  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 utilise 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
$\tau\approx(6.9\pm0.3)\,\mathrm{Gyr}(1+\tanh((330\,\mathrm{d}-P)/(400\pm90)\mathrm{d})$.
Our results compare well with previous calibrations using smaller datasets as
well as the period-age properties of Local Group cluster members. This
calibration opens the possibility of accurately characterising the star
formation and the impact of different evolutionary processes throughout the
Local Group.
