Erratum: Joint Instability of Latitudinal Differential Rotation and Toroidal Magnetic Fields below the Solar Convection Zone. II. Instability for Toroidal Fields That Have a Node between the Equator and Pole

Details Erratum: Joint Instability of Latitudinal Differential Rotation and Toroidal Magnetic Fields below the Solar Convection Zone. II. Instability for Toroidal Fields That Have a Node between the Equator and Pole Erratum: Joint Instability of Latitudinal Differential Rotation and Toroidal Magnetic Fields below the Solar Convection Zone. II. Instability for Toroidal Fields That Have a Node between the Equator and Pole

May 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000apj...534.1020g&link_type=abstract

The Astrophysical Journal, Volume 534, Issue 2, pp. 1020-1020.

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There is a repeated error in certain equations in the papers by Peter A. Gilman and Peter A. Fox, ``Joint Instability of Latitudinal Differential Rotation and Toroidal Magnetic Fields below the Solar Convection Zone. II. Instability for Toroidal Fields That Have a Node between the Equator and Pole'' (510, 1018 [1999]) (GF) Mausumi Dikpati and Peter A. Gilman, ``Joint Instability of Latitudinal Differential Rotation and Concentrated Toroidal Fields below the Solar Convection Zone'' (512, 417 [1999]) (DG) and Peter A. Gilman and Mausumi Dikpati, ``Joint Instability of Latitudinal Differential Rotation and Concentrated Toroidal Fields below the Solar Convection Zone. II. Instability of Narrow Bands at All Latitudes'' (528, 552 [2000]) (GD). In GF, equation (3), DG, equation (24), and GD, equation (3), all are missing an additive term that multiplies the variable H. The correct total factor multiplying H is {1/(1-μ2) ( 2 - m2/(1-μ2) + 1/S[2c(ωo-c) + μ d/dμ(S/(1-μ2)]} The second term, involving S in the denominator, is missing in these papers. As a consequence, the expression for k2, shown in equation (6) of GF and equation (10) of DG, is also missing this term. The correct expression for k2 in both cases is 1/(1-μ2) ( 2 - m2/(1-μ2) + ((1/2S)(d2S/dμ2)) + 1/S[2c(ωo-c) + μ d/dμ(S/(1-μ2)] No results or conclusions are affected in any of these papers, because the equations containing errors are used only to identify the location of singular points, where the effective wavenumber increases without bound. All of these singular points are the same in the erroneous forms as in the correct forms, being determined principally by the roots of S. But obviously, if the erroneous forms are used for other purposes, incorrect conclusions might be reached. The authors are indebted to Paul Cally for discovering this error.

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