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The surroundings of HII 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. We aim to investigate the density structure of envelopes surrounding HII 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. Column density and temperature images derived from Herschel data were used together to model the structure of HII 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. The four hot bubbles associated with H II regions are surrounded by dense, cold, and neutral gas envelopes. The radial density profiles are reminiscent of those of low-mass protostellar envelopes. The inner parts of envelopes of all four HII regions could be free-falling because they display shallow density profiles. As for their outer parts, the two compact HII regions show a density profile, which is typical of the equilibrium structure of an isothermal sphere. In contrast, the central UCHii region shows a steeper outer profile, that could be interpreted as material being forced to collapse. 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, texp, 0.1Myr,for the dense UCHII and compact HII regions and 0.35 Myr for the extended HII region. The envelope transition radii between the shallow and steeper density profiles are used to estimate the time elapsed since the formation of the first proto stellar embryo, Tinf : 1Myr, for the ultra-compact, 1.5 / 3Myr for the compact, and greater than 6Myr for the extended HII regions.
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Astronomy &Astrophysics manuscript no. MonR2RegHII c
ESO 2015
July 3, 2015
From forced collapse to H ii region expansion in Mon R2:
Envelope density structure and age determination with Herschel?
P. Didelon1, F. Motte1, P. Tremblin1,2,3, T. Hill1, S. Hony1,4, M. Hennemann1, P. Hennebelle1, L. D. Anderson5,
F. Galliano1, N. Schneider1,6, T. Rayner7, K. Rygl8, F. Louvet1, A. Zavagno9, V. Könyves1, M. Sauvage1,, Ph. André1,
S. Bontemps6, N. Peretto1,7, M. Grin7,10, M. González1, V. Lebouteiller1, D. Arzoumanian1, J.-P. Bernard11,
M. Benedettini12, J. Di Francesco13,14 , A. Men’shchikov1, V . Minier1, Q. Nguy˜
ˆ
en Luong1, P. Palmeirim1,
S. Pezzuto12, A. Rivera-Ingraham15, D. Russeil9, D. Ward-Thompson7,16, and G. J. White17
(Aliations can be found after the references)
July 2015
ABSTRACT
Context. The surroundings of H ii regions can have a profound influence on their development, morphology and evolution. This paper
explores the eect of the environment on Hii 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 are used together to model the structure of H ii bubbles
and their surrounding envelopes. The resulting observational constraints are 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, partly embedded
into filaments. The envelope 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 as they display shallow density profiles : ρ(r)rqwith q61.5. As for
their outer parts, the two compact H ii regions show a ρ(r)r2profile, which is typical of the equilibrium structure of a Singular
Isothermal Sphere. In contrast, the central UCH ii region shows a steeper outer profile, ρ(r)r2.5, 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: texp 0.1 Myr for the dense UCH ii and compact H ii regions and 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 into account their surrounding neutral envelopes with slowly decreasing density profiles. 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: tinf 1 Myr for the ultra-compact, 1.53 Myr for the compact and greater than 6 Myr for the extended
Hii 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 eects.
Key words. ISM: individual objects (Mon R2) – Stars: protostars – ISM: filaments – ISM: structure ISM: dust, extinction, H ii Region
1. Introduction
Molecular cloud complexes forming high-mass stars are heated
and structured by newly born massive stars and nearby OB clus-
ters. This is especially noticeable in recent Herschel observa-
tions obtained as part of the HOBYS key programme, dedi-
cated to high-mass star formation (Motte et al. 2010, 2012,
see http://hobys-herschel.cea.fr). The high-resolution (from 600
to 3600), high-sensitivity observations obtained by Herschel pro-
vide, through spectral energy distribution (SED) fitting, access to
temperature and column density maps covering entire molecular
cloud complexes. It has allowed us to make, for the first time,
a detailed and quantitative link between the spatial and thermal
?Herschel is an ESA space observatory with science instruments pro-
vided by European-led Principal Investigator consortia and with impor-
tant participation from NASA
structure of molecular clouds. Heating eects of OB-type star
clusters are now clearly observed to develop over tens of parsecs
and up to the high, i.e. 105cm3, densities of starless cores
(Schneider et al. 2010b; Hill et al. 2012; Roccatagliata et al.
2013). Cloud compression and shaping, long known at low- to
intermediate-densities, was recently reported to lead to the cre-
ation of very high-density filaments hosting massive dense cores
(105106cm3, Minier et al. 2013; Tremblin et al. 2013). While
triggered star formation is obvious around isolated H ii regions
(Zavagno et al. 2010; Anderson et al. 2012; Deharveng et al.
2012), it is not yet unambiguously established to operate across
whole cloud complexes (see Schneider et al. 2010b; Hill et al.
2012).
The Mon R2 complex hosts a group of B-type stars, three of
them associated with a reflection nebula (van den Bergh 1966).
Located 830 pc from the Sun, it spreads over 2 deg (30 pc
Article number, page 1 of 25
A&A proofs: manuscript no. MonR2RegHII
at this distance) along an east-west axis and has an age of
16×106yr (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 (13×106yr, 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 outflow (Richardson
et al. 1988; Meyers-Rice & Lada 1991; Xie & Goldsmith 1994)
oriented NW-SE approximately aligned with the rotation axis of
the full cloud found by Loren (1977). The 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 s1. This typical line
profile of infall has also been seen locally in CO and marginally
in 13CO near the central UCH ii region thanks to higher reso-
lution observations (Tang et al. 2013). Younger objects such as
molecular clumps seen e.g. in CO, H2CO, HCN have been ob-
served in this molecular cloud (e.g. Giannakopoulou et al. 1997).
In this paper, we constrain the evolutionary stages of the
Mon R2 H ii regions through their impact on the temperature
and the evolution of the density structure of their surrounding
neutral gas envelopes. The evolution and growth of the H ii re-
gion as a function of age depends strongly on the density struc-
ture of the surrounding environment. If a simple expansion at
the thermal sound speed determines their sizes, the number of
UCH ii regions observed in the galaxy exceeds expectations.
This is the so-called lifetime problem (Wood & Churchwell
1989b; Churchwell 2002) partly arising from a mean density
and a mean ionising flux representative of a sample but per-
haps not adapted to individual object. In order to precisely as-
sess the UCH ii lifetime problem, we need an accurate measure
of the observed density profile of the neutral envelope outside of
the ionised gas A goal of this paper is to use the sensitive Her-
schel FIR (Far Infra Red) and submm photometry of the com-
pact H ii regions in MonR2 to constrain these profiles and subse-
quently estimate the H ii regions ages based on measured profiles
and the corresponding average density. Moreover, Herschel
measurements are sensitive enough so that we can even inves-
tigate significant changes in the density profile with radial dis-
tance. Such changes may be signposts of dynamical processes,
such as infall or external compression.
The paper is organised as follows. Herschel data, associated
column density and dust temperature images, and additional data
are presented in Sec. 2. Section 3 gives the basic properties of
Hii regions and the density structure of their surrounding en-
velopes. These constraints are used to estimate H ii region expan-
sion in Sec. 4 and the age of the protostellar accretion in Sec. 5,
to finally get a complete view of the formation history of these
B-type stars.
Fig. 1: Three-colour Herschel image of the Mon R2 molecular
complex using 70 µm (blue), 160 µm (green) and 250 µm (red)
maps. The shortest wavelength (blue) reveals the hot dust asso-
ciated with H ii regions and protostars. The longest wavelength
(red) shows the cold, dense cloud structures, displaying to a fila-
ment network. The dashed rectangle locates the four H ii region
area shown in Fig. 2
2. Data
2.1. Observations and data reduction
Mon R2 was observed by Herschel (Pilbratt et al. 2010) on
September 4, 2010 (OBSIDs: 1342204052/3), as part of the
HOBYS key programme (Motte et al. 2010). The parallel-
scan mode was used with the slow scan-speed (2000/s), allow-
ing simultaneous observations with the PACS (70 and 160µm;
Poglitsch et al. 2010) and SPIRE (250, 350, 500 µm; Grin et al.
2010) instruments at five bands. To diminish scanning artefacts,
two nearly perpendicular coverages of 1.1×1.1were obtained.
The data were reduced with version 8.0.2280 of HIPE1Stan-
dard steps of the default pipeline up to level-1, including calibra-
tion and deglitching, were applied to all data. The pipeline was
further applied (level-2), including destriping and map making,
for SPIRE data. To produce level-2 PACS images, we used the
Scanamorphos software package2v13 which performs baseline
and drift removal before regriding (Roussel 2012). The resulting
maps are shown in Rayner et al. (in prep.). The map angular res-
olutions are 600 3600, which correspond to 0.025 0.15 pc at the
distance of Mon R2.
The 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
eects (see the bluish spots in Fig. 1). These H ii regions develop
1HIPE is a joint development software by the Herschel Science
Ground Segment Consortium, consisting of ESA, the NASA Herschel
Science Center, and the HIFI, PACS, and SPIRE consortia.
2http://www2.iap.fr/users/roussel/herschel/index.html
Article number, page 2 of 25
P. Didelon et al.: Mon R2 H ii regions structure and age from Herschel
Fig. 2: Dust Temperature (colours in aand contours in b) and column density (colours in band contours in a) maps of the central
part of the Mon R2 molecular cloud complex, covering the center, western, eastern and northern H ii regions with 3600 resolution.
The heating sources of H ii regions are indicated by a cross and with their name taken from Racine (1968) and Downes et al. (1975).
Smoothed temperature and column density contours are 17.5, 18.5, and 21.5 K and 7 ×1021, 1.5×1022 , 5 ×1022 and 1.8×1023 cm2.
into a clearly structured environment characterised by cloud fil-
aments.
2.2. Column density & dust temperature maps
The columm density and dust temperature maps of Mon R2 were
drawn using pixel-by-pixel SED fitting to a modified blackbody
function with a single dust temperature (Hill et al. 2009). We use
a dust opacity law similar to that of Hildebrand (1983), assuming
a dust spectral index of β=2 and a gas-to-dust ratio of 100, so
that dust opacity per unit mass column density is given by κν=
0.1 (ν/1000 GHz)βcm2g1, as already used in most HOBYS
studies (e.g. Motte et al. 2010; Nguyen-Lu’o’ng et al. 2013). The
70 µm emission is likely tracing small grains in hot PDRs and so
excluded from the fits as it does not trace the cold dust used to
measure the gas column density (Hill et al. 2012).
We constructed both the four band (T4B) and three band (T3B )
temperature images and associated column density maps by ei-
ther using the four reddest bands (160 to 500µm) or only the
160, 250, and 350 µm bands of Herschel (cf. Hill et al. 2011,
2012). Prior to fitting, the data were convolved to the 3600 or 2500
resolution of the 500 µm (resp. 350 µm) band and the zero o-
sets, obtained from comparison with Planck and IRAS (Bernard
et al. 2010), were applied to the individual bands. The quality of
a SED fit was assessed using χ2minimisation. Given the high-
quality of the Herschel data, a reliable fit can be done even when
dropping the 500 µm data point. For most of the mapped points,
which have medium column density and average dust temper-
ature values, NH2 and Tdust values are only decreased by 10%
and increased 5% respectively between T4B and T3B. In the fol-
lowing, we used the column density or temperature maps built
from the four longest Herschel wavelengths, except when ex-
plicitly stated. The high-resolution T3B,I70µm, and I160µmmaps
have only been used for size measurements, not for profiles slope
determinations.
The resulting column density map shows that the central
UCH ii region has a structure that dominates the whole cloud,
with column densities up to NH2 2×1023 cm2(see Figs. 2b
and 12). In its immediate surroundings, i.e. 1 pc east and west
as well as 2.5 pc north, the temperature map of Fig. 2a shows
two less dense H ii regions and one extended H ii region, respec-
tively. The name and the spectral type of the stars which are cre-
ating these four H ii regions are taken from Racine (1968) and
Downes et al. (1975). They are associated with reflection neb-
ulae and are called IRS1, BD-06 1418 (vdB69), BD-06 1415
(vdB67), and HD 42004 (vdB68) (see Figs. 2a-b and Table 1).
The central UCH ii region is located at the junction of three main
filaments and a few fainter ones, giving the overall impression of
a ‘connecting hub’ (Fig. 2b). The three other H ii regions are de-
Article number, page 3 of 25
A&A proofs: manuscript no. MonR2RegHII
veloping within this filament web and within the UCH ii cloud
envelope, which complicates the study of their density structure.
The dust temperature image of Figs. 2a and 13 shows that
the mean temperature of the cloud is about 13.5 K and that
it increases up to 27 K within the three compact and ultra-
compact H ii regions. Dust temperature maps are only tracing
the colder, very large grains, and are not sensitive to hotter
dust present within H ii regions (see Anderson et al. 2012,
Fig. 7). The temperature obtained from FIR Herschel SED
corresponds to dust heated in the shell/PDR and thus directly
relates to the size of the ionised bubble.
