Stochastic Fluctuations in a Babcock‐Leighton Model of the Solar Cycle

Charbonneau, Paul; Dikpati, Mausumi

doi:10.1086/317142

Cited by 171 publications

(199 citation statements)

References 57 publications

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“…Assuming a sinusoidal behavior with an additional 33% increase in flow velocity at the peak gives an amplitude of about 1.2 m s À1 for the average counterflow at the base of the SCZ toward the equator. Variations in this flow speed from cycle to cycle should be quite large, as judged by the variations seen at 25 in Figure 3, a result consistent with the dynamo modeling of Charbonneau & Dikpati (2000) and Wang et al (2002).…”

Section: Observations Analyses and Resultssupporting

confidence: 79%

“…Fluctuations in the meridional flow (Hathaway 1996), believed to be a product of turbulent convection, have also successfully accounted for variations in the solar cycle that are superposed on the otherwise stable 11 yr periodicity (Charbonneau & Dikpati 2000;Wang et al 2002). From this it has been conjectured that the meridional circulation acts like a solar clock to set the cycle period.…”

Section: Introductionmentioning

confidence: 95%

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Evidence That a Deep Meridional Flow Sets the Sunspot Cycle Period

Hathaway

Nandy

Wilson

et al. 2003

ApJ

149

119

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Sunspots appear on the Sun in two bands on either side of the equator that drift toward lower latitudes as each sunspot cycle progresses. We examine the drift of the centroid of the sunspot area toward the equator in each hemisphere from 1874 to 2002 and find that the drift rate slows as the centroid approaches the equator. We compare the drift rate at sunspot cycle maximum with the period of each cycle for each hemisphere and find a highly significant anticorrelation: hemispheres with faster drift rates have shorter periods. These observations are consistent with a meridional counterflow deep within the Sun as the primary driver of the migration toward the equator and the period associated with the sunspot cycle. We also find that the drift rate at maximum is significantly correlated with the amplitude of the following cycle, a prediction of dynamo models that employ a deep meridional flow toward the equator. Our results indicate an amplitude of about 1.2 m s À1 for the meridional flow velocity at the base of the solar convection zone.

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Section: Observations Analyses and Resultssupporting

confidence: 79%

Section: Introductionmentioning

confidence: 95%

Evidence That a Deep Meridional Flow Sets the Sunspot Cycle Period

Hathaway

Nandy

Wilson

et al. 2003

ApJ

149

119

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“…This suggests that if the tilt angles are large, then the next cycle will be short. The fact that the correlation of tilt with the length of the next cycle is significant, but is poor with the strength of the next cycle is consistent with the finding that the length and strength of a cycle are poorly correlated (r c = −0.37, Charbonneau & Dikpati 2000; and r c = −0.35, Solanki et al 2002). Now, tilt angles influence the amount of magnetic flux reaching the poles (Baumann et al 2004) and the polar magnetic flux during activity minimum has been found to be one of the proxies that best predicts the strength of the next cycle (Makarov et al 1989;.…”

Section: Relationships With the Following Cyclesupporting

confidence: 81%

Sunspot group tilt angles and the strength of the solar cycle

Dasi-Espuig¹,

Solanki

Krivova³

et al. 2010

A&A

218

232

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Context. It is well known that the tilt angles of active regions increase with their latitude (Joy's law). It has never been checked before, however, whether the average tilt angles change from one cycle to the next. Flux transport models show the importance of tilt angles for the reversal and build up of magnetic flux at the poles, which is in turn correlated to the strength of the next cycle. Aims. Here we analyse time series of tilt angle measurements and look for a possible relationship of the tilt angles with other solar cycle parameters, in order to glean information on the solar dynamo and to estimate their potential for predicting solar activity. Methods. We employed tilt angle data from Mount Wilson and Kodaikanal observatories covering solar cycles 15 to 21. We analyse the latitudinal distribution of the tilt angles (Joy's law), their variation from cycle to cycle, and their relationship to other solar cycle parameters, such as the strength (or total area covered by sunspots in a cycle), amplitude, and length. Results. The two main results of our analysis follow. 1. We find an anti-correlation between the mean normalised tilt angle of a given cycle and the strength (or amplitude) of that cycle, with a correlation coefficient of r c = −0.95 (99.9% confidence level) and r c = −0.93 (99.76% confidence level) for Mount Wilson and Kodaikanal data, respectively. 2. The product of the cycle's averaged tilt angle and the strength of the same cycle displays a significant correlation with the strength of the next cycle (r c = 0.65 at 89% confidence level and r c = 0.70 at 92% confidence level for Mount Wilson and Kodaikanal data, respectively). An even better correlation is obtained between the source term of the poloidal flux in Babcock-Leighton-type dynamos (which contains the tilt angle) and the amplitude of the next cycle. Further we confirm the linear relationship (Joy's law) between the tilt angle and latitude with slopes of 0.26 and 0.28 for Mount Wilson and Kodaikanal data, respectively. In addition, we obtain good positive correlations between the normalised-areaweighted tilt angle and the length of the following cycle, whereas the strength or the amplitude of the next cycle does not appear to be correlated to the tilt angles of the current cycle alone. Conclusions. The results of this study indicate that, in combination with the cycle strength, the active region tilt angles play an important role in building up the polar fields at cycle minimum.

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“…In particular, we can expect the time delay due to the advection by the meridional flow (which has a characteristic time-scale of a few solar cycles, see for example Charbonneau & Dikpati 2000) to be much more effective on the behaviour of the dynamo-generated magnetic field. As a consequence, it is mainly the effect of meridional flow which has been tested in previous models (e.g.…”

Section: Discussionmentioning

confidence: 99%

Buoyancy-induced time delays in Babcock-Leighton flux-transport dynamo models

Jouve¹,

Proctor²,

Lesur³

2010

A&A

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Context. The Sun is a magnetic star whose cyclic activity is thought to be linked to internal dynamo mechanisms. A combination of numerical modelling with various levels of complexity is an efficient and accurate tool to investigate such intricate dynamical processes. Aims. We investigate the role of the magnetic buoyancy process in 2D Babcock-Leighton dynamo models, by modelling more accurately the surface source term for poloidal field. Methods. To do so, we reintroduce in mean-field models the results of full 3D MHD calculations of the non-linear evolution of a rising flux tube in a convective shell. More specifically, the Babcock-Leighton source term is modified to take into account the delay introduced by the rise time of the toroidal structures from the base of the convection zone to the solar surface. Results. We find that the time delays introduced in the equations produce large temporal modulation of the cycle amplitude even when strong and thus rapidly rising flux tubes are considered. Aperiodic modulations of the solar cycle appear after a sequence of period doubling bifurcations typical of non-linear systems. The strong effects introduced even by small delays is found to be due to the dependence of the delays on the magnetic field strength at the base of the convection zone, the modulation being much less when time delays remain constant. We do not find any significant influence on the cycle period except when the delays are made artificially strong. Conclusions. A possible new origin of the solar cycle variability is here revealed. This modulated activity and the resulting butterfly diagram are then more compatible with observations than what the standard Babcock-Leighton model produces.

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Stochastic Fluctuations in a Babcock‐Leighton Model of the Solar Cycle

Cited by 171 publications

References 57 publications

Evidence That a Deep Meridional Flow Sets the Sunspot Cycle Period

Evidence That a Deep Meridional Flow Sets the Sunspot Cycle Period

Sunspot group tilt angles and the strength of the solar cycle

Buoyancy-induced time delays in Babcock-Leighton flux-transport dynamo models

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