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Protostellar
evolution
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Timescales
Collapse
Evolution
Deuterium burning
Rotation
Disks
Observations of disks and protostars
Peter Schilke
Inside out collapse
Peter Schilke
Inside out collapse
3
s
m0 v
Inside-out collapse: the central mass M ∗ t =
t
G
2G M ∗ t 
u r , t =−
( free-fall velocity)
r
and the accretion rate
3
3/ 2
m0 v s
T
2
−6
Ṁ =4  r  u=
≈2×10 M ⊙
G
10 K
5
so it takes about 5×10 years for 1 M ⊙

 
Peter Schilke
Protostellar development timescale
Kelvin­Helmholtz timescale:
(timescale for which a star can create its luminosity out of gravitational energy): KH =
m
E g =G
r
dE g
dt
2
Eg
dE g /dt
M
R
with m= , r =
2
2
2
=L
GM
KH =
2RL
Peter Schilke
Mass­Luminosity Relation: L ∝ M3.2
Mass­Radius relation: R ∝ M0.6
Peter Schilke
K­H Timescale: KH ∝ M­1.8
detailed models
Peter Schilke
Palla & Stahler (1990)
tKH=tacc
dM/dt=10-5 MO/yr
r
Ze
oe
ag
m
n
ai
ce
en
qu
se
Sun
Timescales
Peter Schilke
Models of star formation
Example:
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collapse of cylindrical, magnetized cloud
gradual collapse and accretion through ambipolar diffusion initially
rapid collapse after cloud becomes magnetically
supercritical
Peter Schilke
Models of star formation
Peter Schilke
Density
Peter Schilke
Evolution
As the clump collapses, the dust becomes
optically thick
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it's not longer isothermal any more
heats up until hydrostatic core (first core) is
formed which is thermally supported
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Mass about 0.05 M⊙
Size about 5 AU
3 ℜT
internal energy U =
M
2 
GM
equal to gravitational energy W =−
R
−1
M
R
 GM
T=
=850 [K]
3ℜ R
0.05 M ⊙ 5 AU

 
Peter Schilke
Central temperature
Peter Schilke
Breakdown of first core
thermal energy per molecule at 2000 K is
about 0.74 eV
dissociation energy of H2 is 4.48 eV
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for quite some time the gravitational energy
goes into dissociation of H2 and NOT into raising the temperature while the density rises
Discussion of Bonnor-Ebert spheres:
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at some critial density the core is unstable to
collapse and cannot be supported thermally any
longer
Peter Schilke
Accretion luminosity
At some point the temperature is high
enough to ionize hydrogen (13.6 eV
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dynamically stable protostar
Radius of several R⊙
Mass 0.1 M⊙
T > 105 K
Accretion on this object still going on
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all energy is converted into Luminosity
   
G M ∗ Ṁ
M∗
R∗
Ṁ
Lacc =
≈60 L⊙ −5
−1
R∗
1 M ⊙ 5 R⊙
10 M ⊙ yr

−1
Peter Schilke
Protostar definition
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Mass gaining star whose luminosity stems
mainly from external accretion.
Dust around the protostar is destroyed (vaporization of grains at 1500 K)
The (optical) radiation is absorbed by the
outer dust shell and re-radiated in the IR
Protostars are invisible in the optical
Peter Schilke
Protostellar structure
Peter Schilke
Temperature structure: inner
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Accretion velocity

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−1/ 2
  
2G M ∗
M∗
−1
v ff =
=280 [km s ]
R∗
1M⊙
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1/ 2
R∗
5 R⊙
which lead to postshock temperatures in
excess of 106 K
UV and X-ray photons absorbed in
(opaque, ionized) radiative precursor
Peter Schilke
Temperature structure: inner
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...which radiates like a blackbody with a
temperature given by the Stefan-Boltzmann
law
2
4
4  R∗  B T eff ≈ L acc
T eff ≈


