Joint inference of the Milky Way’s star formation history and initial mass function from <i>Gaia</i> all-sky <i>G</i> &lt; 13 data

Context. Despite the fundamental importance of the star formation history (SFH) and the initial mass function (IMF) in the description of the Milky Way, their consistent and robust derivation is still elusive. Recent and accurate astrometry and photometry collected by the Gaia satellite provide the natural framework to consolidate these ingredients in our local Galactic environment. Aims. We aim to simultaneously infer the IMF and the SFH of the Galactic disc by comparing Gaia data with the mock catalogue resulting from the Besançon population synthesis model (BGM). Our goal is also to estimate the impact of the systematics present in current stellar evolutionary models (SEMs) on this inference. Methods. We used a new implementation of the BGM fast approximate simulations (BGM FASt) framework to fit the seven-million-star Gaia DR3 all-sky G &lt; 13 colour–magnitude diagram (CMD) to the most up-to-date dynamically self-consistent BGM. Results. Our derived SFH supports an abrupt decrease in star formation approximately 1–1.5 Gyr ago followed by a significant enhancement with a wide plateau in the range of 2–6 Gyr ago. A remarkable hiatus appears around 5–7 Gyr ago, with a ∼ 1 Gyr shift depending on the set of stellar models. A complex evolution at ages older than 8 Gyr deserves further investigation. Precise but discrepant values using different SEMs are found for the power-law indices of the IMF. In our fiducial execution with PARSEC SEM, the slope takes a value of α 2 = 1.45 -0.12 +0.19 for the range [0.5–1.53] M ⊙ , while for masses larger than 1.53 M ⊙ we obtain α 3 = 1.98 -0.05 +0.13 Using STAREVOL SEM, the inferred values are α 2 = 2.48 -0.11 +0.09 and α 3 = 1.64 -0.02 +0.15 . We find the solution with PARSEC to have a significantly higher likelihood than that obtained with STAREVOL. Conclusions. The current implementation of the BGM FASt framework is ready to address executions fitting all-sky Gaia data up to an apparent limiting magnitude of 14–17. This will naturally allow us to derive both a reliable SFH for the early epochs of the Galactic disc evolution and a precise slope for the IMF at low masses.