  This research studies the intricate interplay between dark and baryonic
matter within hybrid neutron stars enriched by anisotropic bosonic dark matter
halos. Our modelling, guided by the equation of state with a free parameter,
reveals diverse mass-radius correlations for these astronomical objects. A
pivotal result is the influence of dark matter characteristics - whether
condensed or dispersed - on the observable attributes of neutron stars based on
their masses. Our investigation into anisotropic models, which offer a notably
authentic representation of dark matter anisotropy, reveals a unique
low-density core halo profile, distinguishing it from alternative approaches.
Insights gleaned from galactic clusters have further refined our understanding
of the bosonic dark matter paradigm. Observational constraints derived from the
dynamics of galaxy clusters have been fundamental in defining the dark matter
particle mass to lie between 0.05 GeV and 0.5 GeV and the scattering length to
range from 0.9 fm to 3 fm. Using terrestrial Bose-Einstein condensate
experiments, we have narrowed down the properties of bosonic dark matter,
especially in the often overlooked 3 to 30 GeV mass range. Our findings fortify
the understanding of dark and baryonic matter synergies in hybrid neutron
stars, establishing a robust foundation for future astrophysical pursuits.
