SFRff=0), by counting all
assuming a mean stellar mass
Myr for Class II protostars.
versus αvir,e for these nearbyr,e values for the four clouds
αvir,e > 10). We also plot thelog with nH,min=400 cm−3
ouds with SFRff=0, SFRff
hough not as rapidly as in theMach number of these clouds
e of 7.7 from our numericalmean temperature in both
ion is expected to be a bit
uds than for the numericalre 15 shows the prediction of4, while the dashed line is thepplied to the clouds fromgures. The number of clouds
low to deﬁne a clear relation
cloud SFRs are approximately

have been carefully derived by Federrath et al. (2016) and thanks
to the well-deﬁned timescale of star formation determined throughthe orbital model of CMZ clouds by Kruijssen et al. (2015), thevalues of SFRff and αvir,e are relatively well determined for theCMZ (Barnes et al. 2017). The SFR value derived by Barnes et al.
(2017), SFRff=0.01–0.04, associated with the value αvir,e=
Paolo
Padoan,Troels etHaugbølle,ke Nordlund,and Søren Frimann
4.3±2.3
from Federrathal. (2016), areÅshownby the shadedin Figure
15. These values for the CMZ are clearly consistent
ApJarea840,48 (2017)with our numerical results and with the prediction of our revised
PN11 model.

292 Supernova Driving. IV. The Star-formation Rate of Molecular Clouds#39
7. Summary and Conclusions
We have studied the SFR as a function of cloud parameters
by generating a large sample of realistic MCs, formed ab initio
in a simulation of SN-driven turbulence in an ISM region of250 pc size. This simulation is a continuation of our previous
SN-driven experiment presented in Papers I, II and III, wherewe had already demonstrated that we could recover MCproperties consistent with the observations. In this work, thanks11larger values of αvir,e.
8. The SFR in the CMZ, estimated with the aid of a study ofthe physical properties of the “Brick” cloud and of anorbital model of the clouds in the CMZ, is also consistent
with our numerical results and our theoretical predictions.

y1olution and theest if the SFR ins well. Althoughessed elsewhere,depletion time ofgalactic values,
ation. The main
lowing.

selected from thestribution, with avalue of approxidecreases withation has a large
cloud variations
rs b, β,and %.
bination of timegas density PDF,
ith a low number
k of statisticalto the transientwith the mostof the timescale.
me of the criticalassume it is theeristic postshockty tail of the gas
ff,cr<tPDF. Thisower than in thers of MCs.
ion, the revised
on with a rather
by the relation
tion is consistent2012), where wends primarily on

lected from thetervals of αvir,e,
1 model, SFRff,αOne of the most valuable ﬁndings of this investigation is thelarge scatter of SFRff, including both large variations fromcloud to cloud, even at comparable values of αvir,e, and time
variations within individual clouds. This result Padoan
has been
et al.
achieved thanks to the very large number of clouds formed
ab initio in the simulation, each contributing to an ensemble ofrealistic initial and boundary conditions with probability 15
distributions that may closely match those of real MCs. The
instantaneous value of the SFRff of a given cloud cannot be
accurately predicted based on the cloud physical parameters,
and can even deviate signiﬁcantly from the prediction of thetheoretical model, because of the ever-changing nature of MCs
embedded in the complex ﬁlamentary structure of the cold
ISM, and the continuous driving by SNe, with occasional
explosions in close proximity or even within the cloud. Despite
this chaotic nature of the SFR in MCs, we have found that an
ensemble average obtained by selecting a very large number ofclouds from many snapshots of the simulation yields values of
SFRff within logarithmic intervals of αvir,e that nicely ﬁt themodel prediction. We conclude that our simulation provides
support for the theoretical framework of turbulent fragmentation, while exposing the chaotic and unpredictable nature of thestar-formation process.

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We thank the anonymous referee for several usefulcomments and corrections that helped us improve the paper.
Computing resources for this work were provided by theNASA High-End Computing (HEC) Program through theNASA Advanced Supercomputing (NAS) Division at Ames
Research Center. P.P. acknowledges support by the Spanish
MINECO under project AYA2014-57134-P. T.H. is supported
by a Sapere Aude Starting Grant from The Danish Council for
Independent Research. Research at Centre for Star and Planet
Formation is funded by the Danish National ResearchFoundation.
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particles. Here, it is worth mentioning that, while producing
realistic SFR values within MCs, this simulation currentlyhasa global SFR corresponding to a gas depletion time of the orderof 1 Gyr, consistent with global galactic values (Bigielet al. 2011). Figure 3 shows the global star-formation
efﬁciency, SFE, versus time (solid line), whereSFE (t ) º M (t ) M(1)and Ms the total mass in sink particles. The depletion time, tdep,
is deﬁned asº=12

