Abstract
Context. Recently, there has been an increased interest in the study of the generation of low-energy cosmic rays (< 1 TeV) in shocks situated on the surface of a protostar or along protostellar jets. These locally accelerated cosmic rays offer an attractive explanation for the high levels of non-thermal emission and ionisation rates observed close to these sources.Aims. The high ionisation rate 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 ionisation rate are measured in the same spatial region, a locally shock-accelerated cosmic-ray flux is sufficient to explain both phenomena.Methods. We assume that relativistic protons and electrons are accelerated according to the first-order Fermi acceleration mechanism, and we calculate their emerging fluxes at the shock surface. These fluxes are used to compute the ionisation rate and the non-thermal emission at centimetre 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, the intensity of the magnetic field, and its degree of turbulence.Results. We demonstrate that the local cosmic-ray acceleration model makes it possible to simultaneously explain the synchrotron emission along the HOPS 370 jet within the FIR 3 region and the ionisation rate observed near the FIR 4 protocluster. In particular, our model constrains the magnetic field strength (∼250−450 μG), its turbulent component (∼20−40 μG), and the jet velocity in the shock reference frame for the three non-thermal sources of the HOPS 370 jet (between 350 km s−1 and 1000 km s−1).Conclusions. Beyond the modelling of the OMC-2 FIR 3/FIR 4 system, we show how the combination of continuum observations at centimetre 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 cosmic rays, without having to resort to shock-generated UV photons.Key words: stars: formation / cosmic rays / ISM: jets and outflows / radio continuum: ISM / acceleration of particles