A tree algorithm reduces multi-component coagulation complexity from O(N^{2d}) to O(d N^d log N) by grouping similar interactions and matches direct-method results in tests with analytic solutions.
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abstract
We present Atacama Large Millimeter/submillimeter Array (ALMA) observations from the 2014 Long Baseline Campaign in dust continuum and spectral line emission from the HL Tau region. The continuum images at wavelengths of 2.9, 1.3, and 0.87 mm have unprecedented angular resolutions of 0.075 arcseconds (10 AU) to 0.025 arcseconds (3.5 AU), revealing an astonishing level of detail in the circumstellar disk surrounding the young solar analogue HL Tau, with a pattern of bright and dark rings observed at all wavelengths. By fitting ellipses to the most distinct rings, we measure precise values for the disk inclination (46.72pm0.05 degrees) and position angle (+138.02pm0.07 degrees). We obtain a high-fidelity image of the 1.0 mm spectral index ($\alpha$), which ranges from $\alpha\sim2.0$ in the optically-thick central peak and two brightest rings, increasing to 2.3-3.0 in the dark rings. The dark rings are not devoid of emission, we estimate a grain emissivity index of 0.8 for the innermost dark ring and lower for subsequent dark rings, consistent with some degree of grain growth and evolution. Additional clues that the rings arise from planet formation include an increase in their central offsets with radius and the presence of numerous orbital resonances. At a resolution of 35 AU, we resolve the molecular component of the disk in HCO+ (1-0) which exhibits a pattern over LSR velocities from 2-12 km/s consistent with Keplerian motion around a ~1.3 solar mass star, although complicated by absorption at low blue-shifted velocities. We also serendipitously detect and resolve the nearby protostars XZ Tau (A/B) and LkHa358 at 2.9 mm.
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representative citing papers
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