Formation of Stars and Planets
Frank H. ShuNational Tsing Hua University
Physics Department NTHU2 March 2005
Outline of Talk
• Origin of solar system – review of classical ideas
• Modern theory of star formation– Four phases of star formation– Contraction of molecular cloud cores– Gravitational collapse and disk formation– The initial mass function– X-wind outflow and YSO jets– The inner disk edge– Migration of planets
Planets Revolve in Mostly Circular Orbits in Same Direction as Sun Spins
Planetary Orbits Nearly Lie in a Single Plane with Exception of Pluto & Mercury
Laplace’s Nebular Hypothesis
Photo Credit: NASA/JPL
Snowline in the Solar Nebula
condensed.stay metals androcks, compounds,Hydrogen vaporize.compundshydrogen
condensed,stay metals and Rocks
Relative Abundance of Condensates
Agglomeration of Planets
The Formed Solar System
Four Phases of Star Formation
• Formation of recognizable cores in Giant Molecular Cloud (GMC) by ambipolardiffusion (AD) and decay of turbulence:
Δt = 1 – 3 Myr• Rotating, magnetized
gravitational collapse:Δt = ?
• Strong jets & bipolar outflows; reversal of gravitational infall:
Δt = 0.1 – 0.4 Myr• Star and protoplanetary
disk with lifetime:Δt = 1 – 5 Myr Shu, Adams, & Lizano (1987)
Equations of Non-Ideal MHDfor an Isothermal Gas
( )
( )
[ ]
0. and 0 toscorrespond MHD Ideal mag). 4 ular(perpendic ionization UVfrom shielded isregion when increasedgreatly
is timecollision ion -Neutral cs.microphysiby specified time)collision ion-(neutral and y)resistivit l(electrica andconst /with
,)(4
)(
,4
,4
1)(21
,0
V
2
2
22
==>
==
⎟⎟⎠
⎞⎜⎜⎝
⎛×∇××+×∇−×∇=××∇+
∂∂
=∇
××∇+∇−−∇=××∇+⎟⎠⎞
⎜⎝⎛∇+
∂∂
=⋅∇+∂∂
τη
τη
πρτη
ρππρ
ρρ
ρρ
A
mkTa
BBBBuBtB
GU
BBaUuuutu
ut
rrr
rrrr
rrrrr
r
Cloud-Core Evolution by Ambipolar Diffusion
Desch & Mouschovias (2001).See also Nakano (1979); Lizano & Shu (1989).
t = 7.1 Myr 15.17 Myr
15.23189 Myr 15.23195 Myr → Reset to 0 (pivotal state).
Displayed time scale for laminarevolution is in conflict withstatistics of starless coresversus cores with stars by factorof 3 - 10 (Lee & Myers1999;Jajina, Adams, & Myers 1999).
Turbulent decay (Myers &Lazarian 1999) and turbulentdiffusion (Zweibel 2002,Fatuzzo & Adams 2002) may reduce actual time to 1 - 3 Myr.
Pivotal t = 0 States: MagnetizedSingular Isothermal Toroids
( )
.sin sin
'
,12''2sin sin
1
.1 sin )( with )(4),( ),(2
),(
0
00
0
2/
02/1
2
2
2
θθ
φθ
φ
φφθ
θθ
θθθθφπθθπ
θρπ
RHdd
HRRRH
dd
HdRG
rarRGrar
−=⎟⎠⎞
⎜⎝⎛
−−=⎥⎦
⎤⎢⎣
⎡⎟⎟⎠
⎞⎜⎜⎝
⎛−
+==Φ= ∫
Li & Shu (1996)
N.B. solution for H = 0: R = 1, Φ= 0 (Shu 1977).0
Magnetic field lines
Isodensitycontours
AD leads to gravomagneto catastrophe, whereby center formally tries toreach infinite density in finite time – seems to be nonlinear attractor state withρ~1/r², B~1/r, Ω~1/r. If we approximate the pivotal state as static, it satisfies
Collapse of H = 0.0, 0.125, 0.25, 0.5 Toroids0
Case H = 0 agrees with knownanalytical solution for SIS(Shu 1977) or numerical simulationswithout B (Boss & Black1982).
GaHM /)1( 975.0 30+=&
Mass infall rate into center:
Note trapping of field at originproduces split monopole with longlever arm for magnetic braking.
Allen, Shu, & Li (2003)
0
Formation of pseudodisk when H > 0as anticipated in perturbationalanalysis by Galli & Shu (1993).
0
gives 0.17 Myr to form 0.5 M star.sun
Mass infall rate doubled if there is initial inward velocity at 0.5 a.
Catastrophic Magnetic Braking if Fields Are Perfectly Frozen
Allen, Li, & Shu (2003) – Initial rotation in range specified by Goodman et al. (1993).Some braking is needed, but frozen-in value is far too much (no Keplerian disk forms).
Andre,Motte, & Bacmann(1999); alsoBoogertet al. (2003)
Low-speedrotatingoutflow (cf. Uchida &Shibata 1985)not high-speed jet
Breakdown of Ideal MHD
⇒
• Low-mass stars need 10 megagauss fields to stop infall from pseudodisk by static levitation (if envelope subcritical).
• Combined with rapid rotation in a surrounding Keplerian disk, such stars need only 2 kilogauss fields to halt infall by X-winds (dynamical levitation).
• Appearance of Keplerian disks requires breakdown of ideal MHD (Allen, Li, & Shu 2003).
• Annihilation of split monopole is replaced by multipoles of stellar field sustained by dynamo action.
• Latter fields are measured in T Tauri stars through Zeeman broadening by Basri, Marcy, & Valenti (1992) and Johns-Krull, Valenti, & Koresko (1999).
