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The role of molecular filaments in the origin of the CMF/IMF
Philippe André CEA Lab. AIM Paris-Saclay
Main collaborators: D. Arzoumanian, V. Könyves, A. Roy, P.
Palmeirim, A. Menshchikov, N. Schneider, Y. Shimajiri, B.
Ladjelate, J. Di Francesco, F. Motte, D. Ward-Thompson, J. Kirk, A.
Bracco + Herschel GBS team
Herschel GBS 160/250/500 µm composite image of Taurus B211/B213
(Palmeirim+2013)
(2007-2010)
HansFest – The Wonders of Star Formation – Edinburgh – 7 Sep
2018
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Herschel has confirmed the presence of a ‘universal’ filamentary
structure in the cold ISM 5 pc
Aquila
Könyves+2010, 15 André+2010
Herschel Gould Belt Survey
5 pc
Cosmic web
50 pc
G49 (« Giant Molecular Filament »)
Herschel Hi-GAL Molinari+2010
K. Wang+2015 Schisano+2014 Ragan+2014 Goodman+2014
Column density, NH2 (cm-2)
Column Density PDF for Aquila GMC
Av ~ 7
PDF after subtracting cores
Num
ber o
f pix
els p
er b
in:
Δ
N/Δ
logN
H2
Könyves et al. 2015
Filaments dominate the mass budget of GMCs at high column
densities cf. Schisano+2014, Könyves+2015
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Nearby filaments have a common inner width ~ 0.1 pc
Outer radius 0.5pc
background
NH
2 [cm
-2]
beam
Radius [pc]
Inner radius ~ 0.05pc
Example of a filament radial profile
~ 5 pc
Herschel 500/250 µm
Network of filaments in IC5146
Possibly linked to sonic scale of turbulence? (cf. Padoan+2001;
Federrath 2016)
Challenging for numerical simulations (cf. R. Smith+2014;
Ntormousi+2016)
D. Arzoumanian+2011 & 2018 [but some width variations along
each filament: Ysard+2013]
Num
ber o
f fila
men
ts p
er b
in
Filament width (FWHM) [pc]
Distribution of mean inner widths for ~ 600 nearby (d <
450pc) filaments
0.1
IC5146 Orion B Aquila Polaris
Ophiuchus Taurus Pipe Musca
Distribution of Jeans lengths
0.1 +- 0.05 pc
Distribution of filament lengths
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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P(k) = AISM k-2.69 + P0
Noise-subtracted, deconvolved power spectrum of Polaris
image
Spatial angular frequency, k [arcmin-1]
Pow
er:
P(k)
[Jy2
/sr]
Miville-Deschênes et al. 2010
MJy
/sr
Is a characteristic filament width consistent with the observed
power spectrum of cloud images?
Panopoulou+2017
Tension with scale-free power spectrum SPIRE 250 µm image of
Polaris
translucent cloud
4 pc
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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A simple experiment Injecting a population of synthetic 0.1 pc
filaments with contrast ~ 50% in SPIRE 250 µm image of Polaris
translucent cloud
A. Roy et al. 2018
4 pc
P(k) = AISM k-2.75 + P0
Spatial angular frequency, k [arcmin-1]
Pow
er:
P(k)
[Jy2
/sr]
Power spectrum of image with synthetic 0.1 pc filaments
Synthetic filaments contribution
Conclusion: Observed power spectra remain consistent with a
characteristic filament width ~ 0.1 pc for realistic filling
factors and filament contrasts
Synthetic
Original
Spatial angular frequency, k [arcmin-1] Res
idua
ls: P
ower
-law
− F
it
Difference from power-law fit
MJy
/sr
4 pc
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Assessment of the reliability of derived filament widths through
extensive tests
Arzoumanian+2018
1 de
g
Populations of synthetic Gaussian-shaped or Plummer-shaped
filaments distributed in realistic background column density
map
Comparison between measured and input distributions of filament
widths : Input distributions of FWHM widths
Color: Measured distributions
FWHM [pc]
Num
ber o
f fila
men
ts
FWHM [pc] FWHM [pc]
δ dist. PL dist. Flat dist. ! No significant bias for
high-contrast filaments (C > 0.5)
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Comprehensive study of HGBS molecular filaments
Arzoumanian+2018
(for 1310 extracted filaments, including 599 `robust’ filaments,
in 8 regions of the GB)
