Image Details
Caption: Figure 7.
Cumulatively time-integrated torque densities from Equation (40) as functions of time, after volume-averaging over the deep RZ, for (a) Case H0, (b) Case M0, (c) Case H6, and (d) Case M6. In the legend, we label the curves by the torque densities, which are understood to be shorthand for the time-integrated and volume-averaged quantities. For instance, ﹩\int \left\langle {\tau }_{{\rm{rs}}}\right\rangle ﹩ is shorthand for ﹩{\int }_{0}^{t}{\left\langle {\tau }_{{\rm{rs}}}\right\rangle }_{{\rm{drz}}}(t^{\prime} )dt^{\prime} ﹩. The vertical dotted lines correspond to the values of t3/4 for each case. For Case H6, note that ﹩{\sigma }_{c}^{-2}{t}_{{\rm{es}}}﹩ ≈ 10,000.
© 2026. The Author(s). Published by the American Astronomical Society.