Three-colour Herschel image of the Mon R2 molecular complex using 70 μ m (blue), 160 μ m (green) and 250 μ m (red) maps. The shortest wavelength (blue) reveals the hot dust associated with H ii regions and protostars. The longest wavelength (red) shows the cold, dense cloud structures, displaying to a filament network. The dashed rectangle locates the four H ii region area shown in Fig. 2 

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... has an age of ∼1 − 6 × 10 6 yr (Herbst & Racine 1976, see Plate V). This reflec- tion nebulae association corresponds to the Mon R2 spur seen in CO ( Wilson et al. 2005). An infrared cluster with a similar age (∼1 − 3 × 10 6 yr, Aspin & Walther 1990;Carpenter et al. 1997), covers the full molecular complex and its H ii region as- sociation area ( Fig. 1 in Gutermuth et al. 2011). The western part of the association hosts the most prominent object in most tracers. This UC H ii region ( Fuente et al. 2010) powered by a B0-type star ( Downes et al. 1975) is associated with the infrared source Mon R2 IRS1 ( Massi et al. 1985;Henning et al. 1992). The UCH ii region drives a large bipolar ...

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... molecular cloud is part of a CO shell with ∼26 pc size whose border encompasses the UCH ii region ( Wilson et al. 2005). The shell center is situated close to VdB72/NGC2182 (Xie & Goldsmith 1994;Wilson et al. 2005) at the border of the temperature and column density map area defined by the Herschel SPIRE and PACS common field of view (see e.g. Fig. 12). Loren (1977) also observed CO mo- tions he interpreted as tracing the global collapse of the molecu- lar cloud, with an infall speed of a few km s −1 . This typical line profile of infall has also been seen locally in CO and marginally in 13 CO near the central UCH ii region thanks to higher reso- lution observations ( Tang et al. ...

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... Herschel 3-colour image of the Mon R2 molecular com- plex shows that the central UCH ii region, seen as a white spot in Fig. 1, is dominating and irradiating its surroundings. Three other H ii regions exhibit similar but less pronounced irradiating effects (see the bluish spots in Fig. 1). These H ii regions develop Racine (1968) and Downes et al. ...

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... Herschel 3-colour image of the Mon R2 molecular com- plex shows that the central UCH ii region, seen as a white spot in Fig. 1, is dominating and irradiating its surroundings. Three other H ii regions exhibit similar but less pronounced irradiating effects (see the bluish spots in Fig. 1). These H ii regions develop Racine (1968) and Downes et al. ...

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... UCH ii re- gion since it is prominent and azimuthally averaged over 2 π ra- dians. The analysis is cruder for the three other H ii regions de- veloping between filaments (see Fig. 2b). For these H ii regions, we have selected inter-filament areas/quadrants best representing the H ii regions and avoiding the ambient filamentary structure (see Fig. 12). By doing so, we aimed to measure the contribu- tion of the H ii region envelope alone. We have checked, mainly in the case of the eastern region, that varying the azimuthal sec- tors selected between the major filaments does not change ei- ther the radii or the slope of the envelopes by more than 20%. However, contamination by other ...

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... first estimated the background column density aris- ing from the ambient cloud using both near-infrared extinc- tion ( Schneider et al. 2011) and the Herschel column density map (Fig.12). They consistently give background levels of A v ∼ 0.5 mag 7 at the edge of the Herschel map. ...

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... 7-8 display the calculated column density pro- files of each of the four aforementioned structural components and the resulting cumulative profile. Figure 12 also locates, with concentric circles, the different components used to constrain the structure of the central UCH ii region. We recall that the background is itself defined as a constant- density plateau: A V ∼ 0.5 mag for all H ii regions. ...

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... ultra-compact to com- pact H ii regions (here the central, eastern, and western regions). Indeed, the H ii bubble sizes and the amount of gas mass col- lected in the shell are so small that their contribution can be almost neglected and high resolution would be needed to ob- serve the narrow shoulder enhancement at the border of the shell (see Fig. D.1). These two components are however definitively needed to reproduce the central column density of the more ex- tended and diffuse, northern Extended H ii region. Figure 8 dis- plays an inner column density plateau and a tentative shoulder of the column density profile, just at the R H ii location. We have estimated an upper limit of ...

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... within decreasing density en- velopes. The results given in Col. 6 of Table 4 agree within 15% with analytical calculations given in Col. 5. The remaining dif- ferences arise from assumptions made in the analytical solutions, which neglect the inertia of the shell and strong external pres- sure. These expansions are illustrated by black lines in Fig. 10- ...

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... configuration im- plicitly assumes a mean envelope density at the initiation of the H ii region expansion which is lower than expected. Figure 10 shows four simulations for the central UC H ii re- gion. The expansion in a decreasing-density envelope with no gravity (black lines) is compared to two simulations including gravity and occuring in constant density envelopes. ...

