Context. In September 2017, the largest X-class flare of solar cycle 24 occurred from the most
active region (AR) of this cycle, AR 12673. This AR attracted much interest because of its …

… values of E div /E have on our results. The original sample of 22 flares for which E div /E
< 0.05 is denoted as S2 in this Appendix. When we increase the threshold to E div /E < 0.085, …

… As an application to solar situations, we compared the morphology of field line helicity on
the photosphere with that of the connectivity-based helicity flux density in two reconstructions of …

… used to estimate non-solenoidality (Pariat et al., 2015; Valori et al., 2016; Pariat et al., 2017;
Polito et al., 2017). Table 1 shows that the low values of \(E_{\mathrm{div}}/E\) are again an …

… which is a measure of how much a numerical model of a magnetic field deviates from
solenoidality; lower values of E div , and consequently of the energy ratio E div /E, indicate a less …

… It then follows from Equation (5) that the difference between E c and \(E'_{\… Pariat (2012):
we first choose the gauge \(\hat{z}\cdot\mathbf{A}=0\) throughout \(\mathcal{V}\), so that the x …

Aims. The main aim of this work is to study the evolution of the recently introduced relative
helicity of the magnetic polarity inversion line (PIL) in a magnetohydrodynamics simulation. …

Aims. Coronal heating through the explosive release of magnetic energy remains an open
problem in solar physics. Recent hydrodynamical models attempt an investigation by placing …

… The FI methods used in this study include that of Pariat et al. (… (E F ) at those times composes
about 14%, 6%, and 2% of E p , respectively. Correspondingly, we find a higher value of E F …

… Unlike E v , E p is a conserved quantity in … to E v , H j to E j , H pj to E p . This is particularly
visible for the current-carrying helicity and the free energy: when H j increases (decreases), E j …