Balmer and Paschen continuum emission as well as Balmer series lines of P Cygni-type profile from H_gamma through H_23 are revealed in the violet spectra of BM Gem, a carbon star associated with an oxygen-rich circumstellar shell (`silicate carbon star) observed with the high dispersion spectrograph (HDS) on the Subaru telescope. The blue-shifted absorption in the Balmer lines indicates the presence of an outflow, the line of sight velocity of which is at least 400 km s^-1, which is the highest outflow velocity observed to date in a carbon star. We argue that the observed unusual features in BM Gem are strong evidence for the presence of a companion, which should form an accretion disk that gives rise to both an ionized gas region and a high velocity, variable outflow. The estimated luminosity of ~0.2 (0.03-0.6) L_sun for the ionized gas can be maintained by a mass accretion rate to a dwarf companion of ~10^-8 M_sun yr^-1, while ~10^-10 M_sun yr^-1 is sufficient for accretion to a white dwarf companion. These accretion rates are feasible for some detached binary configurations on the basis of the Bond-Hoyle type accretion process. We concluded that the carbon star BM Gem is in a detached binary system with a companion of low mass and low luminosity. However, we are unable to determine whether this companion object is a dwarf or a white dwarf. The upper limits for binary separation are 210 AU and 930 AU for a dwarf and a white dwarf, respectively. We also note that the observed features of BM Gem mimic those of Mira (omi Cet), which may suggest actual similarities in their binary configurations and circumstellar structures.
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