Abstract
We study how active-region-scale flux tubes rise buoyantly from the base of the convection zone to near the solar surface by embedding a thin flux tube model in a rotating spherical shell of solar-like turbulent convection. These toroidal flux tubes that we simulate range in magnetic field strength from 15 kG to 100 kG at initial latitudes of 1 degree to 40 degrees in both hemispheres. This article expands upon Weber, Fan, and Miesch (Astrophys. J., 741, 11, 2011) (Article 1) with the inclusion of tubes with magnetic flux of 10^20 Mx and 10^21 Mx, and more simulations of the previously investigated case of 10^22 Mx, sampling more convective flows than the previous article, greatly improving statistics. Observed properties of active regions are compared to properties of the simulated emerging flux tubes, including: the tilt of active regions in accordance with Joy's Law as in Article 1, and in addition the scatter of tilt angles about the Joy's Law trend, the most commonly occurring tilt angle, the rotation rate of the emerging loops with respect to the surrounding plasma, and the nature of the magnetic field at the flux tube apex. We discuss how these diagnostic properties constrain the initial field strength of the active region flux tubes at the bottom of the solar convection zone, and suggest that flux tubes of initial magnetic field strengths of \geq 40 kG are good candidates for the progenitors of large (10^21 Mx to 10^22 Mx) solar active regions, which agrees with the results from Article 1 for flux tubes of 10^22 Mx. With the addition of more magnetic flux values and more simulations, we find that for all magnetic field strengths, the emerging tubes show a positive Joy's Law trend, and that this trend does not show a statistically significant dependence on the magnetic flux.
Highlights
The toroidal magnetic field responsible for the emergence of solar active regions is believed to be generated by a dynamo mechanism at or near the base of the convection zone (e.g. Spiegel and Weiss, 1980; van Ballegooijen, 1982; Moreno-Insertis, Schüssler, and FerrizMas, 1992; Gilman, 2000; Charbonneau, 2010)
For simulated flux tubes of all magnetic field strengths considered and fluxes of 1021 Mx and 1022 Mx (Figure 6(b)), as these are most likely the magnetic flux strengths required to produce sunspot groups that can be identified in white light, we find a slope of mA = 0.34 ± 0.02, which does fall within the range of tilt angles that Dasi-Espuig et al (2010) find given the uncertainties on the slope
By embedding the thin flux tube model in a three-dimensional, turbulent, convective velocity field representing the solar convective envelope, we study how convection can influence the properties of emerging active-region flux tubes
Summary
The toroidal magnetic field responsible for the emergence of solar active regions is believed to be generated by a dynamo mechanism at or near the base of the convection zone (e.g. Spiegel and Weiss, 1980; van Ballegooijen, 1982; Moreno-Insertis, Schüssler, and FerrizMas, 1992; Gilman, 2000; Charbonneau, 2010). Recent simulations of solar-like stars that rotate three times the current solar rate have shown that a rotating convective envelope can generate a dynamo that consists of opposite polarity magnetic wreaths in two hemispheres, which span the depth of the convection zone (Brown et al, 2010) When portions of these wreaths become strong enough, ≈ 35 kG or greater, a buoyant magnetic loop develops, which rises through the convecting fluid in which it is embedded (Nelson et al, 2011). Weber, Fan, and Miesch, 2011 (hereafter Article 1) incorporate a thin flux tube model in a (separately computed) rotating three-dimensional convective velocity field representative of the solar convective envelope, in an effort to study the effects of turbulent solar-like convection on the dynamic evolution of active-region scale emerging flux tubes.
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