Galactic archaeology with asteroseismic ages II. Confirmation of a delayed gas infall using Bayesian analysis based on MCMC methods

Context. With the wealth of information from large surveys and observational campaigns in the contemporary era, it is critical to properly exploit the data to constrain the parameters of Galactic chemical evolution models and quantify the associated uncertainties. Aims. We aim to constrain the two-infall chemical evolution models for the solar annulus using the measured chemical abundance ratios and seismically inferred age of stars in the APOKASC sample. Recently, in revised two-infall chemical evolution models, a significant delay of similar to 4.3 Gyr has been invoked between the two episodes of gas accretion. In this work, we wish to test its robustness and statistically confirm and quantify the delay. Methods. We took a novel approach, using Bayesian framework based on Markov chain Monte Carlo methods to fit the two-infall chemical evolution models to the data. Results. In addition to fitting the data for stars in the APOKASC sample, our best fit models also reproduce other important observational constraints of the chemical evolution of the disk: i) present day stellar surface density; ii) present-day supernova and star formation rates; iii) the metallicity distribution function; and iv) solar abundance values. We find a significant delay between the two gas accretion episodes for various models explored with different values for the star formation efficiencies. The values for the delay lie in the range 4.5-5.5 Gyr. Conclusions. The results suggest that the APOKASC sample carries the signature of a delayed gas-rich merger, with dilution being the main process determining the shape of low-alpha stars in the abundance ratios space.