By Lee Hartmann
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Additional info for Accretion Processes in Star Formation, 2nd Edition (Cambridge Astrophysics)
Gravitational acceleration toward the center of a thin sheet (solid curve) or filament (dotted curve) as a function of position in units of the sheet radius R or filament length 2l (measured from the filament center). From Burkert and Hartmann (2004). 33) and thus tc = δr = v R πG 1/2 . 34) This estimate reproduces the numerical results for of the time it takes for the edge of the circular sheet to fall to the center. The important feature is that tc is independent of the size of the region δr ; this means that larger scales must be moving at larger velocities, which makes it difficult to fragment on small scales.
Note that this does not mean that older stars are not present in a given star-forming region. There are many examples where older associations abut a younger population – for example, when stellar winds, ionization, and/or supernovae pile up material, triggering a second generation of star formation (see following section). What does seem to be true is that once gas becomes compressed sufficiently, star formation ensues within 1 Myr or less; otherwise we would see many molecular clouds without any star formation, which is in contradiction with observations (Ballesteros-Paredes & Hartmann 2007).
Cold, dark molecular gas fragments by some unknown process into self-gravitating cloudlets of a few solar masses. These cloudlets or cores evolve into a critical configuration where they cannot support themselves against gravity, and nearly collapse at free-fall. Because of the rapidity of this collapse, any angular momentum transfer must be relatively inefficient, and any initial rotation of the cloud results in collapse to a multiple star system, or to a disk, or both. Since it seems rather unlikely that Protostar Debris disk T Tauri star Log mass accretion rate (solar masses/yr) FU Ori outburst 10–4 EXor outburst?