Despite its importance for the evolution and final end states of stars, the physics of stellar angular momentum transport remains poorly understood. Recent advances in ensemble asteroseismology has yielded measurements of core rotation in many ascending red giant branch stars (RGB) \cite{Mosser_2012}. The main result (Fig~\ref{period}) is that the cores of these stars are rotating at least 10 times slower than what is predicted by state-of-the art models \citep{Cantiello_2014}. Moreover, detailed asteroseismic modeling shows that the bulk of radial differential rotation is localized in the radiative region between the H-burning shell and the bottom of the convective envelope \cite{Klion_2016}. 

The magnetorotational instability (MRI) has been extensively studied in the context of angular momentum transport in accretion disks. However, it is not clear what role--if any--it might play in the radiative regions of differentially rotating stars. The existing literature is limited \cite{Kagan_2014,Wheeler_2015}, and attempts to simulate this mechanism in stellar interiors have not yielded complete results appropriate for inclusion in stellar evolution codes. 

We propose to investigate the role of the MRI in stars using simulations that account for the important physical ingredients of stellar radiative regions: stable radial stratification, mean molecular weight gradients, differential rotation, and magnetic fields. These effects are parameterized by the Brunt-V\"ais\"al\"a frequency $N$, background gradient $\nabla_{\mu}$, shear parameter $q = d\log \Omega/d\log R$, and plasma $\beta$. \citet{Menou_2004} emphasized the importance \emph{double-diffusive} effects in the stellar MRI. These effects occur when there is an imbalance between the microphysical dissipation of momentum $\nu$, magnetic field $\eta$, and heat $\chi$. In their analysis, they note that double diffusive effects can both stabilize and destabilize depending on the relative ratio of these coefficients. Here, we will carefully consider the effects of double-diffusive effects by a series of fast, linear solutions to characterize the parameter space most relevant to stellar parameters. 

Using the \href{http://dedalus-project.org/}{Dedalus framework}, we will simulate the MRI in a simplified geometry to extract effective torques over a range of parameters. We will then implement these results in a 1D implementation in the \href{http://mesa.sourceforge.net}{MESA} code to test against the full set of observations available: the core rotation of red giants, the solar core rotation profile, and the final spin rate of compact remnants. 

This project is extremely ambitious owing to the many length scales that must be resolved simultaneously and the very large parameter space to be spanned. However, we have at our disposal the ideal tools to make significant progress: the spectral magnetohydrodynamic simulation framework Dedalus and the extremely flexible stellar evolution code MESA. Dedalus provides an excellent platform to study the MRI in stellar interiors: it can be adapted to include the new terms and its spectral accuracy ensures that the widest possible dynamic range for a given resolution (Fig.~\ref{Dedalus}). Thanks to the extraordinary results from Kepler asteroseismology and the versatility of the open stellar evolution code MESA, we will be able to immediately test our results against the observations. This project could lead to a novel theory for internal angular momentum transport in stellar interiors, and, among other results, to updated predictions for SN and GRB progenitors.

Both the Dedalus and MESA codes are fully open, so our results will be fully testable and reproducible by the astrophysics community. We will publish not only our results, but also our input files and configuration for both codes.