2.3. Radio fluxes and spectral type of exciting stars
We first estimate the spectral type of exciting stars from their ra-
dio fluxes. To do so, we looked for 21cm radio continuum flux
in the NVSS images (Condon et al. 1998) as well as the corre-
sponding catalogue.3The three compact H ii regions delineated
by colours and the temperature contours of Fig. 2 all harbour one
single compact 21 cm source (see Table 1). The more developed
northern H ii region contains several 21 cm sources, whose cu-
mulated flux can account for the total integrated emission of the
region. We calculated the associated Lyman continuum photon
emission, using the NVSS 21 cm flux listed in Table 1 and the
formulae below, taken from e.g. Martín-Hernández et al. (2005):
NLyc =7.6×1046 s1× Sν
Jy !Te
104K1
3 d
kpc !2
×b(ν, Te)1,(1)
where Sνis the integrated flux density at the radio frequency ν,
Teis the electron temperature, dis the distance to the source, and
the function b(ν, Te) is defined by
b(ν, Te)=1+0.3195 log Te
104K0.213 log ν
GHz .(2)
Quireza et al. (2006) determined, from radio recombina-
tion lines, an electron temperature of 8600 K for the central
UCH ii region. We adopt the same temperature for the other
Hii regions since this Tevalue is close to the mean value found
for H ii regions (see e.g. Quireza et al. 2006, Table 1). Using the
NLyc estimates of Table 1 and the calibration proposed by Pana-
gia (1973), we assumed that a single source excites the H ii re-
gions of Mon R2 and estimated their spectral type (see Table 1).
These radio spectral types, from B2.5 to B1, perfectly agree with
those deduced from the visual spectra of Racine (1968) 4(see Ta-
ble 1). We calculated NLyc for the Mon R2 UCH ii region using
six other radio fluxes with wavelengths from 1 to 75 cm available
in Vizier. They all have radio spectral types ranging from O9.5 to
B0, also in agreement with previous estimates (Massi et al. 1985;
Downes et al. 1975). The concordance of spectral types derived
from flux at dierent radio wavelengths including the shortest
ones, confirm the free-free origin of the centimer fluxes with a
limited synchrotron contamination.
2.4. Hii region type classification
Wood & Churchwell (1989b, end of Sect. 4.a and Sect. 4.c.xi)
have previously classified Mon R2 as an UCHii region. Consid-
ering the sizes and densities determined in Sect. 3.2, we define
3NVSS : NRAO VLA Sky Survey, http://www.cv.nrao.edu/nvss/
4The spectral types from Herbst & Racine (1976) were not used be-
cause they misidentified vdB 68 and vdB 69 (see Loren 1977, note.1)
and because Racine (1968) used better spectral resolution
the morphological type of the four H ii regions. The values from
the central H ii region (ρe=3.2×103cm3,RHii =0.09 pc)
are compatible with the range of oberved values for UCH ii re-
gions (e.g. Hindson et al. 2012), ρe=0.34 1.03 ×104cm3
and RHii =0.04 0.11 pc. It agrees with the classification ob-
tained from IRAS fluxes5. The western and eastern H ii regions
have similar small sizes (around 0.1 pc) but lower densities (<
1000 cm3) which we assume to be more characteristic of Com-
pact H ii regions. The northern H ii region is larger (close to 1
pc) and has a very low density (<100 cm3) typical of Extended
Hii regions.
3. Modelling of the H ii regions environment
The initial dense cloud structures inside which the high-mass
protostars have been formed and the H ii regions that have de-
veloped could have been considerably modified by both the pro-
tostellar collapse and the H ii region ionisation. The bubble and
shell created by the expansion of H ii region retains information
about its age, and the mean density of the inner protostellar en-
velope whose gas has been ionised or collected. We hereafter
investigate all of the components necessary to describe the en-
vironment of H ii regions. The density model is presented in
Sect. 3.1. We first focus on the inner components that are di-
rectly associated with H ii regions, and which are generally stud-
ied at cm-wave radio, optical, or near-infrared wavelengths (see
Sect. 3.2 and 3.3). We then characterise in detail the component
best studied by our Herschel data, namely the surrounding cold
neutral envelope (Sect. 3.4). We finally jointly use all available
pieces of information to perform a complete density modelling
in Sect. 3.5.
Fig. 3: A H ii region and its surroundings four components spher-
ical model and radial profile of density(right). The ionised bub-
ble is first surrounded by the shell containing all of the swept-up
material. The neutral envelope is made of two parts with dier-
ent density gradient finally merging into the background. The
short dashed line represents the extrapolation of the inner enve-
lope before the ionisation expansion and collect processing.
5The MonR2 IRAS fluxes donwloaded from Simbad (F12 =470 Jy,
F25 =4100 Jy, F60 =13070 Jy and F100 =20200 Jy) fulfill the Wood
& Churchwell (1989a) and Kurtz et al. (1994) criteria : log(F25/F12 )=
0.94 >0.57, log(F60/F12 )=1.44 >1.3 and F100 >1000. Jy.
Article number, page 4 of 25
P. Didelon et al.: Mon R2 H ii regions structure and age from Herschel
Table 1: Properties of the four H ii region bubbles of Mon R2
Region name Type Exciting star from visual spectra Ionisation from 21 cm free-free RHii ρe
Ident. Sp.T. AV[mag] S21cm [mJy] NLyc [s1] Sp.T. [pc] [cm3]
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
central UC IRS1 - - 4114. 2.4×1047 B0 0.09 ±0.01 3200
western (vdB67) Compact BD-06 1415 B1 2.7 27.4 1.6×1045 B1 0.11 ±0.01 200
eastern (vdB69) Compact BD-06 1418 B2.5 1.7 2.2 1.3×1044 B2.5 0.08 ±0.01 100
northern (vdB68) Extended HD 42004 B1.5 1.6 38. 2.2×1045 B1 0.8±0.05 10
Notes: The Mon R2 UCH ii region is also called G213.71-12.6 or IRAS 06052-0622. Spectral types in Cols. 4 and 8 are given by
Racine (1968) from visual spectra and from NLyc estimates derived from NVSS 21 cm data and Eq. 1 (see Cols. 6-7). Extinction
given in Col. 5 are estimated from E(B-V) given by Herbst & Racine (1976). The radii and electron density of the H ii region
bubbles (Cols. 9-10) are estimated from the Herschel dust temperature and column density images (see Sects. 3.2-3.5).
3.1. Model of Hii regions and their surroundings
Modelling of the observed column density and temperature
structure of H ii regions and their surroundings (Fig. 2) requires
four density components (see Fig. 3) : a central ionised bub-
ble, a shell concentrating almost all of the collected molecular
gas, a protostellar envelope decreasing in density and a back-
ground. The background corresponds to the molecular cloud in-
side which the H ii region is embedded. The three other compo-
nents are proper characteristics of the H ii region and its enve-
lope. The envelopes of the three Compact and UC Hii regions
are not correctly described by a single power law, but require
two broken power laws similar to that of the inside-out collapse
protostellar model (Shu 1977; Dalba & Stahler 2012; Gong &
Ostriker 2013).
3.2. Hii regions extent
Hii region sizes are important to measure because they constrain
the age and evolution of the regions. Sizes are generally com-
puted from Hαor radio continuum observations that directly
trace the ionised gas. Such data are not always available poten-
tially Hαcould be attenuated for the youngest HII regions, and
radio continuum survey are frequently of relatively low resolu-
tion. We can instead use Herschel temperature maps as well as
70 µm and 160 µm images to estimate the size of the H ii regions.
The extent of all four H ii regions can clearly be seen on the
dust temperature map shown in Fig. 2a. This is an indirect mea-
sure since the Herschel map is traces the temperature of big dust
grains dominant in dense gas, and which reprocess the heating of
photo-dissociation regions (PDRs) associated with H ii regions.
Note also that such a dust temperature map provides the temper-
ature averaged over the hot bubbles in the H ii region and colder
material seen along the same line of sight. This is particularly
clear when inspecting the western H ii region, powered by BD-
06 1415, since its temperature structure is diluted and distorted
by the filament crossing its southern part. We used both the T4B
and T3B temperature images with 3600 and 2500 resolutions. For
the large northern Extended H ii region, the T4B map alone would
be sucient since the angular resolution is not an issue. For the
three other H ii regions, we need to use the T3B map as well as
70 µm and 160 µm maps where intensities are used as tempera-
ture proxies (see discussion by Compiègne et al. 2011; Galliano
et al. 2011). The 70 µm emission traces the hot dust and small
grains in hot PDRs, which mark the borders of H ii regions and
thus define their spatial extent.
Despite the inhomogeneous and filamentary cloud environ-
ment of the Mon R2 H ii regions, the heated bubbles have a
relatively circular morphology (see Fig. 2a). This is probably
Fig. 4: Dust temperature radial profiles of the central UCH ii re-
gion showing a steep outer part and a flatter inner region. Note
the agreement of the measurements done on the 3-band tempera-
ture map, T3B (red and magenta lines and points), and the 4-band
temperature map, T4B (yellow and pink lines and points).
due to the ionisation expansion which easily blows away fila-
ments and dense structures (e.g. Minier et al. 2013). In order
to more precisely define the H ii region sizes, we computed tem-
perature radial profiles, azimuthally averaged around the heating
and ionising stars, which are shown in Figs. 2a-b. The result-
ing temperature profiles of the four H ii regions share the same
general shape: a slowly-decreasing central part surrounded by an
envelope where the temperature follows a more steeply decreas-
ing power law (see e.g. Fig. 4). We used the intersection of these
two temperature structures to measure the radius of the flat in-
ner part, which we use as an estimator of the H ii region radius,
RHii (see Table 1). At the junction between the two temperature
components, data scattering and deviation from a flat inner part
leads to uncertainties of about 15%. The higher-resolution T3B,
70 µm, and 160 µm maps confirm the derived RHii values and
reach a confidence level of 10% uncertainty.
For the (small) central UCH ii region, the radial profiles of
the T3B and T4B temperatures are shown in Fig. 4. The flux pro-
files obtained from the 70 µm and 160 µm images with 600 and
1200 resolutions are shown in Fig. 5. These four dierent esti-
mators display similar radial shapes for the H ii region and give
consistent size values: RHii '0.09, 0.08, 0.09, and 0.09 pc for
70 µm, 160 µm, T3B, and T4B respectively. Similarly concordant
measurements are found for the fully-resolved northern H ii re-
gion in the T4B and T3B maps: RHii '(0.85 ±0.05) pc. Inter-
Article number, page 5 of 25
A&A proofs: manuscript no. MonR2RegHII
Fig. 5: Radial intensity profiles of the central UCH ii region
showing the measurements done at 70 µm (blue points) and
160 µm (green points) taking advantage of the PACS highest res-
olution, compared with the 3-band temperature (T3B) and the
4-band temperature (T4B) data given by the black arrow. The
160 µm profile decreases less in the inner part of the envelope
(pink line) than in its outer part (yellow line). Since 160 µm
emission is sensitive to dust temperature and density, this be-
haviour is probably related to the two dierent slopes found for
the density profile of the envelope characterised in Sect. 3.4.1.
The slope change indeed occurs at similar RInfall radius.
estingly, for the central UCHii region, the derived RHii value of
0.09 pc is in excellent agreement with the one deduced from
H42αRRL measurements (0.08 pc, see Pilleri et al. 2012),
showing that hot dust and ionised gas are spatially related. Ra-
dio continuum data and infrared [Ne II] line also give similar
sizes and shapes (Massi et al. 1985; Jae et al. 2003).
Using Lyman flux (Table 1 Column 7) and H ii region size
(Table 1 Column 9) we compute with Eq. 5 the corresponding
electron density ρe, given in column 10.
3.3. Hii region shells and their contribution to column density
Dense shells have been observed around evolved H ii regions
within simple and low-column density background environ-
ments (e.g. Deharveng et al. 2005; Churchwell et al. 2007; An-
derson et al. 2012). The ‘collect-and-collapse’ scenario proposes
that the material ionised by UV flux of OB-type stars is in-
deed eciently sweeping up some neutral gas originally located
within the present H ii region extent and developing a shell at the
periphery of H ii bubbles (Elmegreen & Lada 1977).
In Appendices D and E we investigate the contribution of this
very narrow component to the column density measured with
Herschel. Appendix D shows the beam dilution of the column
density expected from the shell shoulder. Appendix E explores
the density attenuation due to bubble and shell expansion in dif-
ferent types of envelope density profile. These two eects com-
bined reduce the importance of the shell and predicts a decreas-
ing of the observed column density of H ii regions with expan-
sion at least in decreasing-density envelopes. The shell of the
central UCH ii region characterized by Pilleri et al. (2014, 2013)
has an unnoticeable contribution to the high column density of
the envelope. Even in the northern region, which is the most ex-
tended and best favourable to the detection of a shell, the shell
characteristics are uncertain due to the filamentary environment
inside which the H ii region developed (see Fig. 8). It shows that
the shell is not a dominant component of the column density
structure of the H ii regions studied here but it cannot a priori be
neglected from modelling.
3.4. The envelope surrounding Hii regions
Among the crucial parameters influencing the expansion of an
Hii region and, the size of the heated/ionised regions, we need
to characterise the density profiles of their neutral envelopes.
We therefore constructed radial column density profiles, by plot-
ting the NH2map around each of the ionising sources shown in
Fig. 2b. Figures 6 shows the column density profiles of the cen-
tral UCH ii and eastern H ii regions, respectively. The colours
used for the dierent radial parts of the profiles are similar to
those used for the temperature profiles of Fig. 4.
Radial column density profiles exhibit relatively flat inner
parts that provide a reliable measurement of the column density
maximum value, NMax
H2 , of the envelope surrounding each of the
four H ii regions (see Table 3, Col.7).
