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 ) \propto r ^ { - q } with q \leqslant 1.5 .
As for their outer parts , the two compact H ii regions show a \rho ( r ) \propto r ^ { -2 } 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 ) \propto 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 _ { \text { exp } } \sim 0.1 Myr , for the dense UCH ii and compact H ii regions and \sim 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 _ { \text { inf } } \sim 1 Myr , for the ultra-compact , 1.5 - 3 Myr for the compact , and greater than \sim 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 .