Fragmentation of massive dense cores down to ~1000 AU: Relation between fragmentation and density structure

1.8 MB·

by  Aina Palau

DraftversionFebruary3,2014
PreprinttypesetusingLATEXstyleemulateapjv.2/16/10
FRAGMENTATIONOFMASSIVEDENSECORESDOWNTO.1000AU:
RELATIONBETWEENFRAGMENTATIONANDDENSITYSTRUCTURE
AinaPalau1,RobertEstalella2,JosepM.Girart1,Asuncio´nFuente3,FrancescoFontani4,BenoitCommerc¸on5,GemmaBusquet6,Sylvain
Bontemps7,8,ÁlvaroSa´nchez-Monge4,9,LuisA.Zapata10,QizhouZhang11,PatrickHennebelle5,JamesdiFrancesco12,13
DraftversionFebruary3,2014
ABSTRACT
4
Inordertoshedlightonthemainphysicalprocessescontrollingfragmentationofmassivedensecores,we
1
present a uniform study of the density structure of 19 massive dense cores, selected to be at similar evolu-
0
tionarystages, forwhichtheir relativefragmentationlevelwas assessed in a previouswork. We inferredthe
2
densitystructureofthe19coresthroughasimultaneousfitoftheradialintensityprofilesat450and850µm

n (or 1.2 mm in two cases) and the Spectral Energy Distribution, assuming spherical symmetry and that the
a density andtemperatureof the coresdecrease with radiusfollowingpower-laws. Even thoughthe estimated
J
fragmentationlevelis strictly speakinga lower limit, its relativevalueis significantandseveraltrendscould

1 be exploredwith our data. We find a weak (inverse)trend of fragmentationlevel and density power-law in-
3 dex,withsteeperdensityprofilestendingtoshowlowerfragmentation,andviceversa. Inaddition,wefinda

trendoffragmentationincreasingwithdensitywithinagivenradius,whicharisesfroma combinationofflat
]
A densityprofileandhighcentraldensityandisconsistentwithJeansfragmentation. Weconsideredtheeffects
ofrotational-to-gravitationalenergyratio,non-thermalvelocitydispersion,andturbulencemodeonthedensity
G
structureofthecores,andfoundthatcompressiveturbulenceseemstoyieldhighercentraldensities. Finally,
. a possible explanation for the origin of cores with concentrated density profiles, which are the cores show-
h
ingnofragmentation,couldbe relatedwith astrongmagneticfield, consistentwith theoutcomeofradiation
p
magnetohydrodynamicsimulations.
-
o Subjectheadings: techniques:highangularresolution—stars: formation—radiocontinuum:ISM—galax-
r ies: starclusters
t
s
a
[ 1. INTRODUCTION the predicted if gravity dominated the dynamics of the col-

lapse (see e.g., Kruijssen 2013 for a review), and the num-
1 One unavoidableingredientin the processofformationof
berofsubcondensationstypicallyembeddedinmassivedense
v intermediate/high-massstarsisthattheyareusuallyfoundas-
coresisagainsmallerbyoneorderofmagnitudethanthepre-
2 sociatedwithclustersoflower-massstars(e.g.,Lada&Lada
dicted from a pure Jeans fragmentation analysis (e.g., Hen-
9 2003;Rivillaetal.2013). However,theprocessyieldingthe
nemannetal.2009;Zhangetal.2009,2011;Bontempsetal.
2 formationoftheseclustersisnotclear,asitremainsambigu-
2010; Longmore et al. 2011; Pillai et al. 2011; Wang et al.
8 oushowacloudcorefragmentstofinallyformacluster. The
. observedstarformationefficiencyisbyfarmuchsmallerthan 2011;Leeetal.2013). Thus,abroadobservationalevidence
1 indicatesthatadditionalphysicalingredientscompetingwith
0
gravitymustplayanimportantroleinthefragmentationpro-
4 [email protected]
cess, suchas angularmomentum,stellar feedback,magnetic
1 1InstitutdeCiènciesdel’Espai(CSIC-IEEC),CampusUAB–Facultat
: deCiències,TorreC5–parell2,08193Bellaterra,Catalunya,Spain fieldsandturbulence.
v 2Departament d’Astronomia i Meteorologia (IEEC-UB), Institut de Numericalsimulationsarebecomingcrucialtoestablishthe
i CiènciesdelCosmos,UniversitatdeBarcelona,MartíiFranquès,1,08028 relative importance of each of these ingredients in the frag-
X Barcelona,Spain mentationprocess. Simulationsof fragmentationof rotating
r 3ObservatorioAstronómicoNacional,P.O.Box112,28803Alcaláde cores with different equations of state show that cores with
a Henares,Madrid,Spain
4Osservatorio Astrofisico diArcetri, INAF,LagoE.Fermi5, 50125, some angular momentum easily fragment into multiple ob-
Firenze,Italy jects(e.g.,Boss&Bodenheimer1979;Bate&Burkert1997)
5LaboratoiredeRadioastronomie, UMRCNRS8112,ÉcoleNormale andthusneedofadditionalmechanismstodecreasethefrag-
SupérieureetObservatoiredeParis,24rueLhomond,75231ParisCedex mentation down to the observed levels (see Goodwin et al.
05,France
2007 and references therein). A crucial ingredient in this
6INAF-IstitutodiAstrofisicaePlanetologiaSpaziali, AreadiRecerca
diTorVergata,ViaFossoCavaliere100,00133,Roma,Italy sense is the presence of a magnetic field. Studies on the ef-
7UniversitédeBordeaux,LAB,UMR5804,33270Floirac,France fects of magnetic fields in the evolution of a collapsing and
8CNRS,LAB,UMR5804,33270Floirac,France rotating core indicate that a strong magnetic field can sup-
9I.PhysikalischesInstitutderUniversitätzuKöln,ZülpicherStraße77, press fragmentation as it constitutes an additional form of
D-50937Köln,Germany
support and also via the so-called ‘magnetic braking’ (e.g.,
10Centro de Radioastronomía y Astrofísica, Universidad Nacional
Hosking&Whitworth2004;Mellon&Li2008;Hennebelle
AutónomadeMéxico,P.O.Box3-72,58090,Morelia,Michoacán,Mex-
ico &Teyssier 2008),whichis veryeffectivein removinga sig-
11Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, nificant part of the initial angular momentum through tor-
Cambridge,MA02138,USA
sional Alfvén waves. Similarly, radiation magnetohydrody-
12DepartmentofPhysics&Astronomy,UniversityofVictoria,POBox
namicsimulationsofturbulentmassivedensecoresshowthat
355,STNCSC,Victoria,BC,V8W3P6,Canada
13NationalResearchCouncilCanada,5071WestSaanichRoad,Victo- the combined effects of radiative feedback (e.g., Krumholz
