Solar cycles vary from 9 to 14 years in length. Over time, however, they never departs from the 11-year average cycle length for more than a couple of cyclesmuch less than a random series would. "It's been said that the sun has a clock and the clock is always adjusted," says Dikpati. She and Charbonneau are the first to succeed in simulating this behavior.
The cycles are caused by changes in the sun's magnetic fields, whose behavior is far more complex than that of the earth. A large-scale, toroidal (doughnut-shaped) magnetic field wraps around the sun's rotational axis like a belt, with the inside edge of the doughnut extending into the solar interior. "The toroidal field is easy to observe," says Charbonneau. "You can see it by looking at sunspots." This field reverses polarity about once every 11 years. The Sun also has a weaker, poloidal (bar-magnet- shaped) fieldthe same shape as the earth's magnetic fieldwhich also flips poles every 11 years. This field is usually inferred from structures in the solar corona rather than measured directly, which is hard to do from the earth's viewing angle.
The theory on why these two fields switch back and forth in sync, Charbonneau explains, is that the poloidal field is transformed into a toroidal field, which then turns back into a poloidal one of the opposite polarity, and so on. Modelers have long been able to reproduce the transformation of a poloidal to a toroidal field. "It's not that hard to model the Sun's fluid center and shear regions," says Charbonneau. "If you shove a magnetic field in [the model], it behaves like a Slinky"the north-south field gets stretched further and further until it wraps around the rotational axis.
The hard part has been understanding and modeling the change back from a toroidal field to a poloidal field. Most solar dynamo models rely on small-scale convective turbulence to do the job, but that would require a relatively weak magnetic field in the solar interior, contrary to observational evidence. Also, with these models, a stronger solar cycle takes longer to dissipate and a weaker one is over soonerthe opposite of reality.
Another type of model, the Babcock-Leighton model, uses a different mechanism. Magnetic fields released by decaying sunspots around the equator are carried poleward by north-south (meridional) plasma flows, and thence to the solar interior. Babcock-Leighton models were developed in the 1960s but, with little observational evidence to back them up, fell into neglect.
Helioseismologythe new science that studies the solar interior by way of acoustic oscillations observed on the surfacehas changed that. "Now explanations for what is happening in the sun are constrained by reality," says Charbonneau. "It turns out that things we thought happened only on the surface happen well into the sun."
Charbonneau and Dikpati constructed a new Babcock-Leighton model with realistic fluid flows from helioseismology data. The model could reproduce many observed features of the solar cycle, such as the movement of sunspot emergence from higher to lower latitudes and the polarity flips. Furthermore, it could reproduce the observed phase relationship between the poloidal and toroidal magnetic components. "So that was very encouraging," says Charbonneau.
The HAO researchers then turned to the problem of reproducing the variable solar cycle. Although meridional flows carry large amounts of magnetic fields over time, they are quite weak, so they can be easily disrupted by the intense turbulent motions within the sun's convective envelope. To model this disruption, Dikpati and Charbonneau introduced random fluctuations into their meridional flows. These fluctuations caused the modeled solar- cycle lengths to vary from about 9 to 14 yearsthe same time span that has been observed in the sun over the centuries.
The average rate at which magnetic fields are transported poleward by the plasma flows is about the same in each solar cycle, no matter how large or small the modeled fluctuations are. Thus, when the flows are disrupted more than usual, the cycle lasts longer but is weaker, and conversely less disruption means a shorter, stronger cycle. Although the largest fluctuations suppress or amplify the transport process for a while, it returns to its average rate within a few cycles, just as the sun does.
Charbonneau and Dikpati have presented their results at conferences "and have always had a lot of interest," Charbonneau says. "We expect that because of our work, and that of Bernard Durney (University of Arizona) and the team at [the Naval Research Laboratory], more people will be using these models."