Dynamical tomography of gravitationally bound systems

TL;DR

This paper develops a method for inferring the dynamical properties of large gravitational systems from incomplete observational data, demonstrating uniqueness and robustness through simulations and a tomography-inspired approach.

Contribution

It introduces a novel inverse problem framework for dynamical systems, establishing solution uniqueness and proposing a new tomography-based comparison method.

Findings

Solution is unique for steady-state systems despite data limitations

Regularization and noise impact solution convergence

A tomography-like method effectively compares observed data with models

Abstract

We study the inverse problem of deducing the dynamical characteristics (such as the potential field) of large systems from kinematic observations. We show that, for a class of steady-state systems, the solution is unique even with fragmentary data, dark matter, or selection (bias) functions. Using spherically symmetric models for simulations, we investigate solution convergence and the roles of data noise and regularization in the inverse problem. We also present a method, analogous to tomography, for comparing the observed data with a model probability distribution such that the latter can be determined.