This paper presents diffraction-limited 1-18 micron images of the young quadruple star system HD 98800 obtained with the W. M. Keck 10-m telescopes using speckle and adaptive optics imaging at near-IR wavelengths and direct imaging at mid-IR wavelengths. The two components of the visual binary, A and B, both themselves spectroscopic binaries, were separable at all wavelengths, allowing us to determine their stellar and circumstellar properties. Combining these observations with spectroscopic data from the literature, we derive an age of 10 Myr, masses of 0.93 and 0.64 M_sun and an inclination angle of 58 deg for the spectroscopic components of HD 98800 B, and an age of 10 Myr and a mass of 1.1 M_sun for HD 98800 Aa. Our data confirm that the large mid-IR excess is entirely associated with HD 98800 B. This excess exhibits a black body temperature of 150 K and a strong 10 micron silicate emission feature. The theoretical equilibrium radius of large, perfectly absorbing, 150 K grains around HD 98800 B is 2.4 AU, suggesting a circum-spectroscopic binary distribution. Our observations set important upper limits on the size of the inner dust radius of ~2 AU (mid-IR data) and on the quantity of scattered light of <10% (H-band data). For an inner radius of 2 AU, the dust distribution must have a height of at least 1 AU to account for the fractional dust luminosity of ~20% L_B. Based on the scattered light limit, the dust grains responsible for the excess emission must have an albedo of <0.33. The presence of the prominent silicate emission feature at 10 microns implies dust grain radii of >2 microns. The total mass of the dust, located in a circumbinary disk around the HD 98800 B, is >0.002 M_earth. The orbital dynamics of the A-B pair are likely responsible for the disk geometry.
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