The sizes of these envelopes, given by the radius at half max-
imum, RHM, were measured on the column density profile and
range from 0.35 pc to 1.5 pc (see Table 3, Col.8).
Assuming a spherical geometry, in agreement with the shape
of H ii regions studied here, for which RHM can be used as a size
estimator we can roughly estimate the observed mean density,
hρobsi, from the maximum of the surface density NMax
H2 , using the
equation:
hρobsi=n
V=π×R2
HM NMax
H2
4
3π×R3
HM
=3
4×NMax
H2
RHM
.(3)
This mean density corresponds to the presently observed state
of the envelope (see Table 3, Col.9). To estimate the initial
mean density of the envelope, ρinitial, before the ionisation starts,
Sect. 3.5 suggests an other way of determination through its ac-
tual maximum density and density profile slope.
Comparison of the central UCH ii region characteristics de-
duced here with the parameters of the model used by Pilleri
et al. (2012) shows good agreement. The model has an enve-
lope size of 0.34 pc, inner radius of 0.08 pc, and a mean density
0.8×105cm3comparable with our estimates : RHii 0.09 pc
RHM 0.35 pc, hρobsi=1.4×105cm3.
3.4.1. Column density profiles
With the model of Fig. 3 in mind, we characterise in detail the
four main components associated with H ii regions and their sur-
roundings. The H ii region bubble, fitted by a yellow line, corre-
sponds to a temperature plateau and has an almost constant col-
umn density in Fig. 6. Surrounding the H ii region, one can find
the cloud envelope, which has a constantly decreasing tempera-
ture profile and splits here into slowly- and sharply-decreasing
NH2parts, fitted by pink and blue lines. As for the eastern H ii re-
gion, the column density is lower and the inner envelope extent
is larger, allowing a better distinction between the dierent en-
velope parts than in the central UCH ii region. In this context,
we define the inner envelope as the part where the column den-
sity slowly decreases and the external envelope as the one with
a steeper decrease (see the pink and blue lines in Fig. 6). The
crossing point between these two envelope components defines
Article number, page 6 of 25
P. Didelon et al.: Mon R2 H ii regions structure and age from Herschel
(a) column density radial profile of the central UCH ii region (b) column density radial profile of the eastern CH ii region
Fig. 6: The H ii region bubble (yellow line and points) is surrounded by a neutral gas envelope which splits into slowly- and sharply-
decreasing NH2parts (pink and blue lines and points). Background is defined by the lower limit of the clouds of grey points. The
resolution corresponding to the Herschel beam at 500µm is illustrated by the black curve in a)
the outer radius of the inner envelope, called RInfall for reason
explained in Sect. 5.2 and whose values are given in Table 3.
The profile analysis is trustworthy for the central UCH ii re-
gion since it is prominent and azimuthally averaged over 2πra-
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 overlying cloud structures can-
not be completely ruled out and some studies of other isolated
prominent H ii regions are necessary to confirm the results pre-
sented in here.
The column density slopes of both the internal and the ex-
ternal envelopes can be well represented by power laws such as
N(θ)θp(see Fig. 6). As the column density is the integration
of the density on the line of sight, we can logically retrieve their
density profiles through the measurement of the column density
profiles. For an single power law density ρ(r)rq, an asymp-
totic approximation leads to a very simple relation between the
qindex and the power law index of the column density profile
described as N(θ)θp:q'p1. This assumption holds
for piecewise power laws matching a large portion of the ob-
served envelopes. It is the case of external envelopes as will be
confirmed in Sect. 3.5. However, for small pieces like the in-
ner envelopes, the conversion from column density to density
power law indices is more complex, (see Yun & Clemens 1991;
Bacmann et al. 2000; Nielbock et al. 2012).
Towards the centre, at impacts parameter6smaller than the
Hii region outer radius, all four density components contribute
to the observed column density. Then a gradual increase of
the impact parameter progressively reduces the number of the
contributing density components. The four structural compo-
6Impact parameter : radial distance from the line of sight to the center.
nents of Fig. 3 were constrained, step by step, from the out-
side/background to the inside/HII region bubble.
We 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 Av
0.5 mag7at the edge of the Herschel map. To minimise the sys-
tematic errors in determining the slope of the outer envelope,
a 0.5 mag background was subtracted from the column density
profiles. For the northern H ii region, although the background
contribution to the observed column density profile is the most
important, the power law slope measured for the envelope re-
mains well-define with p possibly ranging from -0.4 to -0.5.
We simultaneously estimated the power law coecients of
the two parts of the envelope, from the slopes (p) measured on
‘background corrected’ column density profiles. We used the re-
lation q'p1 to measure the density profile slopes (q) of the
outer envelope and obtain a first guess for the inner envelope. Ta-
bles 3 and 2 list some of the parameters derived from our column
density structural analysis.
The outer envelope of the two compact eastern and western
Hii regions displays a column density index of pout ' −1 with
an uncertainty of 0.2 (3σ), which corresponds to a ρ(r)r2
density law. The central UCH ii region itself exhibits a steeper
density gradient in its outer envelope, with qout ' −2.5. In prac-
tice, the uncertainties are such that the slopes are well defined
within an uncertaintiy of about 10% or 0.2, clearly allowing the
distinction between ρ(r)r2and ρ(r)r1.5or ρ(r)r2.5
power laws. This is a clear improvement from the studies made
before Herschel from single band sub-millimeter observations
(e.g. Motte & André 2001; Beuther et al. 2002; Mueller et al.
2002).
The northern H ii region, whose envelope does not split into
an inner and outer parts, has a decreasing density profile up to
0.8 pc with a power law coecient of q' −1.5.
The internal envelopes of the central, eastern, and western
Hii regions have a column density profile with power law coe-
cients pin ' −0.35±0.2, but the conversion is not straigthforward
7We used the relation by Bohlin et al. (1978) to transform Herschel
NH2measurements into AVvalues in mag unities, Av'1021 cm2×NH2.
Article number, page 7 of 25
A&A proofs: manuscript no. MonR2RegHII
Table 2: Comparison of the properties of the neutral envelopes surrounding the four H ii regions of Mon R2
Direct fits on observed NH2 profiles Calculated Fits of reconstructed NH2 profiles
Region name NH2(1pc) qout qin RInfall ρ1pc ρ1pc qout qin RInfall
[cm2] [pc] [cm3] [cm3] [pc]
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
central 1.5×1022 2.71.3 0.25 ±.05 2000.±200.1900 ±250 2.75 0.85 ±.35 0.3±.1
western 3.5×1021 1.81.55 0.5±.1 300.±50.370 ±50 1.91.45 ±(.1) 0.5±.1
eastern 4.×1021 2.21.3 0.8±.2 470.±50.430 ±50 2.45 .4±0.2 1.±.2
northern 2.×1021 1.5 - 125.±25.105 ±30 1.45 ±.15 -
Notes: Cols. 2-5 are directly fitted from the observed column density profiles while Cols. 7-10 are adjusted from modelled
column density profiles reconstructed from fixed density profiles. Density profile indices and infall radius Cols.3-5 and Cols.8-
10 are defined in Sect. 3.4.1-3.5 and Fig. 3. The envelope density at 1 pc of Col. 6 is calculated with Eqs.B.3 and B.4 from
Cols.2-5 data while the value given in Col. 7 is taken from the density model.
and the density modelling made in Sect. 3.5 is needed to derived
correct values.
3.5. Density modelling
We here perform a complete modelling of the observed column
density profiles to adjust and evaluate the relative strength and
the characteristics of the components used to describe H ii re-
gions and their surroundings. We modelled four dierent com-
ponents along the line of sight to reconstruct the observed col-
umn density profile. We used the size and density profiles de-
rived in previous sections and listed in Table 3 to numerically
integrate between proper limits, along dierent lines of sight,
the radial density profiles of the background, envelope (external
then internal), H ii region shell, and bubble. For a direct com-
parison with observed profiles, we convolved the modeled col-
umn density profiles with the 3600 resolution of the Herschel NH2
maps. Figures 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 dierent 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: AV0.5 mag for all H ii regions. The back-
ground, even if faint, has an important relative contribution to-
wards the outer part of the H ii region structure, where the enve-
lope reaches low values. For the northern Hii region, the back-
ground contribution to the observed column density profile is
almost equal to that of the envelope, as it can be seen on the
reconstructed profile of Fig. 8.
Our goal is to estimate for each of the four H ii regions in
Mon R2, the absolute densities of the envelope, shell, and H ii re-
gion bubble (see Tables 1-3).
We adjusted our model to the complete column density pro-
file, progressively adding the necessary components : outer en-
velope, inner envelope, shell and bubble, the latter first assumed
to be empty. In Table 2 we compare the results directly obtained
from observationnal data and from data modelling.
We first modeled the density profile observed at radii greater
than 1 pc, dominated by the outer envelope density. We jointly
adjusted the density at 1 pc, ρ1and the density power law slope,
qout. The qout values derived from the q=p1 relation are in
excellent agreement with the fitted ones. The ρ1values obtained
are very similar to those calculated with Eqs.B.3 and B.4 from
the column density values at 1 pc and the appropriate qout val-
ues. Our results prove that the asymptotic assumption is correct
for the outer envelope component. The characteristics of the in-
Fig. 7: Column density profile of the central UCH ii region (cyan
diamonds with σerrors bars) compared to models with all com-
ponents illustrated in Fig. 3. The neutral envelope with two den-
sity gradients or with a single one are shown by a black line and
a dotted black line respectively An envelope model with a sin-
gle density gradient cannot match the observed data. Individual
components after convolution by the beam are shown by ma-
genta, red, green, and blue dashed lines, for the bubble, shell,
envelope and background.. The continuous red line shows the
unconvolved shell profile at an infinite resolution.
Fig. 8: Column density profile for northern H ii region and its
four components coded with the same colours as in Fig. 7. The
dotted green line corresponding to the sum of the envelope and
background contributions matches well with observed data.
Article number, page 8 of 25
P. Didelon et al.: Mon R2 H ii regions structure and age from Herschel
Table 3: Properties of the neutral envelopes surrounding the four H ii regions of Mon R2
Region name RInfall Rout ρ(r)rqInfall NMax
H2 RHM hρobsiρenv(1pc) ρenv (RHii)
[pc] [pc] qin qout age [Myr] [cm2] [pc] [cm3] [cm3] [cm3]
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)
central .3±.1 2.5±.5.85 ±.35 2.7.51.5 2.×1023 0.35 1.4×1052000 ±300 1.5×105
western .5±.1 3.±1.1.5±.15 1.8.82.5 16.×1021 0.4 9.×103350 ±50 12000
eastern .9±.2 2.5±1..4±.22.3 1.44.4 7.×1021 0.9 1.6.×103450 ±50 1200
northern >2 2.5±.51.45 ±.15 - >3.10.3.×1021 1.5 300.115 ±30 150
Notes: Cols. 2-5 describe the density profile of the neutral envelopes surrounding Hii regions by listing the radius separating
the inner and outer envelope components, the outer radius and the density power law slopes of the two envelope components.
Uncertainties (3σ) on qout are estimated to be 0.2. Col. 6 gives the time elapsed since the beginning of infall and protostellar
collapse. It is calculated from RInfall (Col. 2) and Eq. 11 with a velocity range from one to three times the sound speed (see
Sect. 5.2) and it has a statistical error of 20%. Cols. 10-11 give the absolute values of the density measured at r=1 pc and at the
RHii radius, from the complete modelling of column density profiles (see Sect. 3.5). Col. 11 is used to estimate, through Eq. 4,
the mean initial neutral gas density before the ignition of an H ii region.
ner envelope, mixed on the line of sight with those of the outer
envelope, is only reachable through modelling.
Figures 7-8 show that once the envelope density structure is
fixed, the modeled column density profile nicely fits the observed
one for radii larger than RHii.
As for the shell and the bubble, they are expected to have
a small influence on the profiles of the 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 diuse, 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 RHii location. We have
estimated an upper limit of the mean density, column density,
and mass for the northern H ii region swept-up shell, assuming a
0.01 pc thickness with a density varying from 50 to 1000 cm3:
Nshell
H2 1.6×1019 cm2, and 3 M. This putative shell is how-
ever dicult to disentangle from the envelope border and the
complex cloud structure in this area.
According to Hosokawa & Inutsuka (2005), the central bub-
ble should be devoid of cold dust in the earliest phase of
Hii region development, roughly corresponding to the Compact
Hii phase. In the case of the central UCH ii region we used the
electron density of 1.6×103cm3(Quireza et al. 2006) as an up-
per limit for the H ii bubble density of neutral gas. Even this rel-
atively high density value results in a negligible contribution to
the modeled column density profile (see Fig. 7). For the northern
Hii region, a low-density (50 cm3) central component needs
to be introduced in the bubble to reconcile the modeled profile
and the observational data. Without it, we would observe a rel-
ative hole/depletion in the center of the column density profile
(see red and green lines in Fig. 8 compared to cyan or black
ones). The uncertainties are such that the exact value of the in-
ner density component of the northern H ii region is not known
better than to a factor of ten. Therefore, our modelling can only
give upper limits densities for the bubble gas content and Hii re-
gion shell.
Table 3 lists the adopted values of the envelopes density char-
acteristics. The envelope density at 1 pc radius, i.e. ρenv(r=1 pc),
which was used to scale the parametrised density profile, de-
fines the absolute level of density in the envelope. It also gives
the density observed at the inner border of the envelope, i.e.
