Interdependence of solar plasma flows and magnetic fields Dr. E.J. Zita AAS 2012 Anchorage, AK.

Interdependence of solar plasma flows and magnetic fields

Dr. E.J. Zita

AAS 2012

Anchorage, AK

AbstractInteractions between flows and magnetic fields in the Sun’s plasma can affect

surface phenomena such as sunspots, can reveal deeper magnetic connections via changes in solar flows and oscillations, and drive dynamics in the long-term solar magnetic cycle, e.g. the recent “weird solar minimum.”

We have observed changes in solar surface flow patterns (Smith et al. 2010) consistent with the Proctor effect, which depends on magnetic field strength and orientation in active regions.

Other investigators have observed relationships between solar torsional oscillations and mean field strengths. Zonal flow velocities correlate roughly with field strengths, and may serve as diagnostics or predictors of solar cycles.

We explore a possible relationship between the Proctor effect and the magnetic interdependence of zonal flows. Our study potentially deepens understanding of fundamental solar magnetic dynamics underlying convection and dynamo processes.

OutlineA. Proctor effect: Simulations predict changes in

flows (v), depending on orientation and strength of local field (B)

B. Hinode data: test for Proctor effect (PE)

C. Observe changes in flows and fields associated with recent extended solar minimum: 1. meridional circulation 2. torsional oscillations

D. Compare flow/field interactions in 1 & 2 with Proctor Effect.

Proctor Effect (PE) predictions

Fig.1a. A simulation mimicking flows in the outer penumbra, with Rayleigh number R

= 80,000, Q = 1000 (proportional to B2

), =120, magnetic Prandtl number = 0.2,

and obliquity = /4, with potential boundary conditions imposed on the magnetic

field.

The tall thin cells give way to a single large cell that also travels rightward.

Fig.1.b. The phase speed vp and mean surface speed u as

functions of obliquity angle of magnetic field lines, for solutions

with R = 66,000 and Chandrasekhar number Q = 10,000. The

waves travel to the right and in the same direction as the mean

surface flow, in this case.

Both speeds increase roughly linearly with angle for < 0.45.

Testing Proctor Effect with Hinode data

Obtain and align velocity fields (v) and magnetic field vectors from Hinode data near active regions

Plot v versus magnetic field inclination angle

Compare to theoretical v() plots

C. Smith et al., 2010

Velocity and magnetic data analysis:

v: C. Smith applied the LMSAL correlation tracking tool (Hurlburt, Shine & Simon 1995) to G-band datasets using a 32x32 grid on the 1024x1024 images. The resulting flow vectors were then averaged over a one-hour time interval. The 2D vector fields obtained are shown below (black & white).

B: The corresponding Hinode vector magnetograms were aligned and binned to a comparable resolution (field strength and inclination angle – not disambiguated).

B strength & inclination, V

Fig.2

Flow versus inclination in fieldFig.3a

AR 10944 (1 Mar.2007)

g B g B

Flows increase in horizontal field regions, as predicted by Proctor Effect simulations

g B g B

Fig.3b

Scatter in flow/inclination plot due to decrease in flow at higher field strength

Fig.4

Hinode data consistent with Proctor Effect

• Flow speed vs. local field inclination plots (Figs.3) show significant scatter. Upper limits suggest an angle dependence consistent with Proctor Effect predictions (Fig.1), with amplitude of ~2 m/s/degree.

• Flow speed vs. field strength plots (Fig.4) show decrease, as expected from magnetic damping of convection. Sorting data by field strength suggests that this effect accounts for the scatter in the inclination plots (Figs.3).

1. Solar Min & Meridional Circulation David Hathaway & Lisa Rightmire (2009 Science)

Meridional circulation vmc is

• faster @ solar min• slower @ solar max (for surface transport models)

Fast vmc suppresses dynamo action & mean B?

1. Connection to Proctor effect?

• Solar min fields more horizontal faster flows

• Solar max fields more vertical slower flows

2. Solar Min & Torsional OscillationsR. Howe et al. (2009 ApJL)

• More strongly magnetic active regions flow faster (zonal flow, “jet stream”, torsional osc.)

• Slow flow band at minimum → longer cycle

• Side effect of dynamo, or geostrophic flow?

• Increasing zonal flows → onset of new cycle

Torsional oscillations || field strengths

2. Connection to Proctor effect?

• Stronger B fields in AR slower horizontal speeds

• Weaker B fields in AR faster horizontal speeds

Stronger B tend to suppress surface flows, especially when fields are vertical (opposite)

Not inconsistent with faster flows in regions of stronger horizontal B fields

Observations:

Solar minimum has * faster meridional circulation, * weaker, more horizontal magnetic fields, and

* slower torsional oscillations

Proctor Effect observed in magnetic active regions: * Faster flows and waves where B fields are more nearly horizontal (and the effect vanishes where fields are perfectly horizontal);

* Slower flows in stronger fields

Similarities:Meridional circulation and Proctor Effect both show faster

flows when field is weaker and more horizontal,

e.g. at solar min

Differences:Torsional oscillations faster stronger fields solar max

Unlike Proctor Effect, except in horizontal field regions.

Questions:Proctor Effect developed in context of magnetoconvection.

To what extent does it apply to meridional circulation? Consider timescales, length scales, , R, Q.

References

• D.H. Hathaway & L. Rightmire, 2010, “Variations in the Sun’s Meridional Flow over a Solar Cycle,” Science 327, 135

• R. Howe, J. Christensen-Dalsgaard, F. Hill, R. Komm, J. Schou, M.J. Thomson, “A Note on the Torsional Oscillation at Solar Minimum,” 2009 ApJ 701, L87

• R.Howe, R.Komm, F.Hill, T.Larson, J.Schou, M.J.Thompson, R.K.Ulrich, “The Torsional Oscillation and the Solar Cycle,” 2009 ASP Conference Series, Vol.416

• N.E. Hurlburt, P.C. Matthews, M.R.E. Proctor, “Nonlinear Compressible Convection in Oblique Magnetic Fields,” 1996, ApJ 457, 933

• M.R.E. Proctor,1992, in Sunspots: Theory and Observations, ed. J.H. Thomas and N.O. Weiss (Dordrecht: Kluwer), 175

• C. Smith, E.J. Zita, N.E. Hurlburt, “Solar Plasma Flows and Convection in Oblique Magnetic Fields,” 2010 APS-NW #Ds1.005

• E.J. Zita et al., “Physics of the weird solar minimum,” 2010 APS-NW #H1.005

Acknowledgements

Christina Smith, graduate of The Evergreen State College, performed the Hinode

data analysis at LMSAL (Lockheed Martin Solar and Astrophysics Laboratory).

Thanks to Dick Shine for assistance and guidance.

This work was supported by NSF grant 0807651,

NASA grants NAS5-38099, NNM07AA01C, NNG04EA00C, and Lockheed Martin

Internal Research Funds.

g B g B