Speaker
Description
The interactions of ultra-high energy cosmic rays (UHECRs) in astrophysical scenarios are in general of stochastic nature. Whether the targets are photon fields (photohadronic) or other nuclei (hadronic), the outcomes of a sequence of interactions are currently obtained via Monte Carlo simulations since the compound distributions are not known. The reason is that, although the outcomes of individual interactions are available, the compound effect of a sequence of interactions has additional variability given that the multiplicity, nature, and energy distributions of the secondaries for each step are also stochastic. Therefore, the compound probability functions, including all these aspects, have only been accessible through Monte Carlo codes where each stochastic quantity is sampled in sequence. The task becomes especially complex when considering UHECR nuclei and the cascades resulting from subsequent interactions of the secondary nuclear species.
This work presents a methodology to obtain the aforementioned compound distributions based on the theory of matrix exponential distributions, thus no need for simulations. The outcome: analytical expressions which require no more inputs than the existing Monte Carlo codes, but provide better precision and considerably reduced computational cost. The inputs can be obtained from the usual sources: experimental data or precomputed tables from interaction generator codes (e.g. SOPHIA for photohadronic; QGSJet, Sybill, EPOSLHC for photohadronic) representing the interaction rate, the multiplicity and the energy distributions of secondaries after one interaction. The expressions presented allow computing the probabilities and energy distributions of different final products, the related statistical moments, and any other statistical quantities that characterize any probability distribution function. Examples are provided of astrophysical relevance (namely UHECR sources and UHECR propagation) and the results are compared to existing Monte Carlo codes such as CRPropa.
