the formation of stars and planets day 4, topic 1: magnetospheric accretion jets and outflows...
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![Page 1: The formation of stars and planets Day 4, Topic 1: Magnetospheric accretion jets and outflows Lecture by: C.P. Dullemond](https://reader036.vdocuments.mx/reader036/viewer/2022062301/56649d595503460f94a39ae8/html5/thumbnails/1.jpg)
The formation of stars and planets
Day 4, Topic 1:
Magnetospheric accretionjets and outflows
Lecture by: C.P. Dullemond
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Boundary layer
At inner radius of disk:
€
Ωdisk =GM
r*3
Assume disk goes all the way down to the stellar surface
If star rotates at less than breakup speed:
€
Ωdisk > Ωstar
Frictional energy release in boundary layer:
€
Lbl = ˙ M 1
2(vdisk − vstarsurf )
2
€
=˙ M r2
2
GM
r3− Ωstar
⎛
⎝ ⎜
⎞
⎠ ⎟
2
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Boundary layer
Friction between disk and star tends to spin up star until
€
Ωdisk ≈ Ωstar
This means that star would rotate at breakup speed (almost zero local gravity at the equator)
For non-rotating star:
€
Lbl =G ˙ M M
2r
€
=Lvisc
€
Lbl <<Lvisc
Ae and Be stars rotate fast
Most stars, however, rotate far below breakup speed
Fstar
accr diskbnd layer
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Magnetospheric accretion
Ghosh & Lamb (1978) for neutron stars.Camenzind (1990), Königl (1991), Shu et al. (1994), Wang (1995) for TT stars
Magnetic pressure:
€
Pm =B
2
8πDynamic pressure:
€
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
€
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 )
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Magnetospheric accretion
Corotation radius
€
rco =GM
Ω*2
⎛
⎝ ⎜
⎞
⎠ ⎟
1/ 3
Spin-up/spin-down
Very rough estimate for spin-up/spin-down:
€
ri < 0.35 rco Spin-up
€
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)
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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.
€
vs =2GM
r*
1−r*
ri
Shock velocity:
Dissipated energy (=accretion luminosity from shock):
€
Laccr = 1−r*
ri
⎛
⎝ ⎜
⎞
⎠ ⎟G ˙ M M
r*
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(m)1 20.40.2
Magnetospheric accretion
Radiation from accretion shock
Calvet & Gullbring (1998)
Stellar spectrum
Radiation from accretion shock
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Measuring the accretion rate
• Veiling of atmospheric lines by continuum of the accretion layer
• Broad (FWHM ~ 200 km/s) H line emission
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Bipolar outflows / jets
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Bipolar outflows
HH47
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Bipolar outflows
HH34
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Bipolar outflows
Outflows also seen in molecular lines:
Molecular outflows
Bachiller et al.
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Bipolar outflows
Jets originatefrom innerregions of protoplanetarydisks
Hubble Space Telescope image
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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
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Bipolar outflows
Terminal shock
Hydrodynamic confinement?
Magnetic confinement
Magneto-centrifugal launching (<AU scale)
Swept-up material (molecular outflow)
Hot bubble of old jet material
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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
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Disk winds
Slingshot effect. Blandford & Payne (1982)
Gravitational potential:
€
Φ=−GM
r2 + z2
Use cylindrical coordinates r,z
€
Φ=−GM
r0
1
2
r
r0
⎛
⎝ ⎜
⎞
⎠ ⎟
2
+r0
r2 + z2
⎡
⎣ ⎢ ⎢
⎤
⎦ ⎥ ⎥
Effective gravitational potential along field line (incl. sling-shot effect):
(courtesy:C. Fendt)
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Disk windsBlandford & Payne (1982)
€
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
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Disk + star: X-wind model of Frank Shu
Shu 1994
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Magnetic field winding - confinement
C. Fendt
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Magnetic field winding - confinement
€
rj =
c
4π∇ ×
r B
€
rf =
1
c
r j ×
r B
Right-hand rule: force points inwards
(courtesy:C. Fendt)
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Hydromagnetic launch of jet from disk
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Kudoh, Matsumoto & Shibata (2003)
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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)
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Observed knot movement
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Hydrodynamic confinement in jet:
Shock only reduces the velocity component perpendicular to shock front. Therefore obliquely shocked gas is deflected toward the shock plane.
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Hydrodynamic confinement in jet:
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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