The shape of volcanic conduits inferred from bubble size distributions

The most intense known explosive volcanic eruptions on Earth are Plinian eruptions of silicic magma. Geospeedometers indicate that Plinian magma erupts from high pressure within the magma chamber at average speeds of 0.001-1 MPa/s. Concurrently dissolved magmatic volatiles, predominantly water, nucleate about one quadrillion bubbles per cubic meter of melt, preserved as vesicles within tephra. Vesicles span several orders of magnitude in size, with power-law size distributions, and vesicularities of approximately 70+-20%. Together these observations have never been explained in a self-consistent manner. Here we demonstrate that the integration of these observations requires that bubble nucleation commences as magma ascends from within the chamber and continues until the magma fragments to produce tephra. We substantiate experimentally that nucleation in rhyolitic melt can occur continuously over prolonged time intervals. We then use integrated modeling of bubble nucleation and fluid dynamics of magma ascent to demonstrate that bubble size distributions in Plinian pyroclasts are the product of continuous nucleation throughout magma ascent at average decompression rates that are consistent with geospeedometers. A necessary requirement is that the transition from magma chamber to volcanic conduit is gradual, resembling a cupola that narrows upward into a conduit, which in turn continues to decrease in size with distance above the chamber.