FN Tau is a rare example of a very low-mass T Tauri star that exhibits a spatially resolved nebulosity in near-infrared scattering light. To directly derive the parameters of a circumstellar disk around FN Tau, observations of dust continuum emission at 340 GHz are carried out with the Submillimeter Array (SMA). A point-like dust continuum emission was detected with a synthesized beam of ~07 in FWHM. From the analysis of the visibility plot, the radius of the emission is estimated to be ≤029, corresponding to 41 AU. This is much smaller than the radius of the nebulosity, 185 for its brighter part at 1.6 μm. The 340 GHz continuum emission observed with the SMA and the photometric data at λ ≤ 70 μm are explained by a power-law disk model whose outer radius and mass are 41 AU and (0.24-5.9) × 10–3 M ☉, respectively, if the exponent of dust mass opacity (β) is assumed to be 0-2. The disk model cannot fully reproduce the flux density at 230 GHz obtained with the IRAM 30 m telescope, suggesting that there is another extended "halo" component that is missed in the SMA observations. By requiring the halo not to be detected with the SMA, the lower limit to the size of the halo is evaluated to be between 174 AU and 574 AU, depending on the assumed β value. This size is comparable to the near-infrared nebulosity, implying that the halo unseen with the SMA corresponds to the origin of the near-infrared nebulosity. The halo can contain mass comparable to or at most 8 times greater than that of the inner power-law disk, but its surface density should be lower than that at the outer edge of the power-law disk by more than 1 order of magnitude. The physical nature of the halo is unclear, but it may be the periphery of a flared circumstellar disk that is not described well in terms of a power-law disk model, or a remnant of a protostellar envelope having flattened structure.
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