G M ∗ Ṁ
4 B R
Ṁ
T eff ≈7300 [K] −5
−1
10 M ⊙ yr
3
∗

1/ 4
1/ 4
−3/ 4
  
1/ 4
M∗
1M⊙
R∗
5 R⊙
Peter Schilke
Temperature structure: outer
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This radiation (of a stellar-like photosphere)
is transmitted through the opacity gap, absorbed by the dust and re-radiated at the
dust photosphere
like a black body with an approximate temperature of 300 K
and radius 14 AU
Peter Schilke
Results of calculations
Peter Schilke
Isotemperature maps
Peter Schilke
Protostellar evolution
Calculated with stellar structure equations
Temperature in interior rises
Nuclear fusion starts: Deuterium burning
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H + 1H →3He + 
when the temperature reaches 106 K
when this happens, the temperature in the interior rises so high that it cannot be transported
by radiation in the (opaque) medium
convection starts in the center
2
Peter Schilke
Mass-radius relation
Peter Schilke
Deuterium burning phase
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There isn't much deuterium ([D/H] = 2.5 10-5)
and it is rapidly exhausted in the interior
supply from outside through convection
total luminosity 12 L⊙
Peter Schilke
Rotation
Rotation cannot be ignored
Magnetic braking is fairly efficient in the
outer parts of a collapsing cloud
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magnetic braking: transport of angular momentum by torsional Alfvén waves
Peter Schilke
Inner part
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Through decoupling of ions and neutrals in
the inner part, magnetic braking is not efficinent in the interior
If the angular momentum is large enough, it
will miss the protostar entirely and hit a disk
range of angular momenta is present in infalling matter at any time
maximum impact distance in the equatorial
plane is known as centrifugal radius cen
that sets the scale for a protostellar disk
Peter Schilke
Orbits
2 3
0
1/ 2
  
vs  t
T
cen ≈
=0.3 AU
16
10 K
0
−14 −1
10
s
2

t
5
10 yrs

3
Peter Schilke
Birth of a disk
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t 0=
a disk is born when infalling gas misses the
protostar
critical time determined using cen = R*
 
16 R∗
1/3
2
0
 
R∗
=3×10 [ yr ]
3⊙
4
1/ 3
−2/ 3
0
−14 −1
 
vs
−1
 vs
10 s
0.3 km s
the mass of the protostar is M = Ṁ t 0 leading to

−1/3
¿
M 0=

16 R∗ v
3
G 
2
0
8 1/ 3
s

=0.2 M ⊙
1/3
 
R∗
3⊙
0
−14 −1
10
s
−2/3
 
vs
0.3 km s
−1

8 /3
Peter Schilke
Disks
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If there is no disk, infalling mass coming
from above and below the midplane will collide there and create a disk
The accretion shock now is on the surface
of the disk as well as on the protostar
there is a radial infall in the disk
Peter Schilke
Streamlines in disks
Peter Schilke
Inner and Outer disks
Peter Schilke
Disk evolution
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Spiral patterns expands with t3
At time t1 = 1.43 t0, the streamlines start
missing the protostar (at a radius of
0.34 cen)
boundary between (tenuous) outer disk and
(dense) inner disk with almost circular orbits
Peter Schilke
Mass transport rate
Peter Schilke
Peter Schilke
Star formation
Peter Schilke
Disk model
Peter Schilke
Observations of disks
Direct
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Optical (silhouette)
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Not deeply embedded objects
Millimeter/Submillimeter
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Dust
Molecular lines
Indirect
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SEDs
Results:
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Sizes ~ 100 AU
Peter Schilke
Disks
MBM12 3C
Jayawardhana et al. 2002
β Pic
HH 30
Peter Schilke
HH 30
Peter Schilke
SEDs
Star
Disk
Peter Schilke
GG Tau – the ring world
Peter Schilke
Disk evaporation: proplyds
Peter Schilke
Physical Structure of PPDs
Irradiation
Dust heating
Gas heating
UV
photons
radiation
Star
dust
IR
Star
.
electron
dust
Irradiation from the central star
heats gas & dust in disks
Peter Schilke
Radiation processes
Peter Schilke
Chemical Structure of PPDs
UV
surface
intermediate
midplane
Surface layer : n~104-5cm-3, T>50K
Photochemistry
Intermediate : n~106-7cm-3, T>40K
Dense cloud chemistry
Midplane
: n>107cm-3, T<20K
Freeze-out
Peter Schilke
Disk chemical structure
Peter Schilke
Excursion: Comets and solar system
Markwick & Charnley 2004
Peter Schilke
Solar disk
Peter Schilke
Structure of solar system
Peter Schilke
Exoplanets
Peter Schilke
Planet formation
Peter Schilke
Planet formation
Peter Schilke
Debris disks
Disks around evolved (but young) stars
Not remnants of protostellar disks
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Dust is blown away
Have to be replenished from destructive
collisions of planetesimals (asteroid-like objects)
Peter Schilke
rogues gallery
τ Ceti
ε Eridani
Vega (α Lyr)
Fomalhaut (α PsA)
β Pic
Peter Schilke
Peter Schilke
Peter Schilke
Peter Schilke