Nanoflare statistics in an active region 3D MHD coronal model

Abstract

Aims. We investigate the statistics for the spatial and temporal distribution of the energy input into the corona in a three-dimensional magneto-hydrodynamical (3D MHD) model. The model describes the temporal evolution of the corona above an observed active region. The model is driven by photospheric granular motions that braid the magnetic field lines. This induces currents that are dissipated, thereby leading to transient heating of the coronal plasma. We evaluate the transient heating as subsequent heating events and analyze their statistics. The results are then interpreted in the context of observed flare statistics and coronal heating mechanisms. Observed solar flares and other smaller transients cover a wide range of energies. The frequency distribution of energies follow a power law, the lower end of the distribution given by the detection limit of current instrumentation. One particular heating mechanism is based on the occurrence of so-called nanoflares, i.e. very low-energy deposition events. Methods. To conduct the numerical experiment we use a high-order finite-difference code that solves the partial differential equations for the conservation of mass, the momentum and energy balance, and the induction equation. The energy balance includes Spitzer heat conduction and optically thin radiative losses in the corona. Results. The temporal and spatial distribution of the Ohmic heating in the 3D MHD model follows a power law and can therefore be understood as a system in a self-organized critical state. The slopes of the power law are similar to the results based on observations of flares and smaller transients. We find that the coronal heating is dominated by events similar to the so-called nanoflares with energies on the order of 10 17 J or 10 24 erg.

What can large-scale magnetohydrodynamic numerical experiments tell us about coronal heating?

“…the review [86]. In the coronal part of the volume, the typical energy released in a threedimensional model is of the order of 10 17 J (or 10 24 erg) [85], which is in the same range as the nanoflares originally predicted by Parker [87].…”

“…This, together with the drop of the heat input per volume, leads to the maximum energy deposition per particle at the base of the corona (see §4b and figure 3). In consequence, Parker's nanoflares will not deliver the same energy throughout the atmosphere, but they will be stronger in lower heights, as found in the more realistic three-dimensional models [85].…”

“…Investigating small volumes of the three-dimensional model (or individual grid cells), the heat input is enhanced sometimes for only a few minutes, depositing the typical energy of a nanoflare, or many events cluster and form a longer-lasting energy deposition covering often 20 min or more [85]; see also figure 4. These clusters of events can be considered to be the same as 'nanoflare storms' [88] that typically last several hundred to several thousand seconds.…”

Solar Extreme UV radiation and quark nugget dark matter model

“…With these preliminary remarks it is fair to say that there is some agreement between different groups [47][48][49][50][51][52] that nanoflares may play a dominate role in heating of solar corona. For example, for the typical parameters assumed in [49] the authors conclude that in order to reproduce the observations the nanoflares must have typical energies W and the frequencies of appearance dN /dt as follows [49]:…”

MHD modeling of coronal loops: the transition region throat

“…Our numerical experiment is devoted to answering a very specific question on the interaction between the coronal heating and the cross section of the transition region. It is complementary to self-consistent 3D MHD descriptions of coronal boxes (Bingert & Peter 2013).…”