Modeling gamma-ray signatures of particle acceleration in stellar clusters from GeV to PeV

TL;DR

The paper investigates gamma-ray signatures from particle acceleration in Young Massive Stellar Clusters (YMSCs), modeling the transport of CRs from wind termination shocks or embedded SNRs to nearby molecular clouds where hadronic pp interactions produce gamma rays. It develops diffusion-based analytic solutions for impulsive and continuous CR injection, derives maximal CR-excess distances and energy-dependent fluxes, and maps the parameter space against LHAASO/H.E.S.S./Fermi-LAT sensitivities. Applying the framework to the W43 region, the study finds that a wind-termination-shock origin better explains the high-energy gamma-ray data than an embedded SNR scenario and derives constraints on diffusion and injection parameters, notably $\alpha\approx2.0$, $\delta\approx0.33$, and $\epsilon\frac{10^{28}}{D_{10}}\sim1$. The results imply that cluster-driven hadronic emission can contribute to the Galactic CR population at high energies and may account for some unidentified LHAASO sources, guiding future searches for cluster–cloud systems.

Abstract

Young massive stellar clusters (YMSCs) have recently regained interest as PeVatron candidates, potentially accounting for the cosmic-ray (CR) knee as alternatives to isolated supernova remnants (SNRs). LHAASO's unique capability to detect photons above 0.1 PeV, hence tracing multi-PeV CRs, can provide critical constraints on galactic acceleration models when combined with H.E.S.S. and Fermi-LAT data. We investigate the transport of particles from YMSCs acceleration sites, namely wind termination shocks (WTS) or embedded SNRs, to nearby dense molecular clouds where proton-proton interactions produce high-energy gamma rays. We determine the necessary conditions, such as the distance between the acceleration site and the target, or the cluster's power and age, for detectable gamma-ray excesses and identify viable systems through parameter space exploration. By comparing with observations, we can constrain key physical parameters including WTS efficiency, diffusion coefficient and injection slope. Our analysis also examines whether some of LHAASO's unidentified sources might correspond to such cluster-cloud systems.

Figures (3)

• Figure 1: Left: Gamma-ray fluxes at 0.3 PeV from impulsive injection: embedded SNRs, $W_{CR}=10^{50} \rm erg$ and age fixed at $t=10^4 \rm years$ (parameter degenerate with $D_{10})$. Right: Gamma-ray fluxes at 0.3 PeV from continuous injection: WTS, $\dot{W}_{CR}= 3 \cdot 10^{37} ~ \rm erg.s^{-1}$. For both plots, the target is a molecular cloud of mass $M_{cloud}=10^5M_{\odot}$ and at d=2kpc from us. In light green is plotted the gamma-ray background from the CR sea interacting with the cloud and in dark green is the LHAASO point-like sensitivity. Case 1,2,3,4 refer respectively to the parameter set 1) $\delta=0.3$, $\alpha=2.0$, $D_{10}=10^{27} \mathrm{cm}^2 \mathrm{s}^{-1}$; 2) $\delta=0.3$, $\alpha=2.1$, $D_{10}=10^{27} \mathrm{cm}^2 \mathrm{s}^{-1}$; 3) $\delta=0.4$, $\alpha=2.0$, $D_{10}=10^{27} \mathrm{cm}^2 \mathrm{s}^{-1}$; 4) $\delta=0.3$, $\alpha=2.0$, $D_{10}=10^{28} \mathrm{cm}^2 \mathrm{s}^{-1}$.
• Figure 2: $\gamma$-ray spectra from a molecular cloud of mass $M_{cloud}=10^5M_{\odot}$, 60pc away from the cluster and at d=2kpc from us. Incoming CRs are accelerated in embedded SNRs ($W_{CR}=10^{50} \rm erg$ and $t=10^5 \rm years$), or in WTS ($\dot{W}_{CR}= 3 \cdot 10^{37} ~ \rm erg.s^{-1}$) or are the CR sea. Parameters are fixed to $\delta=0.3$, $\alpha=2.0$, $D_{10}=10^{27} \mathrm{cm}^2 \mathrm{s}^{-1}$. Point-like differential sensitivity of LHAASO, CTA North and Fermi-LAT are shown in dashed lines.
• Figure 3: Left:$\gamma$-ray significiance map of LHAASO J1848-0153u between 25 and 100 TeV, with star cluster W43 main in the center. Right:$\gamma$-ray spectra fitted to LHAASO J1848-0153u and the corresponding Fermi datapoints derived in Yang2020. Emissions are computed for a molecular cloud of mass $M_{cloud}=10^6M_{\odot}$ at d=5.5kpc from us, where incoming CRs are accelerated in embedded SNRs or in WTS. For WTS, the parameters used are $\dot{W}_{CR}=~ 3 \epsilon_w \times 10^{38} \rm~erg/s$, $R=75\rm ~pc$, $\delta=0.33$, $\alpha=2.0$, $D_{10}=10^{27} \mathrm{cm}^2 \mathrm{s}^{-1}$ while for SNR: $W_{CR}=2\times 10^{50} \rm erg$, $t=3 \times 10^4 ~ \rm yrs$, $R=55\rm ~pc$, $\delta=0.3$, $\alpha=2.0$, $D_{10}=3 \times 10^{27} \mathrm{cm}^2 \mathrm{s}^{-1}$.