ria,BCV9E2E7,Canada et al. 2007; Peters et al. 2011) and magnetic field can sum
2 Palauetal.
to efficiently suppressfragmentation(e.g., Hennebelle et al. locitydispersion(althoughtheselasttwopropertiesshouldbe
2011,Commerçonetal.2011;Myersetal.2013),yieldinga studied in a larger sample), and find no clear trend of frag-
bettermatchwiththeobservations(e.g.,Palauetal.2013).In mentation level with any of these core properties. In that
addition, submillimeter observationsshow that the magnetic work,twomainpropertiesofthecoresremainedtobestudied
field is importantin the dynamicalevolutionand fragmenta- in relation to fragmentation, mainly the magnetic field and
tion of massive dense cores (e.g., Girart et al. 2009, 2013; the density structure. While the magnetic field cannot cur-
Hezareh et al. 2013). Another ingredient which is probably rently be assessed in this sample in a uniformway, the den-
playingaroleinthefragmentationprocessissupersonictur- sity structurehas been studied in roughlyhalf of the sample
bulence. Theoretical studies show that turbulence generates (e.g.,Beutheretal.2002a;Muelleretal.2002;Crimieretal.
densitystructuresduetosupersonicshocksthatcompressand 2010; van der Tak et al. 2013), but the methodologyused is
fragmentthe gas efficiently, especially for large Mach num- differentforeachwork,castingsomedoubtonthevalidityof
bers (e.g., Padoan et al. 2001, Schmeja & Klessen 2004; anycomparison.Herewepresentauniformstudyoftheden-
Vázquez-Semadeni et al. 2007). More recently it has been sitystructureofeachcoreinthesampleofPalauetal.(2013),
shown that the turbulence mode, solenoidal or compressive aimingataccuratelyassessingitsimpactonthefragmentation
(e.g.,Federrathetal.2008),affectsdifferentlythecloudstruc- level.
tureandfragmentation.Solenoidalturbulencecorrespondsto In Section 2 we present the sample of cores and the data
a null divergence of the driving force (divergence-free)and used to extract the submillimeter intensity profiles and the
arisesfromgalacticrotationandmagneto-rotationalinstabili- SpectralEnergyDistributions(SEDs),andwealsopresentthe
ties,andseemstobeatworkintheRosetteandPolarisFlare envelopemodelusedtofitthesedatasimultaneouslyforeach
clouds (e.g., Hily-Blant et al. 2008; Federrath et al. 2010). core; in Section 3, we presentthe results of our fits; in Sec-
Compressiveturbulencecorrespondstoanullcurlofthedriv- tion 4, we discuss the possible trend between fragmentation
ing force (curl-free) and can be produced by expanding su- levelanddensitystructure. Finally,in Section5 wesumma-
pernovashellsorHIIregions(e.g.,Federrathetal.2010),as rizeourmainconclusions.
seeninthePipeNebulaandtheOrionBcloud(Perettoetal.
2012;Schneideretal.2013).Numericalsimulationscompar- 2. DATAANDMETHODOLOGY
ingbothtypesofturbulenceindicatethatcompressiveturbu- 2.1. Data
lencepromotesfragmentationandgenerateshighdensitycon-
Weaimatstudyingthedensitystructureofthe18massive
traststructures,whilesolenoidalturbulenceslowsfragmenta-
dense cores presented in Palau et al. (2013)plus DR21-OH,
tiondownand keepsa smoothdensity structurein the cloud
a massive dense core for which fragmentation has been re-
(e.g.,Federrathetal.2010;Girichidisetal.2011).
centlystudiedatsimilarmasssensitivitiesandspatialresolu-
Inadditiontothesephysicalagentsopposingtogravity,the
tion by Girart et al. (2013). Among the total number of 19
outcomeofnumericalsimulationsalsodependsonthegeom-
massivedensecores,16ofthemareidentifiedassubmillime-
etryandphysicalpropertiesofthecollapsingcore,inpartic-
ter sources in the catalog of Di Francesco et al. (2008) and
ular the density profile. Hydrodynamical simulations show
thushaveJamesClerkMaxwellTelescope(JCMT14)850and
that highly concentrated cores (e.g., n r 2) lead to the
H2 ∝ − 450µmdataavailable(seeDiFrancescoetal.2008forade-
formation of one single massive star, while flat density pro-
taileddescriptionontheobservations).Forthethreecoresnot
files (n r 1 or flatter) produce an important number of
H2 ∝ − included in Di Francesco et al. catalog, IRAS22198+6336,
low-mass stars (e.g., Myhill & Kaula 1992; Burkert et al.
CygX-N12and CygX-N63(followinglabeling of Bontemps
1997; Girichidis et al. 2011). This trend appears to be seen
etal.2010),weusedthesubmillimeterdataofJennessetal.
inhighresolutionobservationsofIRDCG28.34+0.06,where
(1995),whoobservedalsothe450and850µmemissionwith
threemassivedensecoreswithdifferentdensityprofilesshow
theJCMT,andtheIRAM30m1.2mmdatafromMotteetal.
varyingdegreesoffragmentation(Zhangetal.2009;Wanget
(2007).Thebeam(main+error)oftheJCMTdatawastaken
al.2011). Finally,thesubstructureofmoleculargaswithina
fromDiFrancescoetal.(2008),andthebeam(main+error)
densecore isdecreasingwith time as thecore turnsgasinto
oftheIRAM30mtelescopeat1.2mmwastakenfromGreve
stars,asshownforexamplebySmithetal.(2009).
etal.(1998). Threeregionsforwhichthe450µm datafrom
From an observational point of view, most of the studies
DiFrancescoetal.(2008)werenotusableweredownloaded
focusing on fragmentationof massive dense cores deal with
from the JCMT archive (IC1396N: m98bu24; AFGL5142:
singleregionsand/ordonotreachhighenoughspatialscales
m96bc57; W3IRS5: m02ac32). The single-dish images at
tostudyindividualfragmentsinthecore( 1000–2000AU;
∼ 450 and 850 µm (1.2 mm) for the 19 cores, together with
e.g.,Longmoreetal.2011;Pillaietal.2011;Miettinen2012;
theinterferometricimagesshowingthefragmentationineach
Beutheretal.2013;Kainulainenetal.2013;Takahashietal.
core,areshownintheAppendix(Figs. 10–13).
