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Multiscale convection _amp; MHD in the quiet photosphere

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Multiscale convection _amp; MHD in the quiet photosphere Powered By Docstoc
					Multiscale convection & MHD
  in the quiet photosphere

 M. Rieutord, F. Rincon, Th. Roudier &
the Toulouse-Tarbes solar physics group
     Laboratoire d’Astrophysique de Toulouse-Tarbes
            CNRS et Université de Toulouse
Talk outline
• Observations     of quiet Sun dynamics
  •   Multiscale convection
  •   Magnetic fields

• Open    questions
  •   Production of magnetic field in the quiet Sun
  •   Large-scale MHD, network and supergranulation formation

• Current   modelling efforts
  •   Simple supergranulation models
  •   Large-scale simulations: hydro & MHD
  •   Turbulent dynamo simulations

• Perspectives
                                                                EST Worshop 2010
A brief recap of quiet Sun dynamics
Multiscale convection: granulation
•   A photometric feature paving the surface (Herschel 1801)
•   L ~ 1 Mm, lifetime ~ 5 min
•   Horizontal velocities ~ a few km/s

                                                        Hinode/SOT
Multiscale convection: supergranulation
•   Discovered by Hart (MNRAS, 1954) w. Dopplergram correlations

•   Pops up mostly in spectroscopy, i. e. Dopplergrams: orange skin
     •   Very weak or no temperature signal            (MDI/SOHO)



•   L ~ 30 Mm, lifetime ~ 1.8 days

•   Horizontal velocities ~ 360 m/s
     •   Velocity signal almost horizontal

•   Supergranules may be shallow
     •   Depth < 5 Mm ? (Duval ‘98, Sekii ’07)

•   Affected by solar rotation
     •   Travelling waves ? (Gizon ‘03)
MDI spectra, supergranulation & turbulence
• Hathaway   et al., Sol. Phys. 2000


                 SG
                l=120      Granulation




                                         EST Worshop 2010
Quiet Sun magnetism: network fields
•   Identified as a distribution of bright points and kG magnetic fields

•   Strongly correlated with the supergranulation pattern
    (Leighton, ApJ1964, Hagenaar et al., ApJ 1997)
     •   L ~15-20 Mm




                                                               EST Worshop 2010
Quiet Sun magnetism: internetwork fields
• “Small-scale”    fields with
  •   Mixed-polarities
  •   Horizontal & vertical components
  •   Scales down to 100km and less

• Typically   50-200 G




                                         (Lites et al., ApJ 2008)




Dominguez-Cerdena et al., A&A 2003)                                 EST Worshop 2010
Open questions and big picture...
 The “standard” picture so far
• Quiet    Sun MHD up to supergranulation scales
                                               λ = 36 Mm
                                                                                    δT < 3 K

                                                           I.N.B
τ =1
5 Mm
                                     300 m/s


                                  30 m/s
           Network

                                                                   d = 20 − 30 Mm

                               Rieutord & Rincon, Liv. Rev. Sol. Phys. (2010)
• But   this picture raises a lot of tricky questions
   •   How does supergranulation originate ?
   •   Do network & internetwork fields have a different physical origin ?
   •   How does SG interact with quiet Sun magnetic fields ?
                                                                                       EST Worshop 2010
  What we have to understand (tentative)
E(k)      LSG ∼ 36 Mm        LG ∼ 1.5 Mm                  η   ∼ 100 m              ν   ∼ 0.1 m
                                                                                                   L
        Supergranulation ?
                               Granulation
                             Injection range                        Pm        1
                                                                    Re       Rm        1




                                        Magnetic energy          Kinetic energy



                 Network to internetwork transition




       Rieutord & Rincon, Liv. Rev. Sol. Phys. (2010)
                                                                        −1
                                                                                                   k
        kSG ∼ 0.17 Mm   −1
                              kG ∼ 4.2 Mm      −1
                                                          kη ∼ 60 km              kν ∼ 60 m   −1



  Deal with a scale ratio of 1 million to solve the problem in full details
                     Focus on small bits of the puzzle !          EST Worshop 2010
1 - Origin of quiet Sun magnetic fields
• Small-scale,    local dynamo action close to the surface ?
  •   Produces disordered magnetic field on minute scales
  •   Interactions with multiscale convection ?

• Links   with the global solar dynamo field ?
  •   Reprocessing of active regions Mm
                          E(k) L ∼ 36
                                 SG
                                      ?            LG ∼ 1.5 Mm                  η   ∼ 100 m             ν   ∼ 0.1 m

                              Supergranulation ?

  •   Emergence of deep fields ?                      Granulation
                                                   Injection range                        Pm    1
                                                                                          Re   Rm           1
  •   Cycle dependence ?