ComputedSteadyX-Wind
Filling All Space Dw MfM && =
311
*
* ≈−−−
=JJ
Jfw
Dτ
Ostriker & Shu (1995) Najita & Shu (1994)
xxww RJv Ω−= 32
Apart from details of massloading onto field lines,only free parameters are
.,, ∗∗ µMM D&
locking).(disk
,
,923.0
2/1
3*
7/1
2
4
x
xx
Dx
RGM
MGMR
Ω=Ω
⎟⎟⎠
⎞⎜⎜⎝
⎛=Ω
⎟⎟⎠
⎞⎜⎜⎝
⎛=
∗
∗
∗
&µ
Multipole Solutions Change Funnel Flow but not X-wind
Mohanty & Shu (2005)
What’s important is trapped flux at X-point (Johns-Krull & Gafford 2002).
Prototypical X-Wind Model
Shu, Najita, Ostriker, & Shang (1995)
fastAlfven
slow
isodensity contour
streamline ) typicallyAU 06.0 1( ≈xR
Gas: YSO Jets Are Often PulsedMagnetic Cycles?
Shang, Glassgold, Shu, & Lizano (2002)
o90=i o60=io30=i
Synthetic Long-Slit Spectra
Shang, Shu, & Glassgold (1998)(km/s)velocity
Position-Velocity Spectrogram
LV2 Microjet in Orion ProplydJet/Counterjet R W Tauri
Henney, O’Dell, Meaburn, & Garrington (2002)Woitas, Ray, Bacciotti, Davis, & Eisloffel (2002)
Relationships Among Core Mass, Stellar Mass, & Turbulence
• Conjecture: Outflows break out when infall weakens and widens after center has accumulated some fraction (50%?) of core mass (1/3 of which is ejected in X-wind). Physical content of Class 0?(Andre, Ward-Thompson & Barsony 1993)
• Stellar mass is therefore defined by X-wind as 1/3 of core mass
• Ambipolar diffusion and turbulence driven by outflowslead to distribution of
that yields core mass function.
Shu, Li, & Allen (2004)
1 (r0) above is 200,000 timesbigger than1 (Rx) below
. /)( 02/3222
00 BGvamM +=
0222 /)( Bva +
. ofon Distributi 20 π≤m
Shang, Ostriker, & Shu (1995)
Attack bymatchedasymptoticexpansions
Core Mass with Magnetic Fields and Turbulence
• Pivotal state produced by AD (Mestel & Spitzer 1956, Nakano 1979, Lizano & Shu 1989, Basu & Mouschovias 1994, Desch & Mouschovias 2004):
• Virial equilibrium:
• Solve for
• Compare with SIS threaded by uniform field:
.22
02
0
02/1
=≡BrMG
ππλ
.)(23
0
2022
0 rGMvaM =+⋅
.)(3 ,)(9
02/1
22
00
2/3
222
0 BGvar
BGvaM +
=+
=
. ,0
2/1
2
00
2/3
42
0 BGar
BGaM ππ
==
Differs from barelybound in factor 2.
M = 1.5 solar mass for a = 0.2 km/s, B = 30μG
0
0
Core mass: part which is supercritical
2
Divide mass by 4 if barely bound
Simple “Derivation” for IMFwhen v >> a
. )( :outflowsBipolar 2dvvdvv −∝Μ
.33
1 :When 3
02/3
40
0*22 v
BGvmMMav ∝=≈>>
2 2
(Shu, Ruden, Lada, & Lizano 1990; Masson & Chernin 1992; Li & Shu 1996)
1993)Fuller & (Myersyr 104-1 2
2
/)3/2(
3/ 50
02/1
03
02/34
0
*
*sf ×≈≈=≈=
vr
BGvm
GvBGvm
MMt π&
,)(3
)( *3/4
**** dMMdvvFdMMM −∝Μ=Ν
grains).dust on pressureradiation of because massesstellar high at steeper ; 0.5 /3at (peak masses teintermediaat IMFSalpeter iswhich sun0
2/342 MBGa ≈π
(Shu, Li, & Allen 2004)
NB: SFE = 1/3 when F = 1 (cf. Lada & Lada 2003).
Schematic IMF
Log (M)
Log [MN(M)]
0-1 +1 +2
stars cores
+3 +4
radiationpressure
wind
browndwarf
v < a
- 4/3 slope
wind
D fusion
wind
H fusion
0mdistribution
Motte et al. (1998, 2001); Testi & Sargent (1998)
The Orion Embedded Cluster
1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0Log Mass (solar masses)
100.0
101.0
102.0
2
3
456789
2
3
456789
Log
N +
Con
stan
tTrapezium Cluster Initial Mass Function
HBL
Sun
Brown Dwarfs
At stellarbirth (Lada& Lada 2003),IMF isgiven by Salpeter (1955) IMF.
Almost 100% of Young Stars in Orion Cluster Are Born with Disks
Discovery of Extrasolar Planets
Marcy webpage
Driven Spiral Density and Bending Waves in Saturn’s Rings
Shu, Cuzzi, & Lissauer (1983)
Implications for planet migration due to planet-disk interaction
Shepherd Satellites Predicted by Goldreich & Tremaine
Photo credit: Cassini-Huygens/NASA
Model Fit to CO Fundamental(v = 1→0, ∆J = )1±
Inferred gas temperature ≤ 1200 K; kinematics gives location of inner disk edge.
Najita et al. (2003)
Size of Inner Hole in RoughAgreement with Disk Locking
Najita et al (2003)
Parking Hot Jupiters
Thank you, everyone!