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At least two active plumes were observed on Neptune's moon Triton during the Voyager 2 flyby in 1989. Models for Triton's plumes have previously been grouped into five hypotheses, two of which are primarily atmospheric phenomena and are generally considered unlikely, and three of which include eruptive processes and are plausible. These hypotheses are compared, including new arguments, such as comparisons based on current understanding of Mars, Enceladus, and Pluto. An eruption model based on a solar-powered, solid-state greenhouse effect was previously considered the leading hypothesis for Triton's plumes, in part due to the proximity of the plumes to the subsolar latitude during the Voyager 2 flyby and the distribution of Triton's fans that are putatively deposits from former plumes. The other two eruption hypotheses are powered by internal heat, not solar insolation. Based on new analyses of the ostensible relation between the latitude of the subsolar point on Triton and the geographic locations of the plumes and fans, we argue that neither the locations of the plumes nor fans are strong evidence in favor of the solar-powered hypothesis. We conclude that all three eruption hypotheses should be considered further. Five tests are presented that could be implemented with remote sensing observations from future spacecraft to confidently distinguish among the eruption hypotheses for Triton's plumes. The five tests are based on the: (1) composition and thickness of Triton's southern hemisphere terrains, (2) composition of fan deposits, (3) distribution of active plumes, (4) distribution of fans, and (5) surface temperature at the locations of plumes and/or fans. The tests are independent, but complementary, and implementable with a single flyby mission such as the Trident mission concept. We note that, in the case of the solar-driven hypothesis, the 2030s and 2040s may be the last ..., Comment: Accepted for publication in Icarus