Jets, Disks, and Protostars

daughterduckUrban and Civil

Nov 15, 2013 (3 years and 6 months ago)

81 views

Jets, Disks, and Protostars

5 May 2003

Astronomy G9001
-

Spring 2003

Prof. Mordecai
-
Mark Mac Low

How does collapse proceed?


Singular isothermal spheres have constant
accretion rates


Observed accretion rates appear to decline
with time (older objects have lower
L
bol
)


Flat inner density profiles for cores give
better fit to observations.


Collapse no longer self
-
similar, so shocks
form.

3
0.975
s
M c G


Accretion shocks

Yorke et al. 1993


Infalling gas shocks when it hits the accretion
disk, and again when it falls from the disk
onto the star


Stellar shock releases most of the luminosity


Disk shock helps determine conditions in
flared disk.

Accretion disks


Form by dissipation in accreting gas


Observed disks have
M ~
10
-
3
M



<< M
*


Inward transport of mass and outward transport
of angular momentum energetically favored.


How can gas on circular orbits move radially?


Either microscopic viscosity or macroscopic
instabilities must be invoked.


Balbus
-
Hawley instabilities can provide viscosity


gravitational instability produces spiral density
waves on macroscopic scales


Gravitational instability will act if B
-
H remains
ineffective while infall continues.

Disk Structure


Nelecting pressure (
Ωr >> c
s
) and disk self
-
gravity, radial force eqn:


So long as M large,
Ω ~ r
-
3/2

(Kepler’s law)


Shear in Keplerian disk


Define a shear stress tensor


If viscosity
ν


0,
torque is exerted



angular momentum transport is then

Shu, Gas Dynamics



2 2
r r GM r
 
3
2
d
r
dr

  
r
d
r
dr




π
2
r
r r dz






T
π
, where mass accretion 2
d d r
dJ
M M rv
dr r
 

   

T
Alpha disk models


Viscous accretion a diffusion process, with



molecular
ν = λ
mfp
c
s
;

in a disk with
r ~

10
14

cm,



λ
mfp

~
10 cm,
c
s

~ 1 km s
-
1
=> ν ~ 10
6

cm
2
s
-
1


so
τ
acc

=
10
22

s ~ 3


10
14

yr!


Some anomalous viscosity must exist. Often
parametrized as
π

=


αP


based on hydro turbulent shear stress


for subsonic turbulence,
δv ~ αc
s


in MHD flow, Maxwell stress


B
-
H inst. numerically gives
α
mag

~
10
-
2


where
π

=


α
mag

P
mag

2
acc
r
 

r r
v v
 
 
 
π
r r
B B
 
 
 
π
Magnetorotational instability


First noted by
Chandrasekhar and Velikhov
in 1950s


ignored until
Balbus & Hawley (1991)
rediscovered it...


Driven by magnetic coupling between orbits


instability criterion
d
Ω/dr < 0

(decreasing ang.
vel.,
not ang. mntm as for hydro rotational instability)


most unstable wavelength


so long as
λ
c
> λ
diss

even very weak
B

drives instability


if
B
so strong that λ
c

>> H,

instability suppressed


Field geometry appears unimportant


May drive dynamo action in disk, increasing
field to strong
-
field limit

c
B


MRI in protostellar disks


MRI suppressed in partly neutral disks if every
neutral not hit by ion at least once per orbit (
Blaes
& Balbus 1998)





Inside a critical radius
R
c
~

0.1 AU collisional
ionization maintains field
coupling (
Gammie 1996)


Outside, CR ionization
keeps surface layer coupled


Accretion limited by layer


Gammie 1996

Simulations of MRI suppression

Hawley & Stone 1998

Sheet formation
occurs in partially
neutral gas

Mac Low et al. 1995

less ionization

time

Gravitational Instability in Disks


Important for both protostellar and galactic disks


Axisymmetric dispersion relation





from linearization of fluid equations in rotating disk


angular momentum decreasing outwards ( )
produces hydro instability


Differential rotation stabilizes Jeans instability


if collapsing regions shear apart in <
t
ff

then stable



2 2 2 2
2
2
3
2
where is the disk surface density, and
1
the square of the epicyclic frequency
s
k c G k
d
r
r dr
   


  
 
 
 
 
2
0


Shu, Gas

Dynamics

Toomre Criterion


Disks with Toomre Q < 1 subject to gravitational
instability at wavelengths around
λ
T


Q

λ / λ
T

1

0

1/2

1

ω
2

> 0 stable

ω
2

< 0 unstable

Shu, Gas Dyn.

stabilized

by rotation

stabilized

by pressure

2
2 2
T
2
s
T
4
1 0, where
4
4 c
and the Toomre parameter Q =
T T
s
Q G
c
G
   

  
 
  
   
   
   
   


Accretion increases surface density
σ, so protostellar disk Q
drops


Gravitational instability drives spiral density waves,
carrying mass and angular momentum.


