The double signature of local cosmic-ray acceleration in star-forming
  regions
  Recently, there has been an increased interest in the study of the generation
of low-energy cosmic rays (CRs; < 1 TeV) in shocks situated on the surface of a
protostar or along protostellar jets. These locally accelerated CRs offer an
attractive explanation for the high levels of non-thermal emission and
ionisation rate, $\zeta$, observed close to these sources. The high $\zeta$
observed in some protostellar sources is generally attributed to
shock-generated UV photons. The aim of this article is to show that when
synchrotron emission and a high $\zeta$ are measured in the same spatial
region, a locally shock-accelerated CR flux is sufficient to explain both
phenomena. We assume that relativistic particles are accelerated according to
the first-order Fermi acceleration mechanism and compute $\zeta$ and the
non-thermal emission at cm wavelengths. We then apply our model to the
star-forming region OMC-2 FIR 3/FIR 4. Using a Bayesian analysis, we constrain
the parameters of the model and estimate the spectral indices of the
non-thermal radio emission. We demonstrate that the local CR acceleration model
makes it possible to simultaneously explain the synchrotron emission along the
HOPS 370 jet within the FIR 3 region and $\zeta$ observed near the FIR 4
protocluster. Our model constrains the magnetic field strength
(~250-450$~\mu$G), its turbulent component (~20-40$~\mu$G), and the jet
velocity in the shock reference frame for the three non-thermal sources of the
HOPS 370 jet (~350-1000 km s$^{-1}$). Beyond the modelling of the OMC-2 FIR
3/FIR 4 system, we show how the combination of continuum observations at cm
wavelengths and molecular transitions is a powerful new tool for the analysis
of star-forming regions: these two types of observations can be simultaneously
interpreted by invoking only the presence of locally accelerated CRs, without
having to resort to shock-generated UV photons.