The Astrophysical Journal, 840:48 (16pp), 2017 May 1

Figure 3. Star-formation efﬁciency vs. time for the whole computational
volume (black thick solid line), and for individual MCs from the simulation,
selected with nH,min=200 cm−3 (blue thin lines) and nH,min=400 cm−3 (redthin lines). The thin line of each cloud covers 1.68 Myr, the time interval
during which the clouds are followed (notice that the SFE for ﬁve MCs withMcl > 2 × 104 Me (nH,min = 200 cm−3) and for six MCs with Mcl>104 Me(nH,min = 400 cm−3) has been plotted with thicker lines). The vertical dottedlines mark the times of the 10 simulation snapshots where the MCs wereselected, at intervals of 1.5 Myr. The short-dashed and long-dashed lines show
SFE vs. time for depletion times tdep=1.5 Gyr starting at t=61 Myr andtdep=0.8 Gyr starting at t=67 Myr, respectively. The two green shaded
areas show two examples of SFE vs. time for tdep=0.05 Gyr, characteristic of
the MCs from the simulation, starting at the ﬁrst and fourth cloud selection
times. This cloud depletion time is evaluated as 1 á (SFRff t ff ) ñ averaged overall clouds with non-zero SFR.

intervals 61–67 Myr and 67–74 Myr. At the same time, theclouds selected in the simulation as described in the following
section exhibits a much steeper time dependence of their local
SFE, as shown by the short thin lines in Figure 3, and by theshaded areas illustrating the average cloud depletion time of

The Astrophysical Journal, 840:48 (16pp), 2017 May 1

Padoan et al.

Padoan et al.

search is carried out at a uniform resolution of 5123 cells, that is, aspatial resolution of 0.49 pc, but the cloud properties are computed
using all the tracer particles identiﬁed within each cloud. Because
the tracers record all the hydrodynamical variables interpolated attheir position, and due to the very large number of tracers inhighdensity regions, MC properties are derived with the hydrodynamical variables sampled at the highest local spatial resolution of
the AMR grid, up to the highest resolution of 0.0076 pc in thedensest regions.
MCs are selected from 10 snapshots, at equal intervals of
1.5 Myr, with the ﬁrst snapshot at 4.0 Myr after the inclusion ofself-gravity in the simulation. Only clouds satisfying thefollowing three conditions are retained: (1) the cloud mass is
Mcl>1000 Me, (2) the rms velocity is σv<4 km s−1(toavoid MCs too strongly affected by recent nearby SNe5), (3)the cloud does not disperse during the next 1.5 Myr, meaningthat it is not doubling its effective size in that time interval (toavoid MCs whose properties are evolving too rapidly). With
these conditions, the number of MCs is reduced from 391 to313, 203 clouds with nH,min=200 cm−3 and 110 clouds withnH,min=400 cm−3. The conditions allow for a better comparison with the SFR model that does not account for transient
processes like SN feedback or cloud dispersal. It may yield asample more suitable for the comparison with the observations
as well,because MCs strongly affected by SNe, or in theFigure 4. Properties of MCs selected from the simulation with density thresholds nH,min=200 cm−3 (empty circles) and nH,min=400 cm−3 (ﬁlled circles). The solid
processandof
being
alsovalues
sufferfroma strong
σv averaged
within logarithmic intervals of Re (upper panels), and the values of αvir,e and βdashedlines aredispersed,
the power-law ﬁtsmay
to the meanof Mcl andaveraged inside logarithmic intervals of Mcl (lower left panel) and σv (lower right panel).
feedbackby H II regions, which is not modeled in thesimulation.
In thefollowing,
we bywill
for each andcloudformedand dispersed
thecompute
SN-driven turbulence,theythe threeis then deﬁned as the following non-dimensional SFR:, and β,
thenon-dimensionalparameters,ﬁlamentary
αvir, %structure
are part of an interconnectedthat expressing
extends
SFRff º SFR [Mtr (t j ) tff ] ,(15)
the outer scaleof the turbulence,
approximatelymagnetic
ratios upof to turbulent,
gravitational,
thermal,and70–100
pc (deAvillez& Breitschwerdt
Joung etestimates
theal. ratiowhereof tff is the free-fall time at the mean density of the cloud.
energies.
Thevirial
parameter,
α , 2007;
2009; Padoan et al. 2016b), so they canvir
hardly be considered as
To evaluate the ﬂuctuations of SFRff, we also measure it within
turbulent
andgravitationalenergiesinaspherical
cloudofwell-deﬁned and long-lived isolated entities. This complex
14 shorter time intervals of length δt=Δt/14=0.12 Myr.
one-dimensional
velocity
dispersion
radius ever-changing
Rcl, mass Mnatureof MCs
is not a major concern
for thisFigure 5 shows SFRff versus αvir,e for our two cloud samples
cl, andwork, as&ourgoal is tocorrelate the SFR with the physical(empty circles). There is a clear trend of decreasing SFR withMcKee1992):σv (Bertoldi
increasing virial parameter, though with a very large scatter. Thescatter increases with increasing αvir,e and must have primarily arandom origin due to variations from cloud to cloud at ﬁxed virial(3) and time variations within each cloud, because we doparameternot detect any strong dependence of SFRff on % or β at constantαvir,e (and the scatter is much smaller in the case of the SFR
predicted by our model using the cloud parameters, as shown in
Figure 11). The origin of this scatter is discussed in Section 5.4,
wheretdyn º R cl sv,3D.
(4) we present our model predictions. To illustrate the amountof time variations, we show in Figure 6 the maximum andMtr (t j ) - Mtr (t j + Dt )minimum values of SFRff measured in the 14 time intervals,SFR º(14)Dt in the case of an idealized
The last equality in (3) is exactδt=0.12 Myr in each cloud. The characteristic scatter of SFRff
due to time variations is over one order of magnitude.
spherical
cloud of uniform density. For more realistic cloud
where, Mtr(t) is the total mass of tracers in the cloud that have not
The mean values of SFRff in logarithmic bins
13 of αvir,e aremass distributions,virial parameteris tjonly
an approxbeen accreted ontothe
sink particles
at the time t, andis the timeshown by the error-bar symbols in Figure 5, where the size ofto ofthe kinetic
jth snapshot
which the cloudistheerror bars is equal to the standard error of the mean (the rms
imationcorrespondingof the ratio
and ingravitationalenergies.
Theidentiﬁed. The SFR per free-fall time (Krumholz & McKee 2005)
divided by thesquare root of the the number of data points inparameter of MCs at a given time, rather than to follow theirlong-term evolution.
2⎛ t ⎞25sSFR
40time2Ek Myrff
To deﬁne thev R clover the⎟ ~Δt=1.68⎜ interval,
aº=vir
after the cloud identiﬁcation,
we2 tonly the totalEmass in theGMcl
3ptrack⎝dyn ⎠
gtracer particles associated with the initial cloud deﬁnition.
We
do not account for the possibility that new gas is accreted to thewhere cloudthe dynamical
time
is deﬁned
or removed fromit duringthat timeasinterval. The SFR isthus

