Upper Limit on the Size of Galactic Halo via Hamiltonian Approach

TL;DR

This paper estimates the maximum size of galactic halos using Hamiltonian dynamical systems, finding that the halo size depends on the sign of a parameter in Weyl gravity and can be constrained by stability of circular orbits.

Contribution

It introduces a Hamiltonian approach to determine the upper limit of galactic halo sizes, incorporating Weyl gravity and stability analysis of orbits.

Findings

Negative halo parameter $\gamma$ yields stable halo sizes within the de Sitter radius.

Positive $\gamma$ results in halo size estimates exceeding the de Sitter radius.

The method provides a new way to constrain galactic halo sizes based on stability criteria.

Abstract

Using the approach of autonomous Hamiltonian dynamical system, we attempt to estimate the as yet unknown upper limit on the size of the galactic halo surrounding galaxies (lenses). The key to determine the size of the halo is to determine the maximum radius up to which stable material circular orbits are admissible. We shall illustrate the approach by considering a solution of the Weyl gravity containing a halo parameter $\gamma$. The upper limit for several observed lenses are calculated for a typical value of $gamma$ for definiteness, with and without the cosmological constant $\Lambda $. These lenses (all having Einstein radius $R_{\text{E}}\approx 10^{23}$ cm) consistently yield an upper limit $R_{\text{max}}^{\text{stable}}$($\simeq 4.25\times 10^{27}$ cm) inside the de Sitter radius only when $\gamma$ is \textit{negative}, while a positive $\gamma$ yields $R_{\text{max}}^{\text{% stable}}$ always exceeding the de Sitter radius.