  We explore the presence of self-interacting bosonic dark matter (DM) within
neutron stars (NSs) in light of the latest mass-radius measurements of the
Neutron Star Interior Composition Explorer (NICER). The bosonic DM is
distributed as a core inside the NS or as a halo around it leading to formation
of a DM admixed NS. We focus on the evolution of the visible and dark radius of
the mixed object due to DM model parameters and fractions. It is shown that DM
core formation reduces the visible radius and the total mass pushing them below
observational limits while halo formation is in favor of the latest mass-radius
observations. Applying joint multi-messenger constraints for the radius and
maximum mass, we scan over parameter space of the bosonic DM model. It turns
out that the maximum mass limit provides a more stringent constraint compare to
the radius one. Our investigation allows for the exclusion of a large portion
of DM fractions for sub-GeV bosons and limited the amount of accumulated DM to
be less than $\sim4\%$ for the mass range $m_{\chi}\gtrsim200$ MeV at the
strong coupling regime $\lambda=\pi$. In this paper, we introduce main features
of the pulse profile corresponding to the DM admixed NS as a novel observable
quantity. We find that the depth of minimum fluxes in the pulse profiles
crucially depend on the amount of DM around NS and its compactness. The
current/future astrophysics missions can test the possibility of the existence
of DM within NSs and break the degeneracies between different scenarios.

High Energy Astrophysical Phenomena;Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology