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Some controversial issues in theories of the solar differential rotation and dynamo

Authors:

Bernard R Durney

Institution:

1. National Solar Observatory, National Optical Astronomy Observatories, 85726, Tucson, AZ, U.S.A.

Abstract:

The following points are discussed:

(i)	The dependence of the angular velocity, $\Omega = \Omega _0 \omega _0 (r) + (\omega _2 )(r)P_2 (\cos \theta )]$ , on the spatial coordinates near the lower boundary, R _c, of the solar convection zone (SCZ) can be obtained from an integration with respect to r of a sound approximation to the azimuthal equation of motion. Here P ₂ (cos ) is the second-order Legendre polynomial and is the polar angle. Estimates of ₀, ₂ (the primes denote derivatives with respect to r), based on the best available values for the Reynolds stresses and anisotropic viscosity coefficients, suggest that ₀ < 0,=">₂ 0 for r = R _c. Since a reliable theory of anisotropic turbulent coefficients does not exist at present, positive values of ₀ are conceivable.
(ii)	In the lower SCZ the latitudinal variations of the superadiabatic gradient vanish if is constant along cylinders. The uniformity of the superadiabatic gradient is, however, inconsequential: the physically meaningful rotation law is the one that insures the uniformity of the convective flux.
(iii)	With the exception of the polar regions, the angular momentum transport in thin azimuthal convective rolls is towards the equator.
(iv)	It is suggested that buoyancy uncorrelates horizontally separated regions in the lower SCZ preventing the generation of magnetic fields with small wave numbers: in consequence, the cycle magnetic field must be generated in a region of weak buoyancy whereas the lower SCZ generates a weak rather stochastic magnetic field. The dependence on rotation of these two types of magnetic field could differ.
(v)	In the context of helioseismology it is customary to expand the perturbations (induced by rotation) of the eigenfrequencies in the following form: $\Delta \nu = L\Sigma _{i = 0}^N a_i P_i ( - m/L)$ , where the notation is standard. The observations reveal that to a good approximation a ₁ is independent of l. It is shown that this is the case if $\xi (r) \equiv \omega _0 (r) - \omega _2 (r)/5$ is constant with r. For a simple viscous, rotating fluid in the steady state (r) is constant with r if the angular momentum loss vanishes. Let J(ri dr) be the angular momentum of a thin shell of radius r and thickness dr. Since $J(r) = \tfrac{8}{3}\pi \rho r^4 \Omega _0 \xi _i (r)$ , the constancy of (r) implies that each shell of radius r has the same angular momentum as if the Sun were rotating uniformly with an angular velocity given by $\Omega = \Omega _0 (\omega _0 - \omega _2 /5)$ . It is discussed whether, alternatively, the observations simply indicate that ₀(r) is a slowly varying function of r.

Operated by the Association of Universities for Research in Astronomy, Inc. under contract with the National Science Foundation.

Keywords:

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