Hard X-Ray Constraints on Small-scale Coronal Heating Events

Much evidence suggests that the solar corona is heated impulsively, meaning that nanoflares may be ubiquitous in quiet and active regions (ARs). Hard X-ray (HXR) observations with unprecedented sensitivity >3 keV are now enabled by focusing instruments. We analyzed data from the Focusing Optics X-ray Solar Imager (FOXSI) rocket and the Nuclear Spectroscopic Telescope Array (NuSTAR) spacecraft to constrain properties of AR nanoflares simulated by the EBTEL field-line-averaged hydrodynamics code. We generated model X-ray spectra by computing differential emission measures for homogeneous nanoflare sequences with heating amplitudes H ₀, durations τ, delay times between events t _N, and filling factors f. The single quiescent AR observed by FOXSI-2 on 2014 December 11 is well fit by nanoflare sequences with heating amplitudes 0.02 erg cm^-3 s^-1 <H ₀ < 13 erg cm^-3 s^-1 and a wide range of delay times and durations. We exclude delays between events shorter than ∼900 s at the 90% confidence level for this region. Three of five regions observed by NuSTAR on 2014 November 1 are well fit by homogeneous nanoflare models, while two regions with higher fluxes are not. Generally, the NuSTAR count spectra are well fit by nanoflare sequences with smaller heating amplitudes, shorter delays, and shorter durations than the allowed FOXSI-2 models. These apparent discrepancies are likely due to differences in spectral coverage between the two instruments and intrinsic differences among the regions. Steady heating (t _N = τ) was ruled out with >99% confidence for all regions observed by either instrument.