   Sub-granulation fields                                      Magnetic energy          Kinetic energy


      Terra Incognita                  Network to internetwork transition



      Can we differentiate ?
                              kSG ∼ 0.17 Mm−1 kG ∼ 4.2 Mm−1                     kη ∼ 60 km−1 EST Worshop60 m−1
                                                                                                   kν ∼ 2010
2 - Large-scale MHD interactions
• SG   and the network may originate in coupled, dynamical way
• How     do quiet Sun fields couple to multiscale convection ?
  •   Near equipartition at SG scales ? Non-local interactions ?
  •   Effective magneto-elastic fluid ? (e.g. Longcope et al. 2003)
                                                                                            ∼ 100 m
  •   ... ?                    E(k)     LSG ∼ 36 Mm        LG ∼ 1.5 Mm                  η


                                      Supergranulation ?
                                                             Granulation
                                                           Injection range                        Pm    1
Large-scale dynamical                                                                             Re   Rm


feedback of quiet Sun
   magnetic fields                                                     Magnetic energy          Kinetic energ



      Terra incognita                          Network to internetwork transition




                                      kSG ∼ 0.17 Mm−1 kG ∼ 4.2 Mm−1                        ∼ Worshop
                                                                                        kηEST60 km−1 2010
Current modelling efforts
Modelling: properties of solar turbulence
• Dimensionless          numbers
   •     Rayleigh = Engine (gravity) / Brakes (viscous + thermal) = O(1022)
   •     Reynolds = Inertia / Viscosity = O(1011)
   •     Prandtl = Viscosity / Diffusion = O(10-6 - 10-4)
   •     Magnetic Prandtl = Viscosity / Resistivity = O(10-5 - 10-2)


                         It’s very   large or very          small


• Solar     convection is hugely turbulent
   •     Impacts mean thermal/density profiles, rotation rates
   •     helps to generate magnetic field through dynamo action

• It’s   impossible to simulate it directly
                                                                              EST Worshop 2010
Granulation modelling
•A    thermal boundary layer effect (Stein & Nordlund, ApJ 1998)
  •   Radiative cooling of hot gas - diffusion-dominated process
         •   non-adiabatic by definition

         •   turbulent dynamics not crucial to obtain thermal structure




• More    idealized models also produce some granulation
                                                                          EST Worshop 2010
Linear and kinematic SG models
• Standard     model: hierarchical linear instabilities
  •   Supergranulation: He II recombination ? (Simon & Leighton, ApJ 1964)
  •   Mesogranulation: He I recombination ? (November & Weiss, ApJ 1988)
  •   Granulation: Hydrogen recombination
• Laminar     view
  •   No turbulence
  •   No energy transfer between scales
                                                     Hydrogen recombines
• Raises    important questions
  •   Is turbulence important ?
                                                       He I recombines
        •   Re = 1010, Ra = 1020 !

  •   How deep does SG extend ?
                                                      He II recombines
                                                                           EST Worshop 2010
Linear and kinematic SG models (2)
• Turbulent       diffusion at sub-supergranulation scales ?
  •   Subsequently assume large-scale solar convection is linear

        •   Simon & Leighton hierarchical picture (ApJ, 1964)

        •   Fixed heat flux magnetoconvection (Rincon & Rieutord ‘05)

        •   Magneto-sheared linear convection (Green & Kosovichev ‘06-’07)

        •   ...

• We   can also decide to forget about the physical dynamics
  •   Make kinematic cork models of multiscale convection
        •   “N-body advective-interaction model” with granular plumes (Rast et al. ’03)

        •   “magnetic N-body diffusion-limited aggregation code” (Crouch et al. ’07)


                                                                              EST Worshop 2010
Multiscale MHD convection: turbulent view
• Simple    linear/kinematic models are not satisfactory

                                      Why ?

• Scale   interactions are important
  •   Reynolds stresses, nonlinear transfers, instabilities
  •   Turbulent transport in general: diff. rotation, turbulent magnetic diffusion...
  •   Interactions with magnetic fields at all scales

• Only    numerical simulations can help
  •   Local (cartesian) / Global (spherical)
  •   Hydro / MHD
  •   Magnetoconvection (uniform field) / dynamo (consistent field production)
                                                                           EST Worshop 2010
Local hydro simulations at SG scales
•   Cattaneo et al., ApJ 2001
     •   Incompressible simulations
     •   Effective simulation box ~30 Mm wide, ~1Mm deep


•   Rincon, Lignières, Rieutord, A&A 2005
     •   Compressible, stratified simulations
     •   Effective simulation box
         ~64 Mm wide, ~2 Mm deep



Coherent mesoscale structures
  but not supergranulation

                                                           EST Worshop 2010
Coherent structures at mesoscales




•

    Surface ~ granules   In depth ~ mesoscales
                                         EST Worshop 2010
Current biggest local experiment
• 96   Mm x 96 Mm x 20 Mm “realistic” simulations
• Includes   He II, He I & H recombination
• No   magnetic field
                                      (Benson et al. 2006, Stein et al. 2007)




                                                                EST Worshop 2010
          Velocity spectra and scales
       • Self-similar                        behaviour at large scales
                               •   No supergranulation                   Stein et al., IAUS 2007

