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The asteroseismic modelling of period spacing patterns from gravito-inertialmodes in stars with a convective core is a high-dimensional problem. We utilisethe measured period spacing pattern of prograde dipole gravity modes (acquiring$\Pi_0$), in combination with the effective temperature ($T_{\rm eff}$) andsurface gravity ($\log g$) derived from spectroscopy, to estimate thefundamental stellar parameters and core properties of 37 $\gamma~$Doradus($\gamma~$Dor) stars whose rotation frequency has been derived from$\textit{Kepler}$ photometry. We make use of two 6D grids of stellar models,one with step core overshooting and one with exponential core overshooting, toevaluate correlations between the three observables $\Pi_0$, $T_{\rm eff}$, and$\log g$ and the mass, age, core overshooting, metallicity, initial hydrogenmass fraction and envelope mixing. We provide multivariate linear model recipesrelating the stellar parameters to be estimated to the three observables($\Pi_0$, $T_{\rm eff}$, $\log g$). We estimate the (core) mass, age, coreovershooting and metallicity of $\gamma~$Dor stars from an ensemble analysisand achieve relative uncertainties of $\sim\!10$ per cent for the parameters.The asteroseismic age determination allows us to conclude that efficientangular momentum transport occurs already early on during the main sequence. Wefind that the nine stars with observed Rossby modes occur across almost theentire main-sequence phase, except close to core-hydrogen exhaustion. Futureimprovements of our work will come from the inclusion of more types of detectedmodes per star, larger samples, and modelling of individual mode frequencies.

Asteroseismic masses, ages, and core properties of $\gamma$ Doradus stars using gravito-inertial dipole modes and spectroscopy