Some controversial issues in theories of the solar differential rotation and dynamo |
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Authors: | Bernard R. Durney |
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Affiliation: | 1. National Solar Observatory, National Optical Astronomy Observatories, 85726, Tucson, AZ, U.S.A.
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Abstract: | The following points are discussed:(i) | The dependence of the angular velocity, , on the spatial coordinates near the lower boundary, Rc, 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 P2 (cos ) is the second-order Legendre polynomial and is the polar angle. Estimates of ![ohgr](/content/MT48776221452X81/xxlarge969.gif) 0, ![ohgr](/content/MT48776221452X81/xxlarge969.gif) 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 ![ohgr](/content/MT48776221452X81/xxlarge969.gif) 0 < 0,=">![ohgr](/content/MT48776221452X81/xxlarge969.gif) 2 0 for r = Rc. Since a reliable theory of anisotropic turbulent coefficients does not exist at present, positive values of ![ohgr](/content/MT48776221452X81/xxlarge969.gif) 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: , where the notation is standard. The observations reveal that to a good approximation a1 is independent of l. It is shown that this is the case if 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 , 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 . 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. |
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