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Astronomy & Astrophysics manuscript no. Kainulainen c© ESO 2009
November 30, 2009
Letter to the Editor
Probing the evolution of molecular cloud structure:
From quiescence to birth
J. Kainulainen1 , H. Beuther1, T. Henning1, and R. Plume2
1 Max-Planck-Institute for Astronomy, Ko¨nigstuhl 17, 69117 Heidelberg, Germany
e-mail: [jtkainul, beuther, henning]@mpia-hd.mpg.de
2 Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
e-mail: plume@ras.ucalgary.ca
Received ; accepted
ABSTRACT
Context. Probability distribution of densities is a fundamental measure of molecular cloud structure, containing information on how
the material arranges itself in molecular clouds.
Aims. We derive the probability density functions (PDFs) of column density for a complete sample of prominent molecular cloud
complexes closer than d . 200 pc. For comparison, additional complexes at d ≈ 250 − 700 pc are included in the study.
Methods. We derive near-infrared dust extinction maps for 23 molecular cloud complexes, using the nicest colour excess mapping
technique and data from the 2MASS archive. The extinction maps are then used to examine the column density PDFs in the clouds.
Results. The column density PDFs of most molecular clouds are well-fitted by log-normal functions at low column densities (0.5 mag
< AV . 3 − 5 mag, or −0.5 < ln AV/AV . 1). However, at higher column densities prominent, power-law-like wings are common.
In particular, we identify a trend among the PDFs: active star-forming clouds always have prominent non-log-normal wings. In
contrast, clouds without active star formation resemble log-normals over the whole observed column density range, or show only low
excess of higher column densities. This trend is also reflected in the cumulative forms of the PDFs, showing that the fraction of high
column density material is significantly larger in star-forming clouds. These observations are in agreement with an evolutionary trend
where turbulent motions are the main cloud-shaping mechanism for quiescent clouds, but the density enhancements induced by them
quickly become dominated by gravity (and other mechanisms) which is strongly reflected by the shape of the column density PDFs.
The dominant role of the turbulence is restricted to the very early stages of molecular cloud evolution, comparable to the onset of
active star formation in the clouds.
Key words. ISM: clouds – ISM: structure – Stars: formation – dust, extinction – evolution
1. Introduction
Star formation takes place exclusively in molecular clouds, or
more precisely, in the most extreme density enhancements of
those clouds. In the current view, the structure of molecular
clouds, and thereby the occurrence of the density enhancements,
is heavily affected by the motions induced by supersonic turbu-
lence (e.g. Scalo et al. 1998). In parallel, the cloud structure is
also crucially affected by the self-gravity of gas and magnetic
fields inside the clouds. The relative strengths of these cloud-
shaping mechanisms are currently under lively debate and re-
garded as one of the critical open questions in the physics of the
interstellar medium (for reviews, see Mac Low & Klessen 2004;
McKee & Ostriker 2007).
The impact of supersonic turbulence for molecular cloud
structure is concretely evidenced by the structural characteristics
of molecular clouds that seem to agree with theoretical predic-
tions and numerical simulations of such turbulence (see e.g. §2.1
in McKee & Ostriker 2007). One particularly important statisti-
cal property is the probability distribution of densities, which
describes the probability of a volume dV to have a density be-
tween [ρ, ρ + dρ]. This distribution is expected to take a log-
normal shape in isothermal, turbulent media not significantly af-
fected by the self-gravity of gas (e.g. Va´zquez-Semadeni 1994;
Padoan et al. 1997; Ostriker et al. 1999). The function plays a
fundamental role in current theories of star formation: it is used
to explain among others the initial mass function of stars, and
the star formation rates and efficiencies of molecular clouds (e.g.
Padoan & Nordlund 2002; Elmegreen 2008).
The log-normality of the probability distributions of den-
sity is reflected also in column densities computed from sim-
ulations (e.g. Ostriker et al. 2001; Va´zquez-Semadeni & Garcı´a
2001; Federrath et al. 2009). Unfortunately, measuring column
densities in molecular clouds is a challenge in astrophysics in
itself. The commonly used methods for deriving column densi-
ties, i.e. measurements of CO line emission, thermal dust emis-
sion, and dust extinction, suffer from various model-dependent
effects, and often probe only narrow ranges of physical condi-
tions (e.g. Goodman et al. 2009; Vasyunina et al. 2009).
