Asteroseismic modelling of the subgiant μ Herculis using SONG data: lifting the degeneracy between age and model input parameters

We model the oscillations of the SONG target $μ$ Herculis to estimate the parameters of the star. The $\ell$ = 1 mixed modes of $μ$ Her provide strong constraints on stellar properties. The mass and age given by our asteroseismic modelling are 1.10$^{+0.11}_{-0.06}$ M$_{\odot}$ and 7.55$^{+0.96}_{-0.79}$ Gyr. The initial helium abundance is also constrained at around $Y_{\rm{init}}$ = 0.28, suggesting a ratio in the elements enrichment law ($ΔY/ΔZ$) around 1.3, which is closed to the solar value. The mixing-length parameter converges to about 1.7, which is $\sim$ 10% lower than the solar value and consistent with the results from hydrodynamic simulations. Our estimates of stellar mass and age agree very well with the previous modelling results with different input physics. Adding asteroseismic information makes these determinations less model-dependent than is typically the case when only surface information is available. Our studies of the model dependence (mass, initial helium and metallicity fractions, and the mixing length parameter) of the age determination indicate that accurate stellar ages ($\lesssim$ 10%) can be expected from asteroseismic modelling for stars similar to $μ$ Her. The $\ell$ = 1 bumped modes, which are sensitive to the mean density of the helium core, provide a useful 'clock' that provides additional constraints on its age.