formation of stars and planets
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Formation of Stars and Planets. Frank H. Shu National Tsing Hua University Arnold Lecture – UC San Diego 6 May 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 - PowerPoint PPT PresentationTRANSCRIPT
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Formation of Stars and Planets
Frank H. ShuNational Tsing Hua University
Arnold Lecture – UC San Diego6 May 2005
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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
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Planets Revolve in Mostly Circular Orbits in Same Direction as Sun Spins
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Planetary Orbits Nearly Lie in a Single Plane with Exception of Pluto & Mercury
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Laplace’s Nebular Hypothesis
Photo Credit: NASA/JPL
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Snowline in the Solar Nebula
condensed.stay metals androcks, compounds,Hydrogen vaporize.compundshydrogen
condensed,stay metals and Rocks
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Relative Abundance of Condensates
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Agglomeration of Planets
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The Formed Solar System
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Four Phases of Star Formation
• Formation of recognizable cores in Giant Molecular Cloud (GMC) by ambipolar diffusion (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)
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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
A
mkTa
BBBBuBtB
GU
BBaUuuutu
ut
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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.
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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
RHdd
HRRRH
dd
HdRG
rarRGrar
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
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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 perturbational analysis by Galli & Shu (1993).
0
gives 0.17 Myr to form 0.5 M star.sunMass infall rate doubled if there is initial inward velocity at 0.5 a.
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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
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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; Shu, Galli, & Lizano 2005).
• 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).
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ComputedSteadyX-Wind
Filling All Space Dw MfM
311
*
*
JJ
Jfw
D
Ostriker & Shu (1995)
Najita & Shu (1994)
xxww RJv 32
Apart from details of massloading onto field lines,only free parameters are
.,, MM D
locking).(disk
,
,923.0
2/1
3*
7/1
2
4
x
xx
Dx
RGM
MGMR
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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).
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Prototypical X-Wind Model
Shu, Najita, Ostriker, & Shang (1995)
fastAlfven
slow
isodensity contour
streamline ) typicallyAU 06.0 1( xR
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Gas: YSO Jets Are Often PulsedMagnetic Cycles?
Shang, Glassgold, Shu, & Lizano (2002)
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Synthetic Long-Slit Spectra
90i
Shang, Shu, & Glassgold (1998)
60i30i
(km/s)velocity
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Position-Velocity Spectrogram
Woitas, Ray, Bacciotti, Davis, & Eisloffel (2002) Henney, O’Dell, Meaburn, & Garrington (2002)
Jet/Counterjet R W Tauri LV2 Microjet in Orion Proplyd
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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 outflows lead to distribution of
that yields core mass function.
. /)( 02/3222
00 BGvamM
0222 /)( Bva
. ofon Distributi 20 m
1 (r0) above is 200,000 timesbigger than1 (Rx) below
Shu, Li, & Allen (2004)
Shang, Ostriker, & Shu (1995)
Attack bymatchedasymptoticexpansions
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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
.)(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
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
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Simple “Derivation” for IMFwhen v >> a
. )( :outflowsBipolar 2dvvdvv
.33
1 :When 3
02/3
40
0*22 v
BGvmMMav
,)(3
)( *3/4
**** dMMdvvFdMMM
1993)Fuller & (Myersyr 104-1 2
2
/)3/2(
3/ 50
02/1
03
02/34
0
*
*sf
vr
BGvm
GvBGvm
MMt
grains).dust on pressureradiation of because massesstellar high at steeper ; 0.5 /3at (peak masses teintermediaat IMFSalpeter iswhich sun0
2/342 MBGa
2 2
NB: SFE = 1/3 when F = 1 (cf. Lada & Lada 2003).
(Shu, Li, & Allen 2004)
(Shu, Ruden, Lada, & Lizano 1990; Masson & Chernin 1992; Li & Shu 1996)
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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)
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The Orion Embedded Cluster
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1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0
Log 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.
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Almost 100% of Young Stars in Orion Cluster Are Born with Disks
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Discovery of Extrasolar Planets
Marcy webpage
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Driven Spiral Density and Bending Waves in Saturn’s Rings
Shu, Cuzzi, & Lissauer (1983)
Implications for planet migration due to planet-disk interaction
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Shepherd Satellites Predicted by Goldreich & Tremaine
Photo credit: Cassini-Huygens/NASA
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Model Fit to CO Fundamental(v = 1→0, ΔJ = )
Najita et al. (2003)
Inferred gas temperature ≤ 1200 K; kinematics gives location of inner disk edge.
1
Is this where oxygen isotope ratios are fixed? (Clayton 2002)
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Size of Inner Hole in Rough Agreement with Disk Locking
Najita et al (2003)
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Parking Hot Jupiters
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Thank you, everyone!