Transcript The formation of stars and planets

The formation of stars and planets
Day 4, Topic 1:
Magnetospheric accretion
jets and outflows
Lecture by: C.P. Dullemond
Boundary layer
Assume disk goes all the way down to the stellar surface
GM
disk 
3
r*
At inner radius of disk:
If star rotates at less than breakup speed:
disk  star
Frictional energy release in boundary layer:


Ýr  GM
1
M
2
Ý (v disk  v starsurf ) 
Lbl  M

 3  star 
2
2  r

2
2
Boundary layer
F
For non-rotating star:
star
accr disk
ÝM
GM
Lbl 
2r
 Lvisc
bnd layer

Friction between disk and star tends to spin up star until

disk  
star
Lbl Lvisc
This means that star would rotate at breakup speed
(almost zero local gravity at the equator)
Ae
 and Be stars rotate fast

Most stars, however, rotate far below breakup speed
Magnetospheric accretion
Alfvén radius
ri
Ghosh & Lamb (1978) for
neutron stars.
Camenzind (1990), Königl
(1991), Shu et al. (1994),
Wang (1995) for TT stars
2
Magnetic pressure:
Dynamic pressure:
B
Pm 
8
Pdyn   c s2  v 2
Gas is loaded onto magnetic field lines (disk is destroyed)
at the radius ri where
 Pm =Pdyn.
4 /7
1/ 7 Ý2 / 7
r


(2GM)
M
 i
*
Königl (1991)
(Here * is stellar magnetic moment, and <1 is a fudge factor, typically =0.5 )
Magnetospheric accretion
Spin-up/spin-down
GM 
rco   2 
 * 
1/ 3
Corotation radius
Very rough estimate for spin-up/spin-down:
ri  0.35rco
ri  0.35rco
Spin-up

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
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.
Free-fall
region
Accretion shock
ri
Shock velocity:
2GM
r*
vs 
1
r*
ri
Dissipated energy (=accretion luminosity from shock):
ÝM
 r*  GM
Laccr  1 

 ri  r*
Magnetospheric accretion
Radiation from accretion shock
Stellar
spectrum
Radiation
from
accretion
shock
0.2
0.4
1
 (m)
2
Calvet & Gullbring (1998)
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 originate
from inner
regions of
protoplanetary
disks
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
Swept-up material
(molecular outflow)
Terminal shock
Hydrodynamic
confinement?
Hot bubble of old jet
material
Magnetic confinement
Magneto-centrifugal
launching (<AU scale)
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)
(courtesy:
C. Fendt)
Use cylindrical
coordinates r,z
GM
Gravitational potential:

Effective gravitational
potential along field line (incl.

sling-shot effect):
  2

GM 1 r
r0
   


2
2
r0 
r  z 
2 r0 

r2  z2
Disk winds
Blandford & Payne (1982)
  2

GM 1 r
r0
   


2
2
r0 
2
r



r

z
0



Infall
Critical angle: 60 degrees
with disk plane. Beyond
that: outflow of matter.
Outflow
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
(courtesy:
C. Fendt)
c
j
B
4
1
f  j B
c
Right-hand rule:
force points
inwards
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:
Turbulent mixing between old jet
material and swept-up environment
(entrainment)
Stand-off shock (most of jet
energy dissipated here)
Contact discontinuity
(boundary between jet
and external medium)
Bow shock
Back flow
Shocked external medium gas
(molecular outflow)
Jet flow much faster than propagation of bow shock.
Jet material much more tenuous than external medium