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
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"
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
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
Large-Scale fields
Makarov, Sivaraman, 1983-1989
α Ω α
R h i.e. high magnetic Reynolds number
not a self-adjoint operator!
(fast time + short waves)
Quantum theory analogues - U potential - E Energy levels
Turning points - E Location of the solution
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!)
Fastest growing mode, short waves!
The simplest form (like ~ Coriolis force)
The leading mode 0: base state is the fastest growing mode!
choice of root Kuzanyan, Sokoloff (1995)
Asymptotic solution 45 o Generation Source (potential) α Envelope of the solution 27 o 80 o Wave number (real part of)
Butterfly diagram (Kuzanyan and Sokoloff 1997)
Reversal of dynamo wave to the pole
(Belvedere, Kuzanyan, Sokoloff 2000)
maximum
SOHO-MDI (Schou et al. 1998) thanks to Sasha Kosovichev http://quake.stanford.edu/~sasha/omega.gif Internal differential rotation nhz
Rotation rate maximum source reversal of the wave maximum 1D solution maximum 2D solution
reversal Distribution of generation sources in 1D model max max
Two waves equatorward poleward related to 1D solution
Sunspot wave and polar faculae
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)
Dependence of the sunspot cycle amplitude of the duration of the phase rise
Solar cycle amplitude versus maximum rate of rise (Dmitrieva, Obridko, Kuzanyan, 2000) prediction 100-114 cycle 23: 121
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
Meridional circulation in dynamo (Popova and Sokoloff, 2010)
Meridional circulation in dynamo (Popova and Sokoloff, 2010)
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!
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.
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
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
Makarov et al. 1987: polar faculae versus sunspot cycle 1987-88: some theoretical modelling with A.A. Ruzmaikin
Observations of polar faculae: phase shift with the sunspots Makarov & Sivaraman (Sol. Phys. 1989)
Makarov et al. (Sol. Phys. 2001) Large-Scale fields and Sunspot Cycle: half-cycle time lag
Hagino, Sakurai, Miyazawa (2004) correletaion of Sunspots and Polar Faculae in the cycle +/- half-cycle (5-6 yr) time lag
Jiang et al. (2007-2009) Radial field: important in the models of flux transport
Magnetic moment: Obridko and Shelting (2009); also Makarov et al. (2002)
More Observational Discussion The Polar Branch of dynamo magnetic activity traveling wave is least studied yet, UNFORTUNATELY.
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
Polar Faculae-2? Sivaraman et al. Sol.Phys. 2008
Polar Faculae? Tlatov Sol.Phys. 2009
Tlatov, Vasil yeva, Pevtsov, ApJ, 2010 Ephemeral Regions in high latitudes: anti-hale polarity
Large-scale field (zonal structures)? Tlatov & Obridko, 2012
http://www.solen.info/solar/ Polar Fields
WSO data
Polar Fields (photo&chromo-sphere) SVM/SOLIS (Kitt Peak); e.g., Raouafi et al. 2008
Polar Fields-2 (photo&chromo-sphere) BBSO; SVM/SOLIS (Kitt Peak); SOHO-MDI e.g., Varsik et al. 2002
Polar Fields-3 (photo&chromo-sphere) HINODE-SP; Ito et al. 2010
How strong are actually the Polar Fields? HINODE-SP; Ito et al. 2010 (Shiota et al. 2012)
More Observational? Extend or verify Makarov & Sivaraman result?
The end, or the time to take a breath THANK YOU спасибо! Gracias! 谢谢! ありがとう!