       • Sharp                         dynamical cut-off at ~ 100 km
                               •   Unresolved turbulent dynamics
Georgobiani et al., ApJ 2007




                                                                                     EST Worshop 2010
Global hydro numerical simulations
• ASH   simulations of a thin stratified shell (DeRosa et al., ApJ 2002)
  • Anelastic
  • Supergranulation-scale motions barely captured by the grid

        •   mesh size ~ 10 Mm
  •   Effective box depth ~ 56 Mm




Supergranulation does not emerge as
     a particular physical scale




                                                                 EST Worshop 2010
Discussion: numerical limitations
• We    don’t have dynamical supergranulation scales yet
   •   In global simulations, supergranulation is at grid scale
   •   In local simulations, supergranulation is at box scale

• Stein   et al. simulations
   •    small-scale turbulent dynamics is sacrificed: dissipation coefficients ?

• Cattaneo      / Rincon et al. simulations
   •   Thermodynamic profiles are not realistic + No radiative transfer

• All   simulations
   •   have an issue with thermal relaxation at supergranulation scales
   •   have no subsurface shear layer
   •   MISS MAGNETIC FIELDS
                                                                          EST Worshop 2010
First large-scale MHD simulations coming
•   Ustyugov 2009: some network-SG formation ?




•   Ongoing efforts by the Stein & Nordlund group
• This     is all very preliminary
     •   Large boxes but fairly low resolutions
     •   B is not consistently produced: e.g. no small-scale dynamo action
                                                                             EST Worshop 2010
Quiet Sun magnetic fields: dynamo action ?
•   Voegler et al., A&A 2007, Schuessler et al., A&A 2008
     •   Turbulent dynamo simulations of solar-like convection (i.e. “realistic”)




                                       Pm ~ 1                               EST Worshop 2010
Turbulent dynamo simulations and Pm
• Turbulent     convection is a small-scale dynamo at large Pm
 (Nordlund et al., ApJ 1992, Brandenburg et al., JFM 1996 - Cattaneo et al., ApJL 1999)
  •   ...but disappears at low Pm in numerical simulations (Ra < 108)




                                                                Cattaneo et al., ApJL 1999

                                                               Bushby et al., private comm.


                                                                                     EST Worshop 2010
Why
•   It is harder to make a small-scale dynamo in a rough velocity field

                                            Schekochihin et al., NJP 2007




                                      Rmc increases at large Re
                                                                  EST Worshop 2010
 The issue




  Current
“solar-like”                            Quiet
simulations                             Sun



               Why is this an issue ?
                                           EST Worshop 2010
“Large” Pm isotropic MHD turbulence
• Re=440,   Rm=440, Pm=1 (Schekochihin et al., NJP 2007)




               v                                    B
                                                           EST Worshop 2010
Low Pm isotropic MHD turbulence
• Re=6200,      Rm=430, Pm=0.07 (Schekochihin et al., NJP 2007)




                   v                                         B
  •   The kinematic field has very different statistical properties
  •   Nobody knows how and at which level this dynamo saturates
                                                                     EST Worshop 2010
Perspectives
Observations: ways to make progress
• Improved      knowledged of the magnetic energy spectrum
   •   Spectral scaling laws for L<1 Mm ? L >10 Mm ?

“Network”                                                    “Internetwork “
  side                                                             side

                                                            Abramenko et al.,
                                                             Sol. Phys. 2001




• Intensity,   scale and geometry of B at subgranulation scales
   •   Spectropolarimetry + Hanle (e.g. Lopez Ariste et al., ApJ 2010)
                                                                         EST Worshop 2010
Numerics: go strongly multiscale !
• Coupled       network / SG simulations
  •   Identify magnetic feedback processes in extended convective domains
         •   Flux expulsion, irradiation effects, magneto-elasticity

• Turbulent      MHD in a uniform field vs. Turbulent dynamo
  •   Does the nonlinear dynamics depend on how the field originates ?
  •   What kind of magnetic spectrum do we expect asymptotically ?

• Saturated      turbulent dynamo action at low Pm and high Rm
  •   Saturation amplitude ? Field structure ?
  •   Structure of the dynamo field at large scales ? (e.g. Malyshkin & Boldyrev ’09)


• Numerical        and theoretical work for the next 20 years
                                                                          EST Worshop 2010
  To be continued and improved...
E(k)     LSG ∼ 36 Mm        LG ∼ 1.5 Mm                           η   ∼ 100 m              ν   ∼ 0.1 m
                                                                                                             L
       Supergranulation ?
                              Granulation
                            Injection range                                 Pm        1
                                                                            Re       Rm        1




                                       Magnetic energy                   Kinetic energy



                Network to internetwork transition




                                                                                −1
                                                                                                             k
       kSG ∼ 0.17 Mm   −1
                             kG ∼ 4.2 Mm      −1
                                                                 kη ∼ 60 km               kν ∼ 60 m     −1



                              Rieutord & Rincon, Liv. Rev. Sol. Phys. (2010)
                                                                                               EST Worshop 2010

				
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posted:11/29/2011
language:English
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