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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:
€
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
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
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 )
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)
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*
(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:
€
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)
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
Disk + star: X-wind model of Frank Shu
Shu 1994
Magnetic field winding - confinement
C. Fendt
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)
Hydromagnetic launch of jet from disk
Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“
benötigt.
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)
Zur Anzeige wird der QuickTime™ Dekompressor „YUV420 codec“
benötigt.
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