For the most nearby molecular clouds, dust extinction mea-
surements in the near-infrared provide sensitivity over a rela-
tively wide dynamical range, starting from N(H2 + H) & 0.5 ×
1021 cm−2 (Lombardi et al. 2006). The highest measurable col-
umn densities depend on the limiting magnitude of near-infrared
data available; using e.g. 2MASS data, column densities of
∼ 25 × 1021 cm−2 are reached (e.g. Kainulainen et al. 2006;
Lombardi et al. 2006). This broad range, together with the in-
dependency of such data on the dust temperature, makes dust
extinction mapping a viable method to study the large-scale,

2 J. Kainulainen et al.: Probing the evolution of molecular cloud structure:
lower-density regions of molecular clouds and thereby to test
the predictions from simulations of supersonic turbulence.
In this Letter, we present the first results of a study where
we utilise a novel near-infrared dust extinction mapping method
to study the structural parameters in a large sample of nearby
molecular clouds. In this paper, we focus on the column den-
sity PDFs in the clouds, the presentation of the maps and fur-
ther analysis is left to a forthcoming paper (Kainulainen et al.
in prep.). Our cloud sample forms a complete set of promi-
nent cloud complexes within 200 pc that have an extent of more
than ∼ 4 pc, or are roughly more massive than ∼ 103 M. For
comparison, the sample includes some additional clouds up to
d ≈ 700 pc. The method we adopt allows us to determine the
column densities over a range that extends to significantly higher
column densities than can be probed by CO line emission (due
to the freeze-out of molecules), enabling study of the structural
parameters in a regime not widely accessed before.
2. Extinction mapping method
We employed the near-infrared dust extinction mapping tech-
nique nicest (Lombardi 2009) to derive extinction maps of
nearby molecular clouds. The method was used in conjunction
with JHKS band photometric data from 2MASS (Skrutskie et al.
2006). In nicest, the near-infrared colours of stars, shining
through molecular clouds, are compared to the colours of stars
in a nearby reference field that is free from extinction and in
which the brightness distribution of stars is similar to the on-
cloud region. This comparison yields estimates of near-infrared
extinction towards the stars in the molecular cloud region. The
extinction values are then used to compute a spatially smoothed
map of extinction through the cloud. In the following, we intro-
duce our practical implementation of the method. For the further
description of the method itself, we refer to Lombardi & Alves
(2001) and Lombardi (2009) (see also Lombardi 2005).
We applied nicest to several fields covering previously
known molecular cloud complexes. The clouds included in the
study are listed in Table 1. As an example, Fig. 1 shows the ex-
tinction map of the Taurus complex. In order to directly com-
pare the maps of different clouds, their physical resolution was
selected to be 0.1 pc (2′ at 170 pc distance). This selection corre-
sponds to the Jeans length for a core at T = 15 K and n = 5×104
cm−3. The distances adopted for the clouds are listed in Table 1.
For the most clouds farther away than 200 pc, we used a physical
resolution of 0.6 pc. The PDFs of these clouds are not directly
comparable to those whose resolution is 0.1 pc.
Stars that are either embedded inside the cloud or on the fore-
ground with respect to it can bias the derived extinction. To min-
imize the contribution of such sources, we used catalogues of
previously identified cloud members from the literature to di-
rectly remove sources. In addition, we used the “sigmaclipping”
iteration, i.e. each source towards which the estimated extinc-
tion differed by more than 5-sigma from the local average was
removed from the sample. Another possible source of bias in
the data is that the background stellar density varies among the
clouds, according to their galactic coordinates. We investigated
the possible effect of this on the PDFs by degrading the back-
ground stellar density of some clouds that are close to the galac-
tic plane and recomputing the extinction maps. As these experi-
ments had no impact on the results shown in Sect. 3, we did not
include any correction for the differences.
The noise in the extinction maps depends on the galactic co-
ordinates and on extinction. Typically, the 3σ-error at low col-
umn densities is 0.5 − 1.5 mag. The extinction measurements
“saturate” at about AV = 25 mag. We note that the fractional
area where AV & 25 mag is small and we are not likely to signif-
icantly miss mass due to an inability to probe higher extinctions.
3. The column density PDFs for nearby clouds
Figure 2 shows the mean-normalised PDFs of logarithmic col-
umn densities for four clouds of the study. Figures 4-6 show
the PDFs for 19 other clouds (online only). In these figures and
throughout this Letter, we have divided our sample in active and
non-active star-forming clouds based on the presence of con-
firmed young stellar objects in the clouds.
