From forced collapse to H II region expansion in Mon R2: Envelope density structure and age determination with Herschel

Context. The surroundings of H II regions can have a profound influence on their development, morphology, and evolution. This paper explores the effect of the environment on H II regions in the MonR2 molecular cloud. Aims. We aim to investigate the density structure of envelopes surrounding H II regions and to determine their collapse and ionisation expansion ages. The Mon R2 molecular cloud is an ideal target since it hosts an H II region association, which has been imaged by the Herschel PACS and SPIRE cameras as part of the HOBYS key programme. Methods. Column density and temperature images derived from Herschel data were used together to model the structure of H II bubbles and their surrounding envelopes. The resulting observational constraints were used to follow the development of the Mon R2 ionised regions with analytical calculations and numerical simulations. Results. The four hot bubbles associated with H II regions are surrounded by dense, cold, and neutral gas envelopes, which are partly embedded in filaments. The envelope's radial density profiles are reminiscent of those of low-mass protostellar envelopes. The inner parts of envelopes of all four H II regions could be free-falling because they display shallow density profiles: rho(r) alpha r(-q) with q <= 1.5. As for their outer parts, the two compact H II regions show rho(r) alpha r(-q) profile, which is typical of the equilibrium structure of a singular isothermal sphere. In contrast, the central UCH II region shows a steeper outer profile, rho(r) alpha r(-2.5), that could be interpreted as material being forced to collapse, where an external agent overwhelms the internal pressure support. Conclusions. The size of the heated bubbles, the spectral type of the irradiating stars, and the mean initial neutral gas density are used to estimate the ionisation expansion time, t(exp) similar to 0.1 Myr, for the dense UCH II and compact H II regions and similar to 0.35 Myr for the extended H II region. Numerical simulations with and without gravity show that the so-called lifetime problem of H II regions is an artefact of theories that do not take their surrounding neutral envelopes with slowly decreasing density profiles into account. The envelope transition radii between the shallow and steeper density profiles are used to estimate the time elapsed since the formation of the first protostellar embryo, t(inf) similar to 1 Myr, for the ultra-compact, 1 : 5 3 Myr for the compact, and greater than similar to 6 Myr for the extended H II regions. These results suggest that the time needed to form a OB-star embryo and to start ionising the cloud, plus the quenching time due to the large gravitational potential amplified by further in-falling material, dominates the ionisation expansion time by a large factor. Accurate determination of the quenching time of H II regions would require additional small-scale observationnal constraints and numerical simulations including 3D geometry effects.