Constraining cosmic ray acceleration in young star clusters using
  multi-wavelength observations
  We use $1$D and $3$D 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 $\rho \propto r^{-1}$), 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 $\gamma$-ray
luminosity ($L_{\rm \gamma}$) can reach $\approx 5\%$ of the mechanical
luminosity ($L_{\rm w}$), independent of the fraction of wind energy ($\sim
1-20\%$) injected into CRs. In contrast, if the forward/reverse shock of a
bubble is the injection site then $L_{\rm \gamma}$ increases linearly with the
CR injection fraction, as expected analytically. We find that the X-ray
luminosity ($L_{\rm x}$) in the forward/reverse shock injection scenario is
$\gtrsim 10^{-3} L_{\rm w}$, which is $\sim 10$ 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 we identify the reverse shock as the most
probable CR injection site, and that thermal conduction is important. We do not
find significant dynamical impact of CRs in our models.
