Towards a fully consistent Milky Way disk model V. The disk model for 4-14 kpc

Context. The semi-analytic Just-Jahreiss (JJ) model of the Galactic disk is a flexible tool for stellar population synthesis with a fine age resolution of 25 Myr. The model has recently been calibrated in the solar neighbourhood against the Gaia DR2 stars. We have identified two star-formation bursts within the last similar to 4 Gyr of the local star-formation rate (SFR) history. Aims. In this work we present a generalised version of the JJ model that incorporates our findings for the solar neighbourhood and is applicable to a wide range of galactocentric distances, 4 kpc less than or similar to R less than or similar to 14 kpc. Methods. The JJ model includes the four flattened and two spheroidal components of the Milky Way, describing it as an axisymmetric system. The thin and thick disks, as well as atomic and molecular gas layers, are assumed to have exponential radial surface density profiles. Spherical stellar halo and dark matter in the form of a cored isothermal sphere are also added to the model. The overall thickness of the thin disk is assumed to be constant at all radii, though model realisations with a flaring disk can also be tested. The adopted radial variation in the thin-disk SFR reflects the inside-out disk growth scenario. Motivated by our findings for the solar neighbourhood, we allow a smooth power-law SFR continuum to be modified by an arbitrary number of Gaussian peaks. Additionally, the vertical kinematics of the stellar populations associated with these episodes of star-formation excess is allowed to differ from the kinematics prescribed by the age-velocity dispersion relation for the thin-disk populations of the same age. Results. We present a public code of the JJ model complemented by the three sets of isochrones generated by the stellar tracks and isochrones with the PAdova and TRieste Stellar Evolution Code (PARSEC), the Modules and Experiments in Stellar Astrophysics (MESA) Isochrones and Stellar Tracks (MIST), and a Bag of Stellar Tracks and Isochrones (BaSTI). Assuming a plausible set of parameters, we take the first step towards calibrating the JJ model at non-solar radii. Using metallicity distributions of the red clump giants from the Apache Point Observatory Galactic Evolution Experiment (APOGEE), we constrain the radial variation of the JJ-model age-metallicity relation and propose a new analytic form for the age-metallicity relation function. Conclusions. The generalised JJ model is a publicly available tool for studying different stellar populations across the Milky Way disk. With its fine age resolution and flexibility, it can be particularly useful for reconstructing the thin-disk SFR, as a variety of different SFR shapes can be constructed within its framework.