We present observations of the HD 15115 debris disk from ALMA at 1.3 mm that capture this intriguing system with the highest resolution ($0.!!^{primeprime}6$ or $29$ AU) at millimeter wavelengths to date. This new ALMA image shows evidence for two rings in the disk separated by a cleared gap. By fitting models directly to the observed visibilities within a MCMC framework, we are able to characterize the millimeter continuum emission and place robust constraints on the disk structure and geometry. In the best-fit model of a power law disk with a Gaussian gap, the disk inner and outer edges are at $43.9pm5.8$ AU ($0.!!^{primeprime}89pm0.!!^{primeprime}12$) and $92.2pm2.4$ AU ($1.!!^{primeprime}88pm0.!!^{primeprime}49$), respectively, with a gap located at $58.9pm4.5$~AU ($1.!!^{primeprime}2pm0.!!^{primeprime}10$) with a fractional depth of $0.88pm0.10$ and a width of $13.8pm5.6$ AU ($0.!!^{primeprime}28pm0.!!^{primeprime}11$). Since we do not see any evidence at millimeter wavelengths for the dramatic east-west asymmetry seen in scattered light, we conclude that this feature most likely results from a mechanism that only affects small grains. Using dynamical modeling and our constraints on the gap properties, we are able to estimate a mass for the possible planet sculpting the gap to be $0.16pm0.06$ $M_text{Jup}$.
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