The Emergence of Toroidal Flux Ropes with Different Twist Rising at the Same Speed

The role of twist in the emergence of magnetic flux ropes into the solar atmosphere has remained unclear for some time. Although many studies have investigated how the photospheric properties of active regions resulting from the simulated emergence of magnetic flux ropes from the convection zone with different twists compare to the observed properties of active regions, these simulations have a wide range of magnetic flux rope radii, depths, and initial configurations, making it challenging to form a complete picture of the role of any one variable in the emergence process. Twist, in particular, has been difficult to analyze because isothermally buoyant magnetic flux ropes with different twists also experience different accelerations. In this paper, we develop an analytical model of a toroidal magnetic flux rope in approximate vertical force balance in the convection zone. We numerically implement this model in a stratified atmosphere, and then subtract off a twist-independent density to make magnetic flux ropes buoyant in a twist-independent way, ensuring that the initial acceleration of each magnetic flux rope is approximately the same. We perform numerical simulations to obtain a parameter study of toroidal magnetic flux ropes with different twist rising at the same speed. We analyze the photospheric and coronal properties of the active regions resulting from the emergence of these magnetic flux ropes, and argue that the Parker instability is responsible for many of the features observed in the simulations.