1. High Altitude Observatory (HAO) – National Center for Atmospheric Research (NCAR) The National Center for Atmospheric Research is operated by the University Corporation for Atmospheric Research under sponsorship of the National Science Foundation. An Equal Opportunity/Affirmative Action Employer. OBSERVATION, DATA ASSIMILATION AND SIMULATION OF GLOBAL SOLAR MAGNETIC FIELDS Mausumi Dikpati High Altitude Observatory, NCAR

2. Observations of the Sun’s global magnetic field evolution with 11 year periodicity

3. HISTORICAL BACKGROUND All global solar dynamo theory can be traced back to papers by Parker, Babcock and Leighton 1.Generation of dynamo waves from differential rotation and helical convection acting on seed magnetic fields (Parker 1955a) 2. Fluxtubes rising due to magnetic buoyancy (Parker 1955b) 3. Polar reversal due to poleward migration of poloidal flux (Babcock 1961; Leighton 1969).

4. FLUX TRANSPORT DYNAMO PROCESSES Choudhuri, Schüssler, & Dikpati, 1995 + Meridional circulation Wang & Sheeley, 1991 Durney, 1995 Dikpati & Charbonneau, 1999 Küker, Rüdiger & Schültz, 2001 And certainly many others <

5. 2D Babcock-Leighton flux-transport dynamos ρv Longitude-averaged alpha-effect Turbulent diffusivity

6. Results Contours: toroidal fields at CZ base Gray-shades: surface radial fields Observed NSO map of longitude-averaged photospheric fields

7. 3D Babcock-Leighton Flux-transport dynamo Deposit spot pairs on the surface in response to dynamo-generated toroidal field at tachocline 3D kinematic dynamo equation Miesch & Dikpati (2014) + S 1. Spot-producing toroidal fields from tachocline center 2. Threshold field strength defined Spot-maker recipe 3. Delay time (and randomness)

8. Spot-maker recipe Field of the bipolar spots at the surface : 3D structure of a bipolar spot is computed by using potential field extrapolation below the surface Gaussian or polynomial profiles with tilt given by Joy’s Law (Stenflo & Kosovichev 2012) Assumption: Spots quickly decouple from deep roots (Schussler & Rempel 2005)

9. Results from 3D Babcock-Leighton Flux-transport Dynamo At low latitudes, small-scale features appear due to eruption of tilted bipolar spots, but their dispersal by diffusion, meridional circulation and differential rotation produces mean poloidal fields Trailing flux drifts towards the poles in a series of streams and cause polar reversal Toroidal field butterfly diagram shows equatorward migration, cycle period is governed by meridional circulation Miesch & Dikpati (2014) see also Yeates & Munoz-Jaramillo (2013)

10. Toroidal, poloidal and nonaxisymmetric magnetic energies Normalization Toroidal magnetic energy: Nonaxisymmetric mag. energy: Poloidal magnetic energy:

11. Unresolved issues with global magnetic fields  Why did we not observe a dipolar corona in the last solar minimum?  What produced an unusually large phase difference (~3 years) between North and South hemispheres’ solar cycles?  What are the statistics and origins of buoyant and coalesced spots, as revealed by SDO/HMI observations? Do GONG magnetograms analysis agree with SDO/HMI?  What if the 2 nd meridional circulation cell in depth is confirmed?  Is solar dynamo on the verge of a paradigm shift?

12. Solar minimum corona during past three cycles  Solar minimum corona is normally a dipolar corona, but it was not at the end of cycle 23  Is it due to large phase difference between North and South cycles during the declining phase of cycle 23 and rising phase of cycle 24?  Global coronal structure is governed by the evolution of dynamo- generated magnetic fields; therefore it is necessary to understand the phase shift between North and South dynamos 1986 1996 2008

13. Phase shift between North and South hemispheres An unusually large phase-shift of ~3 years between North and South in cycle 24 was observed Polar fields took much longer than normal to reverse, but the North reversed about a year before the South. Sun et al. (2014)

14. Causes of phase shift between solar cycles in North and South hemispheres Phase shift can be caused by North-South asymmetries in dynamo ingredients, such as in (i)Babcock-Leighton poloidal source (Belucz et al. 2013), (ii) Meridional circulation profile and speed (Belucz & Dikpati 2013) (iii) Inflow cells associated with active regions (Shetye et al. 2015, see also Cameron & Schussler 2012). But, what physics initiates the North-South asymmetry in the dynamo ingredients?

