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!