[Paper Review] BGM FASt: Besan\c{c}on Galaxy Model for Big Data. Simultaneous inference of the IMF, SFH and density in the Solar Neighbourhood

R. Mor, A. C. Robin+2 more|arXiv (Cornell University)|Sep 10, 2018

Stellar, planetary, and galactic studies57 references11 citations

TL;DR

This paper introduces BGM FASt, a fast, scalable framework based on the Besançon Galaxy Model that enables simultaneous multi-parameter inference of the initial mass function (IMF), star formation history (SFH), and stellar density in the solar neighbourhood using approximate Bayesian computation (ABC). Leveraging pre-sampled simulations and a reweighting scheme, BGM FASt achieves ~10⁴ speedup over standard BGM while accurately reproducing key observables like colour-magnitude diagrams, yielding a thin-disc SFH decreasing over time, a present-day star formation rate of 1.2±0.2 M⊙/yr, a total stellar mass density of 0.051+0.002−0.005 M⊙/pc³, and a composite IMF slope of α₂=2.1+0.1−0.3 between 0.5 and 1.53 M⊙.

ABSTRACT

We develop a new theoretical framework to generate Besan\c{c}on 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 $1.2 \pm 0.2 M_\odot/yr$. The resulting total stellar mass density in the Solar Neighbourhood is $0.051_{-0.005}^{+0.002} M_\odot/pc^3$ and the local dark matter density is $0.012 \pm 0.001 M_\odot/pc^3$. For the composite IMF we obtain a slope of $\alpha_2={2.1}_{-0.3}^{+0.1}$ in the mass range between $0.5 M_\odot$ 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.

Motivation & Objective

• To address the computational bottleneck of traditional Milky Way modelling when exploring large parameter spaces with modern Bayesian inference.
• To develop a fast, scalable simulation framework compatible with big data platforms like Apache Spark and Hadoop for handling large surveys such as Gaia.
• To enable simultaneous inference of multiple fundamental Galactic parameters—IMF, SFH, and stellar mass density—using observational data from Tycho-2.
• To validate the performance of the new framework against standard BGM simulations while maintaining dynamical consistency.
• To demonstrate the framework's utility in constraining the local IMF, SFH, and density using real photometric and astrometric data.

Proposed method

• The BGM FASt framework uses a pre-sampled simulation (Mother Simulation) based on the standard Besançon Galaxy Model (BGM Std) as a foundation.
• It applies a reweighting scheme to adjust the simulated stellar populations according to new parameter values (e.g., IMF, SFH, density laws) without re-running the full simulation.
• The method assumes that the distribution function of stars in the Galaxy can be described by an analytical expression, enabling efficient parameter space exploration.
• It integrates with the Approximate Bayesian Computation (ABC) algorithm to compare synthetic colour-magnitude diagrams (CMDs) with observed Tycho-2 data, automating parameter inference.
• The framework is implemented on Apache Spark and Hadoop, enabling distributed, high-performance computation on big data infrastructures like the Gaia Data Analytics Framework (GDAF).
• Dynamical consistency is preserved by ensuring local dynamical statistical equilibrium (LDSE) is maintained via analytical constraints, validated against full BGM Std simulations.

Experimental results

Research questions

• RQ1 Can a fast, scalable simulation framework be developed to enable efficient multi-parameter inference of Galactic parameters using large survey data?
• RQ2 How accurately can BGM FASt reproduce key observables like CMDs and stellar distributions compared to the standard BGM?
• RQ3 What are the inferred values of the initial mass function (IMF), star formation history (SFH), and stellar mass density in the solar neighbourhood using Tycho-2 data?
• RQ4 How do systematic uncertainties—particularly from extinction maps—affect the inferred IMF slope at high masses?
• RQ5 To what extent can the framework be extended to include non-parametric SFHs, metallicity-dependent IMFs, or time-evolving disc structures?

Key findings

• BGM FASt achieves a ~10⁴ speedup over the standard BGM code while maintaining excellent agreement in simulated colour-magnitude diagrams and stellar distributions.
• The inferred star formation history in the solar neighbourhood shows a decreasing trend over time, with a current star formation rate of 1.2±0.2 M⊙/yr.
• The total stellar mass density in the solar neighbourhood is 0.051+0.002−0.005 M⊙/pc³, and the local dark matter density is 0.012±0.001 M⊙/pc³.
• For the composite IMF, the slope in the 0.5–1.53 M⊙ range is α₂=2.1+0.1−0.3, consistent with a Salpeter-like slope.
• The IMF slope at high masses (4 M⊙) is highly sensitive to the extinction map: α₃=3.7+0.2−0.2 with the Drimmel map and α₃=2.9+0.2−0.2 with the Stilism map, both rejecting a Salpeter slope at ~3σ.
• The radial scale length of the thin disc is poorly constrained (e.g., 2151+421−247 pc with Stilism map), and the SFH shape is degenerate with the choice of extinction map, though the current star formation rate remains robust.