Stochastic modelling of cosmic-ray sources for Galactic diffuse emissions

Abstract

Galactic diffuse emissions in gamma rays and neutrinos arise from interactions of cosmic rays with the interstellar medium and probe the cosmic-ray intensity away from the Solar system. Model predictions for those are influenced by the properties of cosmic-ray sources, and understanding the impact of cosmic-ray sources on Galactic diffuse emissions is key for interpreting measurements by LHAASO, Tibet AS-gamma, IceCube, and the upcoming SWGO. We consider supernova remnants as prototypical cosmic-ray sources and study the impact of their discreteness on the Galactic diffuse emissions in different source injection and near-source transport models in a stochastic Monte Carlo study. Three lessons exemplify the results of our simulations: First, the distributions of Galactic diffuse emission intensities can be described by a mixture model of stable laws and Gaussian distributions. Second, the maximal deviations caused by discrete sources across the sky depend on energy, reaching typically tens of percent in burst-like and energy-dependent escape scenarios but order unity or larger in a time-dependent diffusion scenario. Third, the additional model uncertainty from source stochasticity is subdominant in burst-like and energy-dependent escape scenarios, but becomes sizeable above some tens of TeV in the time-dependent diffusion scenario, where it can help reconcile model predictions with LHAASO measurements. With increased spatial resolution, especially at energies beyond tens of TeV, measurements of Galactic diffuse emissions can be expected to constrain source models and locate cosmic ray sources.

Figures (23)

• Figure 1: This schematic overview illustrates the stochastic modelling of CR sources (upper half) and how to obtain GDE predictions and contrasts it to the smooth source model (lower half). In the left panels, the source distribution is illustrated. While point sources can be seen in the stochastic case, the source distribution is a smooth continuum in the smooth case. The position of the Sun is marked with a red cross. In the next step to the right, the CR proton intensities a few kiloparsecs around the Sun are shown as an illustration for the different imprints of the source distributions. The intensity distribution is patchier and imprints of individual sources can be seen by eye. From the CR proton intensities throughout the Galaxy, hadronic GDEs can be predicted for both models. The relative difference between them reveals imprints of individual sources and allows us to study the influence of the stochastic nature of sources quantitatively.
• Figure 2: For one specific realisation in the burst-like scenario, we show the relative difference of GDEs from the smooth model predictions (left) and the proton intensities at 1PeV around the position of the Sun integrated along the $z$-direction (right). The red arrow points towards the Galactic centre, which is in the centre of the sky map on the left. The region marked in the sky map by a grey circle can be explained by the excess proton intensities marked by the crosses in the figure on the right.
• Figure 3: Burst-like scenario. Sky maps at two different energies are shown (10GeV left and 100TeV right). The first row shows the sample means over the $1\,000$ realisations. The remaining rows show the relative deviations of three of those source realisations from this mean, used as an approximation for the smooth model prediction (Eq. \ref{['eq:smooth approx intensity']}). The colour bars are symmetric and saturate at $\pm 5%$ (10GeV) and $\pm 15%$ (100TeV). The numbers on either end of the colour bars indicate the maximum relative deviations for each sky map.
• Figure 4: Energy-dependent escape scenario. This panel shows the relative differences in the energy-dependent escape scenario for the same three source configurations as in Fig. \ref{['fig:1a']}.
• Figure 5: Time-dependent diffusion scenario. This panel shows the relative differences in the time-dependent diffusion scenario for the same three source configurations as in Fig. \ref{['fig:1a']} The confinement around the sources leads to more extreme deviations. The colour bars are symmetric and saturate at $\pm 50%$ (10GeV) and $\pm 100%$ (100TeV). They are linear up to $\pm 5%$ (10GeV) and $\pm 10%$ (100TeV) and logarithmic beyond that.