We present Subaru/HiCIAO H-band high-contrast images of the debris disk around HIP 79977, whose pres- ence was recently inferred from an infrared excess. Our images resolve the disk for the first time, allowing characterization of its shape, size, and dust grain properties. We use angular differential imaging (ADI) to reveal the disk geometry in unpolarized light out to a radius of ~2, as well as polarized differential imaging (PDI) to measure the degree of scattering polarization out to ~1.5. In order to strike a favorable balance between suppression of the stellar halo and conservation of disk flux, we explore the application of principal component analysis (PCA) to both ADI and reference star subtraction. This allows accurate forward modeling of the effects of data reduction on simulated disk images, and thus direct comparison with the imaged disk. The resulting best-fit values and well-fitting intervals for the model parameters are a surface brightness power-law slope of S_out = -3.2 [-3.6,-2.9], an inclination of i = 84{deg} [81{deg},86{deg}], a high Henyey-Greenstein forward-scattering parameter of g = 0.45 [0.35, 0.60], and a non-significant disk-star offset of u = 3.0 [-1.5, 7.5] AU = 24 [-13, 61] mas along the line of nodes. Furthermore, the tangential linear polarization along the disk rises from ~10% at 0.5 to ~45% at 1.5. These measurements paint a consistent picture of a disk of dust grains produced by collisional cascades and blown out to larger radii by stellar radiation pressure.
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