Seismic modelling of subgiant stars: Testing different grid interpolation methods

¹ Instituto de Astrofísica e Ciências do Espaço, Universidade do Porto, CAUP, Rua das Estrelas, 4150-762 Porto, Portugal
² Departamento de Física e Astronomia, Faculdade de Ciências da Universidade do Porto, Rua do Campo Alegre, s/n, 4169-007 Porto, Portugal
³ Université Côte d’Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, Nice, France
⁴ IRAP, Université de Toulouse, CNRS, CNES, UPS, 14 avenue Edouard Belin, 31400 Toulouse, France
⁵ LIRA, Observatoire de Paris, Université PSL, Sorbonne Université, Université Paris Cité, CY Cergy Paris Université, CNRS, 92190 Meudon, France

^⋆ Corresponding author; miguel.clara@astro.up.pt

Received: 25 April 2024
Accepted: 19 December 2024

Abstract

Context. Grid-based modelling techniques have enabled the determination of stellar properties with great precision. The emergence of mixed modes during the subgiant phase, whose frequencies are characterised by a fast evolution with age, can potentially enable a precise determination of stellar properties, a key goal for future missions such as PLATO. However, current modelling techniques often consider grids that lack the resolution to properly account for the fast mode frequency evolution, consequently requiring the use of interpolation algorithms to cover the parameter space in between the grid models when applying model-data comparison methods.

Aims. We aim to reproduce the ℓ = 1 mode frequencies within the accuracy limits associated with the typical observational errors (∼0.1 μHz) through interpolation on a grid of subgiant models.

Methods. With that aim, we used variations of a two-step interpolation algorithm that considered linear and cubic splines interpolation methods and different age proxies (physical age, scaled age, and central density).

Results. The best results were obtained using an algorithm that considers cubic splines interpolation along tracks, linear interpolation across tracks, and central density ρ_c as the age proxy. This combination yielded, on average, an absolute error of 0.14 μHz but reached maximum absolute errors on the interpolated frequencies of 1.2 μHz for some models, which is an order of magnitude higher than the typical observational errors. Furthermore, we investigated the impact on the accuracy of the interpolation from changes in the physical properties of the stars, showing, in particular, how the addition of core overshoot can significantly affect the interpolation results.