Brunt-Vaisala growth rate and the radial emergence of equipartition fields

Details Brunt-Vaisala growth rate and the radial emergence of equipartition fields Brunt-Vaisala growth rate and the radial emergence of equipartition fields

Apr 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995apj...443..444d&link_type=abstract

Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 443, no. 1, p. 444-449

Astronomy and Astrophysics

Astronomy

1

Astronomical Models, Brunt-Vaisala Frequency, Equipartition Theorem, Growth, Magnetic Flux, Magnetohydrodynamics, Solar Convection (Astronomy), Solar Magnetic Field, Coriolis Effect, Dynamo Theory, Flux Pinning, Latitude, Photosphere, Sunspots

Scientific paper

It is believed that the dynamo operates in the overshoot region at the base of the solar convection zone (CZ), and the magnetic features we see at the surface are formed when flux tubes rise through the CZ and appear at the photosphere. Studies of dynamics of flux tubes have pointed out that 10 kG tubes, which are nearly in energy equipartition with the velocity field at the base of the CZ, are weakly buoyant and hence overwhelmed by the Coriolis force. They move parallel to the rotation axis and emerge at very high latitudes, well above the sunspot zone, which makes it difficult to explain the formation of sunspots. Influence of the Coriolis force was found to be overcome only if flux tubes were stronger than roughly a 100 kG. The Brunt-Vaisala growth rate (we define as the square root of the absolute value of N2; where N is the Brunt-Vaisala frequency) of the CZ plays an imporatnt role in the dynamics of rising flux tubes. In an isothermal rise, when the flux tube is in thermal equilibrium with its surroundings, absolute value of N2 is shown to play a negligible role. However, in an adiabatic rise the role of absolute value of N2 is dominant; if absolute value of N2 is larger than roughly 10-12/sq sec in the lower CZ, magnetic buoyancy is shown to rise exponentially as the flux tube emerges. Further if absolute value of N2 greater than 4 x 10-11/sq sec, the exponential rise is sufficiently rapid to enable equipartition fields to overcome the influence of the Coriolis force and emerge rapidly. In the CZ of the solar model of Christensen-Dalsgaard, Proffitt, & Thompson (1993; model CPT) equipartition fields are found to emerge at high latitudes. However, an increase of absolute value of N2 in the lower CZ, on average, roughly by a factor of 8 would make them emerge radially to sunspot latitudes. If this is possible, there would be no need for the dynamo to produce extraordinarily strong fields to explain the formation of sunspots. Conversely, if such a large absolute value of N2 is not possible for the lower layers of the CZ, then our results actually reinforce the conclusion in previous work that field strengths at the CZ base of order 100 kG are necessary for sunspot strength magnetic fields to emerge at sunspot latitudes.

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