DR

This paper investigates the accuracy and physical basis of key asteroseismic scaling relations, focusing on the $ riangle u - ar{ ho}$ and $ u_{ m max} - u_{ m c}$ relations, using stellar models and 3D simulations.

Contribution

It analyzes the uncertainties in the $ riangle u - ar{ ho}$ relation and clarifies the physical understanding of the $ u_{ m max} - u_{ m c}$ relation with 3D simulations.

Findings

Uncertainties in the $ riangle u - ar{ ho}$ relation are explored using stellar models.

The physical basis of the $ u_{ m max} - u_{ m c}$ relation is confirmed, with deviations due to convection complexities.

Departure from observed relations is linked to non-adiabatic processes and convection modeling.

Abstract

Scaling relations between asteroseismic quantities and stellar parameters are essential tools for studying stellar structure and evolution. We will address two of them, namely, the relation between the large frequency separation ($\Delta \nu$) and the mean density ($\bar{\rho}$) as well as the relation between the frequency of the maximum in the power spectrum of solar-like oscillations ($\nu_{\rm max}$) and the cut-off frequency ($\nu_{\rm c}$). For the first relation, we will consider the possible sources of uncertainties and explore them with the help of a grid of stellar models. For the second one, we will show that the basic physical picture is understood and that departure from the observed relation arises from the complexity of non-adiabatic processes involving time-dependent treatment of convection. This will be further discussed on the basis of a set of 3D hydrodynamical simulation of surface convection.