2013). Recently, Bontemps et al. (2010) study a sample of
Inordertocharacterizethespatialstructureofthemassive
sixmassivedensecoresinCygnusXandconductedaconsis-
dense cores, we computed the circularly averaged radial in-
tent analysis for all the regions, finding cores with a variety
tensityprofile,inringsof4 width,asafunctionofthepro-
of fragmentation levels. A subsequent study by Palau et al. ′′
jecteddistancefromthe corecenteratboth850and450µm
(2013)focusedonalistof18massivedensecores(including
whenpossible,andappliedthemodeldescribedinFig.1and
Bontempsetal.2010sources),andobservedwithsimilarspa-
Section 2.2. The intensity profiles at 850 and 450 µm are
tialresolution( 1000AU),sensitivity(downto 0.3 M ),
and field of vie∼w ( 0.1 pc of diameter), again r∼eveals d⊙if- shownin Figs. 2–5. Ascan beseen inthe figures, theemis-
∼ sionispartiallyresolvedforallthecores,revealingtheexis-
ferentfragmentationlevels,withabout 30%oftheregions
∼
showingnofragmentationatall. Palauetal.(2013)studypos-
14TheJamesClerkMaxwellTelescopeisoperatedbytheJointAstronomy
sible correlationsbetween the fragmentationlevel and prop-
Centre on behalf of the Science and Technology Facilities Council of the
ertiesofthecoressuchasmass,averagedensity,evolutionary UnitedKingdom,theNetherlandsOrganisationforScientificResearch,and
indicators,rotational-to-gravitationalenergyandturbulentve- theNationalResearchCouncilofCanada.
Fragmentationofmassivecoresdownto 1000AU 3
∼
The apertures where fluxes were assessed were figured out
b axis
fromtheliteratureoradoptedasreportedintheusedcatalogs
and references(see above), and for peak intensities we took
thebeamasapertureradius.
z dz 2.2. Model
dr
b We modeledthethermalemissionofthe coresatmillime-
r
terandsubmillimeterwavelengthswithasphericallysymmet-
observer
ric envelope of gas and dust, with density and temperature
z axis
decreasing with radius. The density and temperature were
assumed to be power-laws of radius, with indices p and q,
ρ = ρ (r/r ) p andT = T (r/r ) q. Forthedustopacitylaw
0 0 − 0 0 −
weassumedthatthedustopacityisapower-lawoffrequency
with index β, κ = κ (ν/ν )β, where ν is an arbitrary refer-
ν 0 0 0
ence frequency. The values used for the dust opacity were
Fig.1.—Sketchofthecoordinate systemusedinthemodeldescribedin
Section2.2. those of Ossenkopf & Henning (1994), for thin ice mantles
ata gasdensityof106 cm 3, i.e.κ = 0.008991cm2 g 1 for
− 0 −
ν =230GHz,beingβafreeparameterofthemodel.
0
tenceofanenvelopeofdecreasingintensitywithradius,even Inthecaseofoptically-thindustemission,intheRayleigh-
at small distances (. 10′′) from the core center. In some Jeansapproximation,andforaninfiniteradiusenvelope,the
cases, the radial profile was calculated in particular angular intensityasafunctionoftheprojecteddistancetothesource
‘sectors’ centeredon the core peak, to avoid strong negative center, I (b), can be derived analytically (see, for instance,
ν
emissionin the maps(NGC7129-FIRS2at450µm), or con- Beltránetal.2002a),andisapower-lawoftheprojecteddis-
taminationfroma nearbystrongcore(W3IRS5)or fromthe tance to the envelope center b, I (b) b1 (p+q), with index
ν −
DR21 ridge (CygX-N48, CygX-N53, DR21-OH). For these 1 (p+q). ∝
caseswedidnotusethevaluesofthefluxdensityat850and −In ourmodel, however,none of the aboveapproximations
450µm listed in Di Francesco’scatalog, butremeasuredthe (optically thin, Rayleigh-Jeans) were made, and there is no
flux densities to assure that we were not including emission analyticalexpressionfortheintensityprofile. Ingeneral,the
fromthenearbycores/ridge.ForthecaseofW3IRS5,thesec- contributionto the radiated intensity from an element of the
torwastakeninthenorth-southdirectionalsotoavoidpossi- envelopeofgeometricaldepthdz,ataradiusrfromthecenter
blecontaminationoffree-freeemissionfromstrongcentime-
(seeFig.1)isgivenby
tersources15. ForthecaseofCygX-N48,weextractedthein-
tthenessittryopnrgoDfilRe2a1vo-OidHincgotrheelcieosn;tfroibruDtiRon21fr-oOmHthanednoCrythg,Xw-hNe5r3e dIν = dIdνz(r)dz= 2ck2ν2 Jν[T(r)]e−τν(b,z)ρ(r)κνdz, (1)
weextractedtheprofileinasectorwithnorestrictionsinthe
where
east-west direction, but allowing it to extend 25′′ in the z
north-southdirection,whichcorrespondstoth∼e a±pproximate τν(b,z)= ρ(r)κνdz′, (2)
widthoftheDR21filamentintheeast-westdirection. Z−∞
The SED of each massive dense core was built from cen- with r = √b2+z2, is the opticaldepthfromthe observerto
timeterwavelengthsupto50–60µm,asthisisapproximately theelementoftheenvelopeataprojecteddistancebandpo-
the wavelength where envelope and disk contributions start sition z along the line of sight (see Fig. 1), and J (T) is the
ν
to be comparable (e.g., Crimier et al. 2010; Commerçon et Planckfunctioninunitsoftemperature,
al.2012),andhereweonlymodeltheenvelopecontribution.
hν/k
To buildthe SEDs we usedthe data compiledin Palau etal.
