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19_-_Star_Formation

# 19_-_Star_Formation - Prospectus Jeans Mass when will a...

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19 Star Formation: all possible complexity and then some! 2 Prospectus • Jean’s Mass, when will a cloud collapses. • The Free Fall. • Kelvin-Helmholtz and the time scale. • Eddington Limit, gravitational potential and luminosity. 3 The way to the main sequence 4 Star Formation Happens in the Dark

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5 The Jeans Radius & Mass •A simple energetic argument can give a rough approximation for the conditions required for a molecular cloud to collapse and form stars. •The virial theorem relates (time-averaged) kinetic to potential energy, for a stable, gravitationally bound system, |U| > 2KE. •This indicates a stability criterion: if the kinetic energy, e.g. temperature, is too low the cloud will collapse under the force of gravity. 1 2 0 15 4 J p kT R G m π μ ρ 5 J J p kT M R G m μ 3 18 J T M M n Θ = Quick & dirty relation. 6 Jeans Mass via the Virial Theorm 2 2 1 2 3 Potential energy & = const 5 3 Kinetic energy 2 3 3 2 note: 2 5 2 15 5 4 c c c p c c c p p J GM U R KE NkT M N m GM M kT U KE R m GM m kT R kT G ρ μ μ μ π ρμ = - = = = = = 7 Jeans Mass via the Crossing time 2 2 2 2 2 1 2 1 Free fall time (squared) Crossing time (squared) 3 1 Set them equal & solve for R 3 3 4 3 9 p p p p J p G m R kT m R G kT kT R G m GM m kT R G m kT τ ρ μ τ μ ρ ρμ π μ ρμ = = = = = 8 Example: Diffuse HI clouds •Calculate the Jeans mass for diffuse clouds: 8 3 100 50 5 10 Sun M M T K n m - < = = × This is much greater than the stellar mass. So why are diffuse clouds are stable? What is preventing their collapse? 2 3 100 50 5 10 H/c 860 Sun J Sun M M T K n m M M < = = ×
9 Example: Molecular cloud cores What is the Jeans mass for a molecular cloud core? Thus these cores should be collapsing under their own gravity, and they are consistent with their association with the sites of star formation. 8 3 2 10 / 1000 150 10 H / 15 Sun J Sun M M T K n cm M M < < = = 10 So why don’t some clouds collapse while other do? • The Giant Molecular Clouds, GMCs, appear to be stable over long periods of time. • If they did collapse they should form very massive stars. • This is a puzzle. Something is preventing the GMC from collapsing. • Rotation and magnetic fields are often mentioned. But they are not obvious solutions. The magnetic fields and rotation become stiffer as the clouds collapse! 11 Once a Cloud begins to Collapse •A collapsing molecular cloud starts off simply: head2right In free-fall, assuming the pressure gradients are too small to have much effect head2right The gas is approximately isothermal, if gas is optically thin so energy can be efficiently radiated away.

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19_-_Star_Formation - Prospectus Jeans Mass when will a...

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