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The Structur and Evolution of Molecular Clouds


									    The Structur and Evolution of
  Molecular Clouds: From Clumps to
          Cores to the IMF
             J.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
            2. The large Scale View

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

• 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, 10 M 
• 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???
 3. Cloud Structures and Self-similarity
A. A categorizationn of molecular cloud structure

• 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 are coherent regions in l-b-v space
• massive star-forming clumps create star clusters
• most clusters are unbound, but most clumps are bound
• Cores are regions where single stars form
• they are gravitationally bound
• material for the star formation can be accreted from the
surrounding ISM
      B. The virial theorem for molecular clouds

                     1 
Virial theorem:        I  2(T  T0 )  M  W
• 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)

           3   1 2      3
  T   ( Pth  v )dV  P Vcl
       Vcl 2   2        2
Vcl                          P
   is the Volume of the cloud, th is the termal pressure,
P is the mean pressure
  T0  P0Vcl               P0   is the surface pressure
                                is the „gravitational“ pressure
  W  3PGVcl             PG

  P  P0  PG (1       )
                   |W |
 mean pressure=surface pressure+wight of material, reduced
by magnetic stress
The magnetic term

• MF play a crucial role in the structure and evolution of MC

First we consider poloidal fields:
                                c 
• Magnetic critical mass: M  
• ratio of mass to the „magnetic critical mass“ is a measure
for relative importance of MF

• M  M  cloud is magnetically subcritical
MF can prevent collapse

• M  M  cloud is magnetically supercritical
 MF cannot prevent collapse

Toroidal fields can provide a confining force
reduce of magnetic critical mass

Are MF super or subcritical?
• cloud B1 (Crutcher 1994): marginally sub and super
• more clouds (Crutcher 1999) super
• McKee(1989), Bertoldi&McKee(1998):  M / M   2
Are molecular clouds gravitationally bound?

The total energy is   E  T  M W
With the virial theorem we can write

          3             M 
                      | W | Vcl
       E   P0  PG 1     
          2                

If there is no magnetic field, the cloud is bound if PG  P0

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
 P0  1.8 *10 Kcm

• 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
           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 cloud
Get 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. Clumps
Williams 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 P  AD / 2
• 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
          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
Upper 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 formation
Lower 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 clusters
Important for efficency and rate of star formation
IMF 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-
• 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 clusters
Search 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

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