Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.arcetri.astro.it/~fmassi/papers/clustvela.upd.ps.gz Äàòà èçìåíåíèÿ: Thu Nov 15 12:54:48 2001 Äàòà èíäåêñèðîâàíèÿ: Sat Dec 22 05:33:04 2007 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: coma

A&A manuscript no.
(will be inserted by hand later)
Your thesaurus codes are:
08.06.2; 08.16.5; 13.09.6; 09.09.1
ASTRONOMY
AND
ASTROPHYSICS
October 26, 1999
Star Formation in the Vela Molecular Clouds
IV. Young embedded star clusters towards D­cloud Class I sources ?
F. Massi 1;2 , D. Lorenzetti 1;3 , T. Giannini 1;2;3 , and F. Vitali 1
1 Osservatorio Astronomico di Roma, Via Frascati 33, I­00040 Monteporzio C. (Rome), Italy
2 Istituto Astronomico, Universit`a ``La Sapienza'', Via Lancisi 29, I­00161 Rome, Italy
3 CNR ­ Istituto di Fisica dello Spazio Interplanetario, Area di Ricerca Tor Vergata, Via Fosso del Cavaliere, I­00133 Rome,
Italy
Received ; Accepted
Abstract. We study the association between embedded
star clusters and young stellar objects believed to be pre­
cursors of intermediate mass stars (2 ! ¸ M ! ¸ 10 M fi ),
within the Vela Molecular Ridge D­cloud. A sample of
12 IRAS­selected Class I sources belonging to the region
was imaged in the near infrared bands JHK and the pho­
tometry used in order to gain information on the stellar
population around these objects. We find a large fraction
of sources with a NIR excess, particularly within fields lo­
cated towards higher luminosity protostars (L bol ? ¸ 10 3
L fi , meaning M ? ¸ 5 M fi according to accretion mod­
els), indicative of the presence of a large number of less
massive young stellar objects. An analysis of the K­source
surface density confirms that the higher luminosity Class I
sources are embedded in young clusters of sizes ¸ 0:1 \Gamma 0:3
pc and volume densities ? ¸ 3000 \Gamma 12000 stars pc \Gamma3 . Con­
versely, the lower luminosity Class I sources (L bol ! 10 3
L fi , i. e., M ! ¸ 5 M fi ) are associated with small groups
of young stellar objects or isolated. This indicates that
intermediate mass star progenitors lie in clusters whose
member richness increases with the progenitor mass it­
self. The Class I sources appear as the most massive and
less evolved objects in the clusters and tend to be located
near the star surface density peaks, suggesting a mass and
age segregation which may be partly explained by models
of competitive accretion. The K luminosity functions of
the clusters are indicative of populations of coeval stars
10 5 --10 6 yr old roughly distributed according to the field
stars initial mass function. A scenario in which clusters
are formed by contraction and fragmentation of molecu­
lar cores, with less massive stars first leaving the birthline,
is proposed.
Key words: Stars: Formation -- Star: Pre­Main Sequence
--Infrared: Sources --ISM: Individual objects (Vela Clouds)
Send offprint requests to: F. Massi
? Based on observations collected at the European Southern
Observatory, Chile
Correspondence to: massi@coma.mporzio.astro.it
1. Introduction
Observational data have pointed out that high mass stars
do not form in isolation but rather tend to be embedded in
clusters, whereas the birth of relatively isolated low mass
stars (M ! ¸ 2 \Gamma 3 M fi ) has been documented in nearby
dark cloud complexes such as ae Ophiuchi and Taurus. Al­
though the main physical processes governing the collapse
of gas and dust clumps and the growth of a single star are
now becoming to be understood, the theoretical picture
fails to account for the origin of aggregates of stars. This
means that, so far, useful information on this topic had to
be gathered through observations. Many authors already
noted the strict association of high mass stars with stellar
density enhancements (e. g., Carpenter et al. 1993, Hil­
lenbrand 1994, Hillenbrand 1995, Hillenbrand et al. 1995),
but it is noteworthy to quote the work of Testi et al. (1997,
1998, 1999) who, carrying out a systematic survey in the
Near Infrared (NIR) bands J , H and K, have shown ev­
idence of source clustering towards Herbig Ae/Be stars,
finding an increase in stellar content from later to earlier
spectral types. As known, these objects are intermediate
mass stars (2 ! ¸ M ! ¸ 10 M fi ) still in their pre­main se­
quence contraction phase; since such young stars are em­
bedded in highly extincted regions, NIR imaging is instru­
mental in disclosing the presence of fainter companions as
reddening is a lesser problem at these wavelengths (e. g.,
AK ¸ 0:1A V ; see Rieke & Lebofsky 1985).
At the same time, NIR surveys of young embedded
clusters are growing more and more numerous (for a com­
prehensive list see Meyer et al. 1999, Clarke et al. 1999,
Elmegreen et al. 1999); some of these studies rely on the
determination of the K luminosity function (KLF) in or­
der to extract information on age, history and initial mass
function (IMF) of the clusters (see, e. g., Lada & Lada
1995). Despite the number of free parameters and the
problems related to both extinction and the statistical

2 F. Massi et al.: Star Formation in the Vela Molecular Clouds
determination of a reliable control KLF (accounting for
foreground and background field stars) to be subtracted
from the observed one in order to obtain the cluster KLF,
this appears as a fast and simple diagnostic tool.
The aim of the present study was to search for clus­
tering evidence in the earliest phases of intermediate mass
stellar evolution and probe the physical properties of very
young aggregates of stars. In this respect, so­called Class
I sources (Lada & Wilking 1984) are thought to repre­
sent protostars still accreting mass (Adams et al. 1987),
thus in an evolutionary phase preceding the pre­main se­
quence contraction of T­Tauri and Herbig Ae/Be stars,
although not in the main accretion phase. The latter, fea­
turing objects also referred to as ``Class 0 sources'', is in
fact extremely short­lived and yields much smaller sam­
ples even within a whole molecular cloud complex. Also,
Class 0 sources are more prominent at mm and sub­mm
wavelength but quite faint in the NIR, thus preventing
their detection at the shorter wavelengths.
Liseau et al. (1992) and Lorenzetti et al. (1993; hereby,
Paper I and Paper II, respectively) built a catalogue of
Class I sources within the Vela Molecular Ridge (VMR)
based on the IRAS Point Source Catalogue (PSC) and
subsequent NIR observations. The VMR is a complex lo­
cated in the southern sky which is composed of at least 3
molecular clouds (named A, C and D) at a distance ¸ 700
pc, and a molecular cloud (named B) at ¸ 2000 pc (see e.
g., Murphy & May 1991 and Paper I). The criteria driving
the source selection are discussed in Paper I and II; at last,
a complete sample of bona fide Class I sources associated
with the VMR down to a limiting flux F š (12¯m) = 1 Jy
in the – = 12 ¯m IRAS band (roughly corresponding to a
lower mass M ? ¸ 1 M fi ) is available. The critical issue that
Far­infrared (FIR) emission could arise from multiple ob­
jects within the somewhat large (¸ 1 0 ) IRAS beam, rather
than a single one, was already addressed in Paper II and
suggested the motivation for this work. In a previous pa­
per (Massi et al. 1999, hereby Paper III), we reported and
commented photometry on JHK images of the 12 Class
I sources belonging to the VMR­D cloud; there we began
to study the star crowding towards the IRAS sources con­
cluding that probably, in most of the fields, FIR emission
is originated by a single young stellar object (YSO), or an
unresolved close pair of them, thus we could find the NIR
counterparts of the IRAS sources.
A study of this sample can benefit from the fact that
all of the 12 sources formed within the same molecular
cloud, hence all of them share the same distance, which
is 700 \Sigma 200 pc, as widely discussed in Paper I. A major
concern is posed by extinction differences both towards
different fields and within a same area, as well, so that a
given mass does not correspond to a fixed NIR magnitude.
Then, also at these wavelengths where reddening is much
reduced, deep surveys are needed in order to completely
sample embedded star populations. Furthermore, for pre­
main sequence stars the luminosity­mass relation depends
on age, with the younger sources displaying higher NIR
fluxes. The occurence of colour excess at these wavelengths
may complicate the picture, too. Hence, the NIR limiting
magnitude for a given mass is also a function of distance,
extinction and age; as a result, the embedded star popula­
tions towards the 12 fields are not homogeneously sampled
because the JHK limiting magnitudes in our images are
roughly the same, whereas ages and extinction are dif­
ferent. On a theoretical point of view, we must also ac­
count for the fact that a comparison of NIR data with
evolutionary tracks is affected not only by the uncertain­
ties inherent in the adopted models, but also by the need
to convert the (time dependent) mass­luminosity relation
into NIR fluxes.
In the present paper, we use the JHK photometric
data reported in Paper III and carry out an in­depth ex­
amination of clustering and stellar populations towards
Class I sources in the VMR­D cloud. Observations and
data reduction are summarized in Sect. 2, whereas Sect. 3
is devoted to the results and data analysis (colour­colour
diagrams, KLF's), which are subsequently discussed in
Sect. 4; our main conclusions are listed in Sect. 5.
2. Observations and data reduction
We selected 12 fields known to contain moderately lumi­
nous [120 ! ¸ L bol =L fi ! ¸ 5600] Class I sources (see Paper
III); so far, these represent a complete flux limited sample
(F š (12¯m) ? 1 Jy) of IRAS selected Class I sources asso­
ciated with the VMR­D molecular cloud. The Spectral En­
ergy Distributions (SED's) were derived in Papers I, II and
III based on IRAS data, mm observations and NIR pho­
tometry. The JHK images were taken in February 1993
on the ESO/MPI 2.2m telescope at La Silla (Chile) with
the IRAC­2 near infrared camera (Moorwood et al. 1992).
Observational techniques, data reduction and photometry
are described in Paper III; for each field, a 2 \Theta 1:6 arcmin 2
frame is available in each of the J , H and K bands. The
limiting magnitudes are J ¸ 18:5 mag, H ¸ 18:0 mag
and K ¸ 17 mag, whereas we estimated a completeness
limit K compl ¸ 15:5 mag (see Paper III). In the follow­
ing, sources with K ! K compl will be referred to as lying
below the completeness limit. The coordinates of the im­
aged fields are given in Table 1, along with IRAS names
and the designation according to the internal classification
adopted in Papers I, II and III.
In order to obtain a field (control) KLF, five refer­
ence sky areas (indicated by us as ref1, ref2, ref3, ref7
and ref8) were imaged in January 1998 with the IRAC­2b
camera at the ESO/MPI 2.2m telescope using the K fil­
ter. These were randomly chosen such as to be located to­
wards the VMR but far from the IRAS sources, in regions
of lower CO(1--0) integrated emission (i.e., lower extinc­
tion), and their locations are indicated in Table 1. For each
field, 3 (dithered) frames of the object and 3 of near skies
were taken with total on­source (and off­source) integra­