Will act in absence of more efficient mechanisms


Very low Q might allow giant planet formation.


direct gravitational condensation proposed


may be impossible to get through intermediate Q regime though,
due to efficient accretion there.


standard giant planet formation mechanism starts with solid
planetesimals building up a 10 M


core followed by accretion of
surrounding disk gas


Brown dwarfs may indeed

form from fragmentation during
collapse (“failed binaries”).

Jets


Where does that angular momentum go?


Surprisingly (= not predicted) much goes into jets


lengths of 1
-
10 pc, inital radii < 100 AU


velocities of a few hundred km s
-
1

(proper motion,
radial velocities of knots)


carry as much as 40% of accreted mass


cold, overdense material


CO outflows carry more mass


driven either by jets, or associated slower disk winds


velocities of 10
-
20 km s
-
1



masses up to a few hundred M


Herbig
-
Haro objects


Jets were first detected in optical line
emission as Herbig
-
Haro objects


H
-
H objects turn out to be shocks
associated with jets


bow shocks


termination shocks


internal knots


tangential & coccoon shocks


line spectrum can be used to
diagnose velocity of shocks

Jet Observations

CO outflows

High resolution
interferometric observations
reveal that at least some CO
outflows tightly correlated
with jets. Others less
collimated. Also jets?

Gueth & Guilleteau 1999

Blandford
-
Payne disk winds



C. Fendt



Gas on magnetic field lines
in a rotating disk acts like
“beads on a wire”






If field lines tilted less than
60
o

from disk, no stable
equilibrium => outflow



2
0
2 2
0 0
0
Effective potential along a field line
1
,
2
where is the footpoint of the field line
GM r r
r z
r r
r z
r
 
 
 
   
 
 

 
 
Jet Propagation


Collimation


Gas dynamical jets are self
-
collimating


However, hydro collimation cannot occur so close to
source


Toroidal fields can collimate MHD jets quickly


Knots in jets


knots found to move faster than surrounding jet


variability in jet luminosity seen at all scales


large pulses overtake small ones, sweeping them up

simulated
IR from
M.D.
Smith

“Hammer Jet”

Time Scales


Free
-
fall time scale


Kelvin
-
Helmholtz time scale (thermal
relaxation: radiation of gravitational energy)




Nuclear timescale



1 2
~1hr for Sun
ff
G
 


2
7
~ 3 10 yr for Sun
KH
GM
RL

 
10
~10 yr for Sun
H
N H He
Mx
E
L



Termination of Accretion


exhaustion of dynamically collapsing
reservoir?


masses determined by molecular cloud
properties?


competition with surrounding stars for a
common reservoir?


termination of accretion?


ionization


jets and winds


disk evaporation and disruption

Protostar formation


Dynamical collapse continues until core becomes
optically thick (dust) allowing pressure to
increase.
n ~
10
12

cm
-
3
, 100 AU


Jeans mass drops, hydrost. equil. reached


radiation from dust photosphere allows quasistatic
evolution


Second dynamical collapse occurs when
temperature rises sufficiently for H
2
to dissociate


Protostar forms when H
-

becomes optically thick.


Luminosity initially only from accretion.


Deuterium burning, then H burning


z

C. Fendt


deeply embedded,
most mass still
accreting


disk visible in IR,
still shrouded


T
-
Tauri star,
w/disk, star, wind


weak
-
line T
-
Tauri
star

Pre
-
Main Sequence Evolution


Protostar is fully convective


fully ionized only in center


Large opacity, small adiabatic temperature gradient


Energy lost through radiative photosphere,
gained by grav. contraction until fusion begins


Fully convective stars with given
M, L

have
maximum stable
R,
minimum
T


Hayashi line on HR diagram


Pre
-
main sequence evolutionary calculations
must include non
-
steady accretion to get
correct starting point
(Wuchterl & Klessen 2001)