Relative field line helicity of a large eruptive solar active region

Abstract: Context. Magnetic helicity is a physical quantity of great importance in the study of astrophysical and natural plasmas. Although a density for helicity cannot be defined, a good proxy for it is field line helicity. The appropriate quantity for use in solar conditions is relative field line helicity (RFLH). Aims. This work aims to study in detail the behaviour of RFLH, for the first time, in a solar active region (AR). Methods. The target active region is the large, eruptive AR 11158. In order to compute RFLH and all other quantities of interest we use a non-linear force-free reconstruction of the AR coronal magnetic field of excelent quality. Results. We find that the photospheric morphology of RFLH is quite different than that of the magnetic field or of the electrical current, and this is not sensitive to the chosen gauge in the computation of RFLH. The value of helicity experiences a large decrease, 25% of its pre-flare value, during an X-class flare of the AR, a change that is also depicted in the photospheric morphology of RFLH. Moreover, the area of this change coincides with the area that encompasses the flux rope, the magnetic structure that later erupted. Conclusions. The use of RFLH can provide important information about the value and location of the magnetic helicity expelled from the solar atmosphere during eruptive events.