Improved Treatment of Bosonic Dark Matter Dynamics in Neutron Stars: Consequences and Constraints

It is conceivable that a bosonic dark matter (DM) with non-gravitational interactions with SM particles will be accumulated at the center of a neutron star (NS) and can lead to black hole formation. In contrast to previous works with a fixed NS temperature, we dynamically determine the formation of Bose-Einstein condensate (BEC) for a given set of DM parameters, namely the DM-neutron scattering cross-section (σχ n), the thermal average of DM annihilation cross-section (σ v) and the DM mass (m_χ). For both non-annihilating and annihilating DM with σ v ≤ 10⁻²⁶~ cm³~ s⁻¹, the BEC forms for m_χ 10 ~ TeV. In case of non-annihilating DM, observations of old NS allow σχ n 10⁻⁵²~ cm² for 10 ~ MeV ≤ mχ 10 ~ GeV (with BEC) and σχ n 10⁻⁴⁷~ cm² for 5 ~ TeV m_χ 30 ~ PeV (without BEC). This analysis shows the mass window, 10 ~ GeV m_χ 5 ~ TeV unconstrained, subject only to direct detection experiments. In the annihilating DM scenario, the exclusion limits on DM parameters become weaker and even vanish for typical WIMP annihilation cross-section. However, the late-time heating of the NS enables us to probe the region with σχ n 10⁻⁴⁷~ cm², using the James Webb Space Telescope in the foreseeable future. When our results are viewed in the context of indirect searches of DM, it provides a lower limit on the σ v, which is sensitive to the DM thermal state.