J (T)= . (3)
(2013),whichincludedfluxdensitiesatdifferentfrequencies ν exp(hν/kT) 1
from IRAS, JCMT/SCUBA, AKARI and IRAM30m data −
Then,theresultingintensityasafunctionoftheprojecteddis-
whenavailable.Inaddition,wemeasuredthefluxdensitiesat
tancetothesource,I (b),hastobeevaluatedas
70µmofcoreswithavailableSpitzer/MIPS2data. Fluxden- ν
sities obtainedin heavily saturatedSpitzer/MIPS2data were I (b)= +zmax dIν(r)dz, (4)
consideredaslowerlimits. Wealsoconsideredaslowerlim- ν dz
itsthemillimeter/submillimeterfluxdensitiesmeasuredwith Z−zmax
an interferometer,as partof the core emission is filtered out where z = b2+r 2 and r is the maximum radius
max max max
andwedidnottakethisintoaccountinourmodel.ForOMC- wherethe modelis calculated. The computationalburdenis
1S we recompiled the SED because the SED in Palau et al. p
(2001); I22198: Sánchez-Monge (2011); NGC2071: Butneretal. (1990);
(2013)wasbuiltforthesource136 355(about 12 north
− ∼ ′′ NGC7129: Eiroaetal. (1998),Fuenteetal. (2001),Crimieretal.(2010);
of the submillimeter peak), while now we have considered CB3: Launhardt, Ward-Thompson & Henning (1997); OMC1-S: Jaffe et
the fluxes associated with the submillimeter peak, as we are al.(1984),Lisetal.(1998),Goldsmith,Bergin&Lis(1997),Zapataetal.
modeling the submillimeter profiles. In addition, we used (2004a,b);AFGL5142: Zhangetal.(2007),Hunteretal.(1999),Sánchez-
theFIR/submillimeter/centimeterfluxesfromtheliterature16. Monge (2011); I05358NE, I22134: Beuther etal. (2002, 2007), Sánchez-
Monge (2011); I20126: Cesaroni et al. (1997, 1999, 2005), Hofner et al.
(1999), Sánchez-Monge (2011); I22134: Sánchez-Monge (2011); HH80:
15 AlthoughRichardsonetal.(1989a)estimatedthecontamination from Fernández-Lópezetal.(2011);W3IRS5:Campbelletal.(1995),Richardson
free-free emissiontobe< 25%at1.1mm,andonly< 3%at800µm,the etal.(1989a);AFGL2591:vanderTaketal.(1999),vanderTak&Menten
centimetersourcesAandBreportedbyTieftrunketal. (1997)arespatially (2005);CygX-N53,N12,N63andN48:Duarte-Cabraletal.(2013);DR21-
overlappingthecoreemissionandweprefertoavoidthem. OH:Harveyetal.(1986),Gearetal.(1988),Richardsonetal.(1989b),Motte
16 IC1396N:Saracenoetal.(1996),Beltránetal.(2002b),Codellaetal. etal.(2007),Arayaetal.(2009),Zapataetal.(2012).
4 Palauetal.
100
850 µm IC1396N 450 µm -8
10
-10
1 -12
-14
0.1
-16
0.01
I22198 -8
10
-10
1 -12
-14
0.1
-16
0.01
) )
-1m N2071-IRS1 -8 -2m
a 100 c
e -10 1
b -s
y 10 -12 g
(J er
sity 1 -14 F/ν
en -16 ν (
t 0.1 g
n o
I N7129-FIR2 -8 l
10
-10
1 -12
-14
0.1
-16
0.01
-8
CB3-mm
10
-10
1 -12
-14
0.1
-16
0.01
10 100 10 100 1 2 3 4 5
10 10 10 10 10
r (arcsec) r (arcsec) λ (µm)
Fig.2.—Bestfitsfor5regionsofthesample(seeTable1fortheexactfittedparameters). Eachrowcorrespondstoonecore,theleft(middle)panelshowsthe
radialintensityprofileat850(450)µm,withtheemptybluecirclescorrespondingtothedata,theblacksolidlinecorrespondingtothemodel,andthedashedred
lineshowingthebeamprofile;panelsontherightshowtheSED,withblueemptycirclesindicatingtheobservedfluxes,thebluefullcirclesindicatingobserved
lowerlimits,theblacksolidlineshowingthemodelforafixedaperture,andtheredsquarescorrespondingtothemodelforthesameaperturewhereeachflux
wasmeasured.
low,sincebothintegrals,thoseofEqs.2and4,canbeevalu- adoptedforradiilargerthantheradiuswherethetemperature
atedsimultaneouslyinasinglerun. distributionofindex qdropsto10K.Regardingthedensity
−
Regarding the temperature distribution of the envelope, distribution,weadopted,asmaximumradiusoftheenvelope
Chandleretal.(1998)derivefromtheexpressionsofScoville r , the radius for which the envelopedensity droppedto a
max
etal.(1976)that,fortheradiativeheatingofadustcloudby value comparableto that of the ambientgas of the intercore
a central luminous source, the temperature power-law index medium,takentobe5000cm 3.
−
qisa functionofthedustemissivityindexβ, q = 2/(4+β). Insummary,thefourfreeparametersofthe modelarethe
However,fortheouterpartoftheenvelopetheexternalheat- dustemissivityindex,β;theenvelopetemperatureattherefer-
ingcanbeimportant,andaconstanttemperatureof10Kwas enceradiusr ,T ;theenvelopedensityatthereferenceradius
0 0
Fragmentationofmassivecoresdownto 1000AU 5
∼
100
850 µm I22172N-1 450 µm -8
10
-10
1 -12
-14
0.1
-16
0.01
OMC1S136 -6
100
-8
10 -10
-12
1
-14
0.1
) )
1 2
-m A5142 -m
-8
a 10 c
e 1
b -10 -s
y 1 g
(J -12 er
y /
sit 0.1 -14 Fν
n ν
e (
t 0.01 -16 g
n o
I I05358NE l
-8
10
-10
1
-12
0.1
-14
0.01 -16
I20126
-8
10
-10
1
-12
0.1
-14
0.01 -16
10 100 10 100 1 2 3 4 5
10 10 10 10 10
r (arcsec) r (arcsec) λ (µm)
Fig.3.—SameasFig.2for5differentcores(Table1).
r ,ρ ;andthedensitypower-lawindex, p. Thereferencera- thesumoftwocircularGaussians(themainanderrorbeams).
0 0
diusr isarbitrary,andhasbeentakenasr =1000AU. Finally, the circularly averaged profile was computed from
0 0
Withthismodelwefittedtheobservedradialintensitypro- theconvolvedmap. Wealsosimulatedtheeffectofthefinite
files at 450 and 850 µm or 1.2 mm, and the observed SED chop throw used in the observationsto cancel the sky emis-
from centimeter wavelengths up to 60 µm simultaneously. sion.Thus,foreachmappositionweestimatedtheoff-source
The uncertainty adopted for the intensity profiles was 20% intensityastheaverageintensityatachop-throwdistanceof
at850µmand1.2mm,and50%at450µm(DiFrancescoet 120 fromthemap(on-source)position,andwecomputedthe
′′
al.2008). Theuncertaintyof thefluxdensitiesused tobuild difference between the on- and off-source intensities. From
theSEDwasadoptedtobe50%. this,wecomputedtheradialprofilecorrectedforchopping.
