Charting galactic accelerations II: how to 'learn' accelerations in the solar neighbourhood

Abstract

Gravitational acceleration fields can be deduced from the collisionless Boltzmann equation, once the distribution function is known. This can be constructed via the method of normalizing flows from datasets of the positions and velocities of stars. Here, we consider application of this technique to the solar neighbourhood. We construct mock data from a linear superposition of multiple 'quasi-isothermal' distribution functions, representing stellar populations in the equilibrium Milky Way disc. We show that given a mock dataset comprising a million stars within 1 kpc of the Sun, the underlying acceleration field can be measured with excellent, sub-percent level accuracy, even in the face of realistic errors and missing line-of-sight velocities. The effects of disequilibrium can lead to bias in the inferred acceleration field. This can be diagnosed by the presence of a phase space spiral, which can be extracted simply and cleanly from the learned distribution function. We carry out a comparison with two other popular methods of finding the local acceleration field (Jeans analysis and 1D distribution function fitting). We show our method most accurately measures accelerations from a given mock dataset, particularly in the presence of disequilibria.

Measuring Galactic Dark Matter through Unsupervised Machine Learning

“…As pointed out in Ref. [60][61][62], as Φ is a function of x only, multiple velocities sampled from p( v| x) at the same x must obey the Boltzmann Equation given the same acceleration a ≡ −∂Φ/∂ x.…”

“…Ref. [62] simulated 10 6 stars within 1 kpc of the Solar location, to be compared with the ∼ 8, 000 stars inside that radius in our dataset. In addition, due to the dominance of disk stars, our dataset is very sparse at higher values of |z|.…”

“…[60] and elaborated in Refs. [61,62]. This method uses the Boltzmann Equation directly, leveraging new machine learning techniques which can accurately estimate high-dimension phase space directly from data.…”

“…Using one million mock stars within 1 kpc of the Sun, drawn from an analytic model of the Milky Way, Ref. [62] further demonstrated that this approach can reconstruct the gravitational acceleration field with high fidelity, even in the presence of realistic measurement errors.…”

“…In this paper, we extend the approach of Refs. [60][61][62] in two important ways. First, we demonstrate for the first time that the numeric solutions for the derivatives of Φ from phase-space density estimators can be extended to the second derivative, and thus the total mass density can be extracted directly from the density estimator.…”