Magnetic Helicity in Emerging Active Regions: A Statistical Study

Yang Liu, Peter W. Schuck

Topics to be discussed.

• Buildup of magnetic relative helicity in two emerging active regions;

• Hemispheric helicity rule: test with HMI data;

• Test with Demoulin and Berger’s hypothesis (Demoulin & Berger, 2003) for helicity flux computation;

• Computation of helicity flux density: which is better: G_A or G_theta?

1. Energy and helicity buildup: Calculation of energy and helicity fluxes

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Evolution of AR11072: emerging and developing to be a simple active region.

AR11072:

1. Separation motion is detected;

2. Upflow is associated with emerging flux, and surrounds the leading sunspot;

3. Simple bipolar active region.

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Bz + Vz (green: upflow, red: downflow)

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Summary:

1. Helicities from the shear-term and emergence-term have the same sign;

2. Shear-term dominant;

3. Upflow and downflow inject oppsite sign helicities. Both are small.

Evolution of AR11158: 1. emerging; 2. separation of leading and following fields; 3. rotation of sunspots; 4. shear motion along the polarity inversion line.

Bz + Vz (green: upflow, red: downflow)

Bz + Vt

Vector B

AR11158:

1. Spinning sunspots;

2. Shear motion along the PIL;

3. Upflows surround sunspots;

4. Highly sheared magnetic field near the PIL.

Summary of AR11158:

1. Same sign of helicity from shear-term and emergence-term;

2. Shear-term dominants;

3. Upflow and downflow contribute helicity with opposite signs.

Energy in the two active regions (left: AR11072, right: AR11158):

1.shear-term and emergence-term are consistent in phase;

2.Both terms well correspond to the flux emergence;

3.Emergence-term is dominant.

1. Energy and helicity buildup: conclusions

• Shear-term contributes most helicity in the corona;• The helicities from shear-term and emergence-term

have the same sign;• Upflow and downflow contribute helicity with the

opposite signs;• Energy flux well corresponds with the flux

emergence;• Emergence-term and shear-term energy fluxes are

consistent in phase; • Emergence-term contributes more energy.

2: Hemispheric helicity rule

• Methodology and data– Select emerging active regions;– Compute the helicity flux;– Integral over time of the emergence process

to obtain the helicity accumulated in the corona in the active region.

A weak hemisphere-preference is found in this 56-active-region sample. 56% of the active regions follow the rule, while 44% against.

Fitting the data with |H| ~ a * Flux ^ alpha yields alpha = 1.91;

Roughly estimate the turn of the twist of the flux by |H| ~ N * Flux^2. The average turn N = 0.055.

2. Hemispheric helicity rule: conclusions

• It is found in a sample of 56 active regions that 56% of them obey the hemispheric rule while 44% violate it;

• Fitting the data with a formula |H| = a * Flux^alpha yields alpha = 1.91;

• Turn of the flux twist is roughly 0.055 in average.

3: Test Demoulin & Berger’s hypothesis (2003)—DB03 hypothesis

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Using DAVE (Schuck 2006)u

AR11072: Both energy flux and helicity from the tracking velocity [u] (DAVE; blue curves) don’t agree with the total fluxes (black curves). This indicates that the DB03 hypothesis is incorrect.

AR11158: Blue curves don’t agree with the black curves, indicating that the DB03 hypothesis is incorrect.

3. DB03 hypothesis: conclusion

• Both cases indicate that the energy and helicity fluxes computed from the tracking-footpoint velocity does not equal to the total fluxes. This indicates that the DB03 hypothesis is incorrect.

4. Computation of helicity density: Two helicity density proxies

Calculate the vector potential

Boundary condition for the Green’s function.

• The periodic Green’s function (G_A-FFT; G_theta-FFT).

• The free-space Green’s function (G_A-FS; G_theta-FS).

Test with MHD data:

As Pariat et al (2005) pointed out that G_A proxy contains fake signals.

Vector B

Test with HMI data: G_A has fake signals.

When the boundary is chosen consistently, both G_A and G_theta yield identical helicity fluxes, as well as two components of the helicity flux (shear-term and emergence-term).

Helicity flux versus zero-padded boundary. N refers to the factor by which the original data is expanded and zero-padded. The zero-paddede data us N x Lx by N x Ly, where Lx and Ly are the width and height of the field of view of the original data. The solid line with asterisks represents the helicity flux computed from G_A-FFT, while the horizontal dashed line refers to the helicity flux from G_A-FS from the original data. The helicity flux from G_A-FFT converges to that from G_A-FS while increasing the padding areas.

4. Computation of helicity flux: conclusions

• Helicity flux density proxy G_A contains fake signal, as Pariat et al. pointed out (2005);

• This fake signal is cancelled out completely when computing the total helicity flux, as well as the two components of the flux (shear-term and emergence-term), by integral over the entire area of the region;

• The difference of the helicity fluxes computed from helicity density proxies G_A and G_theta is not due to the fake signal that G_A introduces as Pariat et al (2005) suggested, but rather due to inconsistency of the boundaries chosen in the Green’s function;

• The helicity flux computed from G_A-FFT converges to that from G_A-FS with increase of the padding area.