Ø Confirmation of the main result of Arzoumanian+2011 with
better statistics and better controlled measurements
Distribution of mean inner widths for 599 filaments
Num
ber o
f fila
men
ts p
er b
in
Filament width (FWHM) [pc]
0.1 0.2 [pc] beam
Example of a filament radial profile in Orion B
NH
2 [cm
-2]
Radius [pc]
Outer width 1.2pc
Inner width ~ 0.09pc
Mean crest-averaged width: 0.1 pc Median crest-averaged width:
0.09 pc Standard deviation: 0.05 pc Inter-quartile range: 0.07
pc
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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~ 75 % of prestellar cores form in filaments, above a column
density threshold NH2 > 7x1021 cm-2
Prestellar cores form primarily within filaments, above a column
density threshold NH2 > 7x1021
cm-2
1021 1022 Aquila curvelet NH2 map (cm
-2)
1
Unbound
Mline /M
line,crit 0.1
Unstable
Prestellar cores form primarily within filaments, above a column
density threshold NH2 > 7x1021
cm-2
~
Prestellar cores form primarily within filaments, above a column
density threshold NH2 > 7x1021
cm-2
- 5 +15
Könyves et al. 2015, A&A
A census of dense cores in the Taurus L1495 cloud 7
in the range 35 ± 14 M⊙ pc−1. Our mean value is abouta factor of
two larger than the value 15 M⊙ pc
−1 foundby Hacar et al. (2013) using N2H
+ observations, and thevalue 17 M⊙ pc−1 found by Schmalzl et al.
(2010) based onnear-infrared extinction measurements. The reason
for thediscrepancy is not clear, but it is significant that all
threeestimates are greater than or equal to the theoretical valueof
16 M⊙ pc
−1 for an isothermal cylinder in pressure equi-librium at 10 K
(Inutsuka & Miyama 1997). This suggeststhat all of the
prestellar cores in L1495 are located in su-percritical filaments,
in agreement with the HGBS findingsin Aquila (André et al. 2010;
Könyves et al. 2015). We notethat none of the above estimates
includes the contributionof the extended power-law wings whose
inclusion further in-creases the estimated line mass. For example,
the line massintegrated over the full filamentary cross section of
the B211filament is 54 M⊙ pc
−1 (Palmeirim et al. 2013), and this isconsistent with an
aperture-based estimate, ∼ 51 M⊙ pc
−1,obtained from our high-resolution column density map
bydividing the total mass of the filament by its length,
afterhaving subtracted the estimated diffuse background.
6.2 Relationship to unbound starless cores
While the majority of our starless cores are
gravitationallyunbound and therefore not prestellar, they
nevertheless canprovide some important information relevant to star
forma-tion. For example, they may represent density
enhancementsresulting from the interstellar turbulence widely
consideredto play a dominant role in the determination of the IMF
(see,for example, Padoan & Nordlund (2002)). The
probabilitydistribution function (PDF) of the gas density produced
bysupersonic turbulent flow of isothermal gas is well approxi-mated
by a lognormal form (Elmegreen & Scalo (2004) andreferences
therein). It is therefore of interest to plot a his-togram of
estimated density values for the L1495 starlesscores, and this
histogram is shown in Fig. 8. These densitiesare mean values,
calculated by dividing the mass of each coreby its total volume,
based on the estimated outer radius,taken to be the deconvolved
FWHM of the source. Thesedensities also correspond to the n(H2)
values listed in TableB2 of Appendix B. For consistency, the same
completenesscorrection was applied to the starless core histogram
as forthe starless CMF in Fig. 5 although, as it turned out,
thecorrection had negligible effect. It can be seen that, in
sharpcontrast to the CMF, the density distribution is
accuratelylognormal except for a tail at high densities. Note
againthat the difference is not a reflection of incompleteness
sinceapplication of the completeness correction discussed in
Ap-pendix A had no appreciable effect.
