Angular Distribution of Gamma Rays Produced in Proton-Proton Collisions

TL;DR

This paper models the joint energy and angular distribution of gamma rays from proton-proton collisions, providing tabulated data, a Python tool, and an analytic formula to improve astrophysical gamma-ray observations interpretation.

Contribution

It introduces detailed calculations of the gamma-ray angular distribution from proton-proton collisions, including a Python tool and an analytic approximation, filling a gap in existing models.

Findings

Provides tabulated $d^2 N_ ext{gamma}/dE d heta$ distributions

Offers a Python tool for easy application

Introduces an analytic formula for the angular distribution

Abstract

Accurate modeling of how high-energy proton-proton collisions produce gamma rays through the decays of pions and other secondaries is needed to correctly interpret astrophysical observations with the Fermi-LAT telescope. In the existing literature on cosmic-ray collisions with gas, the focus is on the gamma-ray yield spectrum, $d N_\gamma/dE$. However, in some situations, the joint energy and angular distribution can be observed, so one needs instead $d^2 N_\gamma/dE \, d\Omega$. We provide calculations of this distribution over the energy range from the pion production threshold to $100~{\rm GeV}$, basing our results on FLUKA simulations. We provide the results in tabular form and provide a Python tool on GitHub to aid in utilization. We also provide an approximate analytic formula that illuminates the underlying physics. We discuss simplified examples where this angular dependence can be observed to illustrate the necessity of taking the joint distribution into account.