ρenv(r=RHii), corresponding to the maximum value measured
now in the envelope. The central density of the eastern Compact
Hii region is a bit weak and atypical. For the northern H ii re-
gion, the inner border of the envelope is at RHii 0.8 pc, and
we can extrapolate the ρ(r)r1.5density profile to a distance
of 0.1 pc: ρestimated(r=0.1 pc) 6.6×103cm3. We also consid-
ered the density at much smaller radii, which would correspond
to the inner radius of the extrapolated protostellar envelope and
the central core density : ρenv(r=0.005 pc /1000 AU), Col. 4 in
Table 4.
All inner envelopes have power law slope smaller or equal to
the expected infall value of 1.5. The values lower than 1.5 could
be due to subfragmentation in the inner envelope. Some indica-
tions of inhomogeneous clumpy structures are indeed revealed
by high-resolution maps (Rayner et al, in prep.). All outer en-
velopes have power law slope greater or equal to the expected
SIS value of 2, corresponding to hydrodynamical equilibrium.
The high value observed for the central H ii region could be due
to additional compresion (Sect. 5.1, App. C). All these density
determination will be used below to estimate the mean initial
neutral gas density before the ignition of an H ii region.
4. Ionisation expansion time
The physical characteristics presented in the previous sections
are used here to constrain the expansion time of the ionisa-
tion bubble in its neutral envelope. In Sect. 4.1, analytical cal-
culations without gravity show that the average initial density,
hρinitiali, is the main parameter dictating the expansion behaviour.
In Sect. 4.2, simulations are compared to analytical results of
Sect. 4.1 to determine the impact of gravity on expansion. In con-
stant high-density envelopes, gravity prevents expansion through
quenching or re-collapse, but in decreasing-density envelope
once the expansion has started the impact of gravity becomes
negligible. We thus conclude in Sect. 4.3 that analytical calcula-
tions without gravity can be used to derive valid ionisation ex-
pansion times.
4.1. Strömgren sphere expansion analytical calculations
Dierences in size between the northern and the western H ii re-
gions, which harbour an exciting star of the same spectral type,
tend to suggest that the northern H ii region is more evolved than
the western one (see Fig. 2a and Table 1). The larger number of
striations observed in the visible image of the northern reflection
Article number, page 9 of 25
A&A proofs: manuscript no. MonR2RegHII
nebula also indicate an older stage of evolution (Thronson et al.
1980; Loren 1977).
To confirm these qualitative statements, we here determine
time dierences in the beginning of the ionisation expansion
Hii regionsfor the four H ii regions. We recall that the deeply
embedded central UCH ii region has no optical counterpart, the
western, eastern and northern H ii regions, respectively associ-
ated with the vdB67, vdB69 and vdB68 nebulae.
4.1.1. Average initial density
The density observed at the inner border of the envelope, i.e.
ρenv(r=RHii), corresponding to the maximum value measured
now in the envelope, can be used to estimate the density the pro-
tostellar envelope had at the time of the ignition of the ionisation,
when averaged within a sphere of RHii radius. Given the inner
density structure observed for the four H ii regions envelopes,
which density gradient is described by ρ(r)rqin , the mean den-
sity of the initial envelope part, which is now mostly collected in
the shell, is given by:
hρinitialiRHii = 3
3qin !×ρenv(r=RHii).(4)
and derived in Appendix A.1. It is the most important parameter
for analytical calculations and its calculated values are given in
Col. 2 of Table 4.
4.1.2. Expansion in an homogenous density static envelope
Spitzer (1978) predicted the expansion law of a Strömgren
sphere, and thus the evolution of the H ii region size with time
in an homegeneous medium (see also Dyson & Williams 1980
and Arthur et al. 2011, Eq. 1). Following Ji et al. (2012), we in-
verted the relation and expressed time since the ignition of the
ionisation as a function of the observed H ii region radius, RHii :
tExp(RHii ,hρinitial i)=4
7×RStr
cs
RHii
RStr !7/4
1
,(5)
where cs=10 km s1is the typical sound speed in ionised gas
and RStr is the radius of the initial Strömgren sphere (Strömgren
1939, 1948). The latter is given by the following equation:
RStr = 3NLyc
4π αBhρinitiali2!1/3
,(6)
or in numerical terms
RStr '301 AU NLyc
1047s1!1/3 hρinitial i
106cm3!2/3
(7)
where hρinitialiis the initial mean density in which the ionization
occurs, NLyc is the number of hydrogen ionising photons from
Lyman continuum and αB=2.6×1013 cm3s1is the hydrogen
recombination coecient to all levels above the ground.
The ionisation ages determined from Eq. 5 strongly de-
pend on the mean initial density, hρinitiali(see its definition in
Sect. 4.1.1), since it defines the initial radius of the ionised
sphere, RStr (see Eq. 6). With the assumption that the expan-
sion develops in a constant-density medium, the ionisation age is
strictly determined by the initial and present sizes of the ionised
region, RStr and RHii (see Eq. 5).
Initial density estimates are very uncertain since they depend
on assumptions made for the gas distribution before protostellar
collapse and its evolution conditions. Nevertheless the envelope
density structure can be approximated by the mean density of
the envelope part, which was travelled through by the ionisation
front expansion and has been collected in the shell.
Considering the maximum density of the dierent H ii re-
gion envelopes at their inner border (RHii) and using Eq. 4, we
calculate an initial mean density (hρinitialiHii ) reported in Col. 2
of Table 4. This value, assumed to be representative of an enve-
lope with an equivalent homogenous constant density, is jointly
used with the ionising flux given in Table 1 to calculate the cor-
responding expansion time with Eq. 5 and is given in Col. 3 of
Table 4. The expansion time of Compact and UC H ii regions are
similar (tExp 20 90 ×103yr), with a range mainly due to dif-
ferent initial densities. The northern Extended H ii region is three
to 15 times older (300×103yr), in line with what is expected
from their size dierences.
4.1.3. Expansion in a density decreasing static envelope
The present study shows that H ii regions develop into protostel-
lar envelopes whose density decreases with radius (see Sect. 3.5,
see also introduction in Immer et al. 2014). The equationgiven
by Spitzer (1978) describing their expansion in a medium of
homogeneous density (Eq. 5) therefore does not directly apply.
We calculated the expansion of an ionised bubble in an envelope
with a density profile following a power law. We included in this
envelope a central core with a rcradius and a constant density of
ρc. The clump density structure thus follows
ρ=
ρcfor rrc
ρ1×rqfor r>rc
with ρc=ρ1×rq
c
(8)
where ρ1is the density at 1 pc deduced from the constructed
density profile or directly measured from the column density at
the same radius (see Sect. 3.5).
The expansion as a function of time in a decreasing enve-
lope is derived by calculations detailed in Appendix.A.2. In close
agreement with previous work by Franco et al. (1990), it is given
by
tq(RHii)=4
72q×r7/4
c
RStr3/4
1
cs
RHii
rc!72q/4
1
(9)
=4
72q×rc
V(rc)
RHii
rc!72q/4
1
with the same definitions as in Eqs. 5-6 and where V(rc)=
(RStr/rc)3/4×csis the shell expansion speed at the homogeneous
core radius rc. For a constant density, which is the Spitzer case,
q=0 and rc=RStr, and Eq. 9 resumes to Eq. 5.
The inner envelope density profiles of the four regions have
gradients which at most corresponds to the free-fall case, with a
power law coecient of q.1.5. For greater values (q>1.5),
Franco et al. (1990) showed that expansion is in a "champagne-
flow" or "cometary/blister" phase. In such cases, there is no ve-
locity damping nor creation of a collected shell (see also Shu
et al. 2002; Whalen & Norman 2006). In contrast, the shell and
low expansion velocity observed for the central UCHii region
(Fuente et al. 2010; Pilleri et al. 2012, 2013, 2014) indicate that
q=1.5 is probably an upper limit. The ionisation front should
then stay behind the infall wave, RHii <RInfall, with the expan-
sion starting at supersonic velocities, classically 10 km s1, but
then being quickly damped to values around the sound speed in
the neutral molecular medium. As a matter of fact, the expansion
Article number, page 10 of 25
P. Didelon et al.: Mon R2 H ii regions structure and age from Herschel
Table 4: Estimations of expansion time for the four H ii regions of Mon R2
Analytical calculations and simulations without gravity Simulations with gravity Adopted
Constant density Decreasing density Constant density Dec.density expansion
Region hρinitialitSpitzer ρctexp (calc) texp (simu.) hρinitialiMax texp (simu) texp (simu) time
[cm3] [kyr] [cm3] [kyr] [kyr] [cm3] [kyr] [kyr] [kyr]
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
central 2 ×10554 2 ×10658 53 1.7×105133 - 90 ±40
western 2.4×10492 1 ×106108 98 1.7×104215 - 150 ±50
eastern 1.5×10323 4 ×10324 23 8 ×103170 24 25 ±5
northern 3 ×102310 2.5×105370 355 5 ×1033700. 370 350 ±50
(2) average initial density derived from Eqs. 4 and 10.
(3) expansion time calculated from Eqs. 5 and 6 and using the average density of Col. 2.
(4) constant density of central core derived from Eq. 8 with ρc=0.005 pc.
(5) expansion time calculated from Eqs. 9 and 6 and using the central density of Col. 4.
(6) expansion time derived from simulations without gravity using a decreasing-density envelope extrapolated up to the central
density (Col. 4). Considered as a lower limit (see introduction of Sect. 4.2).
(7) maximum constant density allowing ionisation expansion in simulations with gravity, (see Sect. 4.2.2).
(8) expansion time calculated by simulations using the maximum constant density of Col. 7. Considered as an upper limit.
(9) expansion time derived from simulations with gravity using a decreasing-density envelope extrapolated up to highest possible
central density (see Sect. 4.2.3).
(10) adopted expansion time (see Sect. 4.2.4 and 4.3). Errors do not take into account any systematic eects such as those due
to small-scale non-3D geometry or density inhomogeneity.
of the central UCH ii slowed down to 1 km s1at 0.08/0.09 pc
(Pilleri et al. 2014, and references therein) far behind the infall
wave situated around 0.3 pc (see Table 3). More generally, in the
case of the four H ii regions of Mon R2, even if the initial ionisa-
tion extension would exceed the central core size RStr >rcioni-
sation would expand in internal infalling envelopes with shallow
(q<1.5) density profiles. The ρ1value used in Eq. 8 corresponds
to the internal envelope, ρint(1pc), and is calculated from the one
observed in the external envelope, ρenv(1pc), by the relation
ρint(1pc) =ρenv(1pc) ×R(qin qout)
Infall (10)
where ρenv(1pc), RInfall,qin , and qout are given in Table 3.
As for the central core, we adopted a size of 0.005 pc
(1000 AU), which is meant to represent the size where the
spherical symmetry is broken. Since 3D eects are beyond the
scope of this paper, gas at small scales (<0.005 pc) is rep-
resented by an homogeneous and constant density medium.
This value is between the typical size of Keplerian disks sur-
rounding low-mass pre-main sequence T Tauri stars (0.001pc,
200 AU, Carmona et al. 2014; Maret et al. 2014; Harsono
et al. 2014) andthe largest disks or flattened envelopes observed
around intermediate- to high-mass Herbig Ae-Be stars ( 0.01 pc,
200 2000 AU, Chini et al. 2006; de Gregorio-Monsalvo et al.
2013; Jeers et al. 2014). Calculations with various rcvalues
in the conditions considered here (q.1.5) show that when
rcRHii, the value of rcdoes not have much influence on the
expansion time of the ionised bubble.
For objects studied here the initial size of the Strömgren
sphere, RStr, is always smaller than the core radius, rc. Therefore
the expansion is decomposed in two phases : the expansion in an
homogenous medium of constant density, ρcfrom RStr up to rc
and the expansion in the decreasing density part of the envelope
between rcand RHii. The expansion time of the first phase in the
central core, tc, is given by the Spitzer formula (Eq. 5) and the
second phase in the decreasing density envelope, td, is given by
Eq. 9. The total expansion time ttexp =tc+td, is given in Col. 5 of
Table 3. It is consistent with the value obtained for an expansion
within an homogenous-density medium with an equivalent mass
(see Col. 3), corroborating the constant-density equivalence hy-
pothesis and the calculation performed in Sect. 4.1.2. Agreement
is better for the Compact or UC H ii regions, which have hρinitiali
closer to ρcthan the Extended northern region.
The time for an H ii region to expand depends strongly on
the density gradient in the inner envelope, through the density
extrapolated for the 0.005 pc core, ρc, which determines the
Strömgren radius, RStr. The gradient index, qin , itself gives the
transit time in the envelope, td. All measures are uncertain, espe-
cially because the H ii region expansion occured in an envelope
whose density may be larger than the one presently observed. If
ionisation expansion took place in a primordial envelope with a
density slope typical of free-fall, qin =1.5, then the calculations
would give a minimum age of 105yr for all three Compact and
UC H ii regions.
4.2. Simulations of Hii regions development with gravity
We used dedicated simulations to assess the impact of a de-
creasing density and the eect of gravity on our estimates of the
ionisation expansion time. We have employed the HERACLES8
code (e.g. González et al. 2007), a three-dimensional (3D) nu-
merical code solving the equations of hydrodynamics and which
has been coupled to ionisation as described in Tremblin et al.
