UC Santa Cruz

The solar corona is an extremely hot, dynamic region of the solar atmosphere. Hard X-ray (HXR) observations of the corona have revealed the temporal and spatial properties of solar flares that release energy between ~10^25 and ~10^33 ergs in active regions. Flare-like events with energies <10^26 ergs have been seen in the quiet Sun by extreme ultraviolet (EUV) and soft X-ray (SXR) instruments. However, non-flaring active regions and quiet coronal regions cannot be imaged by the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI), the current solar-dedicated HXR observatory, due to a lack of sensitivity and dynamic range.

Even in the absence of heating and particle acceleration from solar flares, the corona maintains an average peak temperature 1--4~MK. This is several hundred times hotter than the photosphere; this discrepancy is known as the coronal heating problem. While the precise physical mechanisms that heat the corona are still unknown, observations at multiple wavelengths can constrain the properties of unresolved impulsive heating events (``nanoflares'') in active regions and the quiet Sun. Until recently, only EUV and SXR data were available to investigate the nature of these events.

Focusing optics that directly image HXRs have recently been used to observe the Sun. The Nuclear Spectroscopic Telescope Array (NuSTAR) satellite is an astrophysics mission that was launched in 2013 and has pointed at the Sun on nine occasions to date. The Focusing Optics X-ray Solar Imager (FOXSI) sounding rocket was designed for solar observing and has flown two times (2012 and 2014). Both NuSTAR and FOXSI have observed non-flaring active regions and quiet Sun regions. In this text two analysis projects will be described in detail: NuSTAR observations of a quiet Sun region and the resulting limits on transient flare-like events, and constraints on the physical properties of nanoflares in active regions observed by NuSTAR and FOXSI.

NuSTAR first observed quiet Sun regions on 2014 November 1, although out-of-view active regions contributed a notable amount of background in the form of single-bounce (unfocused) X-rays. These data are used to search for quiet Sun transient brightenings on time scales of 30, 60, and 100 s and set upper limits on emission in two energy bands. 2.5--4 keV limits are expressed as the temperature T and emission measure EM of a thermal plasma, and 10--20 keV limits as model-independent photon fluxes. The limits in both bands are well below previous HXR microflare detections, though not low enough to detect events of equivalent T and EM as quiet Sun brightenings seen in previous soft X-ray observations. Future observations during solar minimum will increase the NuSTAR sensitivity by over two orders of magnitude due to higher instrument livetime and reduced background.

Active region spectra from the FOXSI-2 sounding rocket and the NuSTAR satellite are used to constrain the physical properties of nanoflares simulated with the EBTEL field-line-averaged hydrodynamics code. X-ray spectra are modeled for various nanoflare heating amplitudes, durations, delay times, and filling factors. Additional constraints on the nanoflare parameter space are determined from energy flux limits and EUV/SXR data. For trains of homogeneous nanoflares, theFOXSI-observed region is well fit by nanoflares with large heating amplitudes >0.02 erg cm^-3 s^-1 and a wide range of delay times and durations. The best fits for this region occur when the delay time is longer than ~1700 s. The NuSTAR-observed regions are not fit as well by the homogeneous nanoflare model, and the good-fit regions of parameter space are fairly different. Three of the NuSTAR-observed regions are fit by smaller heating amplitudes <0.02-0.04 erg cm^-3 s^-1 and shorter delay times, and the other two regions are not well-fit at all. Additional studies of active regions observed by HXR instruments are needed to determine if similar nanoflare distributions can provide good fits to a range of ARs.