rms Mach number is the ratio of the three-dimensional rms
velocity and the sound speed, cs:
7

al parameter for all thew the values of αvir,e ofby the solid line are thels of αvir,e. The dashedmodel computed with thegiven by Equation (28).
h a smaller exponential
e plot. The ﬁlled circlesr panel) and the six MCs

mean values follow
el (see Section 5.3)
m the simulation,
eement is nearlyh the lower-density
ghtly smaller mean
y one standard errorthe model). The
ly at large values ofthe mean values of
r of data points perll be small, if mostlues of αvir,e of theanel shows that ample with nH,min=FRff=0, even aton drops to 5% in). We ﬁnd that only
Figure 7 shows that<5×103 Me or
her nH,min samples
ots in Figure 7 rises
the scatter in SFRffThe average values
in the two samples

14292 Low-mass young stellar population and star formation history of the cluster IC#40 1805 in the W4 H II region
Neelam Panwar, M. R. Samal, A. K. Pandey, J. Jose, W. P. Chen, D. K. Ojha, K. Ogura, H. P. Singh and R. K. Yadav
MNRAS 468, 2684 (2017)
背景：• 小質量星もそのおよそ半数はmassive young clusters or
OB associationsの中で誕生する• 大質量星の影響はあるか？
例 質量関数、星形成効率、若い星のまわりの円盤の進化• IC 1805（距離~2.0kpc）: HII領域W4の中心にある若い散開星団 W4の中はOB星の星風により空洞化 bright-rimmedcloudsが見られる
観測データ：• CFHT: deep V- and R-band images (検出限界0.2 Msun）• Spitzer: IRAC (3.6, 4.5, 5.8, 8.0 micron) and MIPS (24micron)• 2MASS: JHKs bands• Chandra: 0.5-8.0 keV
結果：
1. YSO候補384星を同定（Class I/II 101星＋Class III 283星）
2. 平均年齢~2.5 Myr、質量0.3-2.5 Msun、cluster半径~5pc2688
3. 質量関数 power index -1.23+-0.23
Salpeter (-1.35) や他の星形成領域とconsistent
4. 円盤進化• 円盤を持たない星は円盤を持つ星より古い• 円盤を持つ星の割合が大質量星の近くで下がるという証拠は（統計の範囲内で）ない
5. IC 1805/W4は巨大なフィラメントから生まれたかもしれない

N. Panwar et al.

155 based on the YSO sample (left-hand panel) and 2MASS√ data (right-hand panel). The continuous curveo the observed data points. The error bars represent ± N errors.

ter. Hence, we also
sc-bearing sourcesn the 2MASS and
Myr for the cluster,using all the YSOs.
is probably due torcumstellar extinconary stages (Josenearly parallel to
es not have muchmstellar extinction
ass 0/I sources, but
PMS sources such
umstellar discs rebservations, whichmention that Joseet of optically visages are largely inl CMDs. A binary
onsequently CMD
ase of equal-massuence in the CMD
ect of binarity caners (∼10 Myr) forNGC 7160; Siciliaoung clusters likethe isochrones arege estimation will
he stars in clusters
Similarly, though
optical bands (e.g.
z-Ledesma, Mundt
lity tends to moven little effect on the5). Despite low difumber of disc-lessad due to the comsince the observed

16