On the inference of stellar ages and convective-core properties in main-sequence solar-like pulsators

Particular diagnostic tools may isolate the signature left on the oscillation frequencies by the presence of a small convective core. Their frequency derivative is expected to provide information about convective core's properties and stellar age. The main goal of this work is to study the potential of the diagnostic tools with regards to the inference of stellar age and stellar core's properties. For that, we computed diagnostic tools and their frequency derivatives from the oscillation frequencies of main-sequence models with masses between 1.0 and $1.6\,{\rm\,M}_{\odot}$ and with different physics. We considered the dependence of the diagnostic tools on stellar age and on the size of the relative discontinuity in the squared sound speed at the edge of the convectively unstable region. We find that the absolute value of the frequency derivatives of the diagnostic tools increases as the star evolves on the main sequence. The fraction of stellar main-sequence evolution for models with masses $>1.2\,{\rm\,M}_{\odot}$ may be estimated from the frequency derivatives of two of the diagnostic tools. For lower mass models, constraints on the convective core's overshoot can potentially be derived based on the analysis of the same derivatives. For at least 35 per cent of our sample of stellar models the frequency derivative of the diagnostic tools takes its maximum absolute value on the frequency range where observed oscillations may be expected.