Title: Improved bounds on the bosonic dark matter with pulsars in the Milky Way

Abstract: Neutron stars (NSs) can be used to constrain dark matter (DM) since a NS can transform into a black hole (BH) if it captures sufficient DM particles and exceeds the Chandrasekhar limit. We extend earlier work and for the first time take into account the Galactic motion of individual NSs, which changes the amount of the captured DM by as large as one to two orders of magnitude. We systematically apply the analysis to 413 NSs in the Milky Way, and constrain the DM particle mass and its interaction with nucleon simultaneously. We find that the most stringent bound is placed by a few NSs and the bound becomes stronger after considering the Galactic motion. The survival of observed NSs already excludes a cross section $\sigma_{nX}\gtrsim 10^{-45} \, {\rm cm}^2$ for DM particles with mass from $100\, {\rm MeV}$ to $10^3 \, {\rm GeV}$. Especially for a mass around $10 \, {\rm GeV}$, the constraint on the cross section is as stringent as $\sigma_{nX}\lesssim 10^{-49} \, {\rm cm}^2$.