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Eddington Sweet CirculationEdit

Eddington-Sweet circulation refers to a slow, large-scale meridional flow inside rotating stars that arises when rotation distorts the star’s internal structure enough to break perfect thermal alignment. Named for two foundational figures, Arthur Eddington and Norman Sweet, this circulation redistributes angular momentum and chemical species within radiative regions of stars. While the phenomenon has a long history in theoretical astrophysics, it remains a point of active debate as models incorporate magnetic fields, waves, and other mixing processes.

In rotating stars, the centrifugal force alters the hydrostatic balance and the geometry of isobaric and isothermal surfaces. The resulting slight baroclinicity drives a slow circulation in which material moves from the poles toward the equator near the surface and then back from the equator to the poles along deeper layers. This meridional transport operates most efficiently in radiative zones, where convection is weak and large-scale flows can persist. The overall effect is to transport angular momentum and to mix chemical elements over stellar lifetimes, influencing surface abundances and the evolution of the star. For a fuller discussion of the surrounding physics, see Stellar rotation and Meridional circulation.

Overview

  • Driving mechanism
    • The circulation is driven by the imbalance created when rotation distorts the star’s equipotential surfaces. In a rotating star, pressure and density gradients do not align perfectly, creating a baroclinic torque that sustains large-scale flows. This is most evident in stable, radiative interiors where vertical motions are limited, allowing a coherent meridional pattern to develop. See for example discussions of Baroclinic torque and how it relates to internal rotation in stars.
  • Physical regime
    • Eddington-Sweet circulation is most relevant in radiative zones of stars with moderate to rapid rotation. In zones where convection dominates, other mixing processes overwhelm the simple meridional flow, so the circulation plays only a secondary role there.
  • Role in transport
    • The circulation contributes to the redistribution of angular momentum and to slow chemical mixing, potentially altering surface compositions over long times. In synthesis with turbulence, diffusion, and, when present, magnetic fields, it forms part of the broader picture of rotational mixing that shapes how a star evolves. See Angular momentum and Rotational mixing for related transport processes.

History and naming

  • Early insight came from the recognition by Arthur Eddington that rotation could modify a star’s interior structure in ways that produce nontrivial mass flows. The mechanistic details were expanded by Norman Sweet, whose work highlighted how slow, global circulations could operate in radiative interiors. Together, their legacy is captured in the term Eddington-Sweet circulation.
  • Over the ensuing decades, the idea was integrated into more formal frameworks of rotational mixing. Notable developments include the refinement of the transport equations by Zahn and subsequent work that incorporated shear instabilities, differential rotation, and, later, magnetic effects. See Zahn's theory of rotational mixing and Stellar evolution for broader context.

Physical basis and modeling

  • Meridional flow as a transport agent
    • In a rotating star, the misalignment between pressure and density surfaces produces a torque that sustains a circulation pattern. Material moves toward regions of lower effective gravity near the poles and returns at depth toward higher latitudes, setting up a global loop that spans substantial portions of the radiative interior.
  • Interaction with other processes
    • The strength and effectiveness of Eddington-Sweet circulation depend on the star’s rotation rate, stratification, and the presence of other transport mechanisms. Shear instabilities, magnetic fields, internal gravity waves, and microscopic diffusion all compete with or enhance the net mixing produced by meridional flows. In models, these interactions are encapsulated in rotational mixing prescriptions and, when appropriate, magnetohydrodynamic (MHD) considerations.

Controversies and debates

  • How important is Eddington-Sweet circulation relative to other mechanisms?
    • Practitioners vary in assessing the dominance of meridional flows versus shear-induced mixing, gravity waves, and magnetic transport. A conservative view emphasizes that weak circulation in many stars makes it a supplementary channel, while more aggressive models assign a larger role to Eddington-Sweet transport in shaping surface abundances and angular momentum distribution. See Rotational mixing for the broader landscape of competing processes.
  • Magnetic fields and their suppressive or transformative role
    • The question of how internal magnetic fields modify or suppress meridional circulation is a central topic. Some theoretical work argues that magnetic stresses enforce more rigid rotation and suppress large-scale circulation, while others suggest magnetism creates alternative pathways for angular momentum transport that can coexist with or enhance mixing. The debate intersects with discussions of the Spruit-Tayler dynamo and related MHD theories in stellar interiors.
  • Observational constraints and interpretation
    • Asteroseismology and spectroscopic studies provide increasingly precise probes of internal rotation and surface composition. Interpreting these data within the Eddington-Sweet framework requires careful separation of multiple overlapping processes. Proponents of a traditional, conservative model stress that classic meridional circulation remains a robust, testable ingredient, while critics point to discrepancies that motivate more complex or supplementary mechanisms.

Current perspective

  • In contemporary modeling, Eddington-Sweet circulation is treated as a foundational component of rotationally induced mixing, particularly in radiative zones of rapidly rotating stars. Its estimated impact is often context-dependent, becoming more consequential when rotation is substantial and when other transport channels are comparatively weak. The enduring value of the concept lies in its clear linkage between rotation, thermal structure, and large-scale transport, even as models evolve to incorporate magnetic fields, waves, and turbulence.

See also