The Radius and Entropy of a Magnetized, Rotating Fully-convective Star:
Analysis With Depth-dependent Mixing Length Theories
L. Ireland, and M. Browning. (2018)cite arxiv:1803.02664Comment: 25 pages, 19 figures, accepted for publication in ApJ.
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 $\alpha_MLT$ (following Cox et al. 1981; Chabrier et al.
2007). We provide formulae linking changes in $\alpha_MLT$ 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 $\alpha_MLT$: 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 $\alpha_MLT$ to these putative MLT reformulations.