Qualitatively, most PDFs show a log-normal-like peak, fol-
lowed by a power-law-like extension at higher column densities.
The strength of the extension varies, being dominant for some
clouds (e.g. Taurus) and absent for others (e.g. Coalsack). For
some clouds, the PDF differs from a log-normal shape also at
very low column densities (see Sect. 4). Directed by theoretical
predictions, we fitted the peaks of the PDFs using log-normal
functions:
p(s) ∼ exp
[
−
(ln AV/AV − m)2
2σ2
]
, (1)
where AV is the mean extinction, and m and σ are the scale and
dispersion in logarithmic units. The fits are shown in Figs. 2 and
4-6. Since it is evident that most PDFs are not well fitted by
log-normals over their entire range, the fit was typically made
over the range s = [−0.5, 1]. The dispersions of the fitted log-
normal functions are shown in Table 1, and they span the range
σs ≈ 0.3 − 0.5. Table 1 also shows the total mass , and the mean
and standard deviation of the pixels above AV = 0 mag. The
total mass was calculated by summing up the extinction values
in the map above AV = 0.5 mag and adopting the standard ratio
of N(H2 + H)/AV = 9.4 × 1020 cm−2 (Bohlin et al. 1978).
Another interesting form of the PDFs is the cumulative form
of the pixel probability distribution, describing the fractional
mass enclosed by an isocontour as a function of column den-
sity (or more precisely, the survival function). The cumulative
PDFs are shown in Fig. 3 for all the clouds of the study. In
this figure, the active star-forming clouds are separated from
quiescent clouds. Clearly, the fraction of mass in high column
density regions is higher in star-forming clouds than in clouds
without star formation. We approximated the average cumula-
tive functions for these two classes as a simple mean of all the
clouds in the class, which resulted in the relation (N/Npeak)SF ≈
(N/Npeak)0.4non−SF. For example, the star-forming clouds then have
roughly one order of magnitude more mass above AV = 5 mag
than non-star-forming clouds and more than three orders of mag-
nitude above AV = 15 mag.
4. Discussion and conclusions
While supersonic turbulence is expected to develop a density
PDF close to a log-normal distribution, prominent deviations
from that shape are predicted in strongly self-gravitating sys-
tems (e.g. Klessen 2000; Federrath et al. 2008). Recent obser-
vational studies have indeed indicated that the column density
PDFs of molecular clouds are close to log-normal distributions.
For example, Lombardi et al. (2006, 2008a) examined the col-
umn density PDFs in the Pipe, Rho Oph, and Lupus molecular
clouds. They concluded that the PDF of Ophiuchus is satisfacto-
rily fitted by a log-normal function, while the PDF of Lupus is
extremely well fitted by it. However, the PDF of Pipe required

J. Kainulainen et al.: Probing the evolution of molecular cloud structure: 3
Fig. 1. Left: Wide-field extinction map of the Taurus molecular cloud complex covering ∼ 7.5◦ × 7.5◦ (∼ 18× 18 pc at d = 140 pc).
The FWHM resolution of the map is 2.4′. Right: The same, but in logarithmic scaling highlighting the low column density regions.
The contour at AV = 4 mag shows the region above which the column density PDF differs from the simple log-normal form. The
crosses show the embedded population of the cloud as listed by Rebull et al. (2009) (colour figures given in the online version).
Fig. 2. Left: Probability density functions (PDFs) of the column density for the non-star-forming clouds Lupus 5 and Coalsack.
Right: The same for the active star-forming clouds Taurus and Lupus 1. The error bars show the
√
N uncertainties. Solid lines show
the fits of log-normal functions to the distributions around the peak, typically over the range ln Av/AV = [−0.5, 1]. The dispersions
of the fitted functions are shown in the panels. The x-axis on top of the panels shows the extinction scale in magnitudes. The vertical
dashed line shows the upper limit of extinction values probed by the extinction mapping method. Similar plots for 19 other clouds
are shown in Figs. 4-6 (online only).
Fig. 3. Cumulative forms of the PDFs shown in Figs. 2 and 4-6.
The curves show the fractional mass above the certain extinction
threshold (abscissae). Solid blue lines are for clouds that show
active star formation and dotted red lines for clouds without ac-
tive star formation.
four log-normal functions, which they suggested originated from
physically distinct components along the line of sight.
