The formation of stars and planets

1
The formation of stars and planets

• Day 2, Topic 3
• Collapsing clouds
• and the
• formation of disks
• Lecture by C.P. Dullemond

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Spherically symmetric free falling cloud
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Inside-out collapse of metastable sphere
(warning strongly exaggerated features)
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Hydrodynamical equations
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Inside-out collapse model of Shu (1977)

• The analytic model
• Starts from singular isothermal sphere
• Models collapse from inside-out
• Applies the trick of self-similarity
• Major drawback
• Singular isothermal sphere is unstable and
  therefore unphysical as an initial condition
• Nevertheless very popular because
• Only existing analytic model for collapse
• Demonstrates much of the physics

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Inside-out collapse model of Shu (1977)
Expansion wave moves outward at sound speed. So a
dimensionless coordinate for self-similarity is
Now solve the equations for ?(x), m(x) and u(x)
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Inside-out collapse model of Shu (1977)
Solution requires one numerical integral. Shu
gives a table.
For any t this can then be converted into the
real solution
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Inside-out collapse model of Shu (1977)
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Inside-out collapse model of Shu (1977)
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Inside-out collapse model of Shu (1977)
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Inside-out collapse model of Shu (1977)
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Inside-out collapse model of Shu (1977)
Stellar mass grows linear in time
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A simple numerical model
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A simple numerical model
Temperature 30 K Outer radius 5000
AU Initial condition BE sphere with ?c
1.2x10-17 g/cm3
?(r)
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A simple numerical model
A more realistic non-static model Make
perturbation, but keep mass the same.
?(r)
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A simple numerical model
?(r)
Strong wobbles, but it remains stable
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Observations of such dynamical behavior
Lada, Bergin, Alves, Huard 2003
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A simple numerical model
Now add a little bit of mass (10) to nudge it
over the BE limit
?(r)
Cloud collapses in a global way (not really
inside-out)
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Maps of pre-stellar cores
Shirley, Evans, Rawlings, Gregersen (2000)
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Maps of class 0 sources
Shirley, Evans, Rawlings, Gregersen (2000)
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Line profile of collapsing cloud
Optically thin emission is symmetric
Blue, i.e. toward the observer
Red, i.e. away from observer
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Line profile of collapsing cloud
But absorption only on observers side (i.e. on
redshifted side)
Flux
?
Blue, i.e. toward the observer
Red, i.e. away from observer
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Collapse of rotating clouds
Infalling gas-parcel falls almost radially
inward, but close to the star, its angular
momentum starts to affect the motion. At that
radius rltltr0 the kinetic energy v2/2 vastly
exceeds the initial kinetic energy. So one can
say that the parcel started almost without energy.
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Collapse of rotating clouds
Radius at which parcel hits the equatorial plane
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Collapse of rotating clouds
For larger ?0 larger re
If rc lt r, then mass is loaded directly onto
the star
If rc gt r, then a disk is formed
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Protostellar disks and jets

• Most of infalling matter falls on the equator and
  forms a disk
• Friction within the disk causes matter to accrete
  onto the star
• Jets are often launched from the inner regions of
  these disks
• A jet penetrates through the infalling cloud and
  opens a cavity

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Spectra of collapsing cloud star disk
Whitney et al. 2003
Class 0
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Spectra of collapsing cloud star disk
Whitney et al. 2003
Class I
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Spectra of collapsing cloud star disk
Whitney et al. 2003
Class II
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Spectra of collapsing cloud star disk
Whitney et al. 2003
Class III