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
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 (10^4 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 bound
Cores
• 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
2
• 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
3
T0 P0Vcl P0 is the surface pressure
2
is the „gravitational“ pressure
W 3PGVcl PG
M
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
G
• 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
Observations:
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
(theoretically)
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
3
P0 1.8 *10 Kcm
4
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
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
processes
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-
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 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