Download Distribution and Properties of the ISM

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
3
accretion rates M   0.975cs G
• Observed accretion rates appear to decline
with time (older objects have lower Lbol)
• Flat inner density profiles for cores give
better fit to observations.
• Collapse no longer self-similar, so shocks
form.
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
Shu, Gas Dynamics
• Nelecting pressure (Ωr >> cs) and disk self2
2
gravity, radial force eqn: r  r   GM r
• So long as M large, Ω ~ r -3/2 (Kepler’s law)
d
3
• Shear in Keplerian disk r
 
dr
2
d
• Define a shear stress tensor πr   r
dr 
• If viscosity ν  0, torque is exertedT  2 r  rπr dz

• angular momentum transport is then
dJ T
M d

, where mass accretion M d  2 rvr
dr r
Alpha disk models
• Viscous accretion a diffusion process, with
2
 acc  r 
• molecular ν = λmfpcs; in a disk with r ~ 1014 cm,
– λmfp ~ 10 cm, cs ~ 1 km s-1 => ν ~ 106 cm2 s-1
– so τacc = 1022 s ~ 3  1014 yr!
• Some anomalous viscosity must exist. Often
parametrized as πrφ = – αP
– based on hydro turbulent shear stress π r     vr v
– for subsonic turbulence, δv ~ αcs
– in MHD flow, Maxwell stress π r     Br B
• B-H inst. numerically gives αmag ~ 10-2
– where
πrφ = – αmag Pmag
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 dΩ/dr < 0 (decreasing ang. vel.,
not ang. mntm as for hydro rotational instability)
– most unstable wavelength c  B
• so long as λc > λdiss even very weak B drives instability
• if B so strong that λc >> H, instability suppressed
• Field geometry appears unimportant
• May drive dynamo action in disk, increasing
field to strong-field limit
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
Rc ~ 0.1 AU collisional
ionization maintains field
coupling (Gammie 1996)
• Outside, CR ionization
keeps surface layer coupled
• Accretion limited by layer
Gammie 1996
time
less ionization
Simulations of MRI suppression
Hawley & Stone 1998
Sheet formation
occurs in partially
neutral gas
Mac Low et al. 1995
Gravitational Instability in Disks
Shu, Gas
Dynamics
• Important for both protostellar and galactic disks
• Axisymmetric dispersion relation
 2   2  k 2cs2  2 G k 
where  is the disk surface density, and
1 d  2 2
the square of the epicyclic frequency   3  r   

r dr 
– from linearization of fluid equations in rotating disk
– angular momentum decreasing outwards ( 2  0 )
produces hydro instability
• Differential rotation stabilizes Jeans instability
– if collapsing regions shear apart in < tff then stable
Toomre Criterion
Q ω2 > 0
1
stable
stabilized
by rotation
stabilized
by pressure
ω2 < 0
0
unstable
1/2
1
λ / λT
Shu, Gas Dyn.
Q  T   T 
4 2G
1
      0, where T 
4    
2
4 cs
 cs
and the Toomre parameter Q =

T  G
2
2
• Disks with Toomre Q < 1 subject to gravitational
instability at wavelengths around λT
• 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
Gueth & Guilleteau 1999
High resolution
interferometric observations
reveal that at least some CO
outflows tightly correlated
with jets. Others less
collimated. Also jets?
Blandford-Payne disk winds
• Gas on magnetic field lines
in a rotating disk acts like
“beads on a wire”
Effective potential along a field line
2


GM 1  r 
r0
   

  r, z   
2
2
r0  2  r0 

r

z

where r0 is the footpoint of the field line
• If field lines tilted less than
60o from disk, no stable
equilibrium => outflow
C. Fendt
• Collimation
Jet Propagation
– 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
“Hammer Jet”
simulated
IR from
M.D.
Smith
Time Scales
• Free-fall time scale  ff   G  ~ 1 hr for Sun
• Kelvin-Helmholtz time scale (thermal
relaxation: radiation of gravitational energy)
1 2
 KH
• Nuclear timescale
GM 2

~ 3  107 yr for Sun
RL
 N  EH  He
MxH
~ 1010 yr for Sun
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 ~ 1012 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 H2 to dissociate
• Protostar forms when H- becomes optically thick.
– Luminosity initially only from accretion.
– Deuterium burning, then H burning
C. Fendt
• deeply embedded,
most mass still
accreting
z
• 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)