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

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


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


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


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)


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


~ 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


cm-2

~


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) …


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


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


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


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


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


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


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)


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


Documents

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