Towards a fully consistent Milky Way disk model: IV. The impact of Gaia DR2 and APOGEE

Aims. We present an updated version of the semi-analytic Just-Jahrei (JJ) model of the Galactic disk and constrain its parameters in the Solar neighbourhood.Methods. The new features of the JJ model include a simple two-component gaseous disk, a star-formation rate (SFR) function of the thick disk that has been extended in time, and a correlation between the kinematics of molecular gas and thin-disk populations. Here, we study the vertical number density profiles and W-velocity distributions determined from similar to 2x10(6) local stars of the second Gaia data release (DR2). We also investigate an apparent Hess diagram of the Gaia DR2 stars selected in a conic volume towards the Galactic poles. Using a stellar evolution library, we synthesise stellar populations with a four-slope broken power-law initial mass function, the SFR, and an age-metallicity relation. The latter is consistently derived with the observed metallicity distribution of the local Red Clump giants from the Apache Point Observatory Galactic Evolution Experiment (APOGEE). Working within a Bayesian approach, we sample the posterior probability distribution in a multidimensional parameter space using the Markov chain Monte Carlo method.Results. We find that the spatial distribution and motion of the Gaia DR2 stars imply two recent SF bursts centered at ages of similar to 0.5 Gyr and similar to 3 Gyr and characterised by a similar to 30% and similar to 55% SF enhancement, respectively, relative to a monotonously declining SFR continuum. The stellar populations associated with this SF excess are found to be dynamically hot for their age: they have W-velocity dispersions of similar to 12.5 km s(-1) and similar to 26 km s(-1). The new JJ model is able to reproduce the local star counts with an accuracy of similar to 5%.Conclusions. Using Gaia DR2 data, we self-consistently constrained 22 parameters of the updated JJ model. Our optimised model predicts two SF bursts within the last similar to 4 Gyr, which may point to recent episodes of gas infall.