On the hadronic origin of the very high energy $γ$-ray emission surrounding the young massive stellar cluster Westerlund 1

TL;DR

The paper investigates whether the very high-energy gamma-ray emission surrounding the young massive cluster Westerlund 1 (Wd 1) can originate from hadronic cosmic rays accelerated at the termination shock (TS) of the cluster wind within a superbubble. It develops a physical model of CR acceleration at the TS, solves the Parker transport equation with a spatially varying diffusion and a TS boundary, and computes the resulting hadronic gamma-ray emission from CR protons interacting with ambient gas, comparing to the HESS J1646-458 data. The key finding is that, with a realistic clumpy gas density in the shocked wind cavity (approximate average density $\rho_2 \sim 1\, \mathrm{cm^{-3}}$) and a modest CR-to-ram-pressure ratio $\xi_{\rm CR} \sim 0.1$, the observed spectrum and radial profile can be reproduced, supporting a hadronic origin; if the cavity gas density follows the classic wind-bubble model with homogeneous gas, the required $\xi_{\rm CR}$ would exceed unity. This work highlights Westerlund 1’s TS as a viable site for CR acceleration up to sub-PeV energies and bolsters the view that young massive clusters contribute significantly to Galactic CRs, while emphasizing the need for nonlinear CR feedback considerations and continued multiwavelength observations to constrain the emission mechanism.

Abstract

The Westerlund 1 (Wd 1) is the most massive known young star cluster in the Galaxy, and an extended $γ$-ray source HESS J1646-458 surrounding it has been detected up to 80 TeV in the very high energy, implying that cosmic rays (CRs) are accelerated effectively in the region. However, the dominant radiation process contributing to the $γ$-ray emission is not well constrained. In the present work, we develop a model of CR acceleration at the termination shock in the superbubble inflated by the interaction of the cluster wind from the Wd 1 with the surrounding interstellar medium. We then calculate the flux and radial profile of $γ$ rays produced by the inelastic collisions of the hadronic CRs with the ambient gas. Our results with reasonable parameters can explain well the spectrum and radial profile of the $γ$-ray emission of HESS J1646-458, and consequently the $γ$-ray emission of HESS J1646-458 is likely to be of hadronic origin.

Figures (6)

• Figure 1: Schematic structure of a superbubble inflated by the cluster wind of a massive star cluster.
• Figure 2: Top: The distribution functions of accelerated CRs at the TS for Kolmogorov ($\delta=1/3$) and Iroshnikov-Kraichnan ($\delta=1/2$) turbulence spectra. The vertical dashed and dotdashed lines show the cutoff momenta of accelerated CRs as defined by Eq. \ref{['eq:pcut']} for Kolmogorov and Iroshnikov-Kraichnan turbulence spectra, respectively. The injection efficiency $\eta_\mathrm{inj}=0.1$, the spatial diffusion coefficient $D_0 = 3\times 10^{25}~\mathrm{cm^2/s}$, and the mass density of external ISM $\rho_0=50~m_p~\mathrm{cm}^{-3}$, while other parameters are specified in Section \ref{['sec:sb']}. Bottom: Same as the top panel but $D_0=1\times 10^{26}~\mathrm{cm^2/s}$.
• Figure 3: Top and bottom panels show the radial profiles of CR distribution functions at different momenta for Kolmogorov ($\delta=1/3$) and Iroshnikov-Kraichnan ($\delta=1/2$) turbulence spectra, respectively. The injection efficiency $\eta_\mathrm{inj}=0.1$, the spatial diffusion coefficient $D_0 = 3\times 10^{25}~\mathrm{cm^2/s}$, and the mass density of external ISM $\rho_0=50~m_p~\mathrm{cm}^{-3}$, while other parameters are specified in Section \ref{['sec:sb']}.
• Figure 4: Top and bottom panels show the spectra of accelerated electrons at the TS and their radial profiles at different energies, respectively, for Kolmogorov ($\delta=1/3$) turbulence spectrum. Dashed and solid lines correspond to the cases with and without energy loss resulting from synchrotron radiation taken into account, respectively. The vertical dashed line at the top panel shows the cutoff momentum of accelerated electrons as defined by Eq. \ref{['eq:pcut']} when synchrotron cooling is not taken into account. For the case that the energy loss due to synchrotron radiation is taken into account, the magnetic field is $B=3~\mathrm{\mu G}$. The injection efficiency $\eta_\mathrm{inj}=0.1$, the spatial diffusion coefficient $D_0 = 3\times 10^{25}~\mathrm{cm^2/s}$, and the mass density of external ISM $\rho_0=50~m_p~\mathrm{cm}^{-3}$, while other parameters are specified in Section \ref{['sec:sb']}.
• Figure 5: The $\gamma$-ray fluxes (top panel) and the radial profiles of $\gamma$-ray intensities above the threshold of 0.37 TeV (bottom panel) for three different models with the external ISM mass density $\rho_0 =$ 30, 40, and 50 $m_p~\mathrm{cm^{-3}}$, respectively. The best-fit ratio of CR to ram pressure $\xi_\mathrm{CR}$ for each model is listed in the last column of Table \ref{['tab:fits']}, when it is assumed that the gas density $\rho_2$ of shocked wind cavity is given by Eq. \ref{['eq:rho-cavity']}. In contrast, when the gas density $\rho_2$ is a free parameter and its best-fit value for each model is listed in the second column of Table \ref{['tab:fits-2']}, we have assumed that $\xi_\mathrm{CR}=0.1$. The spatial diffusion coefficient $D_0=3\times 10^{25}~\mathrm{cm^2/s}$, while other parameters are specified in Section \ref{['sec:sb']}. The data points of HESS J1646-458 are taken from HC2022.