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Abstract We present the first interferometric imaging of molecular line emission from the Ring Nebula, NGC 6720, in the form of Submillimeter Array (SMA) observations of COJ = 2 → 1 emission. The SMA¹²CO(2–1) mapping data, with ∼3″ spatial resolution and 2 km s⁻¹velocity resolution, provide an unprecedentedly detailed, 3D view of the Ring’s clumpy molecular envelope. The emission morphology displayed in the velocity-integrated SMA¹²CO(2–1) image closely resembles the morphologies of near-IR H₂and polycyclic aromatic hydrocarbon emission as revealed in recent JWST/NIRCam imaging of NGC 6720. The SMA¹²CO(2–1) data demonstrate that the molecular gas is found within a geometrically thin layer that immediately surrounds the ionized gas imaged by Hubble Space Telescope and JWST. A simple, geometric model of the¹²CO(2–1) emission data shows that the intrinsic structure of NGC 6720’s molecular envelope closely resembles a truncated, triaxial ellipsoid that is viewed close to pole-on, and that the dynamical age of the molecular envelope is ∼6000 yr. The SMA¹²CO(2–1) mapping data furthermore reveal that some of the faint, filamentary features seen projected in the Ring’s interior in JWST imaging are in fact fast-moving polar knots or bullets with radial velocities of ±45–50 km s⁻¹relative to the systemic velocity, and that the hot progenitor star remnant is positioned at the precise geometric center of the clumpy, ellipsoidal molecular shell. We assert that the Ring’s molecular envelope represents the “fossil” remnant of a relatively sudden mass ejection ∼6000 yr ago that terminated the progenitor star’s asymptotic giant branch (AGB) evolution, and that this ellipsoidal envelope of AGB ejecta was then punctured by fast, collimated polar outflows or jets resulting from interactions between the progenitor and one or more companion stars. Such an evolutionary scenario may describe most if not all molecule-rich, “Ring-like” planetary nebulae. 

Abstract Flare frequency distributions represent a key approach to addressing one of the largest problems in solar and stellar physics: determining the mechanism that counterintuitively heats coronae to temperatures that are orders of magnitude hotter than the corresponding photospheres. It is widely accepted that the magnetic field is responsible for the heating, but there are two competing mechanisms that could explain it: nanoflares or Alfvén waves. To date, neither can be directly observed. Nanoflares are, by definition, extremely small, but their aggregate energy release could represent a substantial heating mechanism, presuming they are sufficiently abundant. One way to test this presumption is via the flare frequency distribution, which describes how often flares of various energies occur. If the slope of the power law fitting the flare frequency distribution is above a critical threshold,α= 2 as established in prior literature, then there should be a sufficient abundance of nanoflares to explain coronal heating. We performed >600 case studies of solar flares, made possible by an unprecedented number of data analysts via three semesters of an undergraduate physics laboratory course. This allowed us to include two crucial, but nontrivial, analysis methods: preflare baseline subtraction and computation of the flare energy, which requires determining flare start and stop times. We aggregated the results of these analyses into a statistical study to determine thatα= 1.63 ± 0.03. This is below the critical threshold, suggesting that Alfvén waves are an important driver of coronal heating.