Jets, Disks, and Protostars

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Jets, Disks, and Protostars

• 5 May 2003
• Astronomy G9001 - Spring 2003
• Prof. Mordecai-Mark Mac Low

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How does collapse proceed?

• Singular isothermal spheres have constant
  accretion rates
• 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.

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Accretion shocks

• 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.

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Accretion disks

• Form by dissipation in accreting gas
• Observed disks have M 10-3 M? ltlt 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.

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Disk Structure
Shu, Gas Dynamics

• Nelecting pressure (Or gtgt cs) and disk
  self-gravity, radial force eqn
• So long as M large, O r -3/2 (Keplers law)
• Shear in Keplerian disk
• Define a shear stress tensor
• If viscosity ? ? 0, torque is exerted
• angular momentum transport is then

6
Alpha disk models

• Viscous accretion a diffusion process, with
• molecular ? ?mfpcs in a disk with r 1014
  cm,
• ?mfp 10 cm, cs 1 km s-1 gt ? 106 cm2
  s-1
• so tacc 1022 s 3 ? 1014 yr!
• Some anomalous viscosity must exist. Often
  parametrized as prf aP
• based on hydro turbulent shear stress
• for subsonic turbulence, dv acs
• in MHD flow, Maxwell stress
• B-H inst. numerically gives amag 10-2
• where prf amag Pmag

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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 dO/dr lt 0 (decreasing ang.
  vel., not ang. mntm as for hydro rotational
  instability)
• most unstable wavelength
• so long as ?c gt ?diss even very weak B drives
  instability
• if B so strong that ?c gtgt H, instability
  suppressed
• Field geometry appears unimportant
• May drive dynamo action in disk, increasing field
  to strong-field limit

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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
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Simulations of MRI suppression
Hawley Stone 1998
Sheet formation occurs in partially neutral gas
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Gravitational Instability in Disks
Shu, Gas Dynamics

• 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 lt tff then
  stable

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Toomre Criterion
Q
?2 gt 0 stable
1
stabilized by rotation
stabilized by pressure
?2 lt 0 unstable
? / ?T
Shu, Gas Dyn.
0
1/2
1

• Disks with Toomre Q lt 1 subject to gravitational
  instability at wavelengths around ?T

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• Accretion increases surface density s, 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).

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Jets

• Where does that angular momentum go?
• Surprisingly ( not predicted) much goes into
  jets
• lengths of 1-10 pc, inital radii lt 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?

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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

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Jet Observations
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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?
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Blandford-Payne disk winds

• Gas on magnetic field lines in a rotating disk
  acts like beads on a wire
• If field lines tilted less than 60o from disk,
  no stable equilibrium gt outflow

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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
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Time Scales

• Free-fall time scale
• Kelvin-Helmholtz time scale (thermal relaxation
  radiation of gravitational energy)
• Nuclear timescale

