Methanol as a diagnostic tool of interstellar clouds II. Modelling high-mass protostellar objects

Context. Fundamental properties of interstellar clouds must be known to investigate the initial conditions of star formation within them and the interaction of newly formed stars with their environment. Methanol has proven to be useful to probe densities and temperatures of various environments within interstellar clouds. Aims. We aim to explore the potential of methanol as a tracer molecule for regions in which high-mass stars are forming or have recently formed, in particular so-called high-mass protostellar objects (HMPOs) and infrared dark clouds (IRDCs). Methods. We present and analyse multi-frequency centimetre and (sub) millimetre single-dish observations of methanol toward a sample of 13 sources that are in the poorly understood earliest phases of evolution of high-mass stars (HMPOs and IRDCs). For each source in our sample, we derive physical parameters such as the kinetic temperature, the spatial density. and the methanol column density. We apply our large velocity gradient modelling and fitting technique that involves fitting a synthetic spectrum to all the measured lines simultaneously. Results. In several sources, we find that more than one physical component is necessary to fit the spectra; moreover, broad non-Gaussian linewidths suggest outflows in many sources from both the IRDC and the HMPO subsamples. Kinetic temperatures are found to be between 10 and 60 K and spatial densities in the range 10(5)-10(6) cm(-3). Hotter, denser cores are found in a few HMPOs, indicating that these sources already harbour hot cores heated by protostars.