The variance in log density may provide information onthe
kinetic energy injection mechanism, the Mach number,and the
magnetic field (Molina et al. 2012). To compareFig. 8 with
turbulence models, however, it must be bornein mind that what we
have plotted is essentially a type ofmass-weighted PDF, as opposed
to the volume-weighted ver-sion usually presented in simulations.
More quantitatively,if we make the simplifying assumption that the
density isuniform within an individual core (as would be the case
for
Figure 6. The locations of prestellar cores (red circles) with
re-spect to filamentary structure, shown with the same field of
viewas for Fig. 1. The image has been rotated such that
equatorialnorth is 52◦ anticlockwise from vertical. The filamentary
struc-ture represents a limited-scale reconstruction, up to a
transversespatial scale of 0.1 pc, obtained using the getfilaments
algorithm(Men’shchikov 2013). The greyscale values correspond to
the to-tal (unfiltered) background line densities within the
boundariesof the reconstructed features, based on an assumed
characteristicfilamentary width of 0.1 pc, and are truncated at an
upper valuecorresponding to 16 M⊙ pc−1 (100% on the greyscale). As
a re-sult, the portions in black have a mass per unit length in
excessof the approximate threshold for cylindrical stability.
pressure-confined clumps5 that probably form the bulk ofthe
unbound core distribution) and assume a mass-radiuslaw of the form
M ∝ Rk, then the core density histogram of
5 We do not, of course, assume that all cores have the same
den-sity. The distribution of core densities would reflect the
range ofexternal pressures.
c⃝ 2002 RAS, MNRAS 000, 1–13
Marsh al. 2016, MNRAS
Taurus B211/3+L1495 Σ > 150 M /pc2
~ getfilaments NH2 map = cores = cores
Also:Bresnahan+2017
(CrA)Benedettini+2018 (Lupus) Ladjelate+2018
(Oph)Könyves+2018 (Orion B) …
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Sharp transition around a fiducial value Av ~ 7 " Σ ~ 150 M pc-2
" M/L ~ 15 M /pc
Strong evidence of a column density “threshold” for the
formation of prestellar cores
CFE(AV) = ΔMcores(AV) / ΔMcloud(AV) Könyves et al. 2018,
A&A
Prestellar CFE as a function of background AV
7
Herschel GBS Orion B
Background column density [Av units]
Cor
e fo
rmat
ion
effic
ienc
y [u
nitle
ss]
20%±5%
Turbulence-regulated models of SF (εff ~ 1%) cf.
Krumholz+2012
André+2010; Könyves+2015
Interpretation: Critical M/L of nearly isothermal cylinders
(Ostriker 1964; Inutsuka & Miyama 1997)
Mline, crit = 2 cs2/G ~ 16 M /pc for T ~ 10 K
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Core Mass Function (CMF) in Aquila Complex
Num
ber o
f cor
es p
er m
ass b
in: Δ
N/Δ
logM
Mass (M )
0.6+/-0.2 M
Jeans mass:
MJeans ~ 0.5 M × (T/10 K)2 × (Σcrit/160 M pc-2)-1
Ø CMF peaks at ~ 0.6 M ≈ Jeans mass in marginally critical
filaments
Filament fragmentation can account for the peak of the
prestellar CMF and the “base” of the IMF
CMF
Inutsuka & Miyama 1997
~ 450 prestellar cores
Ø CMF peaks at ~ 0.6 M ≈ Jeans mass in marginally critical
filamentsØ Close link of the prestellar CMF to the stellar IMF: M★
~ 0.4 × Mcore Ø Characteristic stellar mass may result from
filament fragmentation
(see also Motte+1998; Alves+2007)
+0.2 -0.1
André+2014 PPVI; Könyves+2015
0.6+/-0.2M
CMF
IMF (Kroupa 2001)
× ε
(Chabrier 2005)
system IMF
