slide1 l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
cattaneo@flash.uchicago.edu PowerPoint Presentation
Download Presentation
cattaneo@flash.uchicago.edu

Loading in 2 Seconds...

play fullscreen
1 / 22

cattaneo@flash.uchicago.edu - PowerPoint PPT Presentation


  • 49 Views
  • Uploaded on

Chicago 2003. The solar dynamo(s). Fausto Cattaneo Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas. cattaneo@flash.uchicago.edu. Chicago 2003. The solar dynamo problem. The solar dynamo is invoked to explain the origin magnetic activity

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'cattaneo@flash.uchicago.edu' - julie


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide1

Chicago 2003

The solar dynamo(s)

Fausto Cattaneo

Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas

cattaneo@flash.uchicago.edu

slide2

Chicago 2003

The solar dynamo problem

The solar dynamo is invoked to explain the origin magnetic activity

Three important features:

  • Wide range of spatial scales. From global scale to limit of resolution
  • Wide range of temporal scales. From centuries to minutes
  • Solar activity is extremely well documented

Models are strongly observationally constrained

slide3

Chicago 2003

Observations

Hale’s polarity law suggests organization on global scale.

Typical size of active regions approx 200,000Km

Typical size of a sunspot

50,000Km

Small magnetic elements show structure down to limit of resolution (approx 0.3")

slide4

Chicago 2003

Observations: large scale

  • Active regions migrate from mid-latitudes to the equator
  • Sunspot polarity opposite in two hemispheres
  • Polarity reversal every 11 years
slide5

Observations: large scale

: stored in ice cores after 2 years in atmosphere

: stored in tree rings after ~30 yrs in atmosphere

14

C

10

Be

Chicago 2003

PROXY DATA OF SOLAR MAGNETIC ACTIVITY AVAILABLE

Beer (2000)

Wagner et al (2001)

Cycle persists through

Maunder Minimum (Beer et al 1998)

slide6

Chicago 2003

Observations: small scale

Two distinct scales of convection (maybe more)

  • Supergranules:
    • not visible in intensity
    • 20,000 km typical size
    • 20 hrs lifetime
    • weak dependence on latitude
  • Granules:
    • strong contrast
    • 1,000km typical size
    • 5 mins lifetime
    • homogeneous in latitude
slide7

Chicago 2003

Observations: small scale

Quiet photospheric flux

  • Network fields
    • emerge as ephemeral regions (possibly)
    • reprocessing time approx 40hrs
    • weak dependence on solar cycle
  • Intra-network magnetic elements
    • possibly unresolved
    • typical lifetime few mins
slide8

Chicago 2003

General dynamo principle

Any three-dimensional, turbulent (chaotic) flow with high magnetic Reynolds number is (extremely) likely to be a dynamo.

  • Reflectionally symmetric flows:
    • Small-scale dynamo action
    • Disordered fields; same correlation length/time as turbulence
    • Generate but not
  • Non-reflectionally symmetric flows:
    • Large-scale dynamo; inverse cascade of magnetic helicity
    • Organized fields; correlation length/time longer than that of turbulence
    • Possibility of
slide9

Chicago 2003

Rotational constraints

In astrophysics lack of reflectional symmetry associated with

(kinetic) helicity  Coriolis force  Rotation

Introduce Rossby radius Ro (in analogy with geophysical flows)

  • Motions or instabilities on scales Ro “feel’’ the rotation.
    • Coriolis force important  helical motions
    • Inverse cascades  large-scale dynamo action
  • Motions or instabilities on scales < Ro do not “feel” the rotation.
    • Coriolis force negligible  non helical turbulence
    • Small-scale dynamo action
slide10

Chicago 2003

Modeling: large-scale generation

Dynamical ingredients

  • Helical motions: Drive the α-effect. Regenerate poloidal fields from toroidal
  • Differential rotation: (with radius and/or latitude) Regenerate toroidal fields from poloidal. Probably confined to the tachocline
  • Magnetic buoyancy: Removes strong toroidal field from region of shear. Responsible for emergence of active regions
  • Turbulence: Provides effective transport
slide11

Chicago 2003

Modeling: helical motions

  • Laminar vs turbulent α-effect:
    • Babcock-Leighton models. α-effect driven by rise and twist of large scale loops and subsequent decay of active regions. Coriolis-force acting on rising loops is crucial. Helical turbulence is irrelevant. Dynamo works because of magnetic buoyancy.
    • Turbulent models. α-effect driven by helical turbulence. Dynamo works in spite of magnetic buoyancy.
  • Nonlinear effects:
    • Turbulent α-effect strongly nonlinearly suppressed
    • Interface dynamos?
    • α-effect is not turbulent (see above)

Cattaneo & Hughes

slide12

Chicago 2003

Modeling: differential rotation

  • Latitudinal differential rotation:
    • Surface differential rotation persists throughout the convection zone
    • Radiative interior in solid body rotation

Schou et al.

