Introduction Molecular clouds are generally: Self-gravitating, Magnetized, Turbulent,

1. 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. 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. 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

4. 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

5. 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)

6. 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

7. 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,..)

8. 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

9. 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

10. 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

11. 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

12. 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