BGM FASt: Besançon Galaxy Model for Big Data. Simultaneous inference of the IMF, SFH and density in the Solar Neighbourhood

Abstract

We develop a new theoretical framework to generate Besançon Galaxy Model fast approximate simulations (BGM FASt) to address fundamental questions of the Galactic structure and evolution performing multi-parameter inference. As a first application of our strategy we simultaneously infer the IMF, the star formation history and the stellar mass density in the Solar Neighbourhood. The BGM FASt strategy is based on a reweighing scheme, that uses a specific pre-sampled simulation, and on the assumption that the distribution function of the generated stars in the Galaxy can be described by an analytical expression. To validate BGM FASt we execute a set of tests. Finally, we use BGM FASt with an approximate Bayesian computation algorithm to obtain the posterior PDF of the inferred parameters, by comparing synthetic versus Tycho-2 colour-magnitude diagrams. Results: The validation shows a very good agreement between BGM FASt and the standard BGM, with BGM FASt being $\approx 10^4$ times faster. By analysing Tycho-2 data we obtain a thin disc star formation history decreasing in time and a present rate of $1.2\pm 0.2M_{\odot }/yr$. The resulting total stellar mass density in the Solar Neighbourhood is $0.051_{-0.005}^{+0.002}{M}_{\odot }/p{c}^3$ and the local dark matter density is $0.012\pm 0.001M_{\odot }/p{c}^3$. For the composite IMF we obtain a slope of ${\alpha }_2={2.1}_{-0.3}^{+0.1}$ in the mass range between $0.5M_{\odot }$ and $1.53M_{\odot }$. The results of the slope at the high mass range are trustable up to $4M_{\odot }$ and highly depend on the choice of the extinction map (obtaining ${\alpha }_3={2.9}_{-0.2}^{+0.2}$ and ${\alpha }_3={3.7}_{-0.2}^{+0.2}$ respectively, for two different extinction maps). Systematic uncertainties are not included. Conclusions: The good performance of BGM FASt demonstrates that it is a very valuable tool to perform multi-parameter inference using Gaia data releases.

Accepted for publication by A&A. 30 pages (23 pages of main body and 7 pages of Appendixes) , 15 figures and 4 tables