Three-dimensional Forward-fit Modeling of the Hard X-Ray and Microwave Emissions of the 2015 June 22 M6.5 Flare

Abstract

The well-established notion of a “common population” of the accelerated electrons simultaneously producing the hard X-ray (HXR) and microwave (MW) emission during the flare impulsive phase has been challenged by some studies reporting the discrepancies between the HXR-inferred and MW-inferred electron energy spectra. The traditional methods of spectral inversion have some problems that can be mainly attributed to the unrealistic and oversimplified treatment of the flare emission. To properly address this problem, we use a nonlinear force-free field (NLFFF) model extrapolated from an observed photospheric magnetogram as input to the three-dimensional, multiwavelength modeling platform GX Simulator and create a unified electron population model that can simultaneously reproduce the observed HXR and MW observations. We model the end of the impulsive phase of the 2015 June 22 M6.5 flare and constrain the modeled electron spatial and energy parameters using observations made by the highest-resolving instruments currently available in two wavelengths, the Reuven Ramaty High Energy Solar Spectroscopic Imager for HXR and the Expanded Owens Valley Solar Array for MW. Our results suggest that the HXR-emitting electron population model fits the standard flare model with a broken power-law spectrum ( keV) that simultaneously produces the HXR footpoint emission and the MW high-frequency emission. The model also includes an “HXR-invisible” population of nonthermal electrons that are trapped in a large volume of magnetic field above the HXR-emitting loops, which is observable by its gyrosynchrotron radiation emitting mainly in the MW low-frequency range.

Gyrosynchrotron Emission Generated by Nonthermal Electrons with the Energy Spectra of a Broken Power Law

“…Along this line of approach, Gary et al (2013) proposed a procedure to diagnose the 3D coronal magnetic field and other parameters, starting from some prescribed values of these parameters, and adjusting them by minimizing the difference between the calculated and the observed 2D maps of microwave emission so as to get the optimal diagnostic results. Similar studies were carried out by other authors (Nindos et al 2000;Kundu et al 2004;Nita et al 2015;Casini et al 2017;Kuroda et al 2018).…”

Incoherent Solar Radio Emission

“…The relationship of these bursts with hard X-rays together with spectral modeling revealed that the trapped electron population was negligible and the radio emission originated directly from the acceleration sites which featured rather strong magnetic fields and densities. In the Kuroda et al (2018) study the microwave and hard Xray observations were successfully fitted with a broken powerlaw spectrum that reproduced the main characteristics of both emissions. The most popular model for the study of electron transport during flares is the "direct precipitation/trap plus precipitation" (DP/TPP) model (see Aschwanden, 2002Aschwanden, , 2004White et al, 2011, and references therein).…”

“…The diagnostic strength of gyrosynchrotron, albeit significant, is not as straightforward as that of gyroresonance; for meaningful results one needs to combine observations (ideally spectroscopic imaging ones) with detailed modeling. In spite of all the complications, modeling of individual flares (e.g., Nindos et al, 2000b;Kundu et al, 2004a;Tzatzakis et al, 2008;Gary et al, 2013Gary et al, , 2018Kuznetsov and Kontar, 2015;Fleishman et al, 2016bFleishman et al, ,c, 2018Kuroda et al, 2018) showed that the magnetic field may lie from less than 200 G (loop top) to about 1700 G (footpoints). Probably the most spectacular result was obtained by Fleishman et al (2020) who modeled spectroscopic imaging observations from Expanded OVSA (EOVSA) and found that the magnetic field decayed at a rate of about 5 G s −1 for 2 min.…”

“…The combination of microwave and hard X-ray observations of flares with state-of-the-art 3D modeling provides a powerful diagnostic of accelerated electrons (e.g., Fleishman et al, 2016a;Kuroda et al, 2018). In the former study several flares were analyzed which, instead of showing the usual broad-band gyrosynchrotron emission produced by electrons trapped in flaring loops, they showed narrow-band gyrosynchrotron spectra (see also Fleishman et al, 2011Fleishman et al, , 2013.…”

Radio observatories and instrumentation used in space weather science and operations

“…Space Weather Space Clim. 2020, 10, 7 Radioheliograph (GRAPH; Ramesh et al, 1998) in southern India, operating at discrete frequencies between 40 MHz and 150 MHz; the Expanded Owens Valley Solar Array (EOVSA; Kuroda et al, 2018) in the USA, performing imaging spectroscopy from 1 GHz to 18 GHz; the Japanese Nobeyama Radioheliograph (NoRH; Nakajima et al, 1994) operating at 17 GHz and 34 GHz, and the Siberian Solar Radio Telescope (SSRT; Grechnev et al, 2003) operating at the single frequency of 5.7 GHz (the location of these and other instruments are shown in Fig. 5).…”