The column density PDFs presented in this Letter show that
simple log-normal functions fit the PDFs poorly when con-
sidering the whole observed column density range, i.e. N =
0.5 − 25 × 1021 cm−2. As seen in Figs. 2 and 4-6, the PDFs of
most clouds deviate from simple log-normality at s & 0.5− 1, or
AV & 2 − 5 mag. Even though the log-normals fit the peaks of
the PDFs well, the excess “wings” at higher column densities are
persistent features of the molecular cloud structure. Likewise,
about half of the clouds show non-log-normal features at low
column densities. It is, however, difficult to ascertain whether the
low column density features are real. It is quite possible that they
are mostly residuals caused by other, physically distinct clouds
along the line of sight. Nevertheless, they can also be real signa-
tures of cloud structure; non-log-normal features at low column
densities have been predicted, related to intermittent fluctuations
in turbulent media (e.g. Federrath et al. 2009). We note that the
number of pixels in the non-log-normal, higher extinction parts
is not small. In fact, the threshold above which the wings be-
come prominent (AV & 2 − 5 mag) is rather low, suggesting that
material related to star formation is dominantly located in the
non-log-normal part of the PDF. This is illustrated in the right
panel of Fig. 1 which shows the extinction map of Taurus with
a contour at AV = 4 mag highlighting the regions belonging to
the non-log-normal wing of the PDF. The figure also shows the

4 J. Kainulainen et al.: Probing the evolution of molecular cloud structure:
Table 1. Molecular cloud properties and the derived parameters
Cloud Da MH2 × 104 AV σdata σ f it NYSOb
Star-forming clouds, physical resolution 0.1 pc
Ophiuchus 1191 0.6 2 4.3 0.48c 300
Taurus 1402 0.81 1.8 1.5 0.49 300
Serpens 2593 3.6 3 2.4 0.51 300
Cha I 1654 0.23 1.3 1.3 0.35 200
Cha II 1504 0.15 1.3 1.0 0.35 50
Lupus III 1551 0.11 1.3 0.9 0.35c 50
CrA cloud 1295 1.2 0.8 1.0 0.44 tens
Lupus I 1551 0.29 1.0 0.7 0.43 tens
LDN1228d 2006 0.23 1.1 0.7 0.32 tens
Pipe 1307 0.95 2.5 1.4 0.29c 15
LDN134 1008 0.13 1.2 0.6 0.39 a few
LDN204d 1191 0.43 1.9 0.8 0.41 a few
LDN1333d 1809 0.57 1.2 0.5 0.38 a few
Non-star-forming clouds, physical resolution 0.1 pc
LDN1719d 1204 0.53 0.6 0.7 0.50
Musca 1504 0.07 1.0 0.7 0.45
Cha III 1504 0.18 1.3 0.8 0.46
Coalsack 15010 0.5 2.7 1.4 0.28
Lupus V 1551 0.36 1.4 0.7 0.42
Star-forming clouds, physical resolution 0.6 pc
Ori A GMC 45011 11 1.4 2.8 0.5 > 2000
Per cloud 26012 2.0 1.7 1.7 0.49 > 100
Ori B GMC 45011 9.0 1.2 1.7 0.59 > 100
Cepheus A 73013 3.5 1.5 1.6 0.47 > 100
California 45014 11 1.4 0.7 0.51 tens
a References: (1) Lombardi et al. (2008b) (2) Torres et al. (2007) (3)
Straizˇys et al. (1996) (4) Knude & Hog (1998) (5) Casey et al. (1998)
(6) Kun (1998) (7) Lombardi et al. (2006) (8) Mattila (1979) (9)
Obayashi et al. (1998) (10) Corradi et al. (1997) (11) Burrows et al.
(1993) (12) Cernis (1993) (13) Crawford et al. (1970) (14) Lada et al.
(2009).
b An order-of-magnitude estimate of the pre-main-sequence star pop-
ulation in the clouds, based on Reipurth (2008).
c No good fit was achieved. A rough estimate is given for reference.
d The most prominent Lynds dark nebula in the region.
known pre-main-sequence stars that clearly concentrate on the
regions of high column density (Rebull et al. 2009).
