Estimating the age–metallicity distribution of a stellar sample from the probability distributions of the individual stars

Estimating age distributions, or star formation histories, of stellar populations in the Milky Way is important in order to study the evolution of trends in elemental abundances and kinematics. We build on previous work to develop an algorithm for estimating the age-metallicity distribution which uses the full age-metallicity probability density functions (PDFs) of individual stars. No assumptions are made about the shape of the underlying distribution, and the only free parameter of the algorithm is used to ensure a smooth solution. In this work, we use individual age-metallicity PDFs from isochrone fitting of stars with known metallicities. The method is tested with synthetic samples and is found to recover the input age-metallicity distribution more accurately than the distribution of individually estimated ages and metallicities. The recovered sample age distribution (SAD) is always more accurate than the distribution of individual ages, also when restricted to the most precise individual ages. By applying the method to the stars in the Geneva-Copenhagen survey, we detect a possible minimum in the star formation history of the Solar neighbourhood at an age of 10 Gyr which is not seen in the distribution of individual ages. Although we apply the method only to age-metallicity distributions, the algorithm is described more generally and can in principle be applied in other parameter spaces. It is also not restricted to individual parameter distributions from isochrone fitting, meaning that an SAD can be estimated based on individual age PDFs from other methods such as asteroseismology or gyrochronology.