FLUKA Simulations of Pion Decay Gamma-Radiation from Energetic Flare Ions

Abstract

Gamma-ray continuum at $> 10 $ > 10 MeV photon energy yields information on $\gtrsim 0.2 $ ≳ 0.2 – 0.3 GeV/nucleon ions at the Sun. We use the general-purpose Monte Carlo code FLUktuierenden KAskade (FLUKA) to model the transport of ions injected into thick and thin target sources, the nuclear processes that give rise to pions and other secondaries and the escape of the resulting photons from the atmosphere. We give examples of photon spectra calculated with a range of different assumptions about the primary ion velocity distribution and the source region. We show that FLUKA gives results for pion decay photon emissivity in agreement with previous treatments. Through the directionality of secondary products, as well as Compton scattering and pair production of photons prior to escaping the Sun, the predicted spectrum depends significantly on the viewing angle. Details of the photon spectrum in the $\approx 100$ ≈ 100 MeV range may constrain the angular distribution of primary ions and the depths at which they interact. We display a set of thick-target spectra produced making various assumptions about the incident ion energy and angular distribution and the viewing angle. If ions are very strongly beamed downward, or ion energies do not extend much above 1 GeV/nucleon, the photon spectrum is highly insensitive to details of the ion distribution. Under the simplest assumptions, flares observed near disc centre should not display significant radiation above 1 GeV photon energy. We give an example application to Fermi Large Area Telescope data from the flare of 12 June 2010.

Modelling magnetised medium particle transport in the guiding centre limit with GEANT4

“…The parameters of the second power-law component are then fixed to give a best fit to the GBM data, which cover the energy range 300 keV -30 MeV. The GEANT4 spectrum alone gives a very good fit to the LAT data above 50 MeV (χ 2 1 ); we recall that MacKinnon et al (2020) find that a fairly wide range of ion distributions can give spectra consistent with these data. The fit to the GBM data is much poorer, however, for several reasons.…”

“…The proton energy of 1 GeV is only just above the threshold for π − production (cf. MacKinnon et al 2020) so the number of these particles is very small. The long run times involved in the NL simulations limit the extent to which this can be investigated, but the NL and GC results are nonetheless in statistical agreement.…”

“…To show the usefulness of this kind of simulation for data interpretation we carried out a first illustrative comparison of the spectrum in Figure 6 with the Fermi Gamma-ray Burst Monitor (GBM) and Large Area Telescope (LAT) data from the flare of 12 June 2010 (Ackermann et al 2012) at time 00:55:40 -00:58:50 UT. These data were previously compared with results of the FLUKA simulations by Tusnski et al (2019) and MacKinnon et al (2020). A rough fit to the data from both instruments was carried out in OSPEX and is shown in Figure 7, combining the GEANT4 template of Figure 6 (right) with two power-law components, one also with exponential turnover.…”

“…Future work will carry out more complete data fitting, and will compare the details of these spectra with those obtained assuming unmagnetised plasma (e.g. MacKinnon et al 2020).…”

“…Kotoku et al (2007) used Geant4 (Agostinelli et al 2003;Allison et al 2006) to simulate electron transport in solar flares and the resulting bremsstrahlung gamma-ray continuum spectra. Ion transport and secondary production in solar flares have also been modelled by Tang & Smith (2010) using Geant4, and by Tusnski et al (2019) and MacKinnon et al (2020) using Fluka (Böhlen et al 2014;Ferrari et al 2005). Geant4 has also been used to study cosmic ray interaction with planetary atmospheres and surfaces (Desorgher et al 2006a;Matthiä et al 2016;Guo et al 2018).…”