Minimum-entropy constraints on galactic potentials

TL;DR

This paper introduces a novel method to constrain galactic gravitational potentials by minimizing the entropy of tracer samples, avoiding detailed modeling of the distribution function, and demonstrates its effectiveness with simulated data.

Contribution

The authors develop an entropy minimization technique to infer gravitational potential parameters without modeling the distribution function, applicable to various integrals of motion.

Findings

Method accurately recovers potential parameters for spherical and axisymmetric models.

Successfully estimates the flattening parameter with 5-10% uncertainty using simulated data.

Provides publicly available Python module for entropy estimation.

Abstract

A tracer sample in a gravitational potential, starting from a generic initial condition, phase-mixes towards a stationary state. This evolution is accompanied by an entropy increase, and the final state is characterized by a distribution function (DF) that depends only on integrals of motion (Jeans' theorem). We present a method to constrain a gravitational potential assuming a stationary (phase mixed) sample by minimizing the entropy the sample would have if it were allowed to phase-mix in trial potentials. This method avoids modeling the DF, and is applicable to any sets of integrals. We provide expressions for the entropy of DFs depending on energy, $f(E)$, energy and angular momentum, $f(E,L)$, or three actions, $f(\vec{J})$, and investigate the bias and statistical uncertainties in their estimates. We show that the method correctly recovers the parameters for spherical and axisymmetric potentials. We also present a methodology to characterize the posterior probability distribution of the parameters with an Approximate Bayesian Computation, indicating a pathway for application to observational data. Using $10^4$ tracers with $10\% (20\%)$-uncertainties in the 6D coordinates, we recover the flattening parameter $q$ of an axisymmetric potential with $\sigma_q/q\sim 5\% (10\%)$. The python module for the entropy estimators, \texttt{tropygal}, is made publicly available.