Solar rotation without convection: the baroclinic engine ✛
Context
For years astrophysicists believed the Sun’s differential rotation—with the equator lapping the poles in 27 days versus 32—was driven by vigorous turbulent convection. Mixing-length theory held that bubbling flows in the convection zone carry heat and angular momentum, sculpting the rotation profile. But helioseismology revealed that convective motions are far weaker than predicted. As Subrahmanyan Chandrasekhar showed, convection fails to develop when the Rayleigh number is subcritical. This discrepancy, known as the convective conundrum, forced a rethink of classic models. If convection is feeble, Reynolds stresses cannot supply the observed equatorial acceleration. The puzzle: what then spins the stellar gas?
Methods
The team performed global hydrodynamic simulations of a rotating spherical shell covering the layer from 0.72 to 0.96 of the Sun’s radius. They used the EULAG-MHD code, which handles anelastic fluids under inverse-square law gravity. A crucial trick: nudging the potential temperature toward a target profile over 2.4–4.9 years. This profile, built from helioseismic inversions, carries a latitudinal entropy gradient that fits the thermal wind balance. They tested a range of stratification, from superadiabatic (unstable) to strongly stable. The plasma was treated as an ideal gas.
Results
All simulations produced a steady differential rotation with faster equator, much like the real Sun, no matter the stratification. The weakly convective and stable runs best matched the observed radial speed increase at low latitudes and the vertical iso-rotation lines at mid-latitudes. Angular momentum diagnostics revealed that meridional circulation—giant cells stretched along the rotation axis—ferries angular momentum equatorward, while Reynolds stresses are sidekicks. In unstable models, vigorous convection shreds the preset baroclinicity, and the rotation slumps toward a cylindrical profile. A thermal balance check showed a ~10% residual between centrifugal and baroclinic terms—this imbalance triggers meridional flows, a process called gyroscopic pumping.
Implications
The results offer a fresh perspective on the nature of solar differential rotation: it may be a manifestation of large-scale barotropic equilibrium rather than a direct consequence of turbulent convection. This aligns with the thermal wind concept and supports the hypothesis of substantially weaker convection in the interior. In this scenario, the convection zone is near marginal stability, and the differential rotation is ‘dictated’ by the global entropy distribution. Interestingly, the Solar wind might also be explained within this balance.
Future development
Future research must uncover the physical mechanism that creates the observed latitudinal entropy gradient. Candidates include rotational modulation of turbulent heat transport, near-surface cooling that triggers ‘entropy rain,’ or a connection to the tachocline. It is also important to investigate how this picture changes with magnetic fields and whether it can sustain the solar dynamo.
Impact
This work impacts our understanding of stellar dynamics, the solar cycle, and magnetohydrodynamics. The proposed mechanism applies to other sun-like stars as well, opening new perspectives for evolution and dynamo models.
Next steps
Magnetohydrodynamic simulations with the proposed baroclinic forcing are needed, along with comparisons to data from other stars obtained via asteroseismology (e.g., Kepler and TESS telescopes).
Key open problems
The paper directly addresses the solar convective conundrum—the mismatch between predicted and observed convective amplitudes. The proposed scenario hints at resolving this discrepancy without overhauling the fundamental laws of physics.
The knowledge machine's view
This section is addressed to the author of the paper and their colleagues. Neighbouring works were found by meaning-based search across our archive, not by word overlap. We do not review: we show the field around the work.
What the work does
The authors performed global hydrodynamic simulations of a rotating spherical shell, varying stratification from unstable to strongly stable, with nudging of potential temperature toward the helioseismic profile. In all models, differential rotation with equatorial acceleration emerged, and in weakly convective and stable cases it reproduced the observed features of solar rotation well. Analysis of the angular momentum balance showed that meridional circulation, rather than Reynolds stresses, plays the leading role, supporting the concept of thermal wind.
Where its strength is
It is shown that differential rotation can result from large-scale barotropic equilibrium set by the global entropy distribution, rather than from strong turbulent convection. This paves the way for models where convection is close to marginal stability and the rotation profile is dictated by the thermal structure.
Where it could go next
- The study shows that meridional circulation transports angular momentum toward the equator. It would be interesting to see how this mechanism works under double-diffusive conditions: in our archive there is an analysis showing that double diffusion may be suppressed in the interiors of giant planets, but for solar parameters its role in maintaining entropy gradients is still unclear.based on: The Unmixed Cocktail: Why Double Diffusion Is Powerless in the Interiors of Giant Planets arXiv:2607.04629v1
- The simulations showed that the residual imbalance between the centrifugal and baroclinic terms drives meridional flows (gyroscopic pumping). It is interesting to compare this mechanism with how rotation affects heat transport in the oceans of icy moons: there too latitudinal inhomogeneity arises, and the parameterization approaches may be similar.based on: Striped Ocean: How Rotation Reshapes Heat on Icy Moons arXiv:2606.22547
Worth trying
- Test how the angular momentum balance changes if double diffusion is added to the model with coefficients estimated for the solar convection zone.
- Apply the gyroscopic pumping parameterization from the work on icy moons to estimate meridional circulation in solar models with different stratifications.
Why this may matter
If differential rotation is indeed set by the thermal structure rather than convective turbulence, this could simplify stellar evolution models and aid in interpreting helioseismic data, as well as clarify the link between rotation and magnetic activity.
Nearby works in our archive
- Striped Ocean: How Rotation Reshapes Heat on Icy Moonssimilarity 0.62
- The Unmixed Cocktail: Why Double Diffusion Is Powerless in the Interiors of Giant Planetssimilarity 0.60
- The Sun's Magnetic Loops: Chaos You Can Measuresimilarity 0.60
- Twisted Crown: How a Magnetic Vortex Rewrites Sunspotssimilarity 0.59
- Why Do Hot Jupiters Swell?similarity 0.59
- Twisted Solar Loop Reveals the Secret of Magnetic Explosionssimilarity 0.58
The closest work in the archive sits at 0.62 by meaning — the usual level for our corpus.
Original abstract
as written by the authors arXiv:2607.19730v1
A combination of recent observations and numerical simulations has called into question whether Sun's interior is characterized by strong turbulent convection, a problem known as convective conundrum. In light of a possible absence of vigorous convective motions, we examine whether the Sun's differential rotation, previously assumed to be tightly coupled to Reynolds stresses, may instead be sustained by the presence of a background latitudinal entropy gradient in thermal wind balance. By performing global hydrodynamical simulations of a rotating spherical shell representing the bulk of the solar convection zone, we demonstrate that solar-like differential rotation can be generated under a variety of thermal stratifications. This work proposes an alternative scenario for the origin of solar differential rotation that accommodates the previously reported discrepancies.
The difference in rotation rate between the equator and the poles is about 0.016% per year — seemingly tiny, but enough for the equator to lap the poles by a full day after just a few rotations.
Key numbers
- equator rotation period: 27 days
- pole rotation period: 32 days
- inner boundary radius: 0.72 R⊙
- outer boundary radius: 0.96 R⊙
- nudging timescale: 2.4–4.9 years