The current helicity in solar active regions derived from vector magnetograph observations for more than 20 years indicates the so-called hemispheric sign rule; the helicity is predominantly negative in the northern hemisphere and positive in the sou
thern hemisphere. In this paper we revisit this property and compare the statistical distribution of current helicity with Gaussian distribution using the method of normal probability paper. The data sample comprises 6630 independent magnetograms obtained at Huairou Solar Observing Station, China, over 1988-2005 which correspond to 983 solar active regions. We found the following. (1) For the most of cases in time-hemisphere domains the distribution of helicity is close to Gaussian. (2) At some domains (some years and hemispheres) we can clearly observe significant departure of the distribution from a single Gaussian, in the form of two- or multi-component distribution. (3) For the most non-single-Gaussian parts of the dataset we see co-existence of two or more components, one of which (often predominant) has a mean value very close to zero, which does not contribute much to the hemispheric sign rule. The other component has relatively large value of helicity that often determines agreement or disagreement with the hemispheric sign rule in accord with the global structure of helicity reported by Zhang et al. (2010).
We consider a quadrature-based eigensolver to find eigenpairs of Hermitian matrices arising in lattice quantum chromodynamics. To reduce the computational cost for finding eigenpairs of such Hermitian matrices, we propose a new technique for solving
shifted linear systems with complex shifts by means of the shifted CG method. Furthermore using integration paths along horizontal lines corresponding to the real axis of the complex plane, the number of iterations for the shifted CG method is also reduced. Some numerical experiments illustrate the accuracy and efficiency of the proposed method by comparison with a conventional method.
Previously unobservable mirror asymmetry of the solar magnetic field -- a key ingredient of the dynamo mechanism which is believed to drive the 11-year activity cycle -- has now been measured. This was achieved through systematic monitoring of solar
active regions carried out for more than 20 years at observatories in Mees, Huairou, and Mitaka. In this paper we report on detailed analysis of vector magnetic field data, obtained at Huairou Solar Observing Station in China. Electric current helicity (the product of current and magnetic field component in the same direction) was estimated from the data and a latitude-time plot of solar helicity during the last two solar cycles has been produced. We find that like sunspots helicity patterns propagate equatorwards but unlike sunspot polarity helicity in each solar hemisphere does not change sign from cycle to cycle - confirming the theory. There are, however, two significant time-latitudinal domains in each cycle when the sign does briefly invert. Our findings shed new light on stellar and planetary dynamos and has yet to be included in the theory.
