The role of molecular filaments in the origin of the CMF/IMF · 2018. 9. 10. · in mind that what we have plotted is essentially a type of mass-weighted PDF, as opposed to the volume-weighted
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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
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
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
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
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
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
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
~ 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
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
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
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
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
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.
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
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
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
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