Intriguingly, our data appear to show a clear trend. All clouds
with active star formation show strong excess of higher column
densities (Figs. 2 and 4). In contrast, almost all quiescent clouds
have PDFs that either are well described by log-normal func-
tions over the entire column density range, or show relatively
low excess of high column densities (Figs. 2 and 5). The trend
is obvious for the lower-mass clouds in our sample, but an indi-
cation of it is seen also among the more massive clouds (Fig. 6):
the active star-forming clouds of Orion have prominent wings
compared to the California nebula, a massive cloud with sig-
nificantly lower star-forming activity (Lada et al. 2009). In the
context of turbulent molecular cloud evolution, these observa-
tions are in agreement with a picture in which the structure of a
molecular cloud in the early stage of its evolution is decisively
shaped by turbulent motions. Hence, its column density PDF is
close to log-normal, like it is the case for the non-active clouds
in our sample. As the cloud evolves, prominent local density en-
hancements can become self-gravitating, which also assembles a
growing fraction of the gas to higher column density structures.
This significantly alters the simple log-normal form of the col-
umn density PDF, and is very concretely demonstrated by the cu-
mulative forms of the PDFs (Fig. 3), showing how dramatically
the fraction of material at high column density increases from
non-active to active clouds. The cumulative PDFs shown in Fig.
3 generalize this trend, suggested earlier by studies of individual
cloud complexes (Cambre´sy 1999; Lombardi et al. 2006, 2008a;
Lada et al. 2009). In the low column density regions of molec-
ular clouds turbulent motions prevail as the dominant structure-
shaping mechanism, as indicated by the log-normal-like parts of
the PDFs. This appears natural, since those are likely to be the
regions where the role of self-gravity remains small.
In this Letter, we have characterised the shape of the column
density PDFs in nearby molecular clouds and demonstrated the
prevalence of non-log-normalities in them. From the PDFs, we
identified a trend that is in agreement with a picture where self-
gravity has a significant role in shaping the cloud structure start-
ing from a very early stage, corresponding to the formation of
first stars in the cloud. An immediate question following these
observations is to what extent similar features are present in the
simulations of supersonic turbulence. This can be directly ad-
dressed by a comparison of our data to simulations that include
self-gravity and follow the evolution of cloud structure as a func-
tion of time (e.g. Offner et al. 2008; Banerjee et al. 2009). The
data presented in this Letter provide a unique set for this pur-
pose, and we are going to address this in a forthcoming paper.
Acknowledgements. The authors would like to thank the referee, L. Cambre´sy,
for the comments that improved the paper, and C. Federrath, R. Banerjee, M.-
M. Mac Low, and R. Klessen for hepful discussions. This research has made
use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet
Propulsion Laboratory, California Institute of Technology, under contract with
the National Aeronautics and Space Administration. This publication makes use
of data products from the Two Micron All Sky Survey, which is a joint project
of the University of Massachusetts and the Infrared Processing and Analysis
Center/California Institute of Technology, funded by the National Aeronautics
and Space Administration and the National Science Foundation.
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J. Kainulainen et al.: Probing the evolution of molecular cloud structure:, Online Material p 1
Fig. 1. Left: Wide-field extinction map of the Taurus molecular cloud complex covering ∼ 7.5◦ × 7.5◦ (∼ 18× 18 pc at d = 140 pc).
The FWHM resolution of the map is 2.4′. Right: The same, but in logarithmic scaling highlighting the low column density regions.
The contour shows the value of AV = 4 mag above which the column density PDF differs from the simple log-normal form. The
crosses show the embedded population of the cloud as listed by Rebull et al. (2009) (colour figures given in the online version).

J. Kainulainen et al.: Probing the evolution of molecular cloud structure:, Online Material p 2
Fig. 4. Probability density functions (PDFs) of a normalised column density for 13 star-forming clouds in the study. The error bars
show the
√
N uncertainties. Solid lines show the fits of lognormal functions to the distributions around the peak, typically over the
range ln Av/AV = [−0.5, 1]. The dispersion of the fitted function is shown in the panels. For some clouds, no reasonable fit was
achieved over any AV range. For those clouds, we show for a reference a function approximating the shape using a dotted line. The
x-axis on top of the panels shows the extinction scale in magnitudes.

J. Kainulainen et al.: Probing the evolution of molecular cloud structure:, Online Material p 3
Fig. 5. Same as Fig. 4, but for clouds we classify as clouds not containing active star formation.
Fig. 6. Same as Fig. 4, but for clouds at varying distances of 250-700 pc. The PDFs are smoothed to the common physical resolution
of 0.6 pc. For Cepheus, two equally good fits are shown.