Inordertocomparethemodelwiththe observedintensity InordertocomparethemodelwiththeobservedSED,for
profile at each wavelength, we computed the intensity map eachdatapointwithwavelengthhigherthan60µmwecom-
fromthemodel,andweconvolveditwiththebeam,givenas putedthe modelflux density by integrationof the modelin-
6 Palauetal.
100
850 µm I22134-1 450 µm -8
10
-10
1 -12
-14
0.1
-16
0.01 -6
100 HH80-81
-8
10 -10
1 -12
-14
0.1
-16
) )
1 2
-m 100 W3IRS5 -6 -m
a c
be 10 -8 -1s
y -10 g
y (J 1 -12 /er
nsit 0.1 -14 νFν
e (
t -16 g
n o
I 100 A2591 -6 l
-8
10
-10
-12
1
-14
0.1
-16
CygX-N53 -8
10
-10
1 -12
-14
0.1
-16
0.01
10 100 10 100 1 2 3 4 5
10 10 10 10 10
r (arcsec) r (arcsec) λ (µm)
Fig.4.—SameasFig.2for5differentcores(Table1).
tensityprofileinsidethereportedapertureusedforeachmea- residualχ2,
surement. Inaddition,forpointswithfrequencybelow1000
GHz,weaddedthefree-freeemissionofanunresolvedsource χ2 n yoibs−ymi od(β,T0,ρ0,p) 2, (5)
with a flux density extrapolatedfrom the data points at cen- ≡ σ
timTehteerwfitatvineglenpgrtohcse.dure was the sampling of the four- where the sum enXic=o1mpasses the pioints of the intensity pro-
dimensional parameter space, using the same procedure as files at850and 450µm, and the pointsof the SED fitted by
that described in Estalella et al. (2012) and Sánchez-Monge the model. The parameter space was searched for the mini-
et al. (2013). For every set of parameters, we computed the mum value of χ2. For each source, the initial search ranges
forthefourparameterswasβ=1.5 1.5,T =300 300K,
0
± ±
ρ =(1.0 1.0) 10 16gcm 3,andp=1.5 1.0.Thesearch
0 − −
± × ±
rangewasreducedafactorof0.8aroundthebestfitvalueof
Fragmentationofmassivecoresdownto 1000AU 7
∼
10
850 µm CygX-N12 450 µm -8
1
-10
0.1 -12
-14
0.01
-16
0.001
CygX-N63 -8
1
-10
0.1 -12
) )
1 2
-m 0.01 -14 -m
a c
e -16 1
b0.001 -s
y (Jy 100 CygX-N48 -8 /erg
sit -10 Fν
n ν
e 10 -12 (
t g
n o
I -14 l
1
-16
0.1
-6
DR21-OH
100 -8
-10
10
-12
1
-14
0.1 -16
10 100 10 100 1 2 3 4 5
10 10 10 10 10
r (arcsec) r (arcsec) λ (µm)
Fig.5.—SameasFig.2forthelast4coresofTable1. ForCygX-N12andCygX-N63theprofileswereextractedfromthe1.2mmimagesofMotteetal.
(2007).
the parametersfoundforeach loop, consistingin 2000sam- widerangeofvalues. Thedustemissivityindexrangesfrom
ples of the parameter space. The final best fit values were 1.0 to 1.9, with a mean value of 1.5. This is comparable
takenafter10loops.Oncethebestfitparameterswerefound, to dust emissivity indices measured in high-mass envelopes
their uncertaintieswere estimated throughthe increase in χ2 (e.g., Mueller et al. 2002; Hill et al. 2006 for temperatures
(seeEstalellaetal.2012,Sánchez-Mongeetal.2013).Weas- between30and50K),andcorrespondstotemperaturepower-
sessedthequalityofthefitsthroughthevalueofthereduced lawindicesrangingfrom0.34to0.40(meanvalue:0.37,con-
chi-square, sistent with Emerson 1988). The fitted values for the tem-
perature at 1000 AU range from 40 to 260 K, with a mean
χ2
χ min . (6) value of 83 K, and correlate with the bolometric luminosity
r ≡ sn 4 17.Therangeofdensitiesat1000AUis(3–30) 10 17gcm 3,
− −
− with a mean value of 8 10 17 gcm 3. F×inally, the in-
In general for all the sources we found fits with χr ≃ 1, or dex of the density pow∼er law× ran−ges from− 1.5 to 2.4, with a
even less, indicating that the errorsof the data were slightly
mean value of 1.85, similar to the results found in previous
overestimated.InFig.14weshowasexample,theparameter
works focused on massive dense cores (e.g., Pirogov et al.
spacearoundthebestfitsolutionforthesourceIC1396N.
2009). The cores with steeper density profiles are I22198,
NGC7129,andI20126,whilethecorespresentingtheflattest
3. RESULTS
profilesareOMC-1S,I05358NE,W3IRS5andCygX-N12.
Figures2-4presentthebestsimultaneousfittothe850and
450µm(or1.2mm)radialintensityprofilesandtheSEDfor 17 Thetemperature at1000AUandthebolometric luminosity correlate
the19massivedensecores. Asummaryofthefittedparame- withaslopeof+0.24, followingapproximately theStephan-Boltzman law
tersispresentedinTable1. Thefourfittedparametersspana (ofslope+0.25,Table1).