F. Massi et al.: Star Formation in the Vela Molecular Clouds 3
Table 1. Coordinates and designations of the observed fields.
IRAS ff(1950.0) ffi(1950.0) Internal
name designation
h m s ffi 0 00
08328­4314 08 32 49.8 ­43 14 15 IRS 62
08375­4109 08 37 31.8 ­41 09 14 IRS 13
08393­4041 08 39 23.4 ­40 41 18 IRS 63
08404­4033 08 40 27.0 ­40 33 22 IRS 14
08429­4055 08 42 54.4 ­40 55 44 IRS 66
08445­4420 08 44 35.6 ­44 20 14 IRS 67
08448­4343 08 44 49.4 ­43 43 27 IRS 17
08470­4243 08 47 00.0 ­42 43 12 IRS 18
08470­4321 08 47 01.3 ­43 21 15 IRS 19
08476­4306 08 47 39.4 ­43 06 01 IRS 20
08477­4359 08 47 47.1 ­43 59 34 IRS 21
08500­4254 08 50 01.2 ­42 54 11 IRS 71
­ 08 39 30.0 ­40 30 00 ref7
­ 08 44 40.0 ­42 56 00 ref3
­ 08 44 50.0 ­43 33 00 ref1
­ 08 47 00.0 ­43 11 00 ref2
­ 08 47 00.0 ­43 30 00 ref8
tion times of 540 sec; a plate scale of 0:49 arcsec/pixel was
selected, resulting in 2 \Theta 2 arcmin 2 imaged sky areas. The
data were reduced using IRAF routines; flat fielding and
bad pixel removal were performed as described in Paper
III. From each object frame, the nearest sky (in time) was
subtracted, resulting in 3 images per field. These were sub­
sequently registered and combined using median filtering
in order to maximize the signal­to­noise ratio. We checked
that this procedure was the most effective in minimizing
residual bias patterns generated by the object­sky subtrac­
tion. Photometry was performed as described in Paper III,
excepted that the aperture radius was set to 3 pixels to
account for the larger FWHM of the PSF with respect
to the images of 1993 (and because of the less crowded
fields). The standard deviation of the measured aperture
corrections is ! ¸ 0:05 mag in all 5 images and that of the
mean values (i.e., the averages of the aperture corrections
used for each single field) is 0:03 mag. Instrumental mag­
nitudes were converted to absolute values by comparison
with ESO standard stars (Bouchet et al. 1989); no correc­
tions for atmospheric absorption were applied, since the
K magnitudes were calibrated using for each set of images
the nearest observations of standard stars. Errors, limiting
magnitudes and completeness limit are similar to those of
the 1993 K images.
3. Results and analysis
3.1. Sources with NIR excess
The nature of the imaged fields can be assessed through an
examination of their J \Gamma H vs. H \Gamma K diagrams (hereafter,
colour­colour diagrams), displayed in Fig. 1. These were
obtained by using the data published in Paper III com­
plemented with JHK magnitudes of a few objects which
remained undetected in the K band (then not reported
in Paper III); open squares indicate star­like sources with
(valid) brightness measurements in all three bands, arrows
indicate lower or upper limits (e. g., upward arrows mark
data points with a defined H \Gamma K value, but a lower limit
at J \Gamma H) and small vertical segments with a horizontal
arrow pointing to the right are used for sources detected
only in the K band (they lie on the right of the H \Gamma K
line defined by the segment, but in principle can have any
value of J \Gamma H and the assigned ones are randomly cho­
sen). Here, we have considered the whole imaged fields
and not smaller ¸ 1 \Theta 1 arcmin 2 areas as done in Paper
III.
Clearly, most of the diagrams exhibit a spread of data
along the reddening band of the main sequence, consis­
tent with high extinction (frequently A V ? ¸ 10 mag), and
a large fraction of objects lie below the reddening band
(i. e., display a NIR excess), a diagram region typically
occupied by YSO's (see, e. g., Lada & Adams 1992). Even
if part of the NIR excess is undoubtedly caused by pho­
tometric noise (i. e., the fluctuations caused by photon
noise for faint sources comparable in fluxes with the sky),
as shown by the presence of points above the reddening
band (a ''forbidden'' region of the diagram for stars) in
a few fields, almost all diagrams display a clear trend to­
wards having objects with a NIR excess. In fact, a closer
examination of detections lying above the reddening band
indicates that most of these are faint sources with large
photometric errors or have some sort of problem (e.g., ly­
ing within a dip generated by the object­sky subtraction
or being heavily affected by bad pixels), whereas a large
fraction of sources with a NIR excess have well defined
colours. If only objects with K ! K compl are considered,
data points above the reddening bands disappear whereas
the spread below them is preserved.
The presence of one or more points on the right upper
corner (just below the reddening band) of most colour­
colour diagrams throughout the examined regions was al­
ready noted in Paper III; they have small photometric er­
rors and correspond to the NIR counterparts of the IRAS
Class I sources. Possible systematic shifts of data points in
some of the colour­colour diagrams (namely, IRS 13, IRS
17, IRS 19 and IRS 21) are discussed in Appendix and do
not appear to affect our conclusions on the large fraction
of objects with a NIR excess.
The large spatial concentration of objects with a NIR
excess and the high degree of extinction towards most of
the IRAS sources suggest that most of the fields contain
young embedded star clusters; moderately luminous Class
I sources seem then to be associated with aggregates of
YSO's, as already noted in Paper III. Whereas clustering
will be addressed in Sect. 3.3, we note that a few fields,
particularly IRS 67, seem to host a very small fraction of
NIR excess objects and may represent regions with iso­

4 F. Massi et al.: Star Formation in the Vela Molecular Clouds
Fig. 1. H \Gamma K vs. J \Gamma H (colour­colour diagrams) for the 12 fields in the VMR­D cloud; open squares indicate sources with
valid detections in all three bands, arrows indicate lower or upper limits (e. g., upward arrows indicate that given J \Gamma H values
are lower limits), and small vertical segments with rightward arrows indicate sources undetected in H and J (i. e., with H \Gamma K
greater than the given value and, in principle, any possible J \Gamma H values). Random J \Gamma H colours have been assigned to the
latter ones, but such as they do not overlap the other data points. The solid line marks the locus of main sequence stars, whereas
the dotted lines represent the reddening law according to Rieke & Lebofsky (1985), with crosses at intervals of AV = 10 mag.
lated (or in small groups) star formation in progress. The
fraction of NIR excess objects (below the completeness
limit) within each frame is an indication of the youthful­
ness of the stellar population imaged; values towards the
12 IRAS sources are therefore reported in Table 3. Objects
exhibiting a NIR excess are here defined as in Sect. 3.4.

