Angular momentum transport in the convection zone of a 3D MHD simulation of a rapidly rotating core-collapse progenitor

Abstract

Rotation and magnetic fields in the cores of evolved massive stars in their final phase are thought to play an important role in the subsequent supernova explosion and the formation of a compact object, especially in hyperenergetic explosions. However, the interplay between rotation, magnetic fields, and convection up to the final collapse is a nonlinear, multidimensional effect that is difficult to capture with standard one-dimensional (1D) stellar evolution models. We quantify the magnetic angular momentum (AM) transport in the convective oxygen burning shell in a three-dimensional (3D) rotating core-collapse progenitor model. We find that the radial direction of magnetic AM transport is directly related to the Rossby number of the convective oxygen shell. We also analyze the magnetic energy, which sets the amplitude of the magnetic AM flux. The magnetic energy is determined both by rotation and the nuclear energy generation rate analogously to low-mass stars like the Sun. Based on these results, we construct a 1D model of magnetic AM transport in the convection zone for the first time in terms of properties of a given stellar evolution model. This model successfully reproduces the AM transport in the 3D model when the convective dynamo is in a quasi-steady state. Notably, our model for radial AM transport is the first to account for inward AM flux. This may result in interesting differences compared to the conventional treatment of magnetic AM transport in stellar evolution models, which assume AM is transported outward by a purely diffusive process.

Figures (5)

• Figure 1: (a) Temporal evolution of Favre averaged rotation rate $\Omega/2\pi$ (blue solid line) and convective velocity $v_\mathrm{conv}$ (orange solid line) in the O shell. The vertical axes for the rotation rate and convective velocity are displayed on the left and right sides, respectively. An inset view on the right side highlights the evolution of the rotation rate $\Omega/2\pi$ during the quasi-steady phase after $300$ s, where the system maintains a statistically steady convective dynamo. (b) Temporal evolution of the Rossby number Ro (blue solid line) and the correlation of Maxwell stress (orange solid line) in the O shell. The vertical axes for the Rossby number and the correlation of Maxwell stress are displayed on the left and right sides, respectively.
• Figure 2: Time–radius diagrams of (a) the correlation between $B_r$ and $B_\phi$ (Eq. \ref{['eq:MS_Cor']}), and (b) the Rossby number Ro, are shown using a cool-to-warm color scale (color bars are shown on the right). The vertical axis indicates radius, and the horizontal axis denotes time. The O shell (the region between two white lines) reaches the quasi-steady states in the convective dynamo at $\approx 300$ s (black dashed line). The black solid line in panel (a) indicates the region where the correlation changes its sign. The black solid line in panel (b) displays the region where Rossby number crosses unity.
• Figure 3: The horizontal axis shows the inverse of the Rossby number, and the vertical axis shows the ratio between the magnetic and kinetic energy. The color of each point indicates the corresponding time in the simulation that satisfies the quasi-steady state condition by the rainbow colorbar ($t =$ 300 – 480 s; Eq. \ref{['eq:QS']}). The black solid line represents the best fit to the quantities taken from the 3D MHD simulation.
• Figure 4: Comparison of our predicted convective energy flux based on the energy partition between convective and Poynting fluxes (Eq. \ref{['eq:KE_Qdot']}) with simulation data. The convective velocity $v_\mathrm{conv}$ in the O shell is shown on the vertical axis against the right-hand side of Eq. (\ref{['eq:KE_Qdot']}) on a log-log scale. The color of each point indicates the corresponding time in the simulation during the quasi-steady-state phase ($t =$ 300 – 480 s). The black line represents a power-law with an index of 1/3.
• Figure 5: The temporal evolution of the angular momentum flux due to the Maxwell stress (Eq. \ref{['eq:AM_Con']}) in the 3D MHD simulation (blue line). Our 1D model, given by Eq. (\ref{['eq:MS_Model']}) is shown by the orange line. The orange shaded region represents the uncertainty of the 1D model, accounting for the combined standard deviation of the model parameters.