Weak spectral features in BL Lacertae objects (BL Lac) often provide a unique opportunity to probe the inner region of this rare type of active galactic nucleus. We present a Hubble Space Telescope/Cosmic Origins Spectrograph observation of the BL Lac H 2356-309. A weak Ly$alpha$ emission line was detected. This is the fourth detection of a weak Ly$alpha$ emission feature in the ultraviolet (UV) band in the so-called high energy peaked BL Lacs, after Stocke et al. Assuming the line-emitting gas is located in the broad line region (BLR) and the ionizing source is the off-axis jet emission, we constrain the Lorentz factor ($Gamma$) of the relativistic jet to be $geq 8.1$ with a maximum viewing angle of 3.6$^circ$. The derived $Gamma$ is somewhat larger than previous measurements of $Gamma approx 3 - 5$, implying a covering factor of $sim$ 3% of the line-emitting gas. Alternatively, the BLR clouds could be optically thin, in which case we constrain the BLR warm gas to be $sim 10^{-5}rm M_{odot}$. We also detected two HI and one OVI absorption lines that are within $|Delta v| < 150rm km s^{-1}$ of the BL Lac object. The OVI and one of the HI absorbers likely coexist due to their nearly identical velocities. We discuss several ionization models and find a photoionization model where the ionizing photon source is the BL Lac object can fit the observed ion column densities with reasonable physical parameters. This absorber can either be located in the interstellar medium of the host galaxy, or in the BLR.
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