F. Massi et al.: Star Formation in the Vela Molecular Clouds 5
Fig. 1. Continued.
3.2. A closer view on VMR­D young stellar population
In order to determine how deeply our observations probe
the parental molecular cores associated with the IRAS
sources, where found clusters are embedded, in Fig. 2 we
have plotted K vs. H \Gamma K (hereafter, mag­colour diagram)
for all NIR sources towards the 12 regions. The dashed
lines mark the completeness limit, whereas the solid lines
display the locus of ZAMS, the zero age main sequence
(from B0 to M5 stars), at a distance of 700 pc; lower and
upper limits are indicated by arrows (e. g., rightward ar­
rows indicate lower limits in H \Gamma K). An extinction of
A V = 20 mag, according to the reddening law given by
Rieke & Lebofsky (1985), is denoted by the large arrow
drawn in the upper left box. Consistently with K photom­
etry, we have adopted a completeness limit for H which
is 1:5 mag lower than the limiting magnitude (see Paper
III). As shown in Figs. 2, 3 and 4, the 12 imaged areas are
characterized by different star populations; we will closely

6 F. Massi et al.: Star Formation in the Vela Molecular Clouds
Fig. 2. K vs. H \Gamma K (mag­colour diagrams) for 10 of the 12 fields; open squares indicate sources with valid detection at H
and K, arrows indicate lower or upper limits (e. g., rightward arrows indicate that given H \Gamma K values are lower limits), the
solid lines mark the locus of zero age main sequence (from B0 to M5 stars) at a distance of 700 pc, whereas the dashed lines
represent the completeness limits. The large arrow in the upper left box indicates an extinction of AV = 20 mag according to
the reddening law given by Rieke & Lebofsky (1985),
examine IRS 67 and IRS 13, which may represent two
opposite cases.
Figure 3 displays the mag­colour diagram for IRS 67,
where we have superimposed isochrones (dot­dashed lines)
of 10 7 yr old pre­main sequence stars (with masses in the
range 0:1--2:5 M fi ) from D'Antona & Mazzitelli (1994) at
different extinctions (from left to right, A V = 0; 10; 20; 30
mag), assuming a distance of 700 pc. An outline of the
method by which the synthetic tracks of D'Antona &
Mazzitelli (1994) have been converted into NIR magni­

F. Massi et al.: Star Formation in the Vela Molecular Clouds 7
Fig. 2. Continued.
tudes versus time relations is given in Testi et al. (1998).
Clearly, almost all sources lie within A V ¸ 10 mag of the
ZAMS up to the K completeness limit, i. e., the embed­
ded star population is well probed down to ¸ 0:3 M fi .
In fact, through the intersection of isochrones and com­
pleteness limit lines it is easy to check that our observa­
tions fully sample 10 7 yr old pre­main sequence stars of
¸ 0:3 M fi at A V = 10 mag and ¸ 0:9 M fi at A V = 20
mag. As we will see later, a decrease in age causes a de­
crease in mass at the completeness limit. An error in the
distance would not critically affect given values; if VMR
was 300 pc closer than assumed, this would mean to ver­
tically shift ZAMS and isochrones upward by ¸ 1 mag,
thus further lowering the mass limits. Conversely, if VMR
lay 300 pc farther than assumed, ZAMS and isochrones
should be shifted downward by ¸ 0:8 mag, yielding a
mass of ¸ 0:6 M fi (A V = 10 mag) at the completeness
limit. Above the completeness limit (below the dashed
line in the mag­colour diagram) we note an increase in
spread around the ZAMS which matches that around the
reddening band in the colour­colour diagram (see Fig. 1),
proving that the latter is caused by photometric noise. In
fact, IRS 67 is characterized by a very large number of
faint sources (K ? 15 mag); i. e. , among the 12 IRAS
and the 5 reference fields listed in Table 1, it exhibits the
largest number of faint sources. The KLF's (see Sect. 3.5)
for imaged fields lying towards regions of low integrated
CO(1--0) emission tend to be composed of a larger number
of objects with K ? 16 mag; since IRS 67 is associated
with the lowest CO(1--0) emission (see Fig. 1 of Paper
III), we deduce that most of the sources above the com­
pleteness limit are background stars. A small population
of embedded objects (A V ¸ 5 mag) is clearly indicated by
the data points below the completeness limit (above the
dashed line) in the mag­colour diagram and we note that
the isolated point on the right­hand corner (K ¸ 11:5
mag) represents the NIR counterpart of the IRAS source.
We also checked that all objects above the completeness
limit (below the dashed line) also fall below the reddening
line for pre­main sequence stars of 0:1 M fi and 3 \Theta 10 6
years old, thus they are mostly too old to be accompanied
by protostellar disks. Hence, IRS 67 probably represents
a region where a single star is forming, at most associated
with a small population of more evolved Class II/Class III
sources.

8 F. Massi et al.: Star Formation in the Vela Molecular Clouds
Fig. 3. K versus H \Gamma K for IRS 67; symbols are the same
used in Fig. 2 and dash­dotted lines mark the locus of pre­
main sequence stars of 10 7 yr old at (from left to right) AV
= 0; 10; 20 and 30 mag for a distance of 700 pc. Masses (in
M fi ) are indicated near the rightmost track.
Similarly, IRS 14, IRS 63 and IRS 66 do appear fully
sampled up to the K completeness limit, with A V ! ¸ 10
mag. Towards the other IRAS sources, the mag­colour
data points seem to extend to the H \Gamma K completeness
limit (the rising part of the dashed line) along the redden­
ing vector, so that stars (or pre­main sequence stars) of
any mass may be missed because of the reddening. Actu­
ally, when considering all sources with positive K detec­
tions (as done in constructing the K luminosity functions),
the data points between the K completeness limit and the
H \Gamma K completeness limit lines are recovered, thus slightly
lowering the mass completeness limit itself.
IRS 13 is representative of the fields displaying a large
spread of colour on the right of the ZAMS (indicating
both high extinction and NIR excess), hence we now ex­
amine its stellar population in greater detail. Figure 4 dis­
plays the mag­colour diagram for IRS 13; similarly to IRS
67, we have superimposed 10 5 yr old pre­main sequence
isochrones (dot­dashed line) from D'Antona & Mazzitelli
(1994) at different extinctions (A V = 0; 10; 20 and 30 mag),
assuming a distance of 700 pc. Clearly, almost all objects
display an A V ? 10 mag (with respect to the ZAMS) and
it is also easy to check that our observations fully sam­
ple 10 5 years old pre­main sequence stars of ¸ 0:1 M fi at
A V = 20 mag and ¸ 0:3 M fi at A V = 30 mag. We note
that a few data points on the right (well above the com­
pleteness limit line) also lie above the reddening line for
10 5 yr pre­main sequence stars of masses 2:5 M fi . The
reddest and brightest one corresponds to source # 29 (see
Paper III), which we identified as a Class I source and
the NIR counterpart of the IRAS source, whereas another
one corresponds to # 25, which also has NIR colours of
a Class I source (Paper III). Then, these objects presum­
ably represent embedded YSO's which may be more mas­
sive than 2:5 M fi ; note, however, that these sources (# 29
and # 25) exhibit, or may be associated with, an intrinsic
NIR excess, thus being displaced rightward and upward
with respect to ''naked'' pre­main sequence stars, making
furtherly difficult to disentangle age and mass from evo­
lutionary effects. Clearly, most of the sources belong to
a population of deeply embedded objects, consistent both
with the location of IRS 13, towards a maximum in CO(1--
0) integrated emission (see Fig. 1 of Paper III), and with
the high inferred extinction (see Papers I and III). In sum­
mary, this region is representative of multiple star forma­
tion associated with a cluster of very young stars and pro­
tostars. The mag­colour diagram clearly shows that only a
few objects with a positive K detection, but above the K
completeness limit, are missed in the H band (the right­
ward arrows). Note also that extremely red and luminous
NIR sources (the NIR counterparts of the IRAS sources;
see Paper III) are present in many of the imaged fields (e.
g., IRS 14, IRS 17, IRS 18, IRS 19 and IRS 62).
It is also interesting to briefly discuss IRS 18; as shown
in the mag­colour diagram of Fig. 2, this region contains a
large number of bright sources. These lie above the redden­
ing line for 10 6 yr old pre­main sequence stars of 2:5 M fi
and most of them are located just towards the cluster con­
taining the IRAS source (see Sect. 3.3). The reddest ob­
jects do exhibit (# 119; Paper III) or may exhibit (# 176,
121 and 138; they have only a lower limit at J as shown in
Paper III) an intrinsic NIR excess, thus making difficult
a comparison with isochrones of pre­main sequence stars
(which do not account for NIR excess). However, both the
spatial concentration and the spread of extinction around
these sources suggest the existence of a cluster of massive
(more than 2:5 M fi or earlier than A0) and young or very
young stars.
Close unresolved pairs of YSO's are not bound to
change the picture outlined in the previous discussion. In
case of two sources with similar NIR fluxes, the only effect
is increasing K by 2:5 log 2 = 0:75 mag (and, obviously,
increasing the number of data points). On the other end,
the most extreme case is that of two sources, one dom­
inating at K and the other at J with opposite spectral
indices; this would result in translating the corresponding
point rightward in the diagram and in introducing a new
point with a higher K and a smaller H \Gamma K. In both cases,
the existence of a young star population is not questioned
and, anyway, close pairs with companions in totally dif­
ferent evolutionary states are expected to be rare, if this
is plausible at all.
In conclusion, we remark that only in 4 out of 12 fields
(IRS 14, IRS 63, IRS 66 and IRS 67), characterized by