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... the density gradient of the inner envelope from that presently observed (q in =0.85, con- tinuous black line) to that expected for free-falling gas (q in =1.5, dotted black line) increases the extrapolated density and thus the expansion time. Figure 11 itself gives the expansion behaviour of five sim- ulations for the northern H ii region. Like in Fig. 10 and with the same colours, three simulations describe expansion within a decreasing density envelope without gravity (black line), and expansion in constant high-and low-density envelopes without gravity (dashed red and continuous cyan curves, respectively). ...

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... density gradient of the inner envelope from that presently observed (q in =0.85, con- tinuous black line) to that expected for free-falling gas (q in =1.5, dotted black line) increases the extrapolated density and thus the expansion time. Figure 11 itself gives the expansion behaviour of five sim- ulations for the northern H ii region. Like in Fig. 10 and with the same colours, three simulations describe expansion within a decreasing density envelope without gravity (black line), and expansion in constant high-and low-density envelopes without gravity (dashed red and continuous cyan curves, respectively). Two additional simulations in a decreasing density envelope with Article ...

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... at three different times. The simu- lation includes the gravity of the central ionising object in a density decreasing envelope with a central core of 0.05 pc and a density of 110 cm −3 at 1 pc. This envelope has a mean den- sity in agreement with the observed characteristics (see Ta- ble 3). It corresponds to the blue continuous curve in Fig. 11. The gravity influence is only noticeable at small scales where gas velocity is negative corresponding to infall, proeminent mainly in the ionised bubble. The effect is less pronounced outside the shell and get weaker when the H ii region size in- creases. Fig. 9: Velocity field from numerical simulations for the North- ern H ii region ...

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... corresponding maximum values of the initial homogeneous constant density and expansion time are given in Cols. 7-8 of Table 4. Figure 10 shows, for the central UC H ii region, the effect of gravity on the expansion in a constant low-density envelope (cyan curve) compared to the expansion in a decreasing den- In black: without gravity and in an envelope of decreas- ing density, which is extrapolated from the observed one up to a constant density within r c = 0.005 pc. In dotted black: without gravity in an envelope of decreasing density with a gradient typ- ical of infall, ρ ∝ r −1.5 . ...

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... this large dis- tance re-collapse will not occur. More realistically, the northern H ii region should have expanded in an envelope with constant density of 300 cm −3 (cyan curve in Fig.11), equal to the initial average density deduced from the envelope presently observed. ...

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... equal to the initial average density deduced from the envelope presently observed. This gives an expansion time of ∼300×10 3 yr. As for the cen- tral UCH ii region the constant-density envelope case has a low density at the center which favors the expansion at the beginning (cyan curve). But at large scales the expansion times of all mod- Fig. 11: Numerical simulations for the northern H ii region. Sim- ulations with and without gravity are in colours and black, re- spectively. Continuous lines correspond to simulations with sim- ilar average initial density, ρ initial = 300 cm −3 . The envelope has a power law decreasing density with the characteristics of the observed one and ...

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... in the case of a constant-density envelope, the initial conditions and the central structure of the H ii region has less impact on the analysis of the old and more developed northern H ii region since the expansion has already taken place for a longer time. This explains why the expansion times are not very different with and without gravity (blue and black continuous lines in Fig.11). The highest central density allowing an H ii region expansion up to the observed size defines the maximum time of 370×10 3 yr (see Col. 9 of Table 4). ...

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... second option is to lower the density of the overall struc- ture, in the northern H ii region case a factor of two is necessary. The density thus decreased by 2, the expansion time is notice- ably reduced as shown by the blue-dashed line in Fig .11. From Eq. 9 (t exp ∝ R Str −3/4 ) and Eq. 6 (R Str ∝ ρ −2/3 ), the expansion time relates to density through its square root: t exp ∝ ρ 1/2 . ...

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... Eq. 9 (t exp ∝ R Str −3/4 ) and Eq. 6 (R Str ∝ ρ −2/3 ), the expansion time relates to density through its square root: t exp ∝ ρ 1/2 . This is in agreement with the time approximately divided by √ 2 be- tween the two cases, ρ 1 and ρ 1 /2 (blue and blue dashed lines in Fig .11). ...

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... large scales, in a decreasing- density envelope with a power law index q 1, once gravity has been overcome by turbulence and expansion occurs, the gravita- tional pressure decreases faster than the turbulent presure and its influence become negligible ( Tremblin et al. 2014a, section 5.1, Eq. 12). Accretion within a rotating envelope can create a lower density zone where infall is driven from the envelope onto a disk or torus, (see Tobin et al. 2008, Fig.10; Hosokawa et al. 2010, Fig.1; Ohashi et al. 2014, Fig.5). ...

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... the gravita- tional pressure decreases faster than the turbulent presure and its influence become negligible ( Tremblin et al. 2014a, section 5.1, Eq. 12). Accretion within a rotating envelope can create a lower density zone where infall is driven from the envelope onto a disk or torus, (see Tobin et al. 2008, Fig.10; Hosokawa et al. 2010, Fig.1; Ohashi et al. 2014, Fig.5). The decreased density near the ionising objet reduces the influence of gravity. It should result in a reduction of the expansion time and decrease of re-collapse probability. Outflow lobes also modify the density structure and the geometry of the envelope (outflow cavity) and thus influ- ence the expansion time. Infalling gas from ...