Observation on Current Helicity and Subsurface Kinetic Helicity in Solar Active Regions Gao Yu Helicity Thinkshop Main Collaborators: Zhang, H. Q., Su, J. T., Xu, H. Q., Zhao, J., Sokoloff, D., Kuzanyan, K., Sakurai, T. Beijing

“Sunspots do not appear at random over the sun’s surface, but are concentrated in two latitude bands on either side of the equator” Hathaway, 2010, Living Rev., Solar Phys.

Parker dynamo model Poloidal Field Toroidal Field α-effect （ “Cyclonic motion” ） （ “Differential rotation” ）

Sokoloff, 2007, Plasma Phys. Control. Fusion,49, B447–B452 Any impovement today?

Helicity in Active Regions Derived From Vector Magnetogram Hemispheric Helicity Sign Rule from magnetic measurement (HSR): In the northern (southern) solar hemisphere, the helicity mainly possesses left (right) handedness (Seehafer 1990; Pevtsov et al. 1995; Wang et al. 1996; Bao & Zhang 1998; Hagino & Sakurai 2004; Zhang et al. 2010; Hao & Zhang 2012); HSR may change during some phase of solar cycle (Bao & Zhang, 2000; Hagino & Sakurai 2005; Zhang et al. 2010; Hao and Zhang 2012). It may provide observations that reveal some CLUES, although it is still far from characterizing the α-effect.

Definition of Main Parameters Vertical electric current, current helicity and average force free field factor:

Effects on interpreting magnetic field from polarized light Calibration accuracy due to measurement on certain filtering position of spectral line FeI Å; Shift of measuring wavelength due to temperature; Magnetic saturation effects for strong longitudinal magnetic field; 180 ◦ ambiguity of transversal azimuth; Projection effects for the transversal field of active region far away from the center of solar disk; Faraday rotations for the transversal azimuth; … Even so, it was proved that some global features of helicity can be obtained by way of statistics.

Estimation on influence of Faraday rotations on azimuth of measured transverse field Bao et al., 2000 Up to now, Huairou Solar Observing Station has sustained vector magnetic field measurement over more than 25 years; Faraday rotations need a quantitative estimation in statistical analysis of current and helicity.

Su and Zhang 2004 Zhang Less Faraday rotation when measuring at the wing of spectral line; 2.Small rotation azimuths but closely relate to field strength and inclination.

Any common distribution of azimuth error in different active regions?

(º) Bz (G) Ψ ( º ) Gao ， Su ， Xu, & Zhang, 2008, MNRAS

Removal of false net current in strong field area (|B z | >500 G) of solar active regions 1.Numbers of active regions ： 983 ， Numbers of Magnetogram ： 6205 ； 2.Time period ： ， 22 nd cycle ： 431 ， 23 rd cycle ： 553 ； Zero false net current justifies a statistical estimation of Faraday rotation effects ；

Evolution of spatial distribution of current helicity over two cycles Average helicity values over 7 degree and overlapping two year period; 95% confidence interval is given by taking each measured point as a freedom degree; The HSR percentage is about 66% (63%) in the 22 nd cycle and 58% (57%) in the 23 rd cycle for H c. Zhang, Sakurai, Pevtsov, Gao, Xu, Sokoloff & Kuzanyan 2010, MNRAS

Net electric current in opposite polarity area of solar active regions Compute net electric current on regions of opposite polarity. Tiny but not trivial net current exists and validates the sign preference of helicity in the solar active regions. Gao, 2013, RAA

Normal Probability Paper applied for distribution of current helicity Gao, Sakurai, Zhang, Kuzanyan & Sokoloff 2012, MNRAS

Bins of statistically significant in butterfly diagram The second Gaussian component of helicity determine whether HSR holds.

Cycle dependence of distribution of vector magnetic field in active regions

α-effect contains two parts of contributions (Pouquet et al., 1976) ： Hydrodynamic helicity: ~ v· (curl v); The advance in helioseismology make the detection of the vector velocity field, thus the kinetic helicity available (Zhao & Kosovichev 2003); Magnetic helicity, in the solar observation (Seehafer, 1990; Pevtsov et al., 1995; Abramenko, Wang, & Yurchishin, 1996; Bao & Zhang 1998): ~ ; NOTE: Sun: Vorticity is observed AFTER current helicity! Earth: Vorticity is usually seen but helical magnetic field is seldomly seen.

Progress in observation The one-to-one statistical comparison between the current and subsurface kinetic helicity of sampling active regions has been performed (Gao, Zhang, & Zhao, 2009; Maurya, Ambastha, & Reddy, 2011). CC: , 0.118, , Data from different instruments have large timing lag.

Observation NOAA AR11158: Observed from 10-Feb 2011 to 16-Feb Lied on -21 deg deg. NOAA AR11283: Observed from 05-Sep 2011 to 09-Sep Lied on +14 deg deg. SDO/HMI: Time-series data ; Vector magnetogram; Subsurface velocity field of flow (Zhao, 2012).

Flow chart for the HMI time–distance helioseismology data-analysis pipeline Zhao et al. 2012, Solar Physics

Evolution of magnetic and velocity field :00:00 UT: FOV: 5.463’  5.043’; Resolution: 0.504’’; Cadence: 12 min Max. |B  |: 2356 G; Max. |B  |: 2570 G _14hr: FOV: 3.04’  2’; Resolution: 1.008’’; Temporal Interval: 4 hr; Max. |V  |: ms -1 ; Max. |V  |: 285 ms -1 ;

Snapshots do not show any clear corresponding features

NOAA AR11158 ： Weighted current helicity and kinetic helicity

NOAA AR11283 ： Weighted current helicity and kinetic helicity

NOAA AR11302 ： Weighted current helicity and kinetic helicity

Summary of main results A statistical estimation of Faraday rotation effects on helicity sign rule for Huairou vector magnetogram has been carried out; Butterfly diagram of two-cycle current helicity were obtained with HSOS data set and indicate more details that are helpful to develop mean field dynamo models; Net current, even if tiny, but exist and their distribution on polarity in active regions keep consistent with the Helicity Sign Rule; Evolution of photospheric current helicity shows a clear correlation with subsurface kinetic helicity, which was derived from independent measurement technique.

Thank you for your attention!