F. Massi et al.: Star Formation in the Vela Molecular Clouds 9
Fig. 4. K versus H \Gamma K for IRS 13; symbols are the same
used in Fig. 2 and dash­dotted lines mark the locus of pre­
main sequence stars of 10 5 yr old at (from left to right) AV =
0; 10; 20 and 30 mag for a distance of 700 pc. Masses (in M fi )
are indicated near the rightmost track.
``low'' extinction (! 10 \Gamma 20 mag), we can confidently as­
sume that the stellar populations are fully sampled both
in the K and in the H bands down to a well defined
mass (i. e., 0:2 M fi ). These may be either older regions,
where star formation is at an end and most of the young
sources have already got rid of the parental material, or
very young regions where star formation is just beginning
in small molecular cloudlets unresolved in the CO(1 \Gamma 0)
observations. When considering the KLF's, however, the
completeness limit in the H band is unimportant (i. e.,
in mag­colour diagrams only the straight line K = 15:5
must be considered), so the lower mass limits are shifted
slightly downward; e. g., for an age of 10 5 yr and a dis­
tance ¸ 700 pc, pre­main sequence stars are fully sampled
down to 0:1 M fi at A V = 20 mag and to 0:4 M fi at A V
= 40 mag, whereas for an age of 10 7 yr pre­main sequence
stars are fully sampled only down to 0:8 M fi at A V = 20
mag. In Table 3 we indicate a rough estimate of maximum
extinction towards each of the 12 fields with respect to the
ZAMS and without considering NIR excess.
3.3. Clustering
Because of their dimensions (¸ 2 0 \Theta 1:6 0 ), our images are
only suitable to search for clustering on small scales (! 0:4
pc); since we expect that all fields are at the same distance
and the limiting magnitudes are roughly the same, extinc­
tion variations remain the major concern. We showed in
the previous section that extinction is not homogeneous
throughout the 12 fields and that the parental molecular
cores are uncompletely probed. As a result, our obser­
vations are more sensitive to massive or young pre­main
sequence stars.
In order to infer clustering, we considered the K im­
ages, where the effects of extinction are minimized. The
surface densities of K sources (stars arcmin \Gamma2 ) within the
12 fields are displayed in Fig. 5; these were obtained by
counting stars in 20 00 \Theta20 00 squares displaced 10 00 from each
other (the Nyquist sampling interval) over each K frame.
Gathering together all obtained counts throughout the 12
fields, we plot the total number of bins with given numbers
of stars per unit cell (of 20 00 \Theta 20 00 ) in Fig 6, and superim­
posed on it a Poissonian function which has a mean value
of 2 stars per unit cell (18.7 stars arcmin \Gamma2 ) and an area
of 750 stars. Clearly, the Poissonian curve fits the peak of
the observed distribution, but not the wing where an ex­
cess of counts does appear. The found mean value yields
¸ 60 stars per frame, which is comparable with the mean
number of stars in the 5 reference fields (ref1­ref8 in Ta­
ble 1), 76 \Sigma 4, considering that because of their reduced
extinction the latter, as we will show, may exhibit an aver­
age number of foreground/background stars greater than
expected towards most of the 12 IRAS sources. Then, the
distribution peak gives a good estimate of the mean den­
sity of field stars; hereafter, we will adopt a value of 20
stars arcmin \Gamma2 . As said, IRS 67 is associated with the low­
est CO(1--0) integrated emission, so it is characterized by
a larger mean field star density, but it is unlike to signifi­
cantly contribute to the wing excess since its bins account
only for 8 % of the total, whereas the number of bins with
counts greater than sky mean+1oe is ? 50 %. Moreover,
if IRS 67 is not included in the sample with the counts
from all imaged areas, the density distribution does not
change and continue to show an excess in the wing. The
histogram of Fig. 6 then indicates that our sample is in­
deed biased towards overpopulated fields, i. e., the imaged
fields contain embedded star clusters.
In order to check that the inclusion of sources above
the completeness limit did not significantly affect the den­
sity contour maps, we repeated the counting procedure
considering only sources with K Ÿ 15:5 mag. Again, we
found that all counts follow a Poissonian distribution with
a mean equal to 1 star per unit cell (¸ 9:4 stars arcmin \Gamma2 )
and excess in the wing. Contour maps delineate the same
patterns as in Fig. 5, except for IRS 66 and IRS 67, where
any peak at a level ? 3oe above the sky disappears. Then,
in the latter two cases clustering is mainly produced by
faint sources above the completeness limit; since, as dis­
cussed in Sect. 3.2, these are essentially background stars
much farther than the VMR, we deduce that no compact
groups of stars are present towards IRS 66 and IRS 67, but
only large scale random fluctuations. In Table 3 we briefly
report a summary of the previous results, indicating where
they point to the presence of clusters. It is interesting to

10 F. Massi et al.: Star Formation in the Vela Molecular Clouds
Fig. 5. Contour maps of stellar surface density (from K images) obtained with square counting bins of 20 00 \Theta 20 00 offset by 10 00 .
Right Ascension and Declination are in offsets (arcsec) from the IRAS uncertainty ellipse centre, except for IRS 13, where the
point (0; 0) coincides with source # 29 (see Paper III). The lowest contour amounts to 20 stars arcmin \Gamma2 , roughly the mean
field density, and the steps are 20 stars arcmin \Gamma2 , corresponding to intervals of ¸ 2oe. Asterisks mark the locations of the IRAS
counterparts identified in Paper III.
note also that the density peak towards IRS 17 tends to
shift closest to the IRAS counterpart when considering
only K sources below the completeness limit. This may be
due to the presence of diffuse emission towards the IRAS
counterpart with a consequent local decrease of limiting
magnitudes (and, of course, of efficiency in detecting faint
sources).
Following Testi et al. (1997) we have investigated the
richness of the found clusters by studying their K­band
source radial density profiles. These are shown in Fig.7;
the radial density n(r) has been determined by counting
all objects with K Ÿ 15:5 mag in 6 00 wide annuli centred on
the counterparts of the IRAS sources identified in Paper
III. It is evident that the fields towards the most lumi­
nous IRAS sources (L bol ? ¸ 10 3 L fi ) show an increase in
radial density at or near r = 0, further confirming the ex­
istence of aggregates of young embedded stars. The error
bars in Fig. 7 indicate a 1oe fluctuation within each annu­
lus, assuming a Poisson statistic. Even when considering
this uncertainty source, density enhancements do appear
as real towards 5 fields (IRS 13, IRS 14, IRS 17, IRS 18,
IRS 19), at least at a 2oe level above the sky, and the fact
they share the same trend reinforce this result. Note that
the presence of diffuse emission around r = 0'', lowering
the local limiting magnitude, degrades the efficiency in
finding NIR objects towards the centre and then the ra­
dial density peak itself. Both IRS 20 and IRS 21 exhibit a
density peak at a radius r ? 0 rather than at r = 0, since,
in these cases, the NIR counterparts of the IRAS sources
are clearly separated from the surface density peaks (see
Fig.5). In 5 fields (IRS 62, IRS 63, IRS 66, IRS 67 and
IRS 71), namely those associated with the IRAS sources
displaying the lowest bolometric luminosities (L bol ! 10 3
L fi ; see Paper III), only a slight, scarcely significant, in­
crease in n(r) towards the centre is apparent. A compari­
son between these results, and a close examination of the
surface density maps (for sources below the completeness
limit) clearly show that the most luminous protostars tend
to be embedded near the centre of clusters (see Table 3).

F. Massi et al.: Star Formation in the Vela Molecular Clouds 11
Fig. 7. Radial density n(r), in stars arcmin \Gamma2 , versus radius (arcsec) for the 12 fields; r = 0 always coincides with the NIR
counterparts of the IRAS sources found in Paper III. The shown error bars indicate the statistical uncertainties.
Testi et al. (1997) discuss the quantity I c =
2ú
R 1
0 [n(r) \Gamma n1 ]rdr, i. e., the number of sources, cor­
rected for foreground/background stars, as an indicator of
cluster richness, where n1 is the asymptotic value of the
radial density, i. e., the sky. In Fig. 8, we show I c versus
the bolometric luminosity L bol of the IRAS sources, given
in Paper III. We determined n1 counting the sources in
the external annuli where the density decrease comes to a
stop. The errors shown in Fig.8 are those obtained prop­
agating the uncertainty on n1 . It is evident that sources
with L bol =L fi ? 10 3 (M=M fi ? 5, according to the
model of Palla & Stahler, 1993) display a clear increase
in richness with L bol ; since the IR emission in fields with
L bol =L fi ? 10 3 is very likely dominated by a single Class
I source (see Paper III), the relationship between I c and
L bol is not simply due to an increase in the number of
emitting sources. Then, a trend exists for the precursors
of intermediate mass stars towards being associated with
aggregates or groups of stars, with more massive objects
being embedded in richer clusters. Hence, our data con­
firm what already found by Testi et al. (1997, 1998, 1999)
for more evolved Herbig Ae/Be stars. Note that the more
extincted fields (i. e., the worse sampled ones) are also
those exhibiting the greatest bolometric luminosity and
richness, thus reinforcing the trend in increase of cluster
richness towards higher mass YSO's.
We have listed in Table 2 the relevant physical param­
eters of the clusters; we have also indicated whether or
not the peak surface density is greater than mean sky+3oe
(where mean sky and oe are those derived from the Pois­
sonian distribution discussed above). Note that, whereas
IRS 13 fails to fulfil this criterion, nevertheless it must be
considered a positively detected cluster since, because of
the high extinction, the mean sky value adopted is prob­
ably too high in this case. Conversely, IRS 66 and IRS
67 show clustering above a 3oe level, but, as noted, this
is probably due to random fluctuations in the number of
background stars which can be more easily detected be­
cause of the smaller extinction, than unrelated with D
cloud. Cluster sizes (2R) have been determined from the
surface density maps of Fig. 5 as
p
(d 1 \Theta d 2 ), where d 1 and
d 2 are maximum and minimum extent at the mean sky+1oe
level (if not otherwise specified), assuming a distance of
700 pc. Maximum surface densities have been determined

