Twists in the flow: revisiting convective mixing in rotating stellar models. I. Effect on the stellar structure

Abstract

Convection and rotation are both key processes in stellar evolution modelling. While standard mixing-length theory (MLT) provides a widely used modelling of convection, it neglects the effects of rotation on convective transport. We investigate how rotating mixing-length theory (R-MLT), which accounts for the influence of rotation on convection, affects the internal structure, convective mixing, and angular momentum transport in stellar models in comparison to the standard non-rotating MLT. Using the MESA stellar structure and evolution software, we model the main-sequence evolution of a 5 M$_{\odot}$ star, for three cases: non-rotating, rotating with standard MLT for modelling convection, and rotating with R-MLT in convection zones, with the initial rotation rate set to 20 percent of the critical (Keplerian) value at the surface for the rotating models. We find that R-MLT reduces both the convective velocity and mixing length in the stellar core, leading to a smaller convective diffusion coefficient and about 20 percent reduction in the extent of the convective overshooting region. While the overall size of the convective core remains nearly unchanged, R-MLT changes the resulting chemical gradient at the core-envelope boundary, shifting the peak of the Brunt-Väisälä frequency and modifying the angular momentum transport in that region. Including the effects of rotation in the treatment of convection through R-MLT introduces measurable structural and transport differences, underscoring the importance of incorporating rotation-convection coupling in models of stars.

Figures (10)

• Figure 1: Mixing coefficients as a function of enclosed mass fraction for a 5 M$_\odot$ main-sequence star at solar metallicity, with an initial rotation rate set to 20 percent of the critical surface rotation rate. Shown are contributions from convection, convective overshoot, and rotationally- induced hydrodynamical instabilities, namely: Eddington–Sweet circulation (ES), Solberg–Hø iland instability (SH), Goldreich–Schubert–Fricke instability (GSF), dynamical shear instability (DSI), and secular shear instability (SSI).
• Figure 2: ZAMS (left) and TAMS (right) profiles of the region containing the inner 40 percent in mass of the three sets of 5 M$_\odot$ stellar models described in Sect. \ref{['sec:methods']}, showing the variation of the MLT variables: convective velocity on the top, mixing length in the middle, and degree of superadiabaticity at the bottom. The solid yellow lines correspond to the non-rotating model, the dashed purple lines correspond to the model with rotation and standard MLT, and the dashed-dotted orange lines correspond to the model with rotation and R-MLT. The vertical dotted line of the corresponding colour in each panel denotes the boundary of the convective core.
• Figure 3: Mixing coefficient (black) and Brunt–Väisälä frequency (blue) for the same region and stellar models as shown in Fig. \ref{['fig:mlt_vars']}. Profiles near the ZAMS are on the left-hand side, with the non-rotating model on the top, the model with rotation and standard MLT in the middle, and the model with rotation and R-MLT at the bottom. The corresponding profiles at the TAMS are displayed in the right-hand panels. Background shading indicates the dominant mixing mechanism in different stellar layers: grey for convection, purple for overshoot, green for the radiative envelope, and orange for the envelope with rotational mixing.
• Figure 4: Rotation frequency profiles for rotating models computed with standard MLT (dark purple) and with R-MLT (yellow) in the convective regions. The corresponding Rossby number profiles are shown in the right panel. Both models begin with nearly identical rotation frequency distributions near the ZAMS (solid lines) but diverge by the TAMS (dashed lines), particularly beyond the fractional mass of about 0.32.
• Figure 5: Left panel: Hertzsprung-Russell (HR) diagram showing the main-sequence evolution of a 5 M$_\odot$ star. Right panel: Evolution of the buoyancy travel time as a function of the hydrogen mass fraction. The solid yellow line represents the non-rotating model computed with standard MLT in the convective zones; the dashed purple line corresponds to the rotating model with rotational mixing in the radiative zones and standard MLT in the convective zones; and the dash-dotted orange line shows the rotating model but with R-MLT instead of standard MLT in the convective zones.