(2012a,b). The mesh is one dimensional in spherical coordinates
with a radius between 0 and 2 pc and a resolution of 2×103pc,
corresponding to 10 000 cells. The boundary conditions are re-
flexive at the inner radius and allow free-flow at the outer radius.
The adiabatic index γdefined as Pργis set to 1.01, allowing
us to treat the hot ionised gas and the cold neutral gas as two
dierent isothermal phases.
The eects considered here are 1) the ionisation expan-
sion and 2) the gravity of the central object. The envelope
is considered at rest at the beginning of the simulation but,
when gravity is taken into account the infalling part of the
envelope has a velocity close to the expected values.
8Available at http://irfu.cea.fr/Projets/Site_heracles
Article number, page 11 of 25
A&A proofs: manuscript no. MonR2RegHII
Our models consider the gravitational eects of the ion-
ising star but not that of the whole cloud, which could col-
lapse under its own gravity. Such gas infall is important but
modelising it is beyond the scope of this paper. It requires
complex 3D turbulent simulations with self-gravity such as
those developed in Geen et al. (in prep.). Their main con-
clusion is that global cloud infall can stall the expansion of
Hii regions but less eciently than 1D arguments. Indeed,
infall gas should generally be inhomogeneous and clumpy,
and the H ii region should expand in directions where less
dense clumps are present.
Realistic winds from early B type stars have been checked
not to quantitatively modify the ionisation expansion time. A
wind cavity in the ionised gaz would indeed only marginally
increase the electronic density.
Important leaking and outflows of ionised matter would
have a noticeable impact and is neither observed in the tem-
perature map as seen by (Anderson et al. 2015) for RCW120
nor in the Hydrogen RRL or the radio data. Disruption of the
molecular cloud thus cannot be important in the UCH ii re-
gion. Moreover the ionising photon flux we used is coming
from the HII region cavity. Any leaking of ionised matter
would decrease the amount of ionised gaz in the cavity and
thus increase the expansion time.
Complex structure and motions of the ionised gas have
been reported by Jae et al. (2003) and modelised by Zhu
et al. (2005, 2008). They argue for tangential motions of the
ionized gas along the the surface of the HII region, which
cannot supress the thermal pressure at the origin of the ex-
pansion evolution. Thermal turbulence of ionised gas, the
prime driver of expansion, is taken into account in simula-
tions. Recent works show that introducing additional tur-
bulence does not aect much the HII region expansion as it
would only weakly increase the expansion time (see Arthur
et al. 2011; Tremblin et al. 2012a; Tremblin et al. 2014b).
Taking into account all these complexities and secondary
eects is out of the scope of present paper since we merely
tried to reproduce a global behavior, using the mean density
at the origin. Detailed studies would require to take into ac-
count departure from spherical symmetry at small scales.
Simulations are based on 1) the density profiles derived
from column density and 2) UV ionizing fluxes deduced from
radio data. Temperature or electronic density are not used
in the initial conditions so any changes of their values would
not aect the simulation results. For comparison, we used the
profiles presented in Sect. 4.1.3 to perform simulations without
gravity of H ii regions expanding 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-
11.
We hereafter investigate the eect of gravity. Section 4.2.1
shows that extrapolating density profiles as done for analyti-
cal calculations of Sect. 4.1.3 would lead to quenching or rec-
ollapse for the central, western, and northern H ii regions. As
for the eastern region, the extrapolated low central density is
not high enough for gravity to impede expansion and expansion
time remains similar. In Sect. 4.2.2, we calculate the maximum
constant-density medium inside which the H ii regions could de-
velop. Unrealistic envelope models with constant density would
induce re-collapse even at large scale, but they provide never-
theless useful upper limits to the ionisation expansion time. The
case of the less dense northern and eastern H ii regions is dis-
cussed again in Sect. 4.2.3, and confirm that once the expansion
starts the gravity influence is negligible, at least in decreasing-
density envelopes. In Sect. 4.2.4, we summarize the results we
obtained from simulations and give estimates of the ionisation
expansion time for the four H ii regions in Mon R2.
4.2.1. Effect of Gravity: quenching or recollapse
Introducing gravity due to the central object in the simulations
results in the quenching (also called "choke o" by Walmsley
1995) of three H ii regions discussed here and which are expand-
ing in high density medium : central, western and northern re-
gions. They cannot develop and are quenched or gravitationally
trapped (Keto 2007), even with the introduction of a realistic
wind support arising from early B-type stars.
The eastern H ii region is not quenched and can develop in
the observed inner envelope, which has a weak density gradi-
ent. The values of hρinitialiand even ρcare lower than the maxi-
mum constant density hρinitialiMax (see Table. 4) explaining why
quenching is not occuring here. In this case of low density enve-
lope the expansion time obtained in simulation without gravity
(23 kyr, see Col.6 of Table 4) is identical when including gravity
in simulation (24 kyr, see Col.9 of Table 4).
To allow expansion of the three H ii regions quenched in sim-
ulations, one needs to decrease the central density of the profile,
ρc. If we keep extrapolating the density profile observed for the
outer envelope (see ρ1in Col.10 of Table 3), the only way is to
increase the constant density core radius, rc. This determines the
maximum central density value, ρcMax, and the corresponding
minimum core radius, rcmin, allowing an H ii region to develop
up to the observed size. For the UC (central) and the Compact
(western) H ii regions, rcmin is larger than RHii corresponding to
an expansion in an homogenous medium of density ρcMax. So,
the highest density observed in the envelope at a radius corre-
sponding to the H ii region size is greater than the maximum
density allowed by this scenario, ρcMax < ρ(RHii), and the radii
of constant density are larger than the actual H ii region sizes,
rc>RHii. Even if these assumptions are unrealistic, they are
useful to determine upper limits.
Another way to reduce the central density, as shown in Eq. 8,
is to keep the same central core radius but decrease the density
of the entire profile through the ρ1value. This configuration im-
plicitly assumes a mean envelope density at the initiation of the
Hii 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. For a con-
stant low-density envelope (cyan curve) expansion can reach the
observed H ii region size. For higher constant density (red dashed
curve) the re-collapse occurs earlier and closer preventing the ex-
pansion up to its present size. Increasing the density gradient of
the inner envelope from that presently observed (qin=0.85, con-
tinuous black line) to that expected for free-falling gas (qin=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 number, page 12 of 25
P. Didelon et al.: Mon R2 H ii regions structure and age from Herschel
gravity are displayed by a blue line for the nominal average ini-
tial density and a dashed blue line for a lower density.
Figure 9 shows the velocity field of a simulation for the
Northern region obtained at three dierent 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 cm3at 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 eect 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 expansion at three dierent time. Simulation is
made with gravity and in an envelope of decreasing density,
which is extrapolated from the observed one up to a constant
density within rc=0.005 pc.
4.2.2. Case of constant-density envelopes
We simulated the expansion in a constant density envelope,
which value could be compared to the initial average density of
the envelope material swept up by the expansion. The latter is
estimated through Eq. 4 (see Col. 2 of Table 4). This approach is
validated in the case of the northern region (see Sect. 4.2.3) and
is shown to be a good approximation for all H ii regions since, for
analytical calculations without gravity, expansion times given in
Cols. 3 and 5 of Table 4 are similar.
The central UC H ii region and the western Compact H ii re-
gion are quenched by gravity when densities are approaching the
initial average density extrapolated from the observed envelope.
For these two regions, we thus decreased the envelope average
density until their H ii regions develop and reach their actual size.
The associated expansion times are then upper limits measured
for the densest, homogeneous and constant density envelopes.
Any density above this value would result in quenching or re-
collapse before reaching the observed size. Any configuration,
allowing expansion up to the observed size leads to a smaller ex-
pansion time. The 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 eect
of gravity on the expansion in a constant low-density envelope
(cyan curve) compared to the expansion in a decreasing den-
Fig. 10: Numerical simulations for the central UC H ii region ex-
pansion. 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 rc=0.005 pc. In dotted black: without
gravity in an envelope of decreasing density with a gradient typ-
ical of infall, ρr1.5. In cyan: with gravity and in an envelope
with a constant density of 1.65×105cm3, just allowing to reach
the observed size (black dashed line). In dashed red: with gravity
and in an envelope with a constant density of 2.5×105cm3, for
which re-collapse occurs before reaching the observed size.
sity envelope constrained by observationnal data, but without
gravity (black line). For higher density (red dashed curve) the
re-collapse occurs, preventing the expansion to reach the ob-
served size. The same recollapse behaviour is observed for the
western Compact H ii region. At the beginning of the expan-
sion,corresponding to small scales, gravity can have a strong in-
fluence. In the case of a constant-density envelope the collected
mass noticeably increases when size grows. The re-collapse of
the shell is thus favoured in a constant-density envelope, but it
more hardly occurs in a more realistic, decreasing-density enve-
lope or at larger size. At the beginning of the expansion, in the
constant-density cases the expansion is faster, even with grav-
ity. This arises from the fact that the central density here is
much smaller than in the case without gravity of extrapolated
envelopes with a decreasing density. When the collected mass
becomes important, the expansion is strongly slowed down by
gravity and even stops. Re-collapse then occurs, at large dis-
tance, but a constant density is unrealistic for such large sizes.
The northern H ii region could expand up to its observed size
in an envelope with a maximum constant density of 5×103cm3.
This density is much higher than the mean value extrapolated
from observations and the observed size would be reached in a
very long and unlikely time of at least 3×106yr. At this large dis-
tance re-collapse will not occur. More realistically, the northern
Hii region should have expanded in an envelope with constant
density of 300 cm3(cyan curve in Fig.11), equal to the initial
average density deduced from the envelope presently observed.
This gives an expansion time of 300×103yr. 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-
Article number, page 13 of 25
A&A proofs: manuscript no. MonR2RegHII
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, hρinitiali=300 cm3. The envelope
has a power law decreasing density with the characteristics of
the observed one and extrapolated to a constant core of radius
0.005 pc (black) and 0.05 pc (dark blue). For the blue-dashed
line, the envelope has a power law decreasing density with an
index corresponding to the observed gradient but with a 50 cm3
density at 1 pc extrapolated to a constant core at 0.005 pc. For the
cyan and red-dashed curve the envelope has a constant density of
300 cm3(cyan), corresponding to the average initial density, or
a higher 2×104cm3density (red dashed), leading to re-collapse.
els calculated for the nominal constant average density envelope
are converging to similar values. The same situation applies to
eastern H ii region. Better estimates of the expansion time can be
obtained for the northern and eastern H ii regions, as shown in
the Sect. 4.2.3.
4.2.3. Case of decreasing-density envelopes
The two options already mentioned in Sect. 4.2.1 to reduce the
central density are suitable for the northern H ii region. The first
option is to increase the radius of the constant density core, rc.
The lower density and larger size of the northern region, al-
lows expansion with gravity without quenching up to the Hii re-
gion size. Nevertheless, the required size of the central core,
rc0.05 pc (10000 AU), is then much larger than those in-
side which we expect a departure from the spherical symmetry
(0.001 pc/200 AU - 0.005 pc/1000 AU). As 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 dierent 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 370×103yr (see Col. 9 of Table 4).
The 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 (texp RStr3/4) and Eq. 6 (RStr ρ2/3), the expansion
time relates to density through its square root: tex p ρ1/2. This
is in agreement with the time approximately divided by 2 be-
tween the two cases, ρ1and ρ1/2 (blue and blue dashed lines in
Fig .11).
In fact the average initial density, hρinitiali, is identical for the
three cases best representing the northern region. Case 1 is the
first option mentioned above in this section, with gravity and an
enlarged central core (blue line), case 2 is the simulation with-
out gravity (black line), and case 3 is for a constant density with
gravity (cyan line). Independently of the gravity inclusion or not
in simulations, these three lines are leading to similar expansion
times. It indicates that the average initial density in which the
Hii region has expanded is one of the important parameter to
estimate expansion time. Once quenching by gravity has been
overruled the expansion is no longer strongly aected by grav-
ity. In details however the configuration with constant density
and gravity is underestimating the expansion time mainly in the
central parts where the density should be much higher than what
is estimated.
For the northern H ii region expansion simulated in a decreas-
ing envelope without gravity gives a minimum expansion time
of 355 kyr. Expansion simulated with gravity in a decreasing-
density envelope with the highest possible central density, gives
a maximum time of 370 kyr. These values define a very nar-
row interval for the expansion time, if extrapolation of the ob-
served envelope toward the interior is valid. Taking into account
the observational uncertainties including those concerning the
small scales structure we conclude that the expansion time of
the northern H ii region should be 350+/-50 kyr.
Even more strikingly, for the eastern H ii region, it is not
needed to increase the default central core radius (0.005 pc),
and the time expansion calculated with gravity (24 kyr) is al-
most identical to the time obtained without gravity (23 kyr). This
shows again that gravity could delay the start of expansion, but
has very small influence on expansion time. This eect is more
pronounced in low-density medium.
4.2.4. Ionisation age and expansion time
Tracing the expansion of H ii regions with gravity and in a
decreasing-density envelope extrapolated from the one observed
at large scales would require complex 2D or even 3D configu-
rations, at least at small scales. At 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). 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 the envelope itself
locally increases the density and reduces the expansion speed
or impeeds it in disk, torus or funnel. All these eects along
Article number, page 14 of 25
P. Didelon et al.: Mon R2 H ii regions structure and age from Herschel
with sporadic accretion (Peters et al. 2010a; Duarte-Cabral et al.
