On the Relationship Between Nanoflare Energy and Delay in the Closed Solar Corona

TL;DR

This study investigates the relationship between nanoflare energies and delays in the solar corona, finding little to no correlation, which suggests complex triggering mechanisms beyond magnetic stress thresholds.

Contribution

It provides the first comprehensive analysis of nanoflare energy-delay correlation using self-consistent 3D simulations and multiple statistical methods, revealing the lack of a simple relationship.

Findings

No significant correlation between nanoflare energy and delay times.

Distribution of the energy-delay relation exponent peaks near zero.

Delays are broadly distributed regardless of energy levels.

Abstract

Determining the relationship between nanoflare energies and their delays is the key for understanding the physical mechanism of the events and the plasma response. Nanoflares analyzed in this study were generated self-consistently via prescribed photospheric motions in a 3D multi-strand simulation of a subset of active region magnetic flux. Energies and durations were quantified using three distinct methods. In this study, we investigated the correlation between nanoflare energies (E) and delays ($\tau_D$) using two non-parametric, rank-based statistical tests. Across all methods, results consistently show little to no correlation. This is further supported by the distribution of the exponent $\alpha$ in the assumed relation $E \propto \tau_D^\alpha$, which peaks near zero, and by broad delay distributions within fixed energy bins. These findings are irrespective of whether delays are correlated with the energy of the preceding or subsequent event. They also hold for a subset of high-energy nanoflares. The absence of correlation suggests that nanoflare onset is not solely determined by a critical value of magnetic stress and may involve triggering by other events, perhaps related to a locally complex topology.