We present ~0.4 resolution images of CO(3-2) and associated continuum emission from the gas-bearing debris disk around the nearby A star 49 Ceti, observed with the Atacama Large Millimeter/Submillimeter Array (ALMA). We analyze the ALMA visibilities in tandem with the broad-band spectral energy distribution to measure the radial surface density profiles of dust and gas emission from the system. The dust surface density decreases with radius between ~100 and 310 au, with a marginally significant enhancement of surface density at a radius of ~110 au. The SED requires an inner disk of small grains in addition to the outer disk of larger grains resolved by ALMA. The gas disk exhibits a surface density profile that increases with radius, contrary to most previous spatially resolved observations of circumstellar gas disks. While ~80% of the CO flux is well described by an axisymmetric power-law disk in Keplerian rotation about the central star, residuals at ~20% of the peak flux exhibit a departure from axisymmetry suggestive of spiral arms or a warp in the gas disk. The radial extent of the gas disk (~220 au) is smaller than that of the dust disk (~300 au), consistent with recent observations of other gas-bearing debris disks. While there are so far only three broad debris disks with well characterized radial dust profiles at millimeter wavelengths, 49 Cetis disk shows a markedly different structure from two radially resolved gas-poor debris disks, implying that the physical processes generating and sculpting the gas and dust are fundamentally different.
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