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The Structur and Evolution of Molecular Clouds: From Clumps to Cores to the IMF J.P.Williams; L. Blitz; C.F.McKee. Introduction Molecular clouds are generally: Self-gravitating, Magnetized, Turbulent, Compressible fluids What do we want to understand in this paper?

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The Structur and Evolution of Molecular Clouds: From Clumps to Cores to the IMFJ.P.Williams; L. Blitz; C.F.McKee

  • 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???

3. Cloud Structures and Self-similarity

A. A categorizationn of molecular cloud structure

  • 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 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

  • 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

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 subcritical
  • MF can prevent collapse
  • 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):
  • (theoretically)

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

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
  • 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

  • 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