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

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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

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• 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
  (lt10)
• General properties
• Most of mass is in giant molecular clouds
• 50pc, n100/cm2,
• 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

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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 (gt104 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

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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

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• 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

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• 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
• Thats 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

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• 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
• StutzkiGüsten recursive tri-axial gaussian
  fits
• Williams, de GeusBlitz 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
• HeyerSchloerb principal component analysis, a
  series of eigenvectors and eigenimages are
  creates which identify small velocity
  flucuasize-linewidth relation
• Langer, WilsonAnderson Laplacian pyramid
  trasform
• Houlahan Scalo algorithm that constructs tree
  for a map

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• D. Clumps
• Williams made a comparative study of two clouds
• Rosetta (starforming) and G216 (not starforming)
• Mass 105 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

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• 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 D1.4 and invariant form
  cloud
• in absence of noise, Dgt1 demostrates that cloud
  boundaries are fractal
• Probality Density Functions (PDFs) can be used
  to describe the distribution of physical
  quantaties
• you dont need clouds, clumps, cores
• density is difficult to measure
• velocity is easier to measure

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• 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 gt BE mass ? star formation
• Lower limit of cloud size
• 0.1pc N100/cm³1M_sun
• close to BE mass at 10K

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• 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-regul
  ated, because most stars form where is no
  photoionization
• accounts for the low average star formation,
  only 10 of mass are sufficiently shielded

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• B.Cores C.The origin of the IMF
• a core forms a single star
• final stage of cloud fragmentation
• average densities n105/cm3
• 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
• AndréNeri and TestiSarfent (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