  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.
