Coronal mass ejections (CMEs) are thought to be the way by which the solar corona expels accumulated magnetic helicity which is injected into the corona via several methods. DeVore (2000) suggests that a significant quantity is injected by the action of differential rotation, however Démoulin et al. (2002b), based on the study of a simple bipolar active region, show that this may not be the case. This paper studies the magnetic helicity evolution in an active region (NOAA 8100) in which the main photospheric polarities rotate around each other during five Carrington rotations. As a result of this changing orientation of the bipole, the helicity injection by differential rotation is not a monotonic function of time. Instead, it experiences a maximum and even a change of sign. In this particular active region, both differential rotation and localized shearing motions are actually depleting the coronal helicity instead of building it. During this period of five solar rotations, a high number of CMEs (35 observed, 65 estimated) erupted from the active region and the helicity carried away has been calculated, assuming that each can be modeled by a twisted flux rope. It is found that the helicity injected by differential rotation (≈ −7 × 10 42 Mx 2 ) into the active region cannot provide the amount of helicity ejected via CMEs, which is a factor 5 to 46 larger and of the opposite sign. Instead, it is proposed that the ejected helicity is provided by the twist in the sub-photospheric part of the magnetic flux tube forming the active region.

We describe the long-term evolution of a bipolar non-Hale active region that was observed from 1995 October to 1996 January. During these four solar rotations the sunspots and subsequent Ñux concentrations, during the decay phase of the region, were observed to move in such a way that by December their orientation conformed to the Hale-Nicholson polarity law. The sigmoidal shape of the observed soft X-ray coronal loops allows us to determine the sense of the twist in the magnetic conÐguration. This sense is conÐrmed by extrapolating the observed photospheric magnetic Ðeld, using a linear force-free approach, and comparing the shape of computed Ðeld lines with the observed coronal loops. This sense of twist agrees with that of the dominant helicity in the solar hemisphere where the region lies, as well as with the evolution observed in the longitudinal magnetogram during the Ðrst rotation. At Ðrst sight the relative motions of the spots may be misinterpreted as the rising of an ) loop deformed by a kink instability, but we deduce from the sense of their relative displacements a handedness for the Ñux-tube axis (writhe) that is opposite to that of the twist in the coronal loops and, therefore, to what is expected for a kink-unstable Ñux tube. After excluding the kink instability, we interpret our observations in terms of a magnetic Ñux tube deformed by external motions while rising through the convective zone. We compare our results with those of other related studies, and we discuss, in particular, whether the kink instability is relevant to explain the peculiar evolution of some active regions.

Photospheric shearing motions are one of the possible ways to inject magnetic helicity into the corona. We explore their efficiency as a function of their particular properties and those of the magnetic field configuration. Based on the work of M. A. Berger, we separate the helicity injection into two terms: twist and writhe. For shearing motions concentrated between the centers of two magnetic polarities the helicity injected by twist and writhe add up, while for spatially more extended shearing motions, such as differential rotation, twist and writhe helicity have opposite signs and partially cancel. This implies that the amount of injected helicity can change in sign with time even if the shear velocity is time independent. We confirm the amount of helicity injected by differential rotation in a bipole in the two particular cases studied by DeVore (2000), and further explore the parameter space on which this injection depends. For a given latitude, tilt and magnetic flux, the generation of helicity is slightly more efficient in young active regions than in decayed ones (up to a factor 2). The helicity injection is mostly affected by the tilt of the AR with respect to the solar equator. The total helicity injected by shearing motions, with both spatial and temporal coherence, is at most equivalent to that of a twisted flux tube having the same magnetic flux and a number of turns of 0.3. In the solar case, where the motions have not such global coherence, the injection of helicity is expected to be much smaller, while for differential rotation this maximum value reduces to 0.2 turns. We conclude that shearing motions are a relatively inefficient way to bring magnetic helicity into the corona (compared to the helicity carried by a significantly twisted flux tube).

Previous studies have found that coronal loops have a nearly uniform thickness, which seems to disagree with the characteristic expansion of active region magnetic fields. This is one of the most intriguing enigmas in solar physics. We here report on the first comprehensive one-to-one comparison of observed loops with corresponding magnetic flux tubes obtained from cotemporal magnetic field extrapolation models. We use EUV images from TRACE, magnetograms from the MDI instrument on SOHO, and linear force-free field extrapolations satisfying ∇×B = αB with α equal to a constant. For each loop, we find the particular value of α that best matches the observed loop axis and then construct flux tubes using different assumed cross sections at one footpoint (circle and ellipses with different orientations). We find that the flux tubes expand with height by typically twice as much as the corresponding loops. We also find that many flux tubes are much wider at one footpoint than the other, whereas the corresponding loops are far more symmetric. It is clear that the actual coronal magnetic field is more complex than the models we have considered. We suggest that the observed symmetry of loops is related to the tangling of elemental magnetic flux strands produced by photospheric convection.