The Structur and Evolution of Molecular Clouds: From Clumps to

Cores to the IMFJ.P.Williams; L. Blitz; C.F.McKee

1. Introduction

Molecular clouds are generally:• Self-gravitating,• Magnetized,• Turbulent,• Compressible fluids

What do we want to understand in this paper?• Physics of molecular clouds till the

starformation

2. The large Scale View

• Detection in Infrared• Possible today: map entire complexes in subarcminute resoltuion

Instruments:• FCARO 14m,NRAO 12m: Focal plane arrays for one dish• IRAM 30m: 4 receivers at different frequencies• IRAM, OVRO, BIMA: advances in interferometry (<10‘‘)

General properties:• Most of mass is in giant molecular clouds• ~50pc, n~100/cm^2, • No larger clouds (disrupted by some physical process)

Outer Galaxy:• no distance ambiguity, less blending of emission more details than in inner galaxy• large regions with little or no CO emission• emission only in spiral arms (28:1) lifetime of MC smaller than arm crossing time ~10^7 years• ??? the same in inner galaxy (maybe 10:1, maybe half of the gas is nonstarforming between the arms)

• HI Halos around the cloud• many small clouds (0.4kpc) become one large one densityinhomogeneities because of star formation or starting condition???

M6510

Categorization:Clouds • MC are regions where the gas is primariliy molecular• almost all MC are detectable in CO• small (100 M_sun) and big ones (>10^4 M_sun)Clumps • Clumps are coherent regions in l-b-v space• massive star-forming clumps create star clusters• most clusters are unbound, but most clumps are boundCores• Cores are regions where single stars form• they are gravitationally bound• material for the star formation can be accreted from the surrounding ISM

3. Cloud Structures and Self-similarityA. A categorizationn of molecular cloud structure

Virial theorem:

• I is the moment of inertia• T is the total kinetic energy, T0 is surface term• M is the magnetic energy• W is the gravitational energy• I can be neglected in clouds not to turbulent (sign)

is the Volume of the cloud, is the termal pressure,

is the mean pressure

is the surface pressure

is the „gravitational“ pressure

mean pressure=surface pressure+wight of material, reduced by magnetic stress

clGVPW 3

clV th VPdVvPTcl 2

3)

2

1

2

3( 2

)||

1(0 W

MPPP G

)(5

3 2

R

GMaW

clVPT 00 2

3

PthPclV

0P

GP

WMTTI )(22

10

B. The virial theorem for molecular clouds

The magnetic term

• MF play a crucial role in the structure and evolution of MC First we consider poloidal fields:

• Magnetic critical mass:

• ratio of mass to the „magnetic critical mass“ is a measure for relative importance of MF

• cloud is magnetically subcriticalMF can prevent collapse

• cloud is magnetically supercritical MF cannot prevent collapse

Toroidal fields can provide a confining forcereduce of magnetic critical mass

Observations:Are MF super or subcritical?• cloud B1 (Crutcher 1994): marginally sub and super• more clouds (Crutcher 1999) super• McKee(1989), Bertoldi&McKee(1998): (theoretically)

MM

MM

G

cM

2/ MM

Are molecular clouds gravitationally bound?

The total energy is

With the virial theorem we can write

If there is no magnetic field, the cloud is bound if

That‘s good approximation for magnetized clouds too. !! We used time averaged virial theorem !!

Surface pressure because of• cosmic rays (neglected, they pervade the cloud)• magnetic pressure• gas pressure

Results:• molecular Clouds are at least marginally bound• in vicinity to sun, they are bound • clumbs are rather confined by pressure• but massive starforming clumbs are rather confined by gravity

WMTE

clG VW

MPPE

||1

2

30

0PPG

340 10*8.1 KcmP

C. Structur analysis techniques

Molecular Clouds can be mapped via• radio spectroscopy of molecular lines (x,y and v, 3-D)• continuum emission from dust (x,y, 2-D)• stellar absorbtion of dust (x,y, 2-D)

There exist many different etchniques:1. decompose data into a set of discrete clumps• Stutzki&Güsten: recursive tri-axial gaussian fits• Williams, de Geus&Blitz: identify peaks trace contours• clumps can be considered as „builiding blocks“ of cloudGet size-linewidth relation, mass spectrum, varitaion in cloud conditions as a function a position• first is to steep, second to flat

2. many more complicated techniques:• Heyer&Schloerb: principal component analysis, „a series of eigenvectors“ and „eigenimages“ are creates which identify small velocity flucuasize-linewidth relation• Langer, Wilson&Anderson: Laplacian pyramid trasform• Houlahan &Scalo: algorithm that constructs tree for a map

Most important results:• self-similar structures• power-law between size and linewidth features• power law of mass spectra• power law has no characteristic scale scalefreeness Description with fractals (even if there filaments, rings,..)

D. ClumpsWilliams made a comparative study of two clouds• Rosetta (starforming) and G216 (not starforming)• Mass ~10^5 M_sun, • resolution spatial 0.7pc, velocity 0.68 km/s• 100 clumps were cataloged• sizes, linewidth and masses were calculated• basic quantities are related by power laws • the same index in each cloud, but different offsets• clumps in nonstarforming cloud are larger Rather change of scale than of nature in clouds• in Rosetta only starformation in cound clumbs Maybe: no bound clumbs in G216 no starformation• what the interclumb medium is remains unclear• pressure bound, grav. bound: density profile is the same

E. Fractal Structures

• self similar structure• supersonic linewidth trubulent motions for which one would expect fractal structure (Mandelbrot 1982)• fractal dimension of a cloud boundary of Perimeter-area relation of map• different studies find D~1.4 and invariant form cloud• in absence of noise, D>1 demostrates that cloud boundaries are fractal

• Probality Density Functions (PDFs) can be used to describe the distribution of physical quantaties• you don‘t need clouds, clumps, cores• density is difficult to measure• velocity is easier to measure

2/DAP

F. Departures from self-similiarity• there is a remarkable selfsimilarity• but as a result there is no difference between clouds with different rates of star formation• selfsimilarity cannot explain detailed starforming processesUpper limit of cloud size:• Def.: Bonnor-Ebert mass: largest gravitationally stable mass at exterior pressure for nonmagnetic sphere• generalization of BE mass gives upper limit for size• if cloud mass > BE mass star formationLower limit of cloud size:

0.1pc; N=100/cm³~1M_sun close to BE mass at 10K

unbound clouds, no star forming selfsimilarity at much smaller sizes

IV. The Connection between cloud structure and star formation

A. Star-forming clumps

Star forming clumbs:• are bound and form most of the stars• form star clustersImportant for efficency and rate of star formationIMF is related to the fragmentation of clumps

• median column density of molecular gas is high in outer galaxy (Heyer 1998)• most of mass of a mol. cloud is in the low c.d. line of sight• such gas is ionized predominately by interstellar far UV-radiation• low-mass star formation is „photoionization-regulated“, because most stars form where is no photoionization• accounts for the low average star formation, only 10% of mass are sufficiently shielded

B.Cores & C.The origin of the IMF

• a core forms a single star • final stage of cloud fragmentation• average densities n~10^5/cm^3• can be observed in high exitation lines, transitions of mol. With large dipole moment, dust cintinuum emission• at milimeter and submilimeter wavelength• surface filling fraction is low, even in starforming clustersSearch for starformation to find cores• André&Neri and Testi&Sarfent (1998) made large array observeys, (are able to find cores too)• they find many young protostars• but also starless, dense condensations

• core mass spectra are steeper than clump mass spectra• it resembles the initial mass function (IMF)• but: one has to show that the starless cores are selfgravitating