Possible explanations of the Maunder minimum from a flux transport dynamo model

arXiv:1101.4342v1 [astro-ph.SR] 23 Jan 2011 Title of your IAU Symposium Proceedings IAU Symposium No. xxx, 2010 A.C. Editor, B.D. Editor & C.E. Editor, eds. c⃝2010 International Astronomical Union DOI: 00.0000/X000000000000000X Possible explanations of the Maunder minimum from a flux transport dynamo model Bidya Binay Karak and Arnab Rai Choudhuri Department of Physics, Indian Institute of Science, Bangalore-560012 email: bidya karak@physics.iisc.ernet.in, arnab@physics.iisc.ernet.in Abstract. We propose that at the beginning of the Maunder minimum the poloidal field or amplitude of meridional circulation or both fell abruptly to low values. With this proposition, a flux transport dynamo model is able to reproduce various important aspects of the historical records of the Maunder minimum remarkably well. Keywords. Sun: activity – Sun: magnetic field, meridional circulation 1. Introduction One important aspect of the solar cycle is the Maunder minimum during 1645–1715 when the solar activity was strongly reduced (Ribes & Nesme-Ribes 1993). It was not an artifact of few observations, but a real phenomenon (Hoyt & Schatten 1996). From the study of historical data (Ribes & Nesme-Ribes 1993), it has been confirmed that the sunspot numbers in both the hemisphere fell abruptly to nearly zero value at the beginning of the Maunder minimum, whereas a few sunspots appeared in the southern hemisphere during the last phase. It is also established from the cosmogenic isotopes data (Beer et al. 1998; Miyahara et al. 2004) that the cyclic oscillations of solar activity continued in the heliosphere at a weaker level during the Maunder minimum, but with a period of 13–15 years instead of the regular 11-year period. The most promising model of studying solar cycle at present is the flux transport dynamo model (Choudhuri et al. 1995; Durney 1995; Dikpati & Charbonneau 1999; Chatterjee et al. 2004). The main sources of irregularities in this model are the stochastic fluctuations in the Babcock–Leighton process of poloidal field generation (Choudhuri 1992; Choudhuri et al. 2007) and the stochastic fluctuations of meridional circulation (hereafter MC) (Hathaway 1996). Therefore we propose that the polar field or amplitude of MC or both decreased at the beginning of Maunder minimum. With this proposition, we use a flux transport dynamo model to reproduce a Maunder minimum. The details of this work can be found in Choudhuri & Karak (2009) and Karak (2010). 2. Methodology We cary out all the analyses with the flux transport dynamo model described in Chat- terjee et al. (2004). To reproduce the Maunder minimum, we perform the following three separate sets of experiments. Similar to Choudhuri et al. (2007), first, we decrease the polar field above 0.8R⊙by a factor γ after stopping the code at a solar minimum. We change the polar field by different amount in two hemispheres. In northern hemisphere, we take γ = 0.0, whereas in southern hemisphere, it is 0.4. In addition, in this calculation, 119 120 Karak & Choudhuri 1640 1650 1660 1670 1680 1690 1700 1710 1720 1730 1740 1750 −60 −40 −20 0 20 40 60 Year Latitude (a) 1640 1650 1660 1670 1680 1690 1700 1710 1720 1730 1740 1750 0 2 4 6 8 10 Year Sunspot number (b) Figure 1. Results covering the Maunder minimum episode. (a) The butterfly diagram. (b) The smoothed sunspot number. The dashed and dotted lines show the sunspot numbers in southern and northern hemispheres, whereas the solid line is the total sunspot number. From Choudhuri & Karak (2009). we decrease the toroidal field by multiplying it everywhere by 0.8 to stop the eruption for some time. This essentially reduces the strong overlap between two cycles in our model (see figure 13 of Chatterjee et al. 2004). After making these changes, we run the model for several cycles without any further change. In the second procedure for reproducing the Maunder minimum, we decrease the amplitude of MC v0 abruptly to a very low value. After keeping it at low value for few years, we again increase it to the usual value but at different rates in two hemispheres. In the northern hemisphere, it is increased at slightly lower rate than the southern hemisphere. Note that in this case we have varied only v0 and no other parameters of the model. We have repeated this calculation in the low diffusivity model of Dikpati & Charbonneau (1999) too. Last, we have included the effect of the fluctuations of polar field along with the fluctuations of MC. We have run the model for different values of γs from 0 to 1 at each values of v0 from a very low value to the average value. Then we find out the critical values of v0 and the corresponding γ factor for which we get a Maunder-like minimum. 3. Results First, we discuss the results from the polar field reduction procedure. It is shown in Fig. 1 (see the caption also). In order to facilitate the comparison with the observation data, we have marked the beginning of Fig. 1 to be the year 1640. From this figure we see that the sudden initiati

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