8 Palauetal.
TABLE1
Best-fitparameterstotheradialprofilesandSEDofthemassivedensecores
D L a T b ρ b
bol 0 0
ID-Source (kpc) (L ) N a βb (K) (gcm 3) pb χb p c Refs.c
mm − r lit
⊙
1-IC1396N 0.75 290 4 1.41 0.19 43 4 (2.8 0.4) 10 17 1.62 0.08 0.580 1.2 1
−
± ± ± × ±
2-I22198d 0.76 340 1.5 1.46 0.31 43 5 (2.8 1.0) 10 17 2.45 0.16 0.885
−
± ± ± × ± − −
3-NGC2071-IRS1 0.42 440 4 1.09 0.21 40 3 (6.1 1.0) 10 17 1.83 0.09 0.534
−
± ± ± × ± − −
4-NGC7129-FIRS2 1.25 460 1 1.55 0.28 47 4 (5.9 1.1) 10 17 2.14 0.11 0.454 1.4 1
−
± ± ± × ±
5-CB3-mm 2.50 700 2 1.42 0.24 58 7 (7.4 1.5) 10 17 2.04 0.10 0.552 2.2 1
−
± ± ± × ±
6-I22172N-IRS1 2.40 830 3 1.49 0.23 75 10 (3.7 0.7) 10 17 1.89 0.08 0.283
−
± ± ± × ± − −
7-OMC-1S 0.45 2000 9 1.42 0.20 86 9 (8.8 1.8) 10 17 1.56 0.10 0.319 ?? 2
−
± ± ± × ±
8-AFGL5142 1.80 2200 7 1.25 0.20 70 7 (1.8 0.2) 10 16 2.00 0.05 0.361
−
± ± ± × ± − −
9-I05358+3543NE 1.80 3100 4 1.28 0.18 62 6 (6.4 1.0) 10 17 1.55 0.05 0.229 >0.8,1.5 3,7
−
± ± ± × ±
10-I20126+4104 1.64 8900 1 1.82 0.24 86 9 (8.4 1.6) 10 17 2.21 0.11 0.607 1.6,1.8,2.2 3,4,5
−
± ± ± × ±
11-I22134-IRS1 2.60 11800 3.5 1.70 0.19 82 8 (3.1 0.5) 10 17 1.76 0.06 0.477 1.3 3
−
± ± ± × ±
12-HH80-81 1.70 21900 3 1.56 0.14 108 10 (4.2 0.6) 10 17 1.78 0.04 0.473
−
± ± ± × ± − −
13-W3IRS5 1.95 140000 3.5 1.04 0.12 260 30 (2.4 0.3) 10 17 1.46 0.04 0.602 1.5,1.4 4,7
−
± ± ± × ±
14-AFGL2591 3.00 190000 1.5 0.96 0.12 250 20 (5.4 0.7) 10 17 1.80 0.03 0.549 1.0,2.0,1.0 4,6,7
−
± ± ± × ±
15-CygX-N53 1.40 300 6 1.55 0.22 45 4 (9.7 1.8) 10 17 1.76 0.07 0.487
−
± ± ± × ± − −
16-CygX-N12e 1.40 320 2.5 1.75 0.26 50 4 (3.3 0.3) 10 17 1.52 0.03 0.376
−
± ± ± × ± − −
17-CygX-N63e 1.40 470 1 1.80 0.33 45 3 (6.5 1.1) 10 17 2.03 0.07 0.570
−
± ± ± × ± − −
18-CygX-N48 1.40 4400 5 1.88 0.18 58 5 (1.0 0.2) 10 16 1.71 0.05 0.459
−
± ± ± × ± − −
19-DR21-OH 1.40 10000 11 1.60 0.26 73 7 (3.1 0.6) 10 16 1.98 0.08 0.808 1.8,1.4 4,7
−
± ± ± × ±
a L takenfromPalauetal.(2013). N isthefragmentationlevel,takenfromPalauetal.(2013)andassessedbyestimatingthenumber
bol mm
ofmillimetersourceswithinafieldofviewof0.1pcofdiameterasdetectedwithamillimeterinterferometerwithamasssensitivityof
0.3M andaspatialresolutionof 1000AU.ForthefourCygnusXcores,N hasbeenrevisedwithrespecttothevaluesgivenin
∼Palauet⊙al.(2013). ∼ mm
b Freeparameterfittedbythemodel: βisthedustemissivityindex; T andρ arethetemperatureanddensityatthereferenceradius,
0 0
1000AU;pisthedensitypowerlawindex;χ isthereducedχasdefinedinequation(6).
r
c Densitypower-lawindexfromdifferentworksintheliterature. Refs: 1: Crimieretal.(2010);2: Mezgeretal.(1990);3: Beutheret
al.(2002); 4: vanderTaketal.(2000); 5: Shinnagaetal.(2008); 6: Muelleretal.(2002); 7: vanderTaketal.(2013). ForI22134,
thereportedvalueistakenfromBeutheretal.(2002)whofittedtwopower-lawindiceswithabreakat32 ,andwegiveheretheouter
′′
power-lawindex. Toconvertfromthereportedintensitypower-lawindextothedensitypowerlawindex,Beutheretal.(2002)adopta
temperaturepower-lawindexof0.4.SimilarforShinnagaetal.(2008),forwhichthepower-lawbreakistakenat12 .
′′
d DigitizeddatafromJennessetal.(1995).
e Sourcesforwhichonlytheradialintensityprofileat1.2mmwasfitted. ForCygX-N63, N wasinferredfromnewPlateaudeBure
mm
observationsinABconfiguration(S.Bontemps,priv.communication).
Once the model was fitted to the data, we inferred differ- Wecomparedourinferreddensitypower-lawindicestothe
entquantities,whicharegivenin Table2. Theradiuswhere results of previous works where a similar methodology was
the densityreaches 5000cm 3, consideredas the ambient appliedfor some of the coresof oursample. In the two last
−
∼
density,rangesfrom0.1to1.0pc. Theregionswithsmallest columns of Table 1 we list p , the density power-law in-
lit
radii were I22198, NGC7129-1 and CygX-N63, in part due dex from the literature, together with the correspondingref-
totheconcentrateddensityprofileinferredfortheseregions, erences.Crimieretal.(2010),vanderTaketal.(2000,2013)
of p & 2. Onthe otherhand, thecoreswith largestradiiare and Mueller et al. (2002)fit one single power-law to the ra-
I05358NEandCygX-N48.Weestimatedthe‘observedmass’ dialintensityprofiles,beingcomparabletotheworkpresented
ofthecorebyintegratingthedensityprofileuptotheobserved here, while Beuther et al. (2002) used two power-laws with
radiusofthecore,whichrangedfrom5to1000M . Inaddi- a break at 32 . Within the regions fitted by the same au-
′′
tion,weestimatedthesurfacedensity(Σ )andt⊙hedensity thors the tendency of flat and concentrated profiles is con-
0.05pc
(n )ofeachcorewithinaradiusof0.05pc,asthisisthe sistent with the results foundin the presentwork(for exam-
0.05pc
radiuswhereweassessedthefragmentationlevel. Wefound ple, IC1396N is flatter than NGC7129-FIRS2 and CB3-mm
thatΣ rangedfrom 0.1upto1.8gcm 2,withamean asinCrimieretal.2010;orI20126ismoreconcentratedthan
0.05pc −
∼
valueof0.6gcm 2. Finally,theradiiwherethetemperature I22134and I05358NEas in Beuther et al. 2002). However,
−
fallsdownto10Krangedfrom0.2to18pc,beingthecores theabsolutevalueofthedensitypower-lawindicescannotbe
withhighertemperature(atreferenceradius)thosewherethis directlycomparedbetweendifferentworksbecauseofthedif-
radiusislarger. ferentmethodsapplied,whichyielddifferencesof0.2–0.4in
the density power-lawindex. The mostimportantdifference
4. DISCUSSION between previous works and this work is the way of deter-
4.1. Comparisonofdensitystructurewithpreviousworks miningthe temperatureprofile. While Muelleret al. (2002),
Fragmentationofmassivecoresdownto 1000AU 9
∼
TABLE2
Inferredandcompiledpropertiesofthedensecores
r a r a M a Σ a n a σ b σ b M b turb.
