The formation of stars and planets

Day 4, Topic 1:

Magnetospheric accretionjets and outflows

Lecture by: C.P. Dullemond

Boundary layer

At inner radius of disk:

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Ωdisk =GM

r*3

Assume disk goes all the way down to the stellar surface

If star rotates at less than breakup speed:

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Ωdisk > Ωstar

Frictional energy release in boundary layer:

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Lbl = ˙ M 1

2(vdisk − vstarsurf )

2

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=˙ M r2

2

GM

r3− Ωstar

⎛

⎝ ⎜

⎞

⎠ ⎟

2

Boundary layer

Friction between disk and star tends to spin up star until

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Ωdisk ≈ Ωstar

This means that star would rotate at breakup speed (almost zero local gravity at the equator)

For non-rotating star:

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Lbl =G ˙ M M

2r

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=Lvisc

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Lbl <<Lvisc

Ae and Be stars rotate fast

Most stars, however, rotate far below breakup speed

Fstar

accr diskbnd layer

Magnetospheric accretion

Ghosh & Lamb (1978) for neutron stars.Camenzind (1990), Königl (1991), Shu et al. (1994), Wang (1995) for TT stars

Magnetic pressure:

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Pm =B

2

8πDynamic pressure:

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Pdyn = ρ cs2 + ρδv 2

Gas is loaded onto magnetic field lines (disk is destroyed) at the radius ri where Pm =Pdyn.

Alfvén radius ri

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ri = βμ*4 / 7(2GM)−1/ 7 ˙ M −2 / 7 Königl (1991)

(Here * is stellar magnetic moment, and <1 is a fudge factor, typically =0.5 )

Magnetospheric accretion

Corotation radius

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rco =GM

Ω*2

⎛

⎝ ⎜

⎞

⎠ ⎟

1/ 3

Spin-up/spin-down

Very rough estimate for spin-up/spin-down:

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ri < 0.35 rco Spin-up

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ri > 0.35 rco Spin-down

Ghosh & Lamb (1977,1978,1979)Königl (1991)

Equilibrium sets stellar rotation rate (if braking/spin-up time is shorter than stellar formation time)

(The concept of magnetic breaking of the sun was already suggested in 1960 by Hoyle, and in a somewhat less plausible way by Alfvén 1954)

Magnetospheric accretion

Free-fall and accretion shock

Free-fall regionAccretion shock

ri

From rA down to star: matter is in supersonic free-fall.

Near the star the matter gets to a halt in a stand-off shock.

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vs =2GM

r*

1−r*

ri

Shock velocity:

Dissipated energy (=accretion luminosity from shock):

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Laccr = 1−r*

ri

⎛

⎝ ⎜

⎞

⎠ ⎟G ˙ M M

r*

(m)1 20.40.2

Magnetospheric accretion

Radiation from accretion shock

Calvet & Gullbring (1998)

Stellar spectrum

Radiation from accretion shock

Measuring the accretion rate

• Veiling of atmospheric lines by continuum of the accretion layer

• Broad (FWHM ~ 200 km/s) H line emission

Bipolar outflows / jets

Bipolar outflows

HH47

Bipolar outflows

HH34

Bipolar outflows

Outflows also seen in molecular lines:

Molecular outflows

Bachiller et al.

Bipolar outflows

Jets originatefrom innerregions of protoplanetarydisks

Hubble Space Telescope image

Bipolar outflows

• Optically detected jets:– Very collimated streams of gas, moving at supersonic

speed (~~100 km/s)– Mostly bipolar, mostly perpendicular to disk

– Jet outflow rate typically 10-9... 10-7 M.

• Molecular outflows:– Detected in CO lines– Often associated with optical jets (i.e. same origin)

– Derived mass: 0.1...170 M: large!• Most of accelerated mass must have been swept up from the

cloud core, rather than originating in mass ejected from the star

Bipolar outflows

Terminal shock

Hydrodynamic confinement?

Magnetic confinement

Magneto-centrifugal launching (<AU scale)

Swept-up material (molecular outflow)

Hot bubble of old jet material

Magnetically threaded disks

Suppose disk is treaded by magnetic field:

Inward motion of gas in disk drags field inward:

B-field aquires angle with disk

Disk winds

Slingshot effect. Blandford & Payne (1982)

Gravitational potential:

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Φ=−GM

r2 + z2

Use cylindrical coordinates r,z

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Φ=−GM

r0

1

2

r

r0

⎛

⎝ ⎜

⎞

⎠ ⎟

2

+r0

r2 + z2

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

Effective gravitational potential along field line (incl. sling-shot effect):

(courtesy:C. Fendt)

Disk windsBlandford & Payne (1982)

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Φ=−GM

r0

1

2

r

r0

⎛

⎝ ⎜

⎞

⎠ ⎟

2

+r0

r2 + z2

⎡

⎣ ⎢ ⎢

⎤

⎦ ⎥ ⎥

Infall Outflow

Critical angle: 60 degrees with disk plane. Beyond that: outflow of matter.

Gas will bend field lines

Disk + star: X-wind model of Frank Shu

Shu 1994

Magnetic field winding - confinement

C. Fendt

Magnetic field winding - confinement

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rj =

c

4π∇ ×

r B

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rf =

1

c

r j ×

r B

Right-hand rule: force points inwards

(courtesy:C. Fendt)

Hydromagnetic launch of jet from disk

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Kudoh, Matsumoto & Shibata (2003)

Hydrodynamic structure of jets

• Jets are surrounded by cocoon of pressurized gas– Cocoon partly made of old jet material, partly by swept

up material from the environment– Jet material moves supersonically

• Head of jet (‘hot spot’) drills through ISM: shock• Often knots seen (Herbig-Haro objects)

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Stone & Norman (1993)

Observed knot movement

Hydrodynamic confinement in jet:

Shock only reduces the velocity component perpendicular to shock front. Therefore obliquely shocked gas is deflected toward the shock plane.

Hydrodynamic confinement in jet:

Head of the jet:

Stand-off shock (most of jet energy dissipated here)

Contact discontinuity (boundary between jet and external medium)

Bow shock

Back flow

Turbulent mixing between old jet material and swept-up environment (entrainment)

Shocked external medium gas(molecular outflow)

Jet flow much faster than propagation of bow shock.Jet material much more tenuous than external medium