Galactic Archaeology with asteroseismic ages. II. Confirmation of a
  delayed gas infall using Bayesian analysis based on MCMC methods
  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. We aim at constraining 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. In the
revised two-infall chemical evolution models by Spitoni et al. (2019), a
significant delay of $\sim 4.3$ Gyr has been invoked between the two episodes
of gas accretion. In this work, we wish to test its robustness and
statistically confirm/quantify the delay. For the first time, a Bayesian
framework based on Markov Chain Monte Carlo methods has been used for fitting
the two-infall chemical evolution models to the data. 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 found 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. The results suggest that the APOKASC sample carries the signature of
delayed gas-rich merger, with the dilution as main process determining the
shape of low-$\alpha$ stars in the abundance ratios space.