2013; De Pree et al. 2014) increase the expansion time uncer-
tainty. A definitive measurement of the ionisation age would thus
require a detailed modelling based on better constraints of phys-
ical parameters, at least at small scales. Unfortunately, the obser-
vational constraints of high-mass protostellar envelope at small
scales (<0.05 pc) are still largely missing. This 3D small-scale
asymmetric geometry could also shorten the quenching time,
that needs to be added to the expansion time to determine the
age of H ii regions and their ionising stars. On the other hand,
confinement by external pressure could also occur at the end of
expansion and thus lengthen the ionisation age. Expansion times
depend on the initial conditions at small scales and especially
ionisation age if the quenching and confinement times are taken
into account. However, the order of magnitude of the expansion
times determined from simulations seem to converge (see Ta-
ble 4).
The simulations performed, with or without gravity for the
eastern and northern H ii regions expanding in low-density en-
velopes, provide expansion times of 25 ±5×103yr and 350 ±
50 ×103yr.
For the central UC and western Compact H ii regions we es-
timated upper and lower limits for the expansion time. Lower
limits correspond to simulations in a decreasing-density enve-
lope without gravity (Table 4, Col. 6). Upper limits are given by
simulations with gravity in an envelope with the highest constant
density (Table 4, Col. 8) avoiding quenching or re-collapse and
allowing to reach the observed size. The ranges of time values
obtained : 90 150 ±50 ×103yr, are consistent with a mean
expansion time of 1 ×105yr. The expansion time of the cen-
tral UC H ii region, 9 ×104yr, is in agreement with the duration
of the warm phase in dedicated chemical models (104-a few
105yr, Treviño-Morales et al. 2014). The chemical model re-
quire a chemistry out of equilibrium and imply a warm phase
duration of less than 106yr.
Expansion times adopted for the dense western Compact and
central UC H ii regions, despite the dependence on unknown
small scale geometry, are equal to within a factor two, converg-
ing to 1-1.5 ×105yr, (Table 4 Col. 10). They are in agreement
with the statistical estimate of the age of C and UC H ii regions
(105yr, Wood & Churchwell 1989b) and ten times larger than
the rough dynamical time (104yr) estimated from the ini-
tial ionised gas velocity. As already stressed by Urquhart et al.
(2013) the order of magnitude of these ages, 3 6×105yr, is
recently confirmed by new statistical lifetimes (3×105yr, Mot-
tram et al. 2011) and supported by a Galactic population synthe-
sis analysis (24×105yr, Davies et al. 2011). The so-called life-
time problem (Wood & Churchwell 1989b; Churchwell 2002;
Peters et al. 2010b) is simply solved here by taking an expan-
sion velocity equal to the sound speed in ionised gas (cs) only at
the beginning. Indeed, in a slowly decreasing-density envelope
(q<1.5) expansion speed is rapidly damped and even stopped
if confinement by external turbulent pressure occurs (Raga et al.
2012).
4.3. Suitable approximations for expansion time estimation
As already mentioned in previous section, gravity does not it-
self strongly aect the expansion time but a delay of expansion
can occur at beginning Similarly Keto (2007) dierentiates the
dynamic behavior of HC and UC H ii regions, which are gravita-
tionnaly dominated, from that of larger Compact and Extended
Hii regions, which thermally dominated. As a matter of fact, in
the low-density conditions of the northern and eastern regions,
simulations with or without gravity give similar expansion times
(see Table 4 Cols. 6 and 9). In the high-density condition of the
central and western regions, the upper limit of expansion times
calculated with gravity (Table 4 Col. 8), even with a rough con-
stant density estimation, are only twice larger than expansion
times obtained without gravity (Table 4 Col. 6).
Even if the average initial densities (hρinitiali, Table 4 Col. 2)
are only roughly estimated, expansion times of the various ana-
lytical calculations and simulations agree (Table 4 Col. 3, 5 and
6). The agreement is better for the small (C and UC) H ii regions,
for which the average initial density is more representative of the
overall past density conditions. Analytical calculations without
gravity using an extrapolation of the observed density envelope
give a good time estimate at least for H ii regions of small sizes.
For the more extended northern H ii region the evaluation made
of the average envelope density at small scales is more question-
able since the remaining envelope has much lower density than
the one at the beginning of expansion. Calculations using more
realistically extrapolated density profiles should be preferred or
other evaluation using the pressure equilibrium and third Larson
law (Tremblin et al. 2014a) could be made.
We conclude that:
- gravity induces quenching which adds a delay before the
Hii region expands, but when it expands the influence of gravity
becomes marginal.
- envelope density profiles could be used to estimate a mini-
mum expansion time from analytical calculations without grav-
ity, and if density is not too high it gives a realistic value.
- the mean initial density is a good estimator of the matter
density surrounding the massive protostar at early stages, and
later collected in the shell by the H ii region expansion. It could
be used to estimate expansion times if density profiles are not
well defined. In any case, it is better suited than the surrounding
cloud density charaterising the external medium.
All realistic time expansion estimates done in this paper are
converging around 1×105yr for the two dense (UC central and
Compact western) H ii regions, 2.5×104yr for the Compact
eastern H ii region, and 3.5×105yr for the Extended northern
Hii region.
5. History of the formation of the B-type stars
powering H ii regions in Mon R2
In Sect. 5.1, we discuss the global infall of the Mon R2 cloud.
In Sect. 5.2, we analyse the two-slope profiles in the framwork
of the inside-out collapse of envelopes and estimate protostellar
infall ages. In Sect. 5.3, we compare the infall and ionisation
ages and propose a global history of massive star formation in
the Mon R2 cloud.
5.1. Cloud global infall
The density structure and infall kinematics discussed here are
probably dominated by the most massive object clearly identi-
fied in Fig. 2b. The envelope profile defined above (see Sect. 3.5)
and their corresponding values given in Table 3 have been used
in Eq. A.2 to estimate a mass of 3500 Min a 2.5 pc radius for
the central UCH ii region. This region exhibits a steeper density
gradient in its outer envelope, with qout ' −2.5, also illustrated
by the cloud structure studied with Probability Density Func-
tion (Rayner et al. in prep.). It suggests compression by external
forces as shown in numerical simulations of Hennebelle et al.
(2003) and outlined in Appendix A. This compressive process
Article number, page 15 of 25
A&A proofs: manuscript no. MonR2RegHII
could be associated with stellar winds and ionisation shocks of
nearby stars like observed in M16 Massive YSO (Young Stel-
lar Object) by Tremblin et al. (2014b) or with globally infalling
gas driven by the dynamic formation of Mon R2 cloud throug
force-fall. Such infalling motions have in fact been observed in
CO by Loren (1977) and clumps with similar masses generally
exhibit active global infall. It is the case of SDC335 which has
a mass of 5500 Min 2.5 pc (Peretto et al. 2013) contain-
ing protostellar object of similar type B1 (Avison et al. 2015)
or in DR21, Clump-14 (DR21-south, 4900 M) and Clump-16
(DR21-north, 3350 M) (Schneider et al. 2010a), all showing
supersonic infall (V=0.5-0.7 km.s1). Moreover the hourglass
morphology of the magnetic field thought to be a signature of
global infall (Carpenter & Hodapp 2008) and Koch et al. (2014)
suggest that Mon R2 is a super critical fast collapsing cloud. The
expected infall velocity gradient, as observed in SDC13 (Peretto
et al. 2014), seems to be a crucial ingredient to generate filament
crossing (Dobashi et al. 2014) characteristic of all the regions
mentioned here and comonly observed in many places.
5.2. Time elapsed since the beginning of the protostellar
infall
The outer envelope of the two Compact eastern and western
Hii regions display a column density index of pout ' −1±0.2,
which corresponds to a ρ(r)r2density law. It recalls the
density distribution of the singular isothermal sphere (SIS, Shu
1977) and that of the cloud structures quasi-statically forming
clumps in numerical simulations with or without turbulence and
magnetic field (e.g. Li & Shu 1996). A similar density distribu-
tion is in fact obtained for clumps forming from subsonic infall
(Dalba & Stahler 2012) or supersonic flows (Gong & Ostriker
2009). This is also reminiscent of the density profiles found for
low-mass and high-mass protostellar envelopes at early stages
(Tsitali et al. 2013) as known for a long time (e.g. Motte & André
2001; Beuther et al. 2002). Numerous pre-main sequence phase
YSOs are found in the Mon R2 cloud, suggesting that a group or
cluster of protostars has most probably formed within the same
area of these four separate envelopes of 2.5-3 pc radius each.
The transition radius between the inner and outer envelope,
RInfall, could be used to locate the front of the infall expansion
wave associated with the protostellar collapse. Indeed, in the
case of an inside-out collapse developing into a static envelope
with a SIS density structure, the envelope matter is free-falling as
soon as the infall front wave travelling outwards reaches its loca-
tion (e.g. Shu 1977). Interestingly, the density profile measured
for the inner envelope surrounding Hii regions is close to that
of free-falling material, ρ(r)r1.5(see Table 3). The transition
radii would correspond to late stages of the protostellar collapse
since they are rather large compared to typical protostellar en-
velopes: RInfall 0.25, 0.5, 0.8, 2 pc versus Rprot 0.03 0.1 pc
(e.g. Motte & André 2001). Note that this free-falling envelope
material may not be able to reach the stars but pile up at the
periphery of the H ii regions, located at RHii .
We assumed below that the infall front wave initiated at the
time of the protostellar embryo formation and propagating out-
wards from the centre can be approximated by RInfall. The latter
was measured to be 0.25, 0.85, and 0.5 pc for the central, eastern,
and western ultra-compact and compact H ii region envelopes
(see Table 3). We used an infall front wave velocity equal to
the isothermal sound speed, as=cs=pk TmH'0.2 km s1,
calculated for T=13.5 K which is the mean cloud temperature
in Mon R2. We then dated the beginning of the protostellar infall
using the following equation:
tInfall =RInfall
cs'4.9×106yr ×RInfall
1 pc ×cs
0.2 km s11
.(11)
It dates back to a few million years ago for the three compact
and ultra-compact H ii regions with tInfall '1.5×106yr for the
UCH ii and tInfall 2.54.5×106yr for the eastern and western
Hii regions. The more developed northern Hii region has an en-
velope that could be fully free-falling up to a radius reaching the
background density (see Table 3). With a value of RInfall >2 pc,
our calculation leads to a minimum infall age of tInfall >107yr.
These ages seem perhaps too long but they are approximate val-
ues since a more complex density, temperature and kinematic
structure is to be expected for a non-isothermal envelope already
globally collapsing at the time of the creation of the first proto-
stellar embryo.
Moreover the static SIS initial conditions are probably far
from realistic for clouds forming high-mass stars, known to be
dynamical entities (Schneider et al. 2010a; Peretto et al. 2013).
Some models examined the protostellar collapse in an infalling
cloud (Larson 1969; Penston 1969; Gong & Ostriker 2009; Keto
et al. 2015). The global inflow speed before protostellar collapse
indeed modifies the rarefaction wave speed, even in subsonic
mode (Dalba & Stahler 2012). In the case of supersonic flows,
the speed increases by a factor 2 to 3 (Gong & Ostriker 2009,
see their section 4.2), dividing the calculated infall time by the
same factor. Supersonic inflows driven by the cloud global col-
lapse, is probable for the central UCH ii region. It is less certain
but still plausible for the other H ii regions which are within the
same infalling cloud but excentred from the infall center.
Infall times are listed in Col. 6 of Table 3. The range of val-
ues illustrates systematics and errors to statistical uncertainties.
Alltogether it gives the following infall times : 1.±.7×106yr
for the central UC H ii region, 1.5±1.×106yr for the western
C H ii region, 3.±1.5×106yr for the eastern C H ii region. De-
ducing the ionisation expansion time estimated in Sect. 4 from
this infall time provides a measure of the time a protostar needs
to reach the high-mass regime associated with the emission of
ionising UV photons, and an eventual ionisation delay due to
quenching or swelling (Hoare & Franco 2007).
5.3. Age comparison and history of OB star formation in
Mon R2
For the dense compact and ultra-compact (western and central)
Hii regions, infall ages derived in Sect. 5.2: are about 10 times
larger than ionisation expansion time tinfall 12×106yr versus
tionisation 12×105yr. As for the eastern Compact Hii region,
infall time is 100 times larger than the ionisation expansion time
:tinfall 3×106yr versus tionisation 25 ×103yr. The infall age
of the northern Extended H ii region is unknown, with a lower
limit of tinfall >14 ×106yr, 30 times larger than the ionisation
expansion time of tionisation 5×105yr. Even if uncertain, the
order of magnitude of these values is probably realistic since the
stellar ages of the B-type star association observed in Mon R2 is
16×106yr (Herbst & Racine 1976; Carpenter et al. 1997),
in agreement with the computed infall ages of the compact and
ultra-compact H ii region envelopes.