15. Two types of spot-emergence SDO/HMI reveals that spots manifest at the surface by their buoyant eruption and also by coalescence at the surface from salt-pepper type small bipoles

16. Difference in properties between coalesced and buoyant spots Buoyant spot (NOAA11948) rotated faster than coalesced spot (NOAA 11588) Total unsigned flux is more for buoyant than coalesced spot The angle of the field to radial varies smoothly with time for the buoyant spot, but strongly fluctuates for the coalesced spot Buoyant Coalesced (Sainz-Dalda, Dikpati, Rajaguru & Judge 2015, in preparation)

17. Statistics and origin of buoyant and coalesced spots SDO/HMI images indicate there were many more coalesced than buoyant spots during early phase of cycle 24 The number of buoyant versus coalesced spots may vary with cycle phase, and from cycle to cycle. GONG magnetograms should be analysed to confirm these two types of spot- emergences in cycle 24 as well as cycle 23 Possible origins: Perhaps all spots originate from tachocline toroidal field, but coalesced spots may have fragmented into small, salt-pepper type bipoles before reaching the surface, which coalesced later to produce spots. Coalesced spots may also be coming from local dynamo action at the surface. In that case Joy’s law tilt can be weak and random, leading to weaker polar fields. Could a change in the proportions of buoyant and coalesced spots cause the low polar field strength in cycle 24?

18. Meridional Circulation is the Biggest Challenge for Flux-transport Dynamos Is meridional circulation single or multiple celled in depth? Single cell reproduces solar cycle features well. But two cells in depth generally do not. Three cells in depth have not been observed, but have been used in simulation of flux-transport dynamos (Hazra, Karak & Choudhuri 2014) to reproduce solar cycle features However many cells there are in depth, the flux-transport dynamo models need equatorward flow near the bottom, where toroidal fields can be held and amplified, to get the correct sense of migration and butterfly diagram

19. Spatial profile of the Sun’s meridional circulation is not settled Observations: Doppler measurments from MWO data indicate poleward surface flow up to ~60 degree latitude, after which it reverses (Ulrich 2010) Time distance heiloseismology using SDO/HMI data indicates two cells stacked in depth (Zhao et al. 2013) Perturbation technique using SoHO/MDI data indicates four cells in latitude (Schad et al. 2013) Ring diagram analysis from GONG data indicate a long primary cell going all the way down to the bottom of convection zone (Kholikov et al. 2014)

20. Spatial profile of the Sun’s meridional circulation is not settled (contd.) Models: Mean-field models produce one long primary cell with poleward surface flow, often associated with a weak reverse flow for a solar-like differential rotation (Ruediger 1989; Rempel 2005; Dikpati 2014) Convective simulations indicate a more complex pattern consisting of multiple cells in latitude and depth, which are non- solarlike (Gilman 1983; Guerrero et al. 2013; Featherstone and Miesch 2015) Antisolar DR; solar-like mc Solar-like DR; non-solarlike mc

21. Can we infer solar meridional circulation by applying data assimilation in solar dynamo models? True state and “synthetic” observation Reconstruction using 1 observation and 16 ensemble members Reconstruction is reasonably good, except for two windows in time For an initial guess far-off from truth, reconstructed state asymptotically converges toward the truth Dikpati, Anderson & Mitra, GRL, 2014

22. Prospects of combining data assimilation technique True state and “synthetic” observation Reconstruction using 1 observation and 16 ensemble members Reconstruction is reasonably good, except for two windows in time For an initial guess far-off from truth, reconstructed state asymptotically converges toward the truth Dikpati, Anderson & Mitra, GRL, 2014