10K max obs 0.05pc 0.05pc noth init noth feedb vir
ID-Source qa (pc) (pc) (M ) (gcm 2) ( 105cm 3) β b (km−s 1) (km−s 1) (M ) α b mod.c R.c
⊙ − × − rot − − ⊙ vir
1-IC1396N 0.37 0.26 0.38 78 0.28 3.6 0.016 c? 1
− − − −
2-I22198 0.37 0.27 0.09 5 0.10 1.3 0.003 0.51 0.46 10 2.4 ?
−
3-N2071-1 0.39 0.17 0.36 80 0.45 5.7 0.066 0.42 0.72 20 1.2 c 2
4-N7129-2 0.36 0.36 0.19 81 0.29 3.6 ?
− − − − − −
5-CB3-mm 0.37 0.56 0.25 169 0.41 5.2 c? 3
− − − − −
6-I22172N 0.36 1.23 0.24 119 0.25 3.2 0.062 0.59 0.58 16 1.8 c? 4
7-OMC-1S 0.37 1.64 0.96 158 1.00 13 0.020 1.15 51 1.3 c 5
−
8-A5142 0.38 0.81 0.42 356 1.04 13 0.011 0.63 1.61 94 2.4 c? 6
9-I05358NE 0.38 0.60 0.79 1480 0.72 9.1 0.005 0.51 0.72 21 0.8 c? 7
10-I20126 0.34 2.51 0.20 68 0.38 4.8 0.004 0.38 2.00 144 10 ?
−
11-I22134 0.35 1.98 0.29 222 0.26 3.2 0.072 0.33 0.40 10 1.0 ?
−
12-HH80-81 0.36 3.64 0.32 333 0.33 4.2 0.041 0.68 0.97 38 3.2 ?
−
13-W3IRS5 0.40 18.5 0.56 971 0.32 4.0 0.021 2.16 175 15 ?
− −
14-A2591 0.40 13.9 0.36 784 0.41 5.2 0.013 1.56 97 6.1 ?
− −
15-Cyg-N53 0.36 0.32 0.56 675 0.81 10 0.41 8 0.3 c 8
− −
16-Cyg-N12 0.35 0.51 0.57 622 0.39 5.0 c 9
− − − − −
17-Cyg-N63 0.34 0.39 0.24 160 0.37 4.6 ?
− − − − − −
18-Cyg-N48 0.34 0.86 0.67 865 0.94 12 0.61 1.06 42 1.2 c 8
−
19-DR21-OH 0.36 1.26 0.58 526 1.83 23 0.240 0.61 1.48 81 1.2 c 8
a Parametersinferred(notfitted)fromthemodeling. qisthetemperaturepower-lawindex,andr istheradiusofthecorewherethe
10K
temperaturehasdroppeddownto 10K;r istheradiusattheassumed‘ambient’densityof5000cm 3;M isthemasscomputed
analyticallyfromthemodelintegr∼atinguntimlatxheradiuswherethedensityprofilecouldbemeasuredfore−achsoobusrce. Σ andn
0.05pc 0.05pc
arethesurfacedensityanddensityinsidearegionof0.05pcofradius.
b β istherotational-to-gravitationalenergyratioasinPalauetal.(2013)andaddingthenewmeasuredvaluesfromNH (1,1)forOMC-
rot 3
1S(Wiseman&Ho1998)andDR21-OH(Mangumetal.1992). σ isthenon-thermalvelocitydispersionforaquiescentnearby
noth init
core(thusafirstapproachtotheinitialvelocitydispersion),asinPalau−etal.(2013)andaddinganewvalueforCygX-N48andDR21-
OH(Mangumetal.1992). σ wasestimatedassumingatemperatureof20K.σ isthenon-thermalvelocitydispersionfor
noth init noth feedb
thestudiedcore(thusincludingo−utflowfeedbackfromthenascentprotostars)fromdatai−ntheliterature(seeSection4.4forreferences).
σ wasestimatedusingthetemperatureatradius0.05pcasinferredfromthemodeledtemperatureprofile(Tables1and2). M
noth feedb vir
andα− = M /M (with M beingthemasswithinaradiusof0.05pc)areassessedusingthenon-thermalvelocitydispersion
vir vir 0.05pc 0.05pc
includingfeedbackfromoutflows.
c ‘Turb. mode’referstotentativeturbulencemodeaccordingtoworksintheliterature: ‘c’indicatesthatadetailedstudyhasbeendone
comparingthepropertiesoftheregionwithsimulationsorstudyingtheProbabilityDensityFunction;‘c?’ indicatesthattheonlyhints
ofpossiblecompressiveturbulencearethattheregionliesattheborderofanexpandingbubble/HIIregion.Referencesaboutturbulence
mode: 1: Beltránetal.(2002b);2;Schneideretal.(2013);3: Sakaietal.(2013);4: Liuetal.(2012);5: López-Sepulcreetal.(2013);
6:Hunteretal.(1995);7:Leurinietal.(2007);8:Schneideretal.(2011);9:Schneideretal.(2006).
