Magnetic helicity and energy budget around large confined and eruptive solar flares

Abstract

Context. In order to better understand the underlying processes and prerequisites for solar activity, it is essential to study the time evolution of the coronal magnetic field of solar active regions (ARs) associated with flare activity. Aims. We investigate the coronal magnetic energy and helicity budgets of ten solar ARs around the times of large flares. In particular, we are interested in a possible relation of the derived quantities to the particular type of the flares that the AR produces, namely, whether they are associated with a CME or whether they are confined (i.e., not accompanied by a CME). Methods. Using an optimization approach, we employed time series of 3D nonlinear force-free magnetic field models of ten ARs, covering a time span of several hours around the time of occurrence of large solar flares (GOES class M1.0 and larger). We subsequently computed the 3D magnetic vector potentials associated to the model 3D coronal magnetic field using a finite-volume method. This allows us to correspondingly compute the coronal magnetic energy and helicity budgets, as well as related (intensive) quantities such as the relative contribution of free magnetic energy, EF/E (energy ratio), the fraction of non-potential (current-carrying) helicity, |HJ|/|HV| (helicity ratio), and the normalized current-carrying helicity, |HJ|/ϕ′2. Results. The total energy and helicity budgets of flare-productive ARs (extensive parameters) cover a broad range of magnitudes, with no obvious relation to the eruptive potential of the individual ARs, that is, whether or not a CME is produced in association with the flare. The intensive eruptivity proxies, EF/E and |HJ|/|HV|, and |HJ|/ϕ′2, however, seem to be distinctly different for ARs that produce CME-associated large flares compared to those which produce confined flares. For the majority of ARs in our sample, we are able to identify characteristic pre-flare magnitudes of the intensive quantities that are clearly associated with subsequent CME-productivity. Conclusions. If the corona of an AR exhibits characteristic values of ⟨|HJ|/|HV|⟩ > 0.1, ⟨EF/E⟩ > 0.2, and ⟨|HJ|/ϕ′2⟩ > 0.005, then the AR is likely to produce large CME-associated flares. Conversely, confined large flares tend to originate from ARs that exhibit coronal values of ⟨|HJ|/|HV|⟩ ≲ 0.1, ⟨EF/E⟩ ≲ 0.1, and ⟨|HJ|/ϕ′2⟩ ≲ 0.002.

Solar Flares and Magnetic Helicity

“…For NOAA AR 12673, which produced the largest X-class flare of solar cycle 24, found that the helicity ratio increased and then relaxed to lower values before and after, respectively, each of the two major X2. Another follow-up study of Gupta et al [2021], with a set of 10 different NOAA-numbered AR samples, shows results supporting that the helicity ratio has a strong ability to indicate the eruptive potential of an AR, albeit with a few exceptions. A further statistical study with more samples is needed.…”

A New Magnetic Parameter of Active Regions Distinguishing Large Eruptive and Confined Solar Flares

“…The idea of the new parameter α/Φ AR can be generalized to "relative non-potentiality", which refers to the ratio of magnetic flux (or other physical quantities) in a flux rope to that in the surrounding magnetic structures (Lin et al 2021). A larger relative non-potentiality indicates a higher probability for a flux rope to erupt Thalmann et al 2019;Gupta et al 2021). Recently, Lin et al (2020) proposed a new relative non-potentiality parameter of the magnetic flux in the highly twisted region relative to its ambient background fields, which demonstrated a moderate ability in discriminating between confined and ejective events.…”

“…It is suggested that eruptive flares tend to occur if the overlying background magnetic fields are weaker or more quickly decay with height (Török & Kliem 2005;Wang & Zhang 2007;Wang et al 2017;Baumgartner et al 2018;Amari et al 2018;Jing et al 2018;Duan et al 2019). Moreover, the magnetic non-potentiality of ARs is thought to be another important factor governing the eruptive character of solar flares (Nindos & Andrews 2004;Liu et al 2016;Cui et al 2018;Vasantharaju et al 2018;Thalmann et al 2019;Avallone & Sun 2020;Gupta et al 2021), such as free magnetic energy, relative helicity, magnetic twists, etc. Statistical studies have shown that CME productivity is correlated with the twist parameter α (Falconer et al 2002(Falconer et al , 2006, which characterizes the degree to which the photospheric magnetic fields of an AR deviate from a potential field (Leka & Skumanich 1999;Yang et al 2012).…”

The effect of spatial sampling on magnetic field modeling and helicity computation

“…For our study, we select three out of the ten ARs analyzed in Gupta et al (2021), namely NOAAs 11158, 11429, and 12673, which hosted the top four solar flares (in terms of peak soft Xray flux) during solar cycle 24 that occurred within ±35 • of the central meridian (see Table 1). The time window for analysis is chosen as in Gupta et al (2021), that is, it covers a time interval of several hours around the occurrence of the X-class flares, as is the time cadence (a 12min time cadence within ±1h around the flare peak time and a 1h cadence otherwise). Data possibly available during the impulsive phases of the flares were not considered due to the limited validity of the force-free assumption during eruptive processes.…”

“…We use time series of vector magnetic field data as originally prepared by Gupta et al (2021), who use hmi.sharp_CEA_720s…”