SIMBAD references

Empirical and theoretical studies have demonstrated that the periods of Mira variable stars are related to their ages. This, together with their brightness in the infrared, makes them powerful probes of the formation and evolution of highly-extincted or distant parts of the Local Group. Here we utilize the Gaia DR3 catalogue of long-period variable candidates to calibrate the period-age relation of the Mira variables. Dynamical models are fitted to the O-rich Mira variable population across the extended solar neighbourhood and then the resulting solar neighbourhood period-kinematic relations are compared to external calibrations of the age-kinematic relations to derive a Mira variable period-age relation of $\tau \approx (6.9\pm 0.3)\, \mathrm{Gyr}(1+\tanh ((330\, \mathrm{d}-P)/(400\pm 90)\mathrm{d})$. Our results compare well with previous calibrations using smaller data sets as well as the period-age properties of Local Group cluster members. This calibration opens the possibility of accurately characterizing the star formation and the impact of different evolutionary processes throughout the Local Group.