23. Potential of EnKF data assimilation for reconstructing spatio-temporal pattern of meridional circulation What happens if the initial guess about the spatial pattern of meridional circulation is wrong? Obviously reconstructed flow-speed is not so good Correct spatial profile Incorrect spatial profile Optimum reconstruction using 160 observations and 192 ensemble members Dikpati, Anderson & Mitra, GRL, 2014; (see also Alex Fournier’s AGU Poster of last fall)

24. Flux-transport dynamos will not work for the Sun if meridional circulation consists of multiple cells in depth (Belucz, Dikpati & Forgacs-Dajka 2015, submitted) See also Jouve & Brun (2007) for another four-celled case

25. What if the 2 nd cell in depth is confirmed? Surface transport mechanism for generation and evolution of polar fields would remain unaffected Polar fields would not be able to get to the bottom to provide the seed for next dynamo cycle. Tachocline toroidal fields would migrate poleward Then a paradigm shift in solar dynamo models is necessary:  Stronger equatorward propagation needs to be created by some other mechanism, by helical flow in the tachocline combined with radial shear.  Tachocline shear needs to suppress small-scale dynamo action in the matter described by Cattaneo & Tobias (2014) However it might be premature to embrace paradigm shift, because:  There is skepticism about 2 nd cell in depth  It is theoretically difficult to produce multiple cells in depth  Another independent analysis using different instrument’s data did not confirm 2 nd cell in depth yet

26. Future measurements of greatest importance Meridional circulation profile, particularly below the outermost 30 megameters, and near the tachocline Departure of thermodynamic structure, particularly density, from spherical symmetry as in “standard” solar model Hypothesis: Every meridional circulation pattern should have a non-spherically symmetric density pattern associated with it 1.Does thermodynamic structure found “match” with meridional circulation observed? 2.Could evidence of 2 nd circulation cell in depth actually be evidence of thermodynamic structure? Or, Are all these helioseismic inferences independent of each other? Questions: Longitude dependent motion and fields in the tachocline: 1.Can large-scale nonaxisymmetric flows and magnetic fields be observed, as found in calculations of global magnetorotational instability of tachocline? 2.Can also the related longitude-dependent thermodynamic structure in the tachocline be observed?

27. Unresolved issues with polar field measurements 1.What is the polar field measurement that dynamo simulations should be compared with? 2.Is there an observed process in polar region regarding polar field strength and evolution that dynamo models are not accounting for? 3.Is it possible to have an instrument flown in an orbit around the Sun that will observe the poles on a regular basis for at least a decade? WSO polar field is the longitude-averaged mean surface line-of-sight field within the polar cap from 65-degree latitude to pole Hinode observations indicate polar regions have many “patches” of magnetic flux > 10^18 Mx, which vary strongly with cycle phase, in addition to many more small patches of weaker fields that do not vary much with cycle phase. So the solar cycle signal is carried only by the big patches. Tsuneta et al (2008)

28. Summary of requirements of new explorations of available data and requirements for new data Large North-South asymmetry in the current cycle is now an important topic of study; extend the study to longitude-dependent features GONG magnetograms need to be analysed for distinguishing buoyant-eruption versus coalescence in cycle 24 first, for calibration with SDO/HMI and then cycle 23 Does a 2 nd cell in depth exist? If so, is it a permanent or intermittent feature? Is the meridional circulation at the bottom of the convection zone poleward or equatorward? If the meridional circulation is poleward at the bottom, then another paradigm shift in solar dynamo is necessary. What form would this paradigm shift take? Search for evidence of nonspherically symmetric thermodynamic structure in the convection zone and tachocline that can be compared with theoretically obtained thermodynamic patterns Measurements of global longitude-dependent flows at the base of the convection zone, which most likely govern the global longitude-dependent magnetic features we see at the surface

29. Thank you