Spatial distribution of secondary electrons' Synchrotron emission: property and implication

TL;DR

The paper tackles the problem of differentiating hadronic from leptonic origins of ultrahigh-energy γ-ray sources by studying the spatial morphology of X-ray synchrotron emission from secondary electrons. It develops a diffusion-based transport framework with $D(E)=D_0\left(E/1\,\mathrm{GeV}\right)^{1/2}$ and $n_0=10\,{\rm cm}^{-3}$ for a source at $d=5$ kpc over $T_{\rm age}=2$ Myr, comparing hadronic and leptonic scenarios and including Klein-Nishina effects. A key finding is that secondary-electron synchrotron can produce a flat X-ray surface-brightness profile (SBP) and distinctive photon-index profiles, offering a morphological diagnostic alongside spectra to identify PeVatrons; the study also shows how an offset molecular cloud can create complex, yet interpretable, γ-ray and X-ray morphologies. Hybrid cases with primary electrons are explored, revealing parameter regimes where X-ray morphology still preserves hadronic signatures. Overall, the work demonstrates that X-ray morphology and spectral behavior together provide a powerful tool for pinpointing the radiation mechanism of UHE γ-ray sources and constraining PeV cosmic-ray accelerators.

Abstract

Galactic $γ$-ray sources can be produced by either high-energy protons via proton-proton collisions or electrons/positrons via inverse Compton scattering. Distinguishing between the hadronic and leptonic origin of $γ$-ray emission in Galactic sources remains challenging. Measurements of non-thermal X-ray spectra of these sources, which could originate from primary electrons in the leptonic scenario or secondary electrons/positrons in the hadronic scenario, have been suggested as an efficient way of discriminating between these scenarios. In this work, we investigate the morphology of the X-ray emission from secondary electrons/positrons. By calculating the surface brightness profile and the photon index profile of X-ray emission, we find that secondary electrons produce a distinctively flat X-ray surface brightness profile. Our results suggest that, in addition to the X-ray spectrum, the X-ray morphology is crucial to determine the radiation mechanism of ultrahigh-energy $γ$-ray sources and help to identify sources of PeV cosmic rays.

Figures (4)

• Figure 1: Normalized electron density distribution (upper panel) and the power-law index profile (lower panel) of secondary electrons in $20-100$ TeV. Different colors correspond to the magnetic field $B=10, 50, 100 ~ \mu$G. The purple dashed line corresponds to the normalized primary electron density in the leptonic scenario at $1 \, \rm \mu G$. The black dotted line corresponds to the normalized distribution of injection rate of secondary electrons $Q_{\rm e}$ at $t=2 \rm Myr$. Both the density and injection rate are normalized at $r= 0.1\,$pc.
• Figure 2: Left: Energy spectrum for hadronic and leptonic scenario. In $\gamma$-ray band, both models satisfy $dN/dE_{\gamma} \propto E_{\gamma}^{-3}$ and $F_{25-100 \text{TeV}}= 1 \times 10^{-12} ~ \rm erg~cm^{-2}s^{-1}$. In the X-ray band, the yellow solid line refers to the synchrotron radiation from primary electrons with $B_{\rm lep}=1 \rm \mu G$. Green solid, dotted-solid and dotted lines refer to the synchrotron radiation from secondary electrons with $B_{\rm had}=100 \rm \mu G$, $50 \rm \mu G$ and $10 \rm \mu G$ respectively. Right: The predicted SBP and photon index profile in 0.5-7 keV with $B_{\rm had}=50 \rm \mu G$, $B_{\rm lep}=1 \rm \mu G$. The diffusion coefficient is assumed to $D_{\rm 0,had}$=$D_{\rm 0,lep}$=$10^{26} \rm cm^2/s$.
• Figure 3: The predicted energy spectrum, SBP and photon index profile in the hybrid case with $B_{\rm hybrid}=50 \rm \mu G$ and $D_{\rm 0,had}$=$D_{\rm 0,lep}$=$10^{26} \rm cm^2/s$. The solid, dash-dot and dotted lines refer to $K_{ep}=10^{-2}, 10^{-3}$ and $10^{-4}$.
• Figure 4: Left: the morphology of emission in hadronic scenario. Right: the corresponding SBPs and photon index profiles along the x-axis in hadronic (black lines) and leptonic (green lines) scenarios. From top to bottom, (a) $25-100$ TeV $\gamma$-ray emission (b) $2-7$ keV X-ray emission.