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Notes: Abstract Observations of photospheric magnetic fields made with vector magnetographs have been used recently to study helicity on the Sun. In this paper we indicate what can and cannot be derived from vector magnetograms, and point out some potential problems in these data that could affect the calculations of `helicity'. Among these problems are magnetic saturation, Faraday rotation, low spectral resolution, and the method of resolving the ambiguity in the azimuth.

Notes: Abstract The largest concentrations of magnetic flux on the Sun occur in active regions. In this paper, the properties of active regions are investigated in terms of the dynamics of magnetic flux tubes which emerge from the base of the solar convection zone, where the solar cycle dynamo is believed to operate, to the photosphere. Flux tube dynamics are computed using the `thin flux tube' approximation, and by using MHD simulation. Simulations of active region emergence and evolution, when compared with the known observed properties of active regions, have yielded the following results: (1) The magnetic field at the base of the convection zone is confined to an approximately toroidal geometry with a field strength in the range (3–10)×104 G. The latitude distribution of the toroidal field at the base of the convection zone is more or less mirrored by the observed active latitudes; there is not a large poleward drift of active regions as they emerge. The time scale for emergence of an active region from the base of the convection zone to the surface is typically 2–4 months. The equatorial gap in the distribution of active regions has two possible origins; if the toroidal field strength is close to 105 G, it is due to the lack of equilibrium solutions at low latitude; if it is closer to 3×104 G, it may be due to modest poleward drift during emergence. (2) The tilt of active regions is due primarily to the Coriolis force acting to twist the diverging flows of the rising flux loops. The dispersion in tilts is caused primarily by the buffeting of flux tubes by convective motions as they rise through the interior. (3) The Coriolis force also bends the active region flux tube shape toward the following (i.e., anti-rotational) direction, resulting in a steeper leg on the following side as compared to the leading side of an active region. When the active region emerges through the photosphere, this results in a more rapid separation of the leading spots away from the magnetic neutral line as compared to the following spots. This bending motion also results in the neutral line being closer to the following magnetic polarity. (4) Active regions behave kinematically after they emerge because of `dynamic disconnection', which occurs because of the lack of a solution to the hydrostatic equilibrium equation once the flux loop has emerged. This could explain why active regions decay once they have emerged, and why the advection-diffusion description of active regions works well after emergence. Smaller flux tubes may undergo `flux tube explosion', a similar process, and provide a source for the constant emergence of small-scale magnetic fields. (5) The slight trend of most active regions to have a negative magnetic twist in the northern hemisphere and positive twist in the south can be accounted for by the action of Coriolis forces on convective eddies, which ultimately writhes active region flux tubes to produce a magnetic twist of the correct sign and amplitude to explain the observations. (6) The properties of the strongly sheared, flare productive δ-spot active regions can be accounted for by the dynamics of highly twisted Ω loops that succumb to the helical kink instability as they emerge through the solar interior.

Notes: Abstract We compare vector magnetograms of active region NOAA 5747 observed by two very different polarimetric instruments: the imaging vector magnetograph of Huairou Solar Observing Station (HSOS) and the Haleakala Stokes Polarimeter of Mees Solar Observatory (MSO). Unlike previous comparative studies, we concentrate our attention on differences in observations and data reduction techniques that can affect the helicity computation. Overall, we find a qualitative agreement between the HSOS and MSO vector magnetograms. The HSOS data show slightly higher field strength, but the distribution of inclination angles is similar in measurements from the two instruments. There is a systematic difference (up to ∼20°) in the azimuths of transverse fields, which is roughly proportional to the longitudinal field strength. We estimate that Faraday rotation in the HSOS magnetograms contributes ∼12° in the azimuth difference if possible sources of error are taken into account. Next, we apply two independent methods to both data sets to resolve 180° azimuth ambiguity and to compute two helicity measures – the force-free field parameter αbest and the current helicity fractional imbalance ρh. The methods agree reasonably well in sign and value of the helicity measures, but the HSOS magnetograms show systematically smaller values of ρh and αbest in agreement with an expected contribution of Faraday rotation. Finally, we discuss the role of Faraday rotation in computation of αbest and ρh and conclude that it does not affect the strength of the hemispheric helicity rule. The strength of the rule appears to be related to a helicity parameter: αbest shows weaker hemispheric asymmetry than ρh.