Subtracting a mean protostellar lifetime of 3 ×105yr
(Duarte-Cabral et al. 2013, see also Schisano et al. 2014 and
references therein) from the infall time measured for the cen-
tral UCH ii region, 1×106yr suggests that ionisation started
7×105yr ago. With an ionisation expansion time of 1×105yr,
Article number, page 16 of 25
P. Didelon et al.: Mon R2 H ii regions structure and age from Herschel
the quenching delay time could be 6±5×105yr. The typ-
ical protostellar lifetime adopted here agrees with the one ob-
tained for the cold phase of Mon R2 in chemical models (105
- 106yr Treviño-Morales et al. 2014), corresponding to col-
lapse (Esplugues et al. 2014). Similar considerations for west-
ern (and eastern) CH ii region give a quenching delay time of
9±6×105yr (resp. 2±1×106yr). These variations could
be interpreted as an increase of the quenching time with increas-
ing spectral type from B0 to B2.5, and thus decreasing number
of ionising photons NLyc. However, given the large uncertainties
of each of these estimates a constant value around 106yr cannot
ruled out.
Besides, the derived infall ages span an order of magnitude
dierence possibly indicating the existence of progressive star
formation in the Mon R2 cloud. None of the ionisation fronts
and none of the infall rarefaction wave arising from the three
Hii regions located at 1–2 pc from the UCH ii region could
however explain the compression of the UCH ii envelope. There
is thus no clear evidence that star formation in the Mon R2 cloud
could have been triggered by older local populations of stars.
Any observed age gradient could only be related to sequential
star formation triggered by an external agent.
6. Conclusions.
We have presented a study of the Mon R2 molecular cloud
based on dust column density and temperature maps built from
Herschel/HOBYS observations and dedicated simuations. Our
main findings can be summarised as follows:
1 - The MonR2 molecular cloud is dominated by gas asso-
ciated with the central UCH ii region. The latter is located at the
crossing of three major filaments while three other H ii regions
develop in their surroundings. The spectral type of ionising stars
as estimated from 21cm fluxes are in very good agreement with
those obtained from visual spectroscopy. They all are early B-
type stars.
2 - The size of ionised regions is estimated by the heating
of big grains (Fig. 2a) and small grains excitation through their
70 µm flux (Fig. 5), in the close surrounding of H ii regions, prob-
ably within the PDR. It ranges from 0.1 pc for Compact and
UCH ii regions to 0.8 pc for the most classical Extended H ii re-
gion.
3 - The H ii regions are surrounded by large and rather dense
neutral gas envelopes, (Renv 23 pc, ρmax
env 3×1025×
105cm3) . At radii from 0.1 pc to a few parsecs the envelope
surrounding H ii regions cannot be considered to have a constant
density. Temperature gradients are also observed in the neutral
gas envelope surrounding the four regions.
4 - In spite of the quite advanced stage of evolution of the
four massive ionising stars studied here the density of the enve-
lope surrounding them keep the imprint of earlier phases of the
gravitational collapse. The density structure is similar to those
expected for individual protostellar objects. For the first time the
power law slope of the density profile is constrainted, accurately
enough to distinguish between inner layers in free fall (ρrw
with w61.5) and external parts that could correspond to an
equilibrium SIS configuration (ρr2).
5 - We interpret the steep density profile of the central
UCH ii region (ρr2.5) as being due to an external pressure
certainly associated with the observed global collapse, which can
be called a forced fall.
6 - The transition radius between ρr1.5(or rwwith w6
1.5) and r2(or rwwith w>2) laws should locate the free-
fall rarefaction wave. Assuming it expands at one to three times
the sound speed we estimate the time since the infall began. An
infall age around a few millions years for these H ii regions is
consistent with current high-mass star formation scenarios.
7 - The density profiles obtained here allow us to deter-
mine the initial conditions of ionisation and its expansion. Ded-
icated 1D simulations show that the envelope density presently
observed at large scale would induce a complete quenching of
the ionisation expansion. A more complex geometry at small
scale and a dynamic scenario are required to explain the present
Hii region development.
8 - The ionisation expansion time deduced here from ana-
lytical calculations and dedicated simulations are in agreement
with statistical ages of the corresponding H ii region. Compact
and UCH ii region expansion time is 1 2×105yr.
9 - Stellar formation in MonR2 seems to be an on-going
process, that started at least 16×106years ago. Global
feedbacks, such as the globall infall of the cloud complex,
certainly have an important role, but no clear evidence of locally
triggered star formation has been found.
Acknowledgements. P.D. thanks Philippe Laurent for his help in calcula-
tion of elliptical integral numerical values. This research has made use
of TOPCAT (Taylor (2005), http://www.starlink.ac.uk/topcat/) and SAOIm-
age/DS9, developed by Smithsonian Astrophysical Observatory" (http://hea-
www.harvard.edu/RD/ds9/). This work profits by data downloaded from the
SIMBAD database, operated at CDS, and the VizieR catalogue access tool (CDS,
Strasbourg, France; Ochsenbein et al. 2000).
SPIRE has been developed by a consortium of institutes led by CardiUniv.
(UK) and including Univ. Lethbridge (Canada); NAOC (China); CEA, LAM
(France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Swe-
den); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK);
Caltech, JPL, NHSC, Univ. Colorado (USA). This development has been sup-
ported by national funding agencies: CSA (Canada); NAOC (China); CEA,
CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC
(UK); and NASA (USA).
PACS has been developed by a consortium of institutes led by MPE (Germany)
and including UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA, LAM
(France); MPIA (Germany); INAF-IFSI/OAA/OAP/OAT, LENS, SISSA (Italy);
IAC (Spain). This development has been supported by the funding agencies
BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Ger-
many), ASI/INAF (Italy), and CICYT/MCYT (Spain).
T.H. was supported by a CEA/Marie-Curie Eurotalents Fellowship. Part of this
work was supported by the ANR (Agence Nationale pour la Recherche) project
‘PROBeS’, number ANR-08-BLAN-0241.
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1Laboratoire AIM, CEA/IRFU CNRS/INSU Université Paris
Diderot, CEA-Saclay, 91191 Gif-sur-Yvette Cedex, France
e-mail: pierre.didelon@cea.fr
2Astrophysics Group, University of Exeter, EX4 4QL Exeter, UK
3Maison de la Simulation, CEA-CNRS-INRIA-UPS-UVSQ, USR
3441, Centre d´ étude de Saclay, 91191 Gif-Sur-Yvette, France
4Universität Heidelberg, Zentrum für Astronomie, Institut für Theo-
retische Astrophysik, Albert-Ueberle-Str. 2, 69120 Heidelberg, Ger-
many
5Department of Physics and Astronomy, West Virginia University,
Morgantown, WV 26506, USA ; Also Adjunct Astronomer at the
National Radio Astronomy Observatory, P.O. Box 2, Green Bank,
WV 24944, USA
6Université de Bordeaux, OASU, Bordeaux, France
7CardiUniversity, Wales, UK
8European Space Research and Technology Centre (ESA-ESTEC),
Keplerlaan 1, PO Box 299, NL-2200 AG Noordwijk, the Nether-
lands
Article number, page 18 of 25
P. Didelon et al.: Mon R2 H ii regions structure and age from Herschel
9Laboratoire d’Astrophysique de Marseille, CNRS/INSU–Université
de Provence, 13388 Marseille cedex 13, France
10 Queen Mary +Westf. College, Dept. of Physics, London, UK
11 CESR, Toulouse, France
12 INAF-Istituto di Astrofisica e Planetologia Spaziali, via Fosso del
Cavaliere 100, I-00133 Rome, Italy
13 National Research Council of Canada, Herzberg Institute of Astro-
physics, 5071 West Saanich Rd., Victoria, BC, V9E 2E7, Canada
14 University of Victoria, Department of Physics and Astronomy, PO
Box 3055, STN CSC, Victoria, BC, V8W 3P6, Canada
15 Université de Toulouse, UPS-OMP, IRAP, F-31028 Toulouse cedex
4, France ; CNRS, IRAP, 9 Avenue colonel Roche, BP 44346, F-
31028 Toulouse cedex 4, France
16 Jeremiah Horrocks Institute, University of Central Lancashire, Pre-
ston, Lancashire, United Kingdom
17 Department of Physical sciences, The Open University, Milton
Keynes, UK ; RALspace, The Rutherford Appleton Laboratory,
Chilton, Didcot, UK
Article number, page 19 of 25
A&A–MonR2RegHII, Online Material p 20
Fig. 12: Column density map showing the azimuthal selection of areas used to characterise the density profiles of the eastern,
western, and northern H ii regions envelopes. The H ii region bubble, the inner, and the outer envelopes of the central UCH ii region,
are outlined with continuous, dashed and dotted circles, whose sizes are given in Tables 1-3. Area of extraction for surroundings
region are shown. Spectral type are taken from (Racine 1968).
A&A–MonR2RegHII, Online Material p 21
Fig. 13: hot regions overall contours of profile extraction on temp. map. Area of extraction for surroundings region are shown.
A&A–MonR2RegHII, Online Material p 22
Appendix A: H ii region expansion in an envelope of
decreasing density with power law profile
Appendix A.1: Mass and average density from a decreasing
power law density profile
Considering a decreasing density distribution described by a
power law with an index q, ρ(r)=ρ1rq, the mass included
within a radius Ris given by :
M(R)=ZR
0
ρ1rq4πr2dr =4πρ1ZR
0
r2qdr (A.1)
as far as q<3, it gives
M(R)=4πρ1
R3q
3q(A.2)
or in numerical terms
M(R)=0.76646 ρ1cm3Rpc3q
3qM(A.3)
the mean density in the sphere of radius R is then given by
hρ(R)i=M(R)3
4πR3= 3
3q!ρ1Rq= 3
3q!ρ(R)(A.4)
and for a gradient typical of infall, q=1.5, it resumes in
hρ(R)i=2ρ1R3/2=2ρ(R)
Appendix A.2: ionisation expansion in a decreasing
power law density profile
We consider here a decreasing density distribution with a
power law of index q and a central core of constant density to
avoid singularity at the orign and mimic a core envelope using
the same definition as in Eq. 8 :
ρ=
ρcfor rrc
ρ1×rqfor r>rc
with ρc=ρ1×rq
c
(A.5)
Considering the density, ρi, and the speed, ci, in the ionised
medium, the speed of the shell V, from the Rankine-Hugoniot
conditions (Eq. B.5, Minier et al. 2013) we get
ρic2
iρ(r)V2(A.6)
using the density profile of (Eqs. 8/A.5), it transforms into :
ρic2
iρ1×rqV2ρc× r
rc!q
V2(A.7)
considering an initial Strömgren radius smaller than the core ra-
dius rc, Eq. 6 and the photon conservation gives :
ρc2RStr3=ρi2r3ρc
ρi
= r
RStr !3/2
(A.8)
Eq. A.7 can then be written:
Vrc
rq/2RStr
r3/4
circq/2R3/4
Str ci 1
r!(32q)/4
(A.9)
Table B.1: Column density dependance to power law index of
decreasing density envelope
Integral I(a)
q analytical numerical Σ1/1pc ζ
1 ln y+py2+a2(1) - -
3/2 2.6218/a2.6/a5.2ρ15.2
2 1/aarctan (y/a)π/2aπρ1π
5/2 1.1985/a31.2/a32.4ρ12.4
3y/apy2+a21/a22ρ12
Notes: (1) Analytical solution diverges at . Integration can
only be done on a spatialy limited size, and analytical values
will depend on the outside radius Rout.
This equation can be integrated to give the radius of the shell,
rshell, as a function of time, with tcthe time at which the shell
reaches rc
rshell =rc
1+72q
4
R3/4
Str
r7/4
c
ci(ttc)
4/(72q)
(A.10)
Eq. A.9 taken at rcallows to define the speed at this place :
V(rc)=Vcci RStr
rc!3/4
(A.11)
and can be introduced in Eq. A.10
rshell =rc 1+72q
4
Vc
rc
(ttc)!4/(72q)
(A.12)
Appendix B: Column density line of sight
calculation from an envelope of decreasing
density with a power law profile
Considering as previously a decreasing density distribution with
a power law of index q : ρ(r)=ρ1rqthe column density as
measured along the yaxis at impact parameter ais given by:
Σ(a)=2Z
0
ρ1rqdy =2ρ1Z
0 qa2+y2!q
dy (B.1)
with I(x)=R
0px2+y2qdy =R
0x2+y2q/2dy
the column density at impact parameter ais then given by
Σ(a)=2ρ1I(a)(B.2)
The analytical integration for integer values of q leads to well-
known integrals already calculated by Yun & Clemens (1991).
Half integers lead to elliptical integrals and their tabulated val-
ues result in a polynomial expression of I(a). The analytical
and numerical values are given in cols. 2 and 3 of Table B.1.
Adopting a value of 1 pc for the impact parameter a, we can
derive a relation between the column density and the density via
Σ1(a=1pc)=2ρ1I(a=1pc). The relation of ρ1as a fonction of
Σ1uses the conversion factor ζcorresponding to the appropriate
qvalue and given in col.5 of Table B.1.
