Asymptotic solutions for dynamo waves and polar activity in the solar cycle Kirill Kuzanyan 1,2)

Transcription

1 Asymptotic solutions for dynamo waves and polar activity in the solar cycle Kirill Kuzanyan 1,2) 1) IZMIRAN, Moscow region, Russia 2) hosted by National Astronomical Observatories,Chinese Academy of Sciences, Beijing,China Prof Hongqi ZHANG Dr Xu Haiqing; Yu GAO

2 When the night comes with the action I just know it's time to go Can't resist the strange attraction From that giantdynamo... ABBA "Summer Night City"

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4 Why asymptotic? Use analytic methods to complement numerical Study of physical mechanism of dynamo itself. Detailed study of parametric space Finding the role of key ingredients (specific factors) one by one

5 General line of studies (step-by-step) 1D model kinematic dynamo 1D nonlinear model 2D kinematic model 1D single-mode model (leading to non-axisymmetric 2D) 2D model with meridional circulation

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7 Large-Scale fields

8 Makarov, Sivaraman,

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10 α Ω α

11 R h i.e. high magnetic Reynolds number

12 not a self-adjoint operator!

13 (fast time + short waves)

14 Quantum theory analogues - U potential - E Energy levels

15 Turning points - E Location of the solution

16 Semi-classical approximation in quantum theory is usually applicable for the base level of energy (leading mode 0) as well as higher order modes. There comes only one turning point! (see V. Maslov: Semi-classical approximationbooks)! short waves! (and the maximum of the solution is not localized at the turning point!)

17 Fastest growing mode, short waves!

18 The simplest form (like ~ Coriolis force)

19 The leading mode 0: base state is the fastest growing mode!

20 choice of root Kuzanyan, Sokoloff (1995)

21 Asymptotic solution 45 o Generation Source (potential) α Envelope of the solution 27 o 80 o Wave number (real part of)

22 Butterfly diagram (Kuzanyan and Sokoloff 1997)

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24 Reversal of dynamo wave to the pole

25 (Belvedere, Kuzanyan, Sokoloff 2000)

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27 maximum

28 SOHO-MDI (Schou et al. 1998) thanks to Sasha Kosovichev Internal differential rotation nhz

29 Rotation rate maximum source reversal of the wave maximum 1D solution maximum 2D solution

30 reversal Distribution of generation sources in 1D model max max

31 Two waves equatorward poleward related to 1D solution

32 Sunspot wave and polar faculae

33 The unit of magnetic field through equipartition energy (Bassom, Kuzanyan, Soward 1999; see also Griffiths, Bassom, Soward and Kuzanyan 2001; Bassom, Kuzanyan, Sokoloff and Soward 2005)

34 Dependence of the sunspot cycle amplitude of the duration of the phase rise

35 Solar cycle amplitude versus maximum rate of rise (Dmitrieva, Obridko, Kuzanyan, 2000) prediction cycle 23: 121

36 Multiple wings of butterfly diagram in active stars Hale s number N H ~ D 1/3 N H =1 N H =2 latitude latitude Cycle number Cycle number

37 Meridional circulation in dynamo (Popova and Sokoloff, 2010)

38 Meridional circulation in dynamo (Popova and Sokoloff, 2010)

39 Summary on studies of basic properties of astrophysical dynamos by WKB asymptotics For the limit of short waves, equivalent to high magnetic Reynolds number we have used the analogue of methods or semi-classical approach in quantum mechanics. The application of the methods provided the estimates of the key trends of solar and stellar dynamos. (1) stability of the solar and stellar magnetic cycle period (2) reversal of the magnetic field dynamo wave to the pole and the equator (3) increase of magnetic activity towards the direction of the dynamo wave propagation (4) propagation of magnetic activity waves mainly along constant internal angular velocity (so-called Yoshimura- Parker law) (5) interaction of the dynamo wave branches across the solar equator (6) excitation of non-axisymmetric structures with dependence on differential rotation profile (7) qualitative change in dynamo waves with meridional circulation and more applications!

40 The two big problems of the solar dynamo Inability of advanced DNS numerical models to correctly reproduce the key details of the dynamo wave-like activity and the cycle Difficulty to use additional observational factors such as parameters of the solar turbulence, magnetic and crosshelicity, meridional flow structure in order to improve simple 1-2 D dynamo models relying upon assumption of the alpha-effect. Helicities are related with the invariant of motions under certain (through drastic) conditions, the hope is that they can be used as observational proxies of the magnetic activity and turbulence beneath the solar photosphere where they are observed.

41 Let us focus on the Pole! Poleward migration of activity Mistery of the large scale magnetic fields Various proxies of the poloidal field Importance in modelling and prediction

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43 Why polar? The polar magnetic fields are further additional observational manifestations of the solar dynamo mechanism. They have been systematically observed for a number of years by means of polar faculae and bright points (see Makarov and Sivaraman, 1981 and afterwards). Further along, the polar branch of the dynamo wave have been theoretically investigated

44 Makarov et al. 1987: polar faculae versus sunspot cycle : some theoretical modelling with A.A. Ruzmaikin

45 Observations of polar faculae: phase shift with the sunspots Makarov & Sivaraman (Sol. Phys. 1989)

46 Makarov et al. (Sol. Phys. 2001) Large-Scale fields and Sunspot Cycle: half-cycle time lag

47 Hagino, Sakurai, Miyazawa (2004) correletaion of Sunspots and Polar Faculae in the cycle +/- half-cycle (5-6 yr) time lag

48 Jiang et al. ( ) Radial field: important in the models of flux transport

49 Magnetic moment: Obridko and Shelting (2009); also Makarov et al. (2002)

50 More Observational Discussion The Polar Branch of dynamo magnetic activity traveling wave is least studied yet, UNFORTUNATELY.

51 Belvedere, Kuzanyan, Sokoloff (2000): analytic 2D dynamo with the two waves (equatorward and poleward ) angular rotation maximum source turning of the wave maximum 1D solution maximum 2D solution after Kuzanyan and Sokoloff (1995): 1D dynamo

52 Polar Faculae-2? Sivaraman et al. Sol.Phys. 2008

53 Polar Faculae? Tlatov Sol.Phys. 2009

54 Tlatov, Vasil yeva, Pevtsov, ApJ, 2010 Ephemeral Regions in high latitudes: anti-hale polarity

55 Large-scale field (zonal structures)? Tlatov & Obridko, 2012

56 Polar Fields

57 WSO data

58 Polar Fields (photo&chromo-sphere) SVM/SOLIS (Kitt Peak); e.g., Raouafi et al. 2008

59 Polar Fields-2 (photo&chromo-sphere) BBSO; SVM/SOLIS (Kitt Peak); SOHO-MDI e.g., Varsik et al. 2002

60 Polar Fields-3 (photo&chromo-sphere) HINODE-SP; Ito et al. 2010

61 How strong are actually the Polar Fields? HINODE-SP; Ito et al (Shiota et al. 2012)

62 More Observational? Extend or verify Makarov & Sivaraman result?

63 The end, or the time to take a breath THANK YOU спасибо! Gracias! 谢谢! ありがとう!