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Abstract Crustal magma chambers can grow to be hundreds to thousands of cubic kilometers, potentially feeding catastrophic caldera‐forming eruptions. Smaller volume chambers are expected to erupt frequently and freeze quickly; a major outstanding question is how magma chambers ever grow to the sizes required to sustain the largest eruptions on Earth. We use a thermo‐mechanical model to investigate the primary factors that govern the extrusive:intrusive ratio in a chamber, and how this relates to eruption frequency, eruption size, and long‐term chamber growth. The model consists of three fundamental timescales: the magma injection timescaleτ_in, the cooling timescaleτ_cool, and the timescale for viscous relaxation of the crustτ_relax. We estimate these timescales using geologic and geophysical data from four volcanoes (Laguna del Maule, Campi Flegrei, Santorini, and Aso) to compare them with the model. In each of these systems,τ_inis much shorter thanτ_cooland slightly shorter thanτ_relax, conditions that in the model are associated with efficient chamber growth and simultaneous eruption. In addition, the model suggests that the magma chambers underlying these volcanoes are growing at rates between ~10⁻⁴and 10⁻² km³/year, speeding up over time as the chamber volume increases. We find scaling relationships for eruption frequency and size that suggest that as chambers grow and volatiles exsolve, eruption frequency decreases but eruption size increases. These scaling relationships provide a good match to the eruptive history from the natural systems, suggesting that the relationships can be used to constrain chamber growth rates and volatile saturation state from the eruptive history alone. 

Abstract We present a model for a coupled magma chamber–dike system to investigate the conditions required to initiate volcanic eruptions and to determine what controls the size of eruptions. The model combines the mechanics of dike propagation with internal chamber dynamics including crystallization, volatile exsolution, and the elastic response of the magma and surrounding crust to pressure changes within the chamber. We find three regimes for dike growth and eruptions: (1) below a critical magma chamber size, eruptions are suppressed because chamber pressure drops to lithostatic before a dike reaches the surface; (2) at an intermediate chamber size, the erupted volume is less than the dike volume (“dike-limited” eruption regime); and (3) above a certain chamber size, dikes can easily reach the surface and the erupted volume follows a classic scaling law, which depends on the attributes of the magma chamber (“chamber-limited” eruption regime). The critical chamber volume for an eruption ranges from ∼0.01 km3 to 10 km3 depending on the water content in the magma, depth of the chamber, and initial overpressure. This implies that the first eruptions at a volcano likely are preceded by a protracted history of magma chamber growth at depth, and that the crust above the magma chamber may have trapped several intrusions or “failed eruptions.” Model results can be combined with field observations of erupted volume, pressure, and crystal and volatile content to provide tighter constraints on parameters such as the eruptible chamber size.