12 F. Massi et al.: Star Formation in the Vela Molecular Clouds
Fig. 6. The frequency distribution of star counts (in stars per
unit cell of 20 00 \Theta 20 00 ) towards all 12 fields, with a Poissonian
curve (mean = 2 stars per unit cell, area 750 stars) superim­
posed.
Fig. 8. The richness indicator Ic versus bolometric luminosity
Lbol=L fi ; error bars represent the propagation of the statistical
uncertainty on the sky determination.
from the maps of Fig. 5, whereas mean surface densities
are the total number of stars in the K image (minus the
sky value) divided by the image field area. Volume densi­
ties are estimated dividing I c by the volume of a sphere
with the same radius as that of the density enhancement
derived from Fig. 7. Note that all density values are lower
limits because of the uncompleteness in the sampling. We
have also indicated the distance d of the IRAS counterpart
from the nearest density peak (using the surface density
maps of sources with K ! 15:5, not shown here).
3.4. Spatial distribution of NIR excess sources
In order to examine the spatial distribution of sources with
a NIR excess, we have plotted their positions, along with
those of sources without an apparent NIR excess, towards
the 12 fields. Figure 9 shows maps of star positions, cen­
tred on the coordinates of the NIR counterparts found in
Paper III. We have defined as having a NIR excess all
sources which lie on the right of the reddening line of an
A0 V star in the colour­colour diagram; in order to account
for errors, we have shifted the reddening line by \Gamma0:1 mag
in J \Gamma H and 0:1 mag in H \Gamma K in the case of IRS 14, IRS
17, IRS 18, IRS 20, IRS 62, IRS 63, IRS 66 and IRS 71,
and by \Gamma0:2 mag in J \Gamma H and 0:2 mag in H \Gamma K in the
case of IRS 13, IRS 19 and IRS 67 (see discussion in Ap­
pendix). We have also added those sources which were not
detected in J or in J and H but could have a NIR excess
or, anyway, are heavily reddened, assuming as a selection
criterion H \Gamma K ? 2 mag (indicated by filled triangles
on the maps). Only objects with K Ÿ 15:5 mag (i. e., be­
low the completeness limit) have been considered. Clearly,
NIR excess sources tend to cluster towards the field cen­
tres, i. e., the identified Class I sources; within IRS 13,
IRS 14 and IRS 17 fields, NIR excess sources display a
much greater clustering degree with respect to the other
ones, whereas towards IRS 18 an aggregation of objects
with and without NIR excess is apparent. IRS 62, IRS 63,
IRS 67 and IRS 71 contain only a few sources with NIR
excess, but concentrated towards the field centre; in IRS
66 only an object with a NIR excess is present (which cor­
respond to that identified as the possible NIR counterpart
of the IRAS source in Paper III). This is summed up in
Table 3. If we determine the volume density of NIR ex­
cess sources within the fields showing a smaller clustering
degree dividing the number of objects by the volume of
a sphere encompassing their projected locations (assumed
at 700 pc), we find e. g., ¸ 5 \Theta 10 4 stars pc \Gamma3 for IRS 62,
¸ 2 \Theta 10 3 stars pc \Gamma3 for IRS 63 and IRS 67 and ¸ 2 \Theta 10 4
stars pc \Gamma3 for IRS 71. Some of these values are comparable
with those listed in Table 2 for the most luminous IRAS
sources, suggesting that the number of cluster members
is a better discriminant for studying the association with
intermediate mass protostars.
We have also studied the radial colour distribution by
averaging J \Gamma H and H \Gamma K in 6 00 wide annuli centred

F. Massi et al.: Star Formation in the Vela Molecular Clouds 13
Table 2. Physical parameters of the identified clusters; 2R indicates the cluster size and d the distance of the IRAS counterpart
from the nearest density peak.
IRAS ? 3oe 2R Maximum Mean Volume Ic d
source detection surface surface density
density density
(pc) (pc \Gamma2 ) (pc \Gamma2 ) (pc \Gamma3 ) (arcsec)
IRS 13 n a 0:1 800 ( c ) 12000 11 \Sigma 1 0
IRS 14 y 0:2 1900 100 3000 13 \Sigma 1 0
IRS 17 y ? 0:2 3400 400 7000 31 \Sigma 1 0
IRS 18 y ? 0:3 4900 1000 12300 28 \Sigma 2 10
IRS 19 y 0:2 2400 170 6700 28 \Sigma 1 5
IRS 20 y 0:2 d 3900 720 10800 23 \Sigma 2 10
IRS 21 y ¸ 0:2 3900 420 9800 21 \Sigma 1 10
IRS 62 y ¸ 0:2 1500 ­ 4500 4 \Sigma 1 12
IRS 63 y ¸ 0:1 1000 ­ 7800 7 \Sigma 1 8
IRS 66 y b ¸ 0:1 1000 84 ­ 1 \Sigma 0 ­
IRS 67 y b 0:1 d 2900 650 ­ 2 \Sigma 0 25
IRS 71 y ? 0:1 e 1200 370 7800 7 \Sigma 1 10
a However, identified as a cluster
b Possible random surface density fluctuation on a large scale
c Too small because of extinction
d At a mean sky +3oe level
e At a mean sky +2oe level
on the NIR counterparts of the IRAS sources, similarly
to what we have done in Sect. 3.3 for determining stellar
radial densities. Generally, a decrease is apparent from the
centre outward; e. g., in IRS 17 the mean J \Gamma H decreases
from ¸ 2:5 mag (r = 0 00 ) to ¸ 0:8 mag (r = 33 00 ), then
slightly increases. In IRS 13, the mean H \Gamma K decreases
from ¸ 3:3 mag (r = 0 00 ) to ¸ 1:5 mag (r = 27 00 ) and the
mean J \Gamma H decreases from ¸ 4:5 mag to ¸ 0:5 mag. Also
in IRS 67 is apparent a decrease in H \Gamma K (from ¸ 1:2 to
¸ 0:3 mag) and in J \Gamma H (from ¸ 1:6 to 0:7 mag). This
is partly caused by the clustering of NIR excess sources
towards the field centres, but it is also an indication that
extinction increases towards the assumed field centres, as
well. Since, as shown, the surface source density increases
towards the NIR counterparts, then the clusters coincide
with extinction peaks, i. e., local maxima in dust and gas
column density.
3.5. K luminosity functions
Following Lada & Lada (1995), we have built the KLF's
for the 12 examined regions in the form of log N vs. K,
where N is the number of K sources in 1 magnitude wide
bins; due to the small numbers of objects per field we used
a greater binning interval than adopted by Lada & Lada
(1995). A control KLF (sky) accounting both for fore­
ground and background field stars was subtracted from
each raw KLF. An ``empirical'' control KLF was obtained
averaging the KLF's of the 5 reference fields observed in
1998 (ref1­ref8 in Table 1). Since these are located to­
wards the VMR, no reddening correction was performed.
In order to test the control KLF, we constructed a simi­
lar distribution using a different technique: we considered
the K images of the 12 fields and those of 4 more fields
belonging to the VMR­D cloud (from our observing runs
of 1993--94), chosen such as to show no apparent source
clustering. Then, we superimposed the 16 raw KLF's and
assumed that in each magnitude bin all 16 values roughly
follow a Poissonian distribution with an excess in the wing
because of the presence of fields containing clusters. At
last, we built a ``statistical'' control KLF averaging the
6 lowest values in each magnitude bins. The two control
KLF's are very similar up to 15 mag, whereas appreciably
differ in the 15--16, 16--17 and 17--18 mag bins, with the
``empirical'' KLF predicting greater values of log N than
the ``statistical'' one. This is caused by the different ex­
tinction towards the 5 reference fields and the 16 VMR­D
fields and the resulting contribution from the background
stars which is greater in the first case; in fact, as dis­
cussed for the stellar population of IRS 67 (see Sect. 3.2),
at K ? 15 mag background stars dominate with respect
to foreground stars (for small reddening). Since extinction
is much larger towards most of the 12 fields than towards
the 5 reference fields, the ``empirical'' control KLF proba­
bly overestimates the true sky KLF, at least in some cases;
however, this happens at and above the completeness limit
and then does not significantly affect the derived local
KLF's (with the exception of IRS 13, as we will show).
Thus we chose to correct the raw KLF's by subtracting
the ``statistical'' control KLF, just to avoid abrupt drops

