A Complete ALMA Map of the Fomalhaut Debris Disk

We present ALMA mosaic observations at 1.3 mm (223 GHz) of the Fomalhaut system with a sensitivity of 14 $\mu$Jy/beam. These observations provide the first millimeter map of the continuum dust emission from the complete outer debris disk with uniform sensitivity, enabling the first conclusive detection of apocenter glow. We adopt a MCMC modeling approach that accounts for the eccentric orbital parameters of a collection of particles within the disk. The outer belt is radially confined with an inner edge of $136.3\pm0.9$ AU and width of $13.5\pm1.8$ AU. We determine a best-fit eccentricity of $0.12\pm0.01$. Assuming a size distribution power law index of $q=3.46\pm 0.09$, we constrain the dust absorptivity power law index $\beta$ to be $0.9<\beta<1.5$. The geometry of the disk is robustly constrained with inclination $65.\!\!^\circ6\pm0.\!\!^\circ3$, position angle $337.\!\!^\circ9\pm0.\!\!^\circ3$, and argument of periastron $22.\!\!^\circ5\pm4.\!\!^\circ3$. Our observations do not confirm any of the azimuthal features found in previous imaging studies of the disk with HST, SCUBA, and ALMA. However, we cannot rule out structures $\leq10$ AU in size or which only affect smaller grains. The central star is clearly detected with a flux density of $0.75\pm0.02$ mJy, significantly lower than predicted by current photospheric models. We discuss the implications of these observations for the directly imaged Fomalhaut b and the inner dust belt detected at infrared wavelengths.