# The Radius and Entropy of a Magnetized, Rotating Fully-convective Star: Analysis With Depth-dependent Mixing Length Theories

## TL;DR

This paper investigates how rotation and magnetic fields affect the size of fully-convective stars using depth-dependent mixing length theories within 1D stellar models, finding magnetic effects could cause radius inflation while rotation has minimal impact.

## Contribution

It introduces a method to mimic rotational and magnetic effects on stellar radii through depth-dependent mixing length parameters in 1D models, linking these to physical processes.

## Key findings

- Rotation has negligible impact on stellar radius.
- Magnetic fields could cause radius inflation.
- Depth-dependent mixing length can replicate effects of rotation and magnetism.

## Abstract

Some low-mass stars appear to have larger radii than predicted by standard 1D structure models; prior work has suggested that inefficient convective heat transport, due to rotation and/or magnetism, may ultimately be responsible. We examine this issue using 1D stellar models constructed using Modules for Experiments in Stellar Astrophysics (MESA). First, we consider standard models that do not explicitly include rotational/magnetic effects, with convective inhibition modeled by decreasing a depth-independent mixing length theory (MLT) parameter $\alpha_{\text{MLT}}$ (following Cox et al. 1981; Chabrier et al. 2007). We provide formulae linking changes in $\alpha_{\text{MLT}}$ to changes in the interior specific entropy, and hence to the stellar radius. Next, we modify the MLT formulation in MESA to mimic explicitly the influence of rotation and magnetism, using formulations suggested by Stevenson (1979) and MacDonald & Mullan (2014) respectively. We find rapid rotation in these models has a negligible impact on stellar structure, primarily because a star's adiabat, and hence its radius, is predominantly affected by layers near the surface; convection is rapid and largely uninfluenced by rotation there. Magnetic fields, if they influenced convective transport in the manner described by MacDonald & Mullan (2014), could lead to more noticeable radius inflation. Finally, we show that these non-standard effects on stellar structure can be fabricated using a depth-dependent $\alpha_{\text{MLT}}$: a non-magnetic, non-rotating model can be produced that is virtually indistinguishable from one that explicitly parameterizes rotation and/or magnetism using the two formulations above. We provide formulae linking the radially-variable $\alpha_{\text{MLT}}$ to these putative MLT reformulations.