FLUKA as a tool for interpreting flare gamma-rays
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Introduction
Energetic ions in flares produce gamma-ray photons via a variety of nuclear processes: the lines from positron annihilation and neutron capture, the many broad and narrow lines from deexcitation of target nuclei, the continuum radiation from the decay products of secondary pions and other mesons (for high enough energy primary ions). If we assume e.g. a power-law energy distribution a process of forward fitting can constrain ion numbers and power-law spectral index, and thus their importance and role in the flare process. The enumeration of these features and the detailed modelling necessary to constrain them were developed over many years by Reuven Ramaty and his colleagues and students, some of whom continue this work. However the same or similar problems have been studied independently in laboratory nuclear and particle physics communities for their own needs. The accumulated knowledge of these efforts is embodied in several large, mature codes: FLUKA, Geant4, MCNP and others. While they have seen a few applications to solar flares we were keen to explore their use further, particularly for the interpretation of gamma-ray spectra.
FLUKA
FLUKA (http://www.fluka.org) is a general purpose Monte Carlo code for studying propagation and secondary production of energetic particles in matter. It has a large user base spanning a wide range of fields: medical physics, environmental science, space physics, cosmic rays, laboratory nuclear and particle physics. It is freely available to registered users but is not open source. It is written in Fortran 77 and needs to be run on a reasonably up-to-date Linux system, or possibly via the Docker encapsulated environment. A GUI, Flair, greatly facilitates practical use. The intention of the authors is that it treats all relevant processes (transport of primary and secondary particles; production of secondaries; photon scattering and absorption), all to the same level of accuracy; it is “not a tool-kit”. Many solar and space physicists will have used Geant4 to e.g. simulate detector response, instrumental backgrounds, etc. Compared to Geant4, FLUKA is probably easier to get going with (especially for ageing Fortran progammers!). Beyond some subroutines that allow a degree of customisation, however, the source code is not routinely accessible to the user so for some purposes it will be less flexible. The practical use of these codes is discussed amusingly in (https://willworkforscience.blogspot.com/2010/10/monte-carlo-programs-in-particle.html). We set up a source of solar (Asplund) composition, injected power-law ion energy distributions $\simE^{-\delta}$ with a range of angular distributions and collected all photons emitted into the backward hemisphere. In the first instance we used the recommended FLUKA technique of “detectors”, software devices that e.g. monitor all particles crossing the boundary between two regions. The resulting photon spectra can be compared with observations, from RHESSI, Fermi and any other missions and the parameters of the primary ion distribution constrained in consequence.
SOL2010-06-12
The GOES M2 event on 12 June 2010 0050 was the first flare to be detected by Fermi ([1]). Gamma-ray photons were detected in both Fermi instruments: lines and continuum in the BGO scintillators of the Gamma-Ray Burst Monitor (GBM), and continuum to about 300 MeV in the Large Area Telescope (LAT). Detectable gamma-radiation lasted about 60s, roughly coincident with the flare impulsive phase. In our FLUKA publications we showed fits to the data from this flare to give examples of what can be done. Tusnski et al. (2019) -ref. [2] - shows a fit to the GBM data from this flare. The model spectrum is obtained from FLUKA by injecting a distribution of protons, alpha-particles and heavier nuclei (C, N, O, Ne, Mg, Al, Si, S, Ca, Fe) with $\delta=4$, distributed isotropically in the downward hemisphere, into a solar target. In the GBM data only the lines at 2.22, 4.44 and 6.13 MeV can be clearly discriminated but the general form of the FLUKA spectrum is in good agreement with the data. In the paper we also show that FLUKA gives detailed results for the deexcitation lines in good agreement with the code based on [3] - thanks to Ron Murphy for a copy. Tusnski et al. were able to give an acceptable fit to combined GBM and LAT data, the first time to our knowledge that a single code has given self-consistent results across the whole of this energy range (<1 - >300 MeV), spanning several different radiation mechanisms. In MacKinnon et al. (2020) we studied in more detail the ~100 MeV continuum radiation produced via decay of secondary pions, going on to look at its dependence on viewing angle. While several sets of primary ion parameters give acceptable fit to the LAT data, some are definitely ruled out and systematic trends in $\chi^2$ values are also interesting. Figure 2 shows the best fit we found to the LAT spectrum, for downward isotropic protons, $\delta=3$ up to a maximum of 1 GeV. A couple of interesting points: • The LAT spectrum below ~50 MeV is not consistent with any pion decay spectrum; it falls off too steeply. There must be primary electrons present to at about this energy. Above 50 MeV the pion decay component from primary ions is dominant, however. On the other hand, the best fits to the spectrum are obtained assuming a primary proton distribution that does not extend above 1 GeV. • The flare took place at a heliocentric angle of ~48 degrees but the best fits are obtained for an event near disk centre. Most likely the magnetic field lines are not vertical, as already suggested by the magnitudes of the deexcitation line redshifts found in the RHESSI data from the 23 July 2003 flare.
Conclusions; next
Our work shows that FLUKA can be a valuable tool for interpreting flare gamma-ray spectra. We are particularly interested in radiation from secondary particles, e.g. sub-mm synchrotron radiation from pion decay electrons and positrons. Detection and interpretation of this radiation should open up a new window on the highest energy processes in flares (with Lorentz gammas of 200 or more, pion decay positrons are certainly the most relativistic particles found during flares). Our next steps will explore these diagnostic possibilities in detail.
References
[1] Ackermann et al. (2012) Fermi Detection of γ-Ray Emission from the M2 Soft X-Ray Flare on 2010 June 12 - NASA/ADS (harvard.edu) [2] Tusnski et al. (2010) Self-consistent Modeling of Gamma-ray Spectra from Solar Flares with the Monte Carlo Simulation Package FLUKA - NASA/ADS (harvard.edu)
[3] Kozlovsky et al. (2002) Nuclear Deexcitation Gamma-Ray Lines from Accelerated Particle Interactions - NASA/ADS (harvard.edu)
[4] MacKinnon et al. (2020) FLUKA Simulations of Pion Decay Gamma-Radiation from Energetic Flare Ions - NASA/ADS (harvard.edu)
