Babcock Model

The Babcock Model describes a mechanism which can explain magnetic and sunspot patterns observed on the Sun.

A modern understanding of sunspots starts with George Ellery Hale, in which magnetic fields and sunspots are linked. Hale suggested that the sunspot cycle period is 22 years, covering two polar reversals of the solar magnetic dipole field.

Butterfly diagram showing paired sunspot pattern. Graph is sunspot Wolf number.

Horace W. Babcock proposed in 1961 a qualitative model for solar dynamics. On the largest scale, the Sun supports an oscillatory magnetic field, with a quasi-steady periodicity of 22 years.^[1][2] This oscillation is known as the Babcock-Leighton dynamo cycle, amounting to the oscillatory exchange of energy between poloidal and toroidal solar magnetic field ingredients. A half dynamo cycle corresponds to a single sunspot solar cycle. At solar-cycle maximum, the external poloidal dipolar magnetic field is near its dynamo-cycle minimum strength, but an internal toroidal quadrupolar field, generated through differential rotation, is near its maximum strength. At this point in the dynamo cycle, buoyant upwelling within the convective zone forces emergence of toroidal magnetic field through the photosphere, giving rise to patches of concentrated magnetic field corresponding to sunspots. During the solar cycle’s declining phase, energy shifts from the internal toroidal magnetic field to the external poloidal field, and sunspots diminish in number. At solar-cycle minimum, the toroidal field is, correspondingly, at minimum strength, sunspots are few in number, and the poloidal field is at its maximum strength. With the rise of the next 11 year sunspot cycle, magnetic energy shifts back from the poloidal to the toroidal field, but with a polarity that is opposite to the previous cycle. The process carries on continuously, and in an idealized, simplified scenario, each 11 year sunspot cycle corresponds to a change in the overall polarity of the Sun's large-scale magnetic field.^[3][4]

• The start of the 22-year cycle begins with a well-established dipole field component aligned along the solar rotational axis. The field lines tend to be held by the highly conductive solar plasma of the solar surface.
• The solar surface plasma rotation rate is different at different latitudes, and the rotation rate is 20 percent faster at the equator than at the poles (one rotation every 27 days). Consequently, the magnetic field lines are wrapped by 20 percent every 27 days.
• After many rotations, the field lines become highly twisted and bundled, increasing their intensity, and the resulting buoyancy lifts the bundle to the solar surface, forming a bipolar field that appears as two spots, being kinks in the field lines.
• The sunspots result from the strong local magnetic fields in the solar surface that exclude the light-emitting solar plasma and appear as darkened spots on the solar surface.
• The leading spot of the bipolar field has the same polarity as the solar hemisphere, and the trailing spot is of opposite polarity. The leading spot of the bipolar field tends to migrate towards the equator, while the trailing spot of opposite polarity migrates towards the solar pole of the respective hemisphere with a resultant reduction of the solar dipole moment. This process of sunspot formation and migration continues until the solar dipole field reverses (after about 11 years).
• The solar dipole field, through similar processes, reverses again at the end of the 22-year cycle.

• The magnetic field of the spot at the equator sometimes weakens, allowing an influx of coronal plasma that increases the internal pressure and forms a magnetic bubble which may burst and produce an ejection of coronal mass, leaving a coronal hole with open field lines. Such a coronal mass ejections are a source of the high-speed solar wind.
• The fluctuations in the bundled fields convert magnetic field energy into plasma heating, producing emission of electromagnetic radiation as intense ultraviolet (UV) and X-rays.

References

• Babcock, H. W. (1961). "The Topology of the Sun's Magnetic Field and the 22-Year Cycle". Astrophys. J. 133 (2): 572–587. Bibcode:1961ApJ...133..572B. doi:10.1086/147060.