Probing dark gauge boson with observations from neutron stars

We present an investigation on the production of light dark gauge bosons by the nucleon bremsstrahlung processes in the core of neutron stars. The dark vector is assumed to be a $U(1)_{B-L}$ gauge boson with a mass much below keV. We calculate the emission rate of the dark vector produced by the nucleon bremsstrahlung in the degenerate nuclear matter. In addition, we take into account the photon-dark vector conversion for the photon luminosity observed at infinity. Combining with the observation of J1856 surface luminosity, we find that a recently discovered excess of J1856 hard x-ray emission in the 2-8 keV energy range by XMM-Newton and Chandra x-ray telescopes could be consistently explained by a dark vector with gauge coupling $e^{\prime}=5.56\times 10^{-15}$, mixing angle $\varepsilon=1.29\times 10^{-9}$, and mass $m_{\gamma^{\prime}}\lesssim 10^{-5}$ eV. We also show that the mixing angle $\varepsilon > 7.97 \times 10^{-9}$ for $m_{\gamma^{\prime}} \lesssim 3 \times 10^{-5}~\rm eV$ and the gauge coupling $e^{\prime} > 4.13 \times 10^{-13}$ for $m_{\gamma^{\prime}} \lesssim 1~\rm keV$ have been excluded at 95% confidence level by the J1856 surface luminosity observation. Our best-fit dark vector model satisfies the current limits on hard x-ray intensities from the Swift and INTEGRAL hard x-ray surveys. Future hard x-ray experiments such as NuSTAR may give a further test on our model.