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Angularfrequency,s[arcmin-1]
P(s)[M
#2/pc]
Powerlawfit
Spa>alfrequency,s[pc-1]
Beam-corrected
Uncorrected
Beameffect
Statistical properties of filament line-mass fluctuations
Meanpowerspectrumslope
80filaments
Nb.offilamentsperbin
α=-1.6±0.3
Powerspectrumindex,α
α = -1.6
Filament’screst
NH2[1021cm-2]
Mline[M
#/pc]
Fluctua>ons
alongcrest
Offset[arcmin]
Distribution of power spectrum slopes consistent with 1D
Kolmogorov spectrum (-5/3)
Powerspectrumofline-massfluctua4ons
Roy+2015
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Core Mass, M/Mmin
dN/d
M
Evolution toward a Salpeter-like core mass function with initial
power spectrum index αobs = -1.6
Inutsuka 2001
Implications for the prestellar CMF and the IMF
A Salpeter IMF can be produced by filament fragmentation
provided turbulence has generated a Kolmo- gorov-like power
spectrum of initial density fluctuations (Inutsuka 2001)
Inutsuka & Miyama 1992, 1997
Squa
re o
f gro
wth
rat
e
Wavenumber
Dispersionrela4oninacylinder
kmax
0kmax" Mmin
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Given filament properties (cf. Arzoumanian+2011, 2013,
2018):
Mline ~ Σfil × Wfil ~ Mline, vir ≡ 2cs,eff2/G with Wfil ~ 0.1
pc
MJeans ~ MBE ~ 1.3 cs,eff4/(G2Σfil) Σfil Mline
ΔN/ΔlogMBE MBE-1.4+-0.2
(Salpeter index: -1.35)
Salpeter-like distribution of characteristic core masses from
distribution of filament line masses Local effective Jeans mass in
a thermally supercritical filament:
ΔN/ΔlogMline Mline-1.4+-0.2
Num
ber o
f fila
men
ts p
er M
line b
in
ΔN
/Δlo
gMlin
e
Mass per unit length, Mline (M /pc)
Distribution of line masses for HGBS filaments
16 M /pc
Full CMF/IMF results from the convolution of the distribution of
filament line masses by the CMF in individual filaments (Y.-N. Lee,
Hennebelle, Chabrier 2017)
cf. André+2014 PPVI
Ph. André – HansFest – Edinburgh – 7 Sep 2018
André, Arzoumanian et al., in prep.
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Median prestellar core mass vs. background column density
Background column density [Av units]
M
edia
n co
re m
ass [
M]
(cor
rect
ed fo
r inc
ompl
eten
ess)
Equivalent line mass of parent filament [M /pc] (Orion B)
Könyves+2018
Lower quartile
16
Median core mass and dispersion of core masses increase with
background column density
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Dependence of the prestellar CMF on background cloud (column)
density
(OrionB) N
umbe
r of c
ores
per
mas
s bin
: ΔN
/Δlo
gM
Mass (M )Könyves+2018 HGBS survey results
Global prestellar CMF
CMF at AV < 7 back
CMF at AV > 7 back
Ø Broader CMF at higher background column densities (i.e.
higher Mline filaments)
Ph. André – HansFest – Edinburgh – 7 Sep 2018
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Summary: A filamentary paradigm for star formation and the
IMF?
Ø Herschel results support a filamentary paradigm for star
formation and the IMF although many issues remain open and/or
strongly debated
Ø Filament fragmentation appears to produce the peak of the
prestellar CMF and likely accounts for the « base » of
the IMF
Ø Salpeter power law of IMF may arise from a combination of two
effects: 1) Salpeter power-law distribution of supercritical
filament M/L (due to accretion ?), 2) differential growth of an
initial Kolmogorov spectrum of density fluctuations along the
filaments
Ph. André – HansFest – Edinburgh – 7 Sep 2018