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We study the effect of cosmic ray (CR) acceleration in the massive compact star cluster Westerlund 1 in light of its recent detection in γ-rays. Recent observations reveal a 1/ r radial distribution of the CR energy density. Here, we theoretically investigate whether or not this profile can help to distinguish between (1) continuous CR acceleration in the star cluster stellar wind-driven shocks and (2) discrete CR acceleration in multiple supernovae (SNe) shocks – which are often debated in the literature. Using idealized two-fluid simulations and exploring different acceleration sites and diffusion coefficients, we obtain the CR energy density profile and luminosity to find the best match for the γ-ray observations. We find that the inferred CR energy density profiles from observations of γ-ray luminosity and mass can be much different from the true radial profile. CR acceleration at either the cluster core region or the wind termination shock can explain the observations, if the diffusion coefficient is κ cr ∼ 1027 cm2 s−1 and a fraction of |${\approx}10-20{{\ \rm per\ cent}}$| of the shock power/post-shock pressure is deposited into the CR component. We also study the possibility of discrete SNe explosions being responsible for CR acceleration and find that with an injection rate of 1 SN in every ∼0.03 Myr, one can explain the observed γ-ray profile. This multiple SN scenario is consistent with X-ray observations only if the thermal conductivity is close to the Spitzer value. [ABSTRACT FROM AUTHOR]

Cosmic rays (CRs) are frequently modelled as an additional fluid in hydrodynamic (HD) and magnetohydrodynamic (MHD) simulations of astrophysical flows. The standard CR two-fluid model is described in terms of three conservation laws (expressing conservation of mass, momentum, and total energy) and one additional equation (for the CR pressure) that cannot be cast in a satisfactory conservative form. The presence of non-conservative terms with spatial derivatives in the model equations prevents a unique weak solution behind a shock. We investigate a number of methods for the numerical solution of the two-fluid equations and find that, in the presence of shock waves, the results generally depend on the numerical details (spatial reconstruction, time stepping, the CFL number, and the adopted discretization). All methods converge to a unique result if the energy partition between the thermal and non-thermal fluids at the shock is prescribed using a subgrid prescription. This highlights the non-uniqueness problem of the two-fluid equations at shocks. From our numerical investigations, we report a robust method for which the solutions are insensitive to the numerical details even in absence of a subgrid prescription, although we recommend a subgrid closure at shocks using results from kinetic theory. The subgrid closure is crucial for a reliable post-shock solution and also its impact on large-scale flows because the shock microphysics that determines CR acceleration is not accurately captured in a fluid approximation. Critical test problems, limitations of fluid modelling, and future directions are discussed. [ABSTRACT FROM AUTHOR]

Using an idealized set-up, we investigate the dynamical role of cosmic rays (CRs) in the early stages of galactic outflows for galaxies of halo masses 108, 1011, and 1012 M⊙. The outflow is launched from a central region in the galactic disc where we consider three different constant star formation rates (0.1, 1, and 10 |$\mathrm{M}_\odot \, \mathrm{yr}^{-1}$|⁠) over a dynamical time-scale of 50 Myr. We determine the temperature distribution of the gas and find that CRs can reduce the temperature of the shocked gas, which is consistent with previous results. However, we show that CRs do not have any noticeable effect on the mass loading by the outflow. We find that CRs can reduce the size of the outflow, which contradicts previous claims of efficient dynamical impact of CRs; however, it is consistent with earlier theoretical models of CR-driven blastwave as well as stellar wind. We discuss the dependence of our results on CR injection prescriptions and compare them with earlier studies. We conclude that in the early stages of galactic outflows the dynamical role of CRs is not important. [ABSTRACT FROM AUTHOR]

Cosmic ray (CR) sources leave signatures in the isotopic abundances of CRs. Current models of Galactic CRs that consider supernovae (SNe) shocks as the main sites of particle acceleration cannot satisfactorily explain the higher 22Ne/20Ne ratio in CRs compared to the interstellar medium. Although stellar winds from massive stars have been invoked, their contribution relative to SNe ejecta has been taken as a free parameter. Here, we present a theoretical calculation of the relative contributions of wind termination shocks (WTSs) and SNe shocks in superbubbles, based on the hydrodynamics of winds in clusters, the standard stellar mass function, and stellar evolution theory. We find that the contribution of WTSs towards the total CR production is at least |$25{{\ \rm per\ cent}}$|⁠ , which rises to |$\gtrsim 50{{\ \rm per\ cent}}$| for young (≲10 Myr) clusters, and explains the observed 22Ne/20Ne ratio. We argue that since the progenitors of apparently isolated supernovae remnants (SNRs) are born in massive star clusters, both WTS and SNe shocks can be integrated into a combined scenario of CRs being accelerated in massive clusters. This scenario is consistent with the observed ratio of SNRs to γ-ray bright (L γ ≳ 1035 erg s−1) star clusters, as predicted by star cluster mass function. Moreover, WTSs can accelerate CRs to PeV energies, and solve other long-standing problems of the standard SN paradigm of CR acceleration. [ABSTRACT FROM AUTHOR]

We use 1D and 3D two-fluid cosmic ray (CR) hydrodynamic simulations to investigate the role of CRs in the vicinity of a compact young star cluster. We model a self-gravitating cloud (density profile ρ∝ r −1), include important thermal and non-thermal processes, and explore two different CR injection scenarios. We show that if internal shocks in the wind-driving region are the main site for CR acceleration, then the resulting γ-ray luminosity (L γ) can reach ≈5 per cent of the mechanical luminosity (L w), independent of the fraction of wind energy (∼1–20 per cent) injected into CRs. In contrast, if the forward/reverse shock of a bubble is the injection site then L γ increases linearly with the CR injection fraction, as expected analytically. We find that the X-ray luminosity (L x) in the forward/reverse shock injection scenario is ≳ 10−3 L w, which is ∼10 times larger than in the central wind-driving injection case. We predict the corresponding range of the synchrotron radio luminosity. We show how multi-wavelength observations can constrain the CR parameters. Comparing the predicted multi-wavelength luminosities with those of 30 Doradus and Westerlund 2 we identify the reverse shock as the most probable CR injection site. We do not find significant dynamical impact of CRs in our models. [ABSTRACT FROM AUTHOR]

Using analytic methods and 1D two-fluid simulations, we study the effect of cosmic rays (CRs) on the dynamics of interstellar superbubbles (ISBs) driven by multiple supernovae (SNe)/stellar winds in OB associations. In addition to CR advection and diffusion, our models include thermal conduction and radiative cooling. We find that CR injection at the reverse shock or within a central wind-driving region can affect the thermal profiles of ISBs and hence their X-ray properties. Even if a small fraction (10-20 per cent) of the total mechanical power is injected into CRs, a significant fraction of the ram pressure at the reverse shock can be transferred to CRs. The energy transfer becomes efficient if (1) the reverse shock gas Mach number exceeds a critical value (Mth ≳ 12) and (2) the CR acceleration time-scale τacc ∼ κcr/v² is shorter than the dynamical time, where κcr is a CR diffusion coefficient and v is the upstream velocity. We show that CR affected bubbles can exhibit a volume-averaged hot gas temperature 1-5 × 106 K, lower by a factor of 2 - 10 than without CRs. Thus, CRs can potentially solve the long-standing problem of the observed low ISB temperatures. [ABSTRACT FROM AUTHOR]