ALMA Reveals an Eccentricity Gradient in the Fomalhaut Debris Disk

Abstract: We present evidence of a negative eccentricity gradient in the debris disk of the nearby A-type main sequence star, Fomalhaut. Fitting to the high-resolution, archival ALMA 1.32 mm continuum data for Fomalhaut (with a synthesised angular resolution of $0.76{\times}0.55''$; 4-6\,au), we present a model that describes the bulk properties of the disk (semi-major axis, width, and geometry) and its asymmetric morphology. The best-fit model incorporates a forced eccentricity gradient that varies with semi-major axis, $e_f\propto a^{n_\mathrm{pow}}$, a generalized form of the parametric models of Lynch & Lovell 2022, with $n_\mathrm{pow}{=}{-1.75}{\pm}0.16$. We show that this model is statistically preferred to models with constant forced and free eccentricities. In comparison to disk models with constant forced eccentricities, negative eccentricity gradient models broaden disk widths at pericenter versus apocenter, and increase disk surface densities at apocenter versus pericenter, both of which are seen in the Fomalhaut disk, and which we collectively term Eccentric Velocity Divergence. We propose single-planet architectures consistent with the model and investigate the stability of the disk over 440 Myr to planet-disk interactions via N-body modeling. We find that Fomalhaut's ring eccentricity plausibly formed during the protoplanetary disk stage, with subsequent planet-disk interactions responsible for carving the disk morphology.