ρ1=Σ1
ζ×1 pc/cm =1000
3.08 ×ζcm3Σ1
1021 cm2(B.3)
The dependance between ζand qis given at the 5% error
level by the following relation
ζ=π
(q1)2/3(B.4)
A&A–MonR2RegHII, Online Material p 23
Table C.1: Envelope density power law slope dependence on
compression at two time step of protostellar stage
φ10 3 1 .3 .1
time step 4 : Class0 start -2.1 -2.1 -2.2 -1.9 -2.
time step 5 : ClassI start -1.5 -1.6 -1.65 -1.7 -1.8
Appendix C: density gradient steepening by
external compression, as seen in simulations
Hennebelle et al. (2003) have made numerical simulations to test
the influence on density profiles of compression induced by ad-
ditional external pressure. The compression is characterised (see
their Eq.12) by a dimensionless factor (φ) wich gives the num-
ber of sound-crossing times needed to double the external pres-
sure. Large φvalues correspond to small compression, called
subsonic and slow pression increase. Hennebelle et al. (2003)
show radial density and velocity profile at five time steps. The
three first ones correspond to prestellar phases, well represented
by Bonnor-Ebert spheres (Bonnor 1956; Ebert 1955). The fourth
step would correspond to the protostellar class 0 phase and the
last one to the beginning of the class I phase (see Andre et al.
2000 for class 0 and class I definitions). For a supersonic com-
pression (φ <1) during the prestellar phase, a density wave is
crossing the core profile towards the interior. For a sonic or sub-
sonic compression (φ>1) the Bonnor-Ebert sphere like profile
is smoothly distorted during prestellar phases leading to a single
power law at protostellar phases.
We measured and give in Table C.1 the variation of the den-
sity profile power law index (q) as a function of the compression
factor φat the two time steps corresponding to the beginning
and the end of class 0 phase, (steps 4 and 5). During the Class
0 phase, the slope of the density profile does not depend on the
compression and remains q =-2, the classical value expected for
hydrostatic equilibrium. At the end of Class 0 phase the slope of
the power law fitting the density profile is correlated to the com-
pression given by the φvalue (see Table C.1). It increases from
1.5, the classical value of a free-falling envelope, to 1.8 when φis
varying from 10 (virtually no compression) to .1 (strongly super-
sonic compression). This 20 % steepening of the density profile
could be one eect occuring also at later stage and larger radii
as observed in the MonR2 central UCH ii region, as advocated in
Sect.5.2.
Appendix D: H ii region swept-up shells and their
contribution to the column density
The ‘collect-and-collapse’ scenario proposes that the ionising
flux of OB-type stars is indeed eciently sweeping up the gas
located within the H ii region extent and developing a shell at the
periphery of H ii bubbles (Elmegreen & Lada 1977).
We here (see also Appendix E) investigate the contribution
of this very narrow component to the column density measured
with Herschel. This contribution should be especially large at
the border of the H ii regions where the line of sight tangentially
crosses the shell.
We thus chose to model the density structure of a shell sur-
rounding an H ii region, similar to that powered by the Mon R2-
IRS1 star. We used a density structure linearly increasing with
the radius, ρ(r)r(see Fig. 3) to mimic those suggested
by the calculations of H ii region expansion (Hosokawa & In-
utsuka 2005, 2006), giving more weight to the shell outer layers,
and a thickness of 0.002 pc as modeled by Pilleri et al. (2013,
Fig. D.1: Contribution of the shell to the column density pro-
file of the central UCH ii region. Its density radial extension is
given by the two dashed black lines. The column density result-
ing from the line of sight accumulation is illustrated by the black
solid line. The shell column density is then convolved with the
Herschel beams (colour dotted lines) to simulate the flux or col-
umn density of the shell (coloured solid lines) observable from
600(70 µm) to 3600 (500 µm) resolutions.
Fig.2). Pilleri et al. (2012, 2013) studied the shell of the central
Mon R2 UCH ii and considered two concentric slabs with ho-
mogeneous density, located at 0.08 pc around the Hii region.
In their model, the photo-dissociation region slab has a density
of 2 ×105cm3and a 6.5×104pc thickness, while the high-
density shell has a 3 ×106cm3density and a 103pc thickness.
We used the densities of these slabs to model the inner and outer
density values of the shell surrounding the central UCH ii region.
Figure D.1 shows the column density result of the central
UCH ii shell calculated with the assumptions above. The two ver-
tical dashed lines show the shell radial extension. Its projection
on the line of sight results in the idealised profile of this shell
(black solid line), flat towards the centre and sharply increasing
to the border. The shell was convolved with the Herschel beams
(see dotted coloured lines in Fig. D.1) to evaluate its contribu-
tion to the fluxes and column density profiles measured towards
this H ii region. The border increase due to the shell seen tangen-
tially is completely smeared out for all Herschel wavelengths
tracing the cold gas density, i.e. for λ160 µm (see Fig. D.1).
The column density profiles measured by Herschel have angular
resolutions too coarse (2500 and 3600), by factors of at least four.
On top of that, the mixing along the line of sight with other den-
sity components such as the envelope and background filaments
makes the centre-to-limb contrast of the shell to be rarely observ-
able. We thus cannot expect to resolve any shell around compact
or ultra-compact H ii regions located at 830 pc. In contrast in the
case of the extended northern H ii region, the relative contribu-
tion of the shell compared to the envelope is more important,
increasing the center-to-limb contrast and allowing a marginal
detection of the shell (see Fig. 8). Therefore, the shell is not a
dominant component of the column density structure of H ii re-
gions and their surroundings but it cannot always be neglected
for its complete bubbleing
A&A–MonR2RegHII, Online Material p 24
Appendix E: Column density dilution on the central
line of sight by shell
Appendix E.1: attenuation by shell in homogenous envelope
We assumed first the simple scenario of a bubble expanding in an
homogenous envelope and for which all the matter initially lo-
cated within a sphere with a RHii radius concentrates in the shell
located at this very same radius. According to numerical simu-
lations, the H ii region swept-up shells have small thicknesses,
Lshell <0.01 pc (e.g. Hosokawa & Inutsuka 2005). The almost
total mass transfer from the bubble to the shell thus leads to the
approximate equation:
Minitial =4
3πRHii
3×ρinitial
=Mshell '4πRHii
2Lshell ×ρshell,(E.1)
where ρinitial is the initial constant density of the envelope and
ρshell the shell density, assumed to be homogeneous. Using the
relation between ρshell and ρinitial given by Eq. E.1, the column
density of the shell, Σshell, measured along the line of sight to-
wards the centre of the region simply relates to that of the initial
gas sphere, Σinitial(r<RHii ), with homogeneous density ρinitial
and radius RHii through:
Σshell = Σobs =2×(Lshell ×ρshell)
'2×(RHii ×ρinitial /3) = Σinitial /3 (E.2)
The column density measured towards the center of H ii regions
with fully developed bubbles is thus expected to be divided by 3
compared to its original value .
ηshell =Σinitial
Σobs
=3.(E.3)
When approaching the border of the H ii region, the line of sight
is crossing a greater part of the shell and the column density
reaches higher values. However as shown in Appendix. D, the
very small size expected for the shell will result in a beam dilu-
tion with very small enhancement usually not observable.
In the case of an H ii region of radius RHii , not fully devel-
oped within an envelope of density ρinitial, to reach its external
radius, Renv, the contribution of the outer residual envelope, Σenv,
needs to be accounted for. The initial column density is now
Σinitial(r<Renv)=2×Renv ×ρinitial . The column density observed
towards the developed Hii bubble would thus be:
Σobs = Σshell + Σenv 'Σinitial /3×RHii
Renv
+ Σinitial ×Renv RHii
Renv
'Σinitial ×3×Renv 2×RHii
3×Renv
,(E.4)
and the decreasing factor or line-of-sight attenuation factor, η,
would be:
η=Σinitial
Σobs '3
32×RHii
Renv
.(E.5)
It can be noticed that for a fully extended H ii region which
reaches the size of the envelope RHii =Renv, the attenuation fac-
tor reaches 3, the value already obtained for the shell alone.
These purely geometrical attenuation factors are weak for the
small compact and ultra-compact H ii regions (η'1.1/1.2), but
start to be noticeable for the more extended northern H ii region
(η'1.5). We could estimated the density of the initial protostel-
lar envelope before the Hii region develops, ρinitial, by correcting
the mean density hρobsi, measured in Sect. 3.4.1 from observed
column density through Eq. 3. The density correction due the
geometrical eect of H ii region expansion is obtained by the
following relation: ρinitial ∼ hρobsi × η.
Appendix E.2: attenuation in envelope of decreasing density
In the more realistic case of an envelope with a decreasing den-
sity gradient, it is expected that the attenuation factor of the col-
umn density by H ii bubbles, η, should be larger than in the case
of a constant-density envelope and constantly increasing as the
Hii region expands.
The mass collected in the shell for the expansion of the
Hii region at a radius RHii is given by Eq. A.2. The density in
the shell of thichness Lshell is then,
ρshell =M(RHii)
4πR2
HiiLshell
=ρ1R1q
Hii
(3 q)×Lshell
the column density observed for this shell at small impact pa-
rameter, near the H ii region center is then :
Σshell (RHii)=ρshell ×Lshell =ρ1
R1q
Hii
3q
The initial value of the column density was
Σinitial (RHii)=ZRHii
0
ρ(r)dr =ZRHii
0
ρ1rqdr =ρ1
R1q
Hii
1q(E.6)
this relation is valid only for q<1 when the value of R1qnear
0 is negligeable. The attenuation by the shell is given by
ηshell =Σinitial
Σobs
=3q
1q.(E.7)
For constant density envelope (q=0) Eq. E.3 is recovered.
To evaluate the attenuation with an existing residual outer
envelope we have to calculate the corresponding column density
contribution,
Σenv (RHii)=ZRenv
RHii
ρ(r)dr =ρ1
1qR1q
env
1 RHii
Renv !1q
(E.8)
then
η=Σinitial (Renv)
Σobs
=Σinitial (Renv)
Σshell (RHii)+ Σenv (RHii)
will give after some calculations
η=3q
32×RHii
Renv 1qq
(E.9)
For a shell reaching the size of the envelope RHii =Renv, Eq. E.9
resumes to Eq. E.7 obtained for the shell alone, and for a constant
density envelope (q=0) it resumes to Eq. E.5
These relations are only valid for q<1, due to the singularity
at origin of the density distribution.
A&A–MonR2RegHII, Online Material p 25
Appendix E.3: attenuation in envelope of decreasing density
with a constant density core
To avoid the singularity at the origin we need to use the density
profil define by Eq.A.5 with a central core of constant density
ρc, and a size of rc.
Following the same calculation as above they give for:
the mass
M(R)=ZR
0
ρ(r)V(r)dr
=Zrc
0
ρ(r)V(r)dr +ZR
rc
ρ(r)V(r)dr
=4πρ1R3q
3q 1q
3rc
R3q!(E.10)
the density in the shell
ρshell =M(RHii)
4πR2
HiiLshell
the shell column density near the center of the H ii region
Σshell (RHii)=ρshell ×Lshell =M(RHii )
4πR2
Hii
=ρ1R1q
3q
1q
3 rc
RHii !3q
(E.11)
the initial value of the column density
Σinitial (RHii)=ρ1R1q
Hii
1q
1q rc
RHii !1q
(E.12)
and then the attenuation by the shell
ηshell =Σinitial
Σobs
=3q
1q×1q(rc/RHii)1q
1q
3(rc/RHii)3q(E.13)
All these relations reduces to the equivalent one of previous sec-
tion for rc=0.
The same calculations as before concerning an existing
residual outer envelope are still applicable here. As showed by
Franco et al. (1990) shell develop only for q<1.5, so q<3 and
the terms rc
RHii 3qin the equations above are always negligible.
Then the calculations give for the attenuation
η=3q
32×RHii
Renv 1qq×
1q rc
RHii !1q
(E.14)
and for rc=0 we recover Eq. E.9
The application to the northern H ii region with appropriate
values of the dierent parameters gives an attenuation factor η'
25, which becomes 100 when the H ii region expansion reaches
the size of the envelope (RHii =Renv).
The formal treatment of the case of the Compact and UC
Hii regions would require to take into account an envelope with
two density gradient, but the attenuation would be as ecient
as for the northern extended H ii region once expansion of these
region would occur.
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It is noted that the Lyman continuum radiation from a cluster of OB stars will drive ionization (I) fronts into nearby neutral material and that an I front should be preceeded by a shock (S) front as it moves into an adjacent molecular cloud near dense nebulae. The gravitational stability of the high-density layer of neutral gas that accumulates between the I and S fronts is investigated to determine whether star formation is likely to occur there. The results show that the shocked neutral layer will become gravitationally unstable after several million years for I-S fronts propagating into molecular clouds of moderate density and that the stars which may form as the layer collapses are likely to be more massive than those which form in unshocked remote parts of the same molecular cloud. It is found that if the stars which eventually form in the shocked layer are OB stars, a new system of I-S fronts will propagate into the remaining cloud after these stars reach the main sequence, and another cycle of OB star formation will be initiated. It is therefore proposed that massive OB stars may be formed in sequential bursts during the lifetime of some large molecular clouds.
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An effort is described to model detailed CO observations of the spatially well-resolved and highly collimated bipolar outflow associated with Mon R2. The models indicate that the extent to which the outflows appear bipolar on the sky depends predominantly on the structure of the velocity field of the outflowing gas. Two of the outflow lobes are very well fitted by a paraboloidal shell model. The model which best fits the velocity structure of the outflow is one whose velocity field is characterized by a velocity power law in which v is proportional to R. Velocity sorting of initially clumpy flow gas due to entrainment by a wind or perhaps an explosion probably gives rise to the observed power law.