Crimier et al. (2010), and van der Tak et al. (2013) calcu- Before comparing the inferred density structure for each
latethetemperatureprofileself-consistentlythroughradiative massivedensecore(estimatedthroughthedensitypower-law
transfer codes, we assume that the temperature profile is re- index p), to the fragmentation level (estimated through the
latedtothedustemissivityindex(Section2.2)andleavethe N parameter, see Table 1 and Palau et al. 2013), we dis-
mm
temperature at a given radius as a free parameter. This is cuss here the main uncertainties in the assessment of these
also different to Beuther et al. (2002) work, who assumed a propertiesand possible biases. First of all we stress thatthe
fixedtemperaturepower-lawindexof0.4. Ourmethodfinds determinationofboth pandN hasbeencarriedoutapply-
mm
ingeneralflattertemperatureprofilescomparedtoCrimieret ing the same methodology and criteria to all the cores and
al.(2010)andvanderTaketal.(2013),yieldinghigherden- thus,althoughtheabsolutevaluesmightbesubjecttodiscus-
sitypower-lawindices. Ontheotherhand,ourmethodisper- sion,therelativevaluebetweentheregionsismeaningfuland
fectly consistentwith the results of Mueller et al. (2002)for validforacomparison. Inparticular,N isalowerlimitto
mm
AFGL2591. Therefore,oncethedifferentmethodologiesare the totalnumberof fragmentsbecauseof fluxmissed bythe
takenintoaccount,ourmethodologyyieldsconsistentresults interferometers,andbecausewearemissingobjectsemitting
with previousworks, and allows to fairly compare the fitted at wavelengthsdifferentto millimeter. However, the sample
parametersfromoneregiontotheother. presented in Palau et al. (2013) was selected applying strict
criteriaforthefilteredemissionanduv-coverage(seecolumn
8 of Table 3 of Palau et al. 2013), constraining this study
4.2. Uncertaintyinthefragmentationlevelandpossible to the most compact fragments (. 5000 AU). Since larger
biasesinthesample non-centrallypeakedstructuresmightbetransient,thisisnot
10 Palauetal.
tationlevelifusedtocomparethedifferentregionsandnotas
anabsolutevalue.
Apossiblebiascouldcomefromthedifferentdistancesin
thesample. However,for16outof19coresdistancesrange
only from 0.8 to 2.5 kpc, and no trend of N , p, or any
mm
of the fitted parametersvs distance is foundin ourdata (Ta-
ble 1), indicating that this is not affecting our conclusions.
Anotherbiascouldarisefromdifferentevolutionarystagesof
thecoresofoursample,assimulationsshowthatthedegreeof
substructureina clouddecreaseswithage(e.g.,Smithetal.
2009). Oursampleisnotlikelydramaticallyaffectedbythis
becausethetargetswereselectedtobeinsimilarevolutionary
stages: alltargetsharboranintermediate/high-massprotostar
detected in the far-infrared, are associated with a strong and
compactmillimeter core, are associated with molecular out-
flows, andhavenotdevelopedan(ultra-)compactHIIregion
yet. The smalldifferencesin evolutionarystage of the cores
ofthissamplewerealsostudiedinPalauetal.(2013)byesti-
matingevolutionaryindicators,andnorelationbetweenN
mm
andtheseindicatorswasfound(seee.g.,Fig. 8BofPalauet
al.2013).
Therefore,nobiasesindistance,evolutionarystageormiss-
ingfragmentsinN shouldbestronglyaffectingtheresults
mm
presentedinthiswork.
4.3. Trendoffragmentationlevelwithdensitypower-law
indexanddensity
In this Section we study the relation between the core pa-
rametersinferredfromthemodelandthefragmentationlevel,
quantifiedthroughthenumberofmillimetersourceswithina
field of view of 0.1 pc (in diameter), N , as in Palau et al.
mm
(2013). We findnotrendofβ, T andtotalmassofthe core
0
with the fragmentation level (Tables 1 and 2). Conversely,
Fig. 6 presents the relation between the density power-law
index p, the central density (at 1000 AU) ρ , and the den-
0
sity within a radius of 0.05 pc, n , with the fragmenta-
0.05pc
tionlevel. Fig.6-arevealsapossibleweaktrendofN with
mm
the density power-law index, with low fragmentation levels
foundmainlyincoreswithsteeperdensityprofiles. Concern-
ing N vs ρ , our sample splits up into two groups, cores
mm 0
with high fragmentation and high ρ , and cores with lower
0
fragmentationandlowρ ,suggestingthathighcentraldensi-
0
ties(inoppositiontoaveragedensity,asassessedinPalauet
al.2013),couldberelatedtothefragmentationlevel.Finally,
thereisacleartrendofhighfragmentationlevelsincoreswith
highn (Fig. 6-c). A closer inspectionof the data using
Fig.6.—Relation between thefitted parameter p(density power-law in- 0.05pc
statistical tests, like the Spearman’s ρ and Kendall’s τ rank
(ddeexn,spitaynewli"tah"i)n,ρ00.0(5depncsitoyfartaadiruasd,iupsaonfel10"0c0")AwUi,thpaNnemlm"b("f)r,aganmdennt0a.0ti5opnc correlationcoefficients,indicatesthatNmmand pshowafaint
level, see Table 1). In the last panel, the Jeans number is calculated as anti-correlation(ρ 0.49, τ 0.3, Pearson’s linear cor-
tMio0n.0E5pffic×cieCnFcyE(/CMFJEea)nso,fa1s7s%um(isnegeamtaeimnpteexrta)t,uarnedotfh2e0grKeeanndstaarsCionrdeicFaotermthae- relation coefficient∼R−∼ −0.3).∼A−s for n0.05pc, it is strongly
correlatedwithN (ρ 0.70,τ 0.54),andthetwoparam-
measurementsinthesimulationsofCommerçonetal.(2011)fortheµ = 2 mm ∼ ∼
(stronglymagnetized)andµ=130(weaklymagnetized)cases.Inallpanels, eters are well described by a linear relationship (R 0.90).
∼
reddotscorrespondtocoreswithhintsofcompressiveturbulence,andblue These relations indicate that the high n likely arise in
0.05pc
dotscorrespondtocoreswithnoassessmentoftheturbulencemodeinthe coreswithratherflat pandalsohighρ .
literature(seeTable2andSection4.4). 0
A trend of high fragmentation level for flat density pro-
files was already suggestedtheoretically by Myhill & Kaula
likelyaffectingourestimateofthefragmentationlevel.Inad- (1992). More recently, Girichidis et al. (2011) show, by
dition,thenumberofinfraredsourceswerecomparedtoN studying the evolution of collapsing non-magnetized turbu-
mm
and were found to be correlated, indicatingthat N is sys- lent massive cores for different initial density profiles, that
mm
tematically underestimatingthe ‘real’ fragmentationlevelof cores with a flat density profile produce a high number of
the corebyonlya factorof 2. Finally, Palauet al. (2013) protostars, while concentrated density profiles rather yield
∼
alsousedradiationMHDsimulationstoshowthatN issen- onemassive protostarin the corecenter. This can be under-
mm
sitive to the original fragmentation of the core. Altogether stoodin the frameworkof Jeansfragmentation,as the larger
suggeststhatN isalreadyagoodindicatorofthefragmen- the density, the smaller the Jeans mass (for a given tem-
mm