Silicate carbon stars show the 10 micron silicate emission, despite their carbon-rich photospheres. They are considered to have circumbinary or circum-companion disks, which serve as a reservoir of oxygen-rich material shed by mass loss in the past. We present N-band spectro-interferometric observations of the silicate carbon star BM Gem using MIDI at the Very Large Telescope Interferometer (VLTI). Our aim is to probe the spatial distribution of oxygen-rich dust with high spatial resolution. BM Gem was observed with VLTI/MIDI at 44--62 m baselines using the UT2-UT3 and UT3-UT4 baseline configurations. The N-band visibilities observed for BM Gem show a steep decrease from 8 to ~10 micron and a gradual increase longward of ~10 micron, reflecting the optically thin silicate emission feature emanating from sub-micron-sized amorphous silicate grains. The differential phases obtained at baselines of ~44--46 m show significant non-zero values (~ -70 degrees) in the central part of the silicate emission feature between ~9 and 11 micron, revealing a photocenter shift and the asymmetric nature of the silicate emitting region. The observed N-band visibilities and differential phases can be fairly explained by a simple geometrical model in which the unresolved star is surrounded by a ring with azimuthal brightness modulation. The best-fit model is characterized by a broad ring (~70 mas across at 10 micron) with a bright region which is offset from the unresolved star by ~20 mas at a position angle of ~280 degrees. This model can be interpreted as a system with a circum-companion disk and is consistent with the spectroscopic signatures of an accretion disk around an unseen companion recently discovered in the violet spectrum of BM Gem.
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