Evolution of the near-core rotation frequency of 2,497 intermediate-mass stars from their dominant gravito-inertial mode

We combined Gaia DR3 and TESS photometric light curves to estimate the internal physical properties of 2,497 gravity-mode pulsators. We relied on asteroseismic properties of Kepler $\gamma\,$Dor and SPB stars to derive the near-core rotation frequency, $f_{\rm rot}$, of the Gaia-discovered pulsators from their dominant prograde dipole gravito-inertial pulsation mode. We offer a recipe based on linear regression to deduce $f_{\rm rot}$ from the dominant gravito-inertial mode frequency. It is applicable to prograde dipole modes with an amplitude above 4mmag and occurring in the sub-inertial regime. By applying it to the 2,497 pulsators, we have increased the sample of intermediate-mass dwarfs with such an asteroseismic observable by a factor of 4. We used the estimate of $f_{\rm rot}$ to deduce spin parameters between 2 and 6, while the sample's near-core rotation rates range from 0.7% to 25% of the critical Keplerian rate. We used $f_{\rm rot}$, along with the Gaia effective temperature and luminosity to deduce the (convective core) mass, radius, and evolutionary stage from grid modelling based on rotating stellar models. We derived a decline of $f_{\rm rot}$ with a factor of 2 during the main-sequence evolution for this population of field stars, which covers a mass range from 1.3M$_\odot$ to 7M$_\odot$. We found observational evidence for an increase in the radial order of excited gravity modes as the stars evolve. For 969 pulsators, we derived an upper limit of the radial differential rotation between the convective core boundary and the surface from Gaia's vbroad measurement and found values up to 5.4. Our recipe for the near-core rotation frequency from the dominant gravito-inertial mode detected in the independent Gaia and TESS light curves is easy to use, facilitates applications to large samples, and allows to map their angular momentum and evolutionary stage in the Milky Way.