  • Radial shear:
    • Concentrated in the tachocline; a thin layer at the bottom of the convection zone
    • Whys is the tachocline so thin? What controls the local dynamics?

No self-consistent model for the solar differential rotation

slide13

Chicago 2003

Modeling: magnetic buoyancy

What is the role of magnetic buoyancy?

  • Babcock-Leighton models:
    • Magnetic buoyancy drives the dynamo
    • Twisting of rising loops under the action of the Coriolis force generates poloidal field from toroidal field
    • Dynamo is essentially non-linear
  • Turbulent models:
    • Magnetic buoyancy limits the growth of the

magnetic field

    • Dynamo can operate in a kinematic regime

Wissink et al.

Do both dynamos coexist? Recovery from Maunder minima?

slide14

Chicago 2003

Modeling: turbulence

How efficiently is turbulent transport?

  • Babcock-Leighton models: Turbulent diffusion causes the dispersal of active regions. Transport of poloidal flux to the poles.
  • Interface models: Turbulent diffusion couples the layers of toroidal and poloidal generation
  • All models:
    • Turbulent pumping helps to keep

the flux in the shear region

    • Turbulence redistributes angular

momentum

    • Etc. etc. etc.

Tobias et al.

slide15

Chicago 2003

Modeling: challenges

No fully self-consistent model exists.

  • Self-consistent model must capture all dynamical ingredients (MHD, anelastic)
  • Geometry is important (sphericity)
  • Operate in nonlinear regime
  • Resolution issues. Smallest resolvable scales are
    • in the inertial range
    • rotationally constrained
    • stratified

Need sophisticated sub-grid models

slide16

Chicago 2003

Modeling: small-scale generation

cold

g

hot

  • Plane parallel layer of fluid
  • Boussinesq approximation
  • Ra=500,000; P=1; Pm=5

Simulations by Lenz & Cattaneo

time evolution

temperature

slide17

Chicago 2003

Rm

Pm=1

Pm =1

IM

Stars

103

simulations

102

Liquid metal experiments

Re

103

107

Modeling: physical parameters

  • Dynamo must operate in the inertial range of the turbulence
  • Driving velocity is rough
  • How do we model MHD behaviour with Pm <<1
slide18

Chicago 2003

Modeling: kinematic and dynamical issues

Pm=1

Pm=0.5

yes

  • Does the dynamo still operate? (kinematic issue)
  • Dynamo may operate but become extremely inefficient (dynamical issue)

Re=550, Rm=550

no

Re=1100, Rm=550

slide19

Chicago 2003

Modeling: magneto-convection

  • Relax requirement that magnetic field be self sustaining (i.e. impose a uniform vertical field)
  • Construct sequence of simulations with externally imposed field, 8 ≥ Pm ≥ 1/8, and S = = 0.25
  • Adjust Ra so that Rm remains “constant”

Simulations by Emonet & Cattaneo

slide20

Chicago 2003

Modeling: magneto-convection

B-field (vertical)

vorticity (vertical)

Pm = 8.0

Pm = 0.125

slide21

Chicago 2003

Modeling: magneto-convection

  • Energy ratio flattens out for Pm < 1
  • PDF’s possibly accumulate for Pm < 1
  • Evidence of regime change in cumulative PDF across Pm=1
  • Possible emergence of Pm independent regime
slide22

Chicago 2003

Summary

Two related but distinct dynamo problems.

  • Large-scale dynamo
    • Reproduce cyclic activity
    • Reproduce migration pattern
    • Reproduce angular momentum distribution (CV and tachocline)
    • Needs substantial advances in computational capabilities
  • Small scale dynamo
    • Non helical generation
    • Small Pm  turbulent dynamo