14 F. Massi et al.: Star Formation in the Vela Molecular Clouds
Fig. 9. Spatial distribution of sources with NIR excess (crosses) and without apparent NIR excess (open squares), along with
objects with lower limits at J (or J and H) and H \Gamma K ? 2 mag (filled triangles); offsets are in arcsec from the locations of the
NIR counterparts identified in Paper III.
above the completeness limit magnitude which are how­
ever unreliable and appear as unrealistic.
All sky­corrected KLF's are shown in Fig. 10; note,
however, that IRS 63, IRS 66, IRS 67 and IRS 71 KLF's (i.
e., fields associated with lower luminosity IRAS sources)
show extremely small numbers of objects below the com­
pleteness limit and then are scarcely significant. The error
bars indicate the logarithm of N \Sigma \DeltaN , where \DeltaN is the
combination of the statistical errors in the true star counts
and the estimated field star counts (sky).
All KLF's are essentially flat; where a significant num­
ber of sources is available, they are represented by a power
law up to a turning point above which the distribution flat­
tens, similarly to what found for pre­main sequence star
clusters (see Lada & Lada 1995). The turning point lies
below the completeness limit (with the exception, at most,
of IRS 17 and IRS 21), so the flattening appears as a real
feature of the KLF's. Unfortunately, all luminosity func­
tions do extend above the completeness limit, confirming
that the low mass end of the stellar population is not ade­
quately sampled; above the completeness limit, the KLF's
fall off. We determined the slopes of the power law end by
fitting a log N = aK \Theta K+ b function to the relevant data
(i. e., below the completeness limit), often excluding the
brightest source; these are reported in Table 3.
4. Discussion
4.1. Properties of the clusters
We have shown in Sect. 3.3 that VMR­D Class I sources
with bolometric luminosities L bol ? ¸ 10 3 L fi are asso­
ciated with stellar density enhancements of sizes 2R ¸
0:1 \Gamma 0:3 pc and star densities ¸ 3000 \Gamma 12300 pc \Gamma3 . Con­
versely, VMR­D Class I sources with bolometric luminosi­
ties L bol ¸ 10 2 L fi exhibits lower degrees of clustering,
and very small or no source aggregation at all in the case
of IRS 66 and IRS 67. Found sizes lie at the lower end
of values generally reported for young embedded clusters;
Carpenter et al. (1993) observed 20 IRAS sources associ­
ated with OB stars in the NIR, finding clusters of radius
ranging from R = 0:18 to R = 0:74 pc. More recently,
Testi et al. (1998) examined 45 fields around Herbig Ae/Be
stars through JHK imaging, evidencing in 22 cases clus­
ters with typical sizes R ¸ 0:2 pc. The Trapezium cluster
has a central core 2R ¸ 0:14 pc sized (Zinnecker et al.
1993), whereas Lada & Lada (1995) find 9 subclusters in
IC 348 ranging from R ¸ 0:1 \Gamma 0:2 pc to R ¸ 0:5 pc for the
main one. In part, the slightly smaller size of the stellar
density enhancements in VMR­D is due to our small im­
aged fields (e. g., towards IRS 17 and IRS 18 the clusters
appear to lie partly out of the images), although in the
case of IRS 13 the smallness may reflect the youthfulness

F. Massi et al.: Star Formation in the Vela Molecular Clouds 15
Fig. 10. K luminosity functions for the 12 fields plotted as histograms of log N vs. the apparent K magnitude, binned at
intervals of 1 mag. Vertical bars indicate the statistical error, whereas solid lines are linear fits to the power law part of the
KLF's. Dashed lines show a linear relation with an angular coefficient of 0:4. A control KLF was subtracted from each raw KLF
in order to minimize the contribution of foreground and background field sources.
Table 3. Summary of cluster properties towards the 12 IRAS sources
IRAS NIR Maximum Clustering NIR Cl. I source KLF
source excess estimated excess towards angular
field source AV source cluster coefficient (aK )
fraction (mag) concentration centre
IRS 13 0.81 ? ¸ 40 y y y 0:17 (! 0:29) a
IRS 14 0.33 ¸ 20 y y y 0:52
IRS 17 0.55 ¸ 40 y y y 0:31
IRS 18 0.15 ¸ 40 y y y 0:33
IRS 19 0.63 ¸ 40 y y y 0:44
IRS 20 0.11 ¸ 30 y y n 0:52
IRS 21 0.34 ¸ 40 y y n 0:25
IRS 62 0.24 ¸ 30 y y n 0:17
IRS 63 0.19 ¸ 20 y y n ­
IRS 66 0.06 ¸ 10 n n n ­
IRS 67 0.20 ¸ 10 n y n ­
IRS 71 0.06 ¸ 30 y(?) y n 0:07
a Without subtracting control KLF
of the whole structure with a lesser degree of dynamical
evolution. Volume stellar densities are in agreement with
the highest values reported for similar regions: Carpenter
et al. (1997) find a central density ¸ 9000 stars pc \Gamma3 for
Monoceros R2 (a cluster 2R ¸ 0:38 pc in size); Zinnecker
et al. (1993) find 10 4 stars pc \Gamma3 for the Trapezium core;
Wilking et al. (1997) find a maximum density ¸ 1950 stars
pc \Gamma3 for R Cr A. Note, however, that a comparison be­
tween different studies is difficult because of differences in

16 F. Massi et al.: Star Formation in the Vela Molecular Clouds
completeness limits, in distances of the regions and, some­
times, even in the adopted definition of dimensions.
4.2. Coeval versus continuous star formation
Figure 9 clearly shows a clustering trend of sources with
intrinsic NIR excess, i. e., there exists an evolutionary seg­
regation. Note that we have been somewhat conservative
in defining the NIR excess, so the clustering of YSO's may
be even more marked. A comparison of the colour­colour
diagrams of Fig. 1 with the study of Lada & Adams (1992)
shows the simultaneous presence of objects with typical
colours of Class I and Class II sources towards the fields
with clusters, i. e., there exist YSO's in different evo­
lutionary states. Statistical argumentations suggest that
the members of each cluster have to be almost coeval.
As we will show later, KLF's associated with the VMR­
D cloud are consistent with a population of stars with a
field­like IMF; if the birth of the less massive members oc­
curred much earlier than that of the more massive ones, we
should have found also rich clusters with low luminosity
(L bol ¸ 10 2 M fi ) Class I sources only. However, clusters
where the birth of very low mass stars preceded that of
the more massive ones would go undetected, since the cat­
alogue of VMR Class I sources barely contains protostars
down to masses M ¸ 1 M fi (see Paper II).
Conversely, if the birth of the most massive star oc­
curred much earlier than that of the less massive ones,
we should have found luminous Class I sources in isola­
tion as well, unless some of the low luminosity objects we
have found towards IRS 62, IRS 63, IRS 66, IRS 67 and
IRS 71 do represent very young massive star progenitors
that still have to accrete most of their final mass. This
seems unlikely, since 1:3­mm continuum fluxes towards
these sources are smaller than towards the high luminos­
ity IRAS sources, indicating that less mass is available in
their circumstellar envelopes (see Fig. 11). Furthermore, if
each of these regions had still to form a cluster, the beam
should enclose a fraction of molecular gas which has not
yet condensed in stars whereas towards the most luminous
IRAS sources it has already been transformed in stellar
mass. Hence, if this was the case, anyway millimetric ob­
servations should detect more flux towards the supposed
``youngest'' (i. e., less luminous) regions. A remarkable ex­
ception is represented by IRS 63, a ``low'' luminosity IRAS
source whose 1:3­mm flux nevertheless suggests an enve­
lope mass of 1--5 M fi (Paper III); its location is indicated
in Fig. 11.
The correlation between bolometric luminosity and
mm­flux shown in Fig. 11, which if taken at face value
indicates that the less luminous IRAS sources do not rep­
resent clusters to be formed, could be alternatively ex­
plained assuming that the distance of the less luminous
sources has been systematically underestimated. Then, in
Fig. 11 we show the effect of distance (dotted lines) on
objects which would have the same 1.3­mm flux (dashed
line) of IRS 18 if lying at its distance. Clearly, the distance
of the less luminous objects should have been underesti­
mated by a factor of 8 in order to fit the relation, and
even if this was true, they would not belong to VMR­D
and the above assessment on coeval formation of stars in
the clusters within this cloud would continue to apply.
However, a larger sample of sources is needed in order to
quantify this argumentation; we have already imaged at
JHK all IRAS­selected Class I source candidates in the
VMR C and D clouds, so a more exhaustive answer will
come from the complete examination of these fields.
As discussed in Sect. 3.3, the most luminous Class I
sources tend to concentrate towards or near the cluster
centres, suggesting a mass (and evolutionary) segregation
within these structures. NIR embedded clusters are gen­
erally believed too young to have undergone dynamical
evolution (see, e. g., Bonnell & Davies 1998), so the mass
segregation must be accounted for otherwise, e. g., by com­
petitive accretion (Bonnell et al. 1997). Hence, if clusters
are formed by contraction and fragmentation of molec­
ular cores, the more evolved YSO's (i. e., the Class II
sources), which are presumably also the lower mass clus­
ter members, in a scenario of coeval star formation must
have stopped to gather matter well before the highest mass
ones (the Class I sources). If the accretion rate is roughly
constant in a same molecular core, e. g., then all proto­
stars may have started to grow roughly at the same time
with those first leaving the birthline characterized by a
lower mass.
4.3. Analysis of the KLF's: age and IMF of the clusters
In order to obtain more details on the age and mass distri­
bution of the members of the young clusters, we studied
their KLF's. As indicated in Table 3, we found KLF's
whose shapes are roughly in agreement with those gen­
erally reported; in fact, Lada & Lada (1995) note a re­
markable similarity among the KLF's of different young
embedded clusters, with slopes aK ¸ 0:40. Although we
used a binning interval twice that adopted by Lada &
Lada (1995), we have checked that this does not signifi­
cantly affect the slope of the log N --K function, thus allow­
ing a comparison between our results and those of Lada
& Lada (1995). Unfortunately, we cannot determine the
spread along the x axis of the KLF's, which according to
Lada & Lada (1995) is related to the age of the stellar
population, since, as already noted, the K completeness
limit is not sufficiently high to enable a complete sam­
pling. Hence, we can only rely on the KLF slopes in order
to derive age information. Furthermore, we caution on the
effects both of extinction and of NIR excess which are only
partially minimized by using 1 mag wide bins.
Lada & Lada (1995) constructed a set of KLF's for
models of pre­main sequence star clusters ranging in age
from 10 6 to 10 7 yr, both in the case of coeval members
and in that of continuous star formation. Since we are

