标题： 矢量暗物质晕：从极化动力学到直接探测 显示英文标题

标题： Vector Dark Matter Halo: From Polarization Dynamics to Direct Detection

摘要： 本研究探讨了矢量暗物质（VDM）在星系外晕中的特征极化形成和演化。 通过数值模拟，我们分析了VDM在不同初始条件下的行为——均匀、各向同性和部分极化。 模拟求解薛定谔-泊松方程，研究自旋密度分布及其在引力坍缩和晕形成过程中的演化。 我们的结果表明，VDM在均匀和各向同性条件下形成晕和中心Proca星，极化密度波动幅度与VDM物质密度相匹配。 在没有初始极化的场景中，自旋密度在晕核心保持稳定，但在外部区域发生波动。 部分极化的初始条件导致总极化保持守恒，核心极化增加会导致外围出现相反的极化。 我们研究了部分极化状态对暗光子直接探测的新后果，即与普通光子动力学混合的VDM。 显示英文摘要

摘要： This study investigates the characteristic polarization formation and evolution of vector dark matter (VDM) in the outer halo of galaxies. By employing numerical simulations, we analyze the behavior of VDM under different initial conditions -- homogeneous, isotropic, and partially polarized. The simulations solve the Schr\"odinger-Poisson equations, examining the spin density distribution and its evolution during gravitational collapse and halo formation. Our results reveal that VDM forms halos and central Proca stars from homogeneous and isotropic conditions, with the polarization density fluctuation amplitude mirroring VDM matter density. In scenarios with no initial polarization, spin density remains stable in the halo core but fluctuates in outer regions. Partially polarized initial conditions lead to a conservation of total polarization, with increased core polarization resulting in opposite polarization in the periphery. We examine the novel consequences of the partially polarized state for direct detection of dark photons, i.e., VDM kinetically mixed with ordinary photons.