Babcock-Leighton Solar Dynamo Model: the Role of Active Region Inflows for The Saturation of the Solar Dynamo
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Date
2018-06-05
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Addis Ababa University
Abstract
Helioseismology has detected that solar photospheric active regions are surrounded by
spatially extended, converging ow with typical ow velocities of 20-30 m/s. They extend
up to 30 degrees from the center of the active region. It has been proposed that this
converging ow may act as a saturation mechanism for the solar dynamo, and as such,
may determine the strength of solar cycles. In this work we explore questions such as:
Are the converging ows towards active regions an e_ective saturation mechanism for
Babcock-Leighton solar dynamo models?
These inows can potentially play an important role in ux-transport models of the
solar cycle. The model of inow towards the active regions is developed within the
framework of the Surface ux Transport And Babcock-LEighton (STABLE) solar dynamo
model. STABLE is designed to capture both the 11-year solar cycle and the evolution of
photospheric magnetic ux with high _delity. The STABLE model solves the kinematic
magnetohydrodynamic (MHD) induction equations in a 3D, rotating, spherical shell. The
induction equation is solved by means of the Anelastic Spherical Harmonic (ASH) code,
which currently serves as the dynamical core for the STABLE model. STABLE uses the
SpotMaker spot deposition algorithm to place bipolar magnetic regions (BMRs) on the
solar surface in response to the dynamo-generated toroidal magnetic _eld. In this way, the
model can be regarded as a uni_cation of BL dynamo models (2.5D in radius/latitude)
and surface ux transport models (2.5D in latitude/longitude) into a more self-consistent
framework that builds on the successes of each while capturing the full 3D structure of
the evolving magnetic _eld. The subsequent evolution of these BMRs due to di_erential
rotation, meridional circulation, inow and turbulent di_usion naturally generates a mean
poloidal _eld as originally described by Babcock (1961) and Leighton (1964).
We veri_ed the STABLE model by reproducing a 2D mean-_eld benchmark and this
model, and reproduces some basic features of the solar cycle including an 11 yr periodicity,
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equatorward migration of toroidal ux in the deep convection zone, and poleward propagation
of poloidal ux at the surface. The poleward-propagating surface ux originates
as trailing ux in BMRs, migrates poleward in multiple non-axisymmetric streams, and
eventually reverses the polar _eld, thus sustaining the dynamo. We also present some
representative dynamo simulations, focusing on the special case of kinematic magnetic
induction and axisymmetric ow _elds. Not all solutions are supercritical; it can be a
challenge for the BL mechanism to sustain the dynamo when the turbulent di_usion near
the surface is _ 1012 cm2 s1. However, if BMRs are su_ciently large, deep, and numerous,
then sustained, cyclic, dynamo solutions can be found that exhibit solar-like features.
Furthermore, we _nd that the shearing of radial magnetic ux by the surface di_erential
rotation can account for most of the net toroidal ux generation in each hemisphere, as
has been recently argued for the Sun by [Cameron and Sch ussler(2015)].
We _nd that inows into active regions can indeed enhance ux cancellation and
regulate the strength of magnetic cycles. We _nd that inows decrease the amplitude of
the polar _eld, relative to a no-inows scenario (that is the tilt angle saturation [Karak
and Miesch(2017)]). Stronger (weaker) inows lead to larger (smaller) reductions of the
polar _eld. Our STABLE simulations show that converging ows toward the BMRs
signi_cantly inhibits the build-up of the polar _eld and provide a non-linear feedback
mechanism capable of saturating the global dynamo of the solar cycle within the Babcock-
Leighton paradigm. To our knowledge this is the _rst 3D Babcock-Leighton model with
explicit BMRs to demonstrate that converging ows can serve as a viable saturation
mechanism for the solar dynamo. We also discuss how the converging ows play a key
role in determining the strength of magnetic cycles.
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Keywords
Babcock-Leighton, Solar Dynamo Modei, Active Region Inflows