F. Massi et al.: Star Formation in the Vela Molecular Clouds 17
Fig. 11. Bolometric flux vs. 1.3 mm flux for 10 out of 12 IRAS
sources. The bolometric flux is measured in solar luminosities
assuming a standard distance of 700 pc. The points correspond­
ing to IRS 14, IRS 18 and IRS 63 are labelled. Dotted lines
indicate the effects of distance on sources which would exhibit
the same flux as IRS 18 (dashed line) when lying at its dis­
tance and have been chosen such as to roughly enclose all data
points (varying the bolometric flux). Crosses on the dotted line
mark, from the dashed line, growing distances 1, 2, 3, 4, 5, 6,
7, 8 and 10 times that of IRS 18.
interested in structures with (possibly) coeval members
which may be younger than 10 6 yr, we also determined
model KLF's but using a simple semi­analytical method.
The KLF can be expressed as:
dN
dK = dN
d log M \Theta
d log M
dK (1)
where the first term on the right side is the IMF; the
second term on the right side was determined fitting a
linear relation to the pre­main sequence star isochrones
in a log M vs. K diagram obtained from the evolutionary
tracks of D'Antona & Mazzitelli (1994), as discussed in
Sect. 3.2. We used the IMF of Miller & Scalo (1979):
dN
d log M = C 0 exp[\GammaC 1 (log M \Gamma C 2 ) 2 ] (2)
where C 0 = 106, C 1 = 1:09 and C 2 = \Gamma1:02 are appropri­
ate for a constant birth rate of field stars and an age of the
Galaxy amounting to 10 12 yr. Recently, the Miller­Scalo
IMF has been criticized (Scalo 1998); however, since we
are interested neither in the detailed shape of IMF's nor in
the lower masses end, its choice is not critical for our pur­
poses. Using the linear fits to the synthetic tracks, given
an age we can express log M as a function of K; at last,
Table 4. Slopes of model KLF's for constant age determined
by a linear fit to the data
Age Angular Angular
coefficient (aK) coefficient (aK)
(Myr) (bin 0.5 mag) (bin 1 mag)
0:1 0:23 0:22
0:3 0:29 0:20
1 0:40 0:33
3 0:32 0:28
10 0:23 0:20
we determined log N vs. K with numerical integrations of
Eq. 1 using 0:5 and 1 mag binning intervals. Linear fits to
the rising part of the model KLF's yielded the slopes given
in Table 4; note that values with 1 mag binning are slightly
smaller than those with 0:5 mag, since the turn­off point
becomes less marked, whereas those with 0:5 mag binning
agree well with those given in Lada & Lada (1995). It can
be also noted that the KLF slope increases with age up to
10 6 yr, then decreases; instead, in the case of continuous
uniform star formation, the KLF slope appears roughly
constant at all ages (Lada & Lada 1995).
As shown in Fig. 10, most of the KLF's are consis­
tent, within errors, with a slope aK = 0:40 thus making
difficult a direct comparison of found values with those
given in Table 4. This adds to the effects of reddening and
NIR excess on the observed KLF's; these have been partly
circumvented by using a large (1 mag) binning interval.
However, we remark that colour­magnitude diagrams (see
Fig. 2 and Table 3) indicate extinction variations (and/or
NIR excess) up to A V = 20\Gamma30 mag (AK ¸ 2\Gamma3 mag) and
more towards some regions. Furthermore, if a significant
fraction of objects is represented by Class I sources, the
adopted mass­luminosity relations (for pre­main sequence
stars) are not appropriate. The KLF's of IRS 13 and IRS
62 fields are much flatter than the other ones; as concern­
ing IRS 13, we noted in Paper III that the sky area towards
this IRAS source appears extremely extincted, with very
few visible stars in the DSS plate (see also Fig. 1). Then,
the control KLF probably overestimates the population
of foreground stars and an upper limit to the slope can
be obtained by fitting a linear relation to the uncorrected
KLF (a K = 0:29). The number of stars towards IRS 62,
on the other hand, is too low to yield a significant fit.
As an effect of the presence of unresolved binaries
within the fields, the linear portion of the KLF's may be
steeper than it appears; anyway, in view of the large sta­
tistical errors, we do not expect this effect to be remark­
able. Furthermore, the slopes could have been increased by
reddening effects. Hence, we did not correct the observed
distribution to account for it, which would have needed
theoretical assumptions, given the lack of observational
data.

18 F. Massi et al.: Star Formation in the Vela Molecular Clouds
As a rule, the brightest source in the KLF's of Fig. 10,
often isolated from the rest of the distribution, represents
the NIR counterpart of the IRAS source, i. e., the dom­
inant Class I source. Exceptions are IRS 18, IRS 20 and
IRS 21 (as for IRS 21 the brightest, isolated object in the
KLF is probably a foreground star); in IRS 62, the bright­
est isolated object corresponds to source # 27 (see Paper
III), which has NIR colours typical of a Class I source
but was not identified as the IRAS counterpart because of
its location with respect to the IRAS uncertainty ellipse.
If the stellar populations are dominated by pre­main se­
quence stars, the brightest object within the KLF is then
peculiar and was not included when fitting the linear re­
lation (with the exceptions of IRS 18 and IRS 20). Given
the uncertainties, the obtained slopes are compatible with
those listed in Table 4, suggesting that the KLF's may be
actually dominated by pre­main sequence stars with an
IMF very similar to that of Miller & Scalo (1979) at the
high mass end, i. e., a field IMF. Because of the difficul­
ties already noted, the slope values are scarcely significant;
more useful is a direct comparison among KLF's.
Figure 12 shows a comparison of KLF's for 9 of the 12
fields; a noticeable issue is that all KLF's roughly share the
same K luminosity range and bear a generic resemblance,
indicating that the assumption of constant distance is in­
deed correct. The peculiarity of the IRS 13 KLF has al­
ready been discussed; the remarkable extinction and the
very high fraction of NIR excess sources in the colour­
colour diagram suggest that this is probably the youngest
field. The KLF slope (a K ! 0:29) would indicate an age
earlier than 10 6 yr. The combined effects of age, extinc­
tion and NIR excess may explain the differences with the
KLF of IRS 17, which can be considered as a typical young
cluster. An opposite case is that of IRS 18, whose KLF is
quite similar to those reported for other young embedded
clusters with continuous star formation (see Lada & Lada
1995). Here, more episodes of star formation may have
taken place and it may represent the older cluster. In fact,
the bright end of the KLF is dominated by a couple of ob­
jects without a NIR excess. This is not random, since a
look at the DSS plate shows a small cluster of visible stars
just towards the IRAS source, i. e., the NIR cluster, east
of a larger stellar aggregate. This is in agreement with
the colour­colour diagram which indicates the presence of
both very reddened stars and NIR excess sources. Then
the KLF is the result of at least two episodes of star for­
mation, with the NIR cluster probably located behind the
visible one.
In spite of their slopes (varying from aK = 0:25 to
aK = 0:52), IRS 17, IRS 20 and IRS 21 share similar
KLF's. the most noticeable differences arising in the high­
est luminosity end of the distributions. Whereas, as con­
cerning IRS 17, the latter is dominated by sources # 57
(the IRAS counterpart) and # 40 (a YSO which is also
a possible jet driving source), the brightest source in the
IRS 21 KLF is probably a foreground star. We noted in
Paper III that the NIR counterpart of IRS 20 is heav­
ily reddened, then it is shifted towards the inner of the
distribution. Undoubtedly IRS 17 is a very young field, as
suggested by the high fraction of NIR excess sources in the
colour­colour diagram and the presence of a collimated jet
(Massi et al. 1997). Given the similarity of KLF's, IRS 20
and IRS 21 appear as quite young clusters, as well.
A resemblance between the KLF's of IRS 14 and IRS
19 also exists; however, whereas the colour­colour diagram
of IRS 14 indicates that it is a more evolved field occu­
pied by a Herbig Ae/Be star (see Paper III) and a group
of Class II sources, with a relatively small extinction, the
colour­colour diagram of IRS 19 is different, displaying a
few objects with colours typical of Class I sources and a
much higher fraction of NIR excess sources (see also Ta­
ble 3). Then, IRS 19 appears younger (i. e., less evolved)
than IRS 14. A rough comparison between pre­main se­
quence tracks (isochrones) and the mag­colour diagram
suggests an age ! ¸ 3\Theta10 6 yr for IRS 14. Finally, IRS 62 and
IRS 71 have extremely flat KLF, with few bright sources
with respect to the other fields; this reflects a shortness of
high mass stars, confirming they host formation of small
groups of lower mass stars.
Qualitatively, the slope of the linear part of the KLF's
seems to increase from the youngest cluster (IRS 13) to
the most evolved one (IRS 14), as predicted by the time
evolution of our model KLF's from 10 5 yr to 10 6 yr. IRS
18 is probably older than IRS 14 itself because of its mul­
tiple episodes of star formation. However, we remark that
defining a cluster age is not straightforward if most or part
of the sources are still in the birthline (as it is the case for
Class I sources), since usually the departure from the lat­
ter is assumed as the starting point. From the analogy
of the observed KLF's with the model KLF's (using pre­
main sequence star tracks), however, we can confirm that
the low mass cluster members are already in the pre­main
sequence phase; if so, the cluster ages we gave are referred
to these stars.
4.4. Final remarks on intermediate mass star formation
At present, our observations cannot help settling the di­
chotomy between two different views on the association
of young massive stars with clusters of less massive com­
panions. A possible scenario is that the physical processes
that lead to their formation need anyway the presence of
clusters of stars, in order to be effective. However, the in­
crease in cluster richness with the bolometric luminosity
of the ``central'' Class I source, evidenced by our data,
may be also explained if stars are randomly assembled
into clusters with a given IMF and spectrum of member­
ship number, as, in that case, the richest ones are more
likely to host massive stars, without discarding the pos­
sibility that high mass stars may also form in isolation,
although very rarely. Bonnell & Clarke (1999) discuss this
scenario, showing that the most critical discriminant be­

