The \textit{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 \textit{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 \textit{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 \textit{JWST} \textit{NIRCam} data, confirming that the beginning of the substellar sequence should be detected in $\omega$\,Centauri in forthcoming observations.