The HST large programme on $\omega$ Centauri -- V. Exploring the
  Ultracool Dwarf Population with Stellar Atmosphere and Evolutionary Modelling
  Brown dwarfs can serve as both clocks and chemical tracers of the
evolutionary history of the Milky Way due to their continuous cooling and high
sensitivity of spectra to composition. We focus on brown dwarfs in globular
clusters that host some of the oldest coeval populations in the galaxy.
Currently, no brown dwarfs in globular clusters have been confirmed, but they
are expected to be uncovered with advanced observational facilities such as
JWST. In this paper we present a new set of stellar models specifically
designed to investigate low-mass stars and brown dwarfs in $\omega$ Centauri --
the largest known globular cluster. The parameters of our models were derived
from iterative fits to HST photometry of the Main Sequence members of the
cluster. Despite the complex distribution of abundances and the presence of
multiple Main Sequences in $\omega$ Centauri, we find that the modal
colour-magnitude distribution can be represented by a single stellar population
with parameters determined in this study. The observed luminosity function is
well-represented by two distinct stellar populations having solar and enhanced
helium mass fractions and a common initial mass function, in agreement with
previous studies. Our analysis confirms that the abundances of individual
chemical elements play a key role in determining the physical properties of
low-mass cluster members. We use our models to draw predictions of brown dwarf
colours and magnitudes in anticipated JWST NIRCam data, confirming that the
beginning of the substellar sequence should be detected in $\omega$ Centauri in
forthcoming observations.