F. Massi et al.: Star Formation in the Vela Molecular Clouds 19
tween the two views is in fact the relative frequency with
which young massive stars are found in small clusters,
whose assessment needs much larger samples than ours.
Another interesting issue would be exploring the relation
between cluster richness and total mass available; we are
carrying out molecular line observations in order to gather
data on the associated cores and discuss this topic.
We conclude with a few remarks on the possibility
that the most massive objects in at least some clusters
may have formed by coalescence rather than accretion. Al­
though preliminary models of this scenario (see Bonnell et
al. 1998) suggest densities of ¸ 10 4 stars pc \Gamma3 as a thresh­
old for coalescence to become an efficient way, which have
been measured towards some of our fields, they must be
furtherly improved before a meaningful comparison with
observational data can be carried out. However, note that
Bonnell et al. (1998) propose that in the framework of this
scenario the most massive stars in a young cluster could
appear as the less evolved ones, as indicated by our obser­
vations. Hence, we cannot rule out this possibility, which
deserves further investigation.
5. Conclusions
We have carried out an accurate examination of JHK
photometric data and K source spatial distributions to­
wards 12 fields in the VMR­D cloud known to contain
Class I sources. This represents a complete sample of IRAS
selected objects of the same kind down to a limiting flux
F š (12¯m) = 1 Jy belonging to VMR­D itself. We have
obtained useful information on star formation processes,
confirming that intermediate­mass stars originate in clus­
ters rather than in isolation. In particular:
1 The highest luminosity Class I sources (L bol ? ¸ 10 3
L fi , corresponding to M ? ¸ 5 M fi according to the
model of Palla & Stahler 1993) are embedded in young
stellar clusters with sizes 2R ¸ 0:1 \Gamma 0:3 pc and stellar
densities 3000 \Gamma 12000 pc \Gamma3 .
2 Smaller luminosity Class I sources (L bol ¸ 10 2 L fi ,
corresponding to M ? ¸ 2 M fi according to the model
of Palla & Stahler 1993) are isolated or associated with
small aggregates of YSO's with stellar densities less
than ¸ 10000 pc \Gamma3 .
3 Using as a richness indicator the number of K sources
in the radial density enhancement of the clusters (I c ),
we found a clear increase in richness with increasing
bolometric luminosity of the IRAS sources, indicating
not only that more massive stars tend to form within
richer clusters, but also that this trend may be already
established at their birth.
4 Sources with a NIR excess tend to concentrate within
the clusters and the dominant Class I source is often
located close to the stellar surface density peak, i. e.,
there appears to exist a mass segregation, as predicted
by competitive accretion models, and an age segrega­
tion.
Fig. 12. Comparison of K luminosity functions (corrected for
the contribution of field stars) for 9 of the 12 regions.
5 the K luminosity functions towards the highest lumi­
nosity Class I sources are quite similar to those re­
ported for young embedded clusters, with a linear in­
creasing part and a flattening. The dominant Class
I source often appears as the brightest object, iso­
lated from the rest of the distribution. KLF slopes
(a K ¸ 0:2 \Gamma 0:5) are consistent with those generally
reported for young embedded clusters (a K ¸ 0:4).
5 The shape of found KLF's is consistent with a stel­
lar population distributed according to a Miller­Scalo
(field) IMF at the high mass end. The KLF slope seems
to increase from the less evolved cluster (IRS 13) to
the more evolved one (IRS 14), in agreement with the
predicted evolution of clusters of coeval pre­main se­

20 F. Massi et al.: Star Formation in the Vela Molecular Clouds
quence stars. IRS 18 appears as the oldest structure,
with a group of visible stars towards the aggregate of
NIR sources.
6 Although defining a cluster age is not straightforward,
since many YSO's are presumably still in the birthline,
the shape and slope of found KLF's do seem to suggest
that the lower mass stars sampled by our observations
are already in the pre­main sequence phase. With re­
spect to these, the cluster ages range from 10 5 to ¸ 10 6
yr, with the exception of IRS 18 which is older.
7 Our data seem to outline a scenario where high­
intermediate mass stars form in clusters with a field­
like IMF; at least the highest mass members are
roughly coeval, although the fragmentation of molecu­
lar cores may have started the contraction of all cluster
members at the same time suggesting that actually all
sources are coeval.
8 We cannot rule out the possibility that some of the
highest mass Class I sources may have formed for co­
alescence of less massive cluster members rather than
accretion. This would explain why the most massive
protostars in a cluster are also the less evolved ones.
Appendix A: Systematic shifts in colour­colour
diagrams
As can be seen in Fig. 1, some colour­colour diagrams
(namely, those for IRS 13 and IRS 19) contain no or only
few points within the reddening band of the main se­
quence, whereas the majority of data falls below it; since
sources within the reddening band should be spread above
and below it with equal probability by photometric errors,
if real this would indicate an exceedingly small number of
foreground (slightly extincted) stars towards these fields
(assuming background ones may be almost absent since
heavily extincted). However, it appears unlikely that field
stars are almost completely lacking (with the possible ex­
ception of IRS 13, towards which DSS plates show only
few stars) and the possible presence of a systematic er­
ror in colours must be discussed. As reported in Paper
III, zero points are well established, so a systematic er­
ror in magnitudes (anyway, at a level of ¸ 0:1 mag) may
only arise due to unaccuracies in the estimated aperture
corrections. Because of the general unavailability in our
fields of sufficiently bright, isolated stars, we determined
mean aperture corrections for each frame (to be added to
the instrumental magnitudes) using small samples of ob­
jects lying in the less crowded areas. The associated un­
certainty (indicated by the standard deviation over each
frame) can amount up to ¸ 0:1 mag (see Paper III). Al­
though variations in the mean aperture corrections from
frame to frame (¸ 0:1 mag) are random, it may happen
that for a given field they cause a bias downward in a
band and upward in another one, thus resulting in a sys­
tematic shift of colours. However, we expect that actually
aperture corrections are roughly equal in the three bands,
since each field was imaged in the same night changing
filters in succession (so that the 3 JHK frames are near
each other in time). Hence, the difference itself in aper­
ture corrections between different bands for the same sky
area may be assumed as an estimate of the corresponding
colour shift.
In fact, according to the previous discussion, it appears
that data points in the colour­colour diagram of IRS 13
should be systematically shifted leftward by 0:18 mag and
upward by 0:1 mag, whereas, as for IRS 19, they should
be shifted leftward by 0:18 mag. We checked that similar
considerations should be applied to IRS 17 and IRS 21
diagrams as well, where data points should be shifted 0:12
mag upward in the first case and 0:08 mag both downward
and rightward in the other. In all cases, after shifting,
the reddening bands appear better matched to the data
points without, however, significantly affect the general
remarks on the large fraction of sources with a NIR excess.
The shortness of reddened and unreddened stars towards
IRS 13 and IRS 19 is then, in part, an artefact of data
reduction.
Acknowledgements. We thank Leonardo Testi for kindly pro­
viding us with the code of the task by which we derived the re­
lationship among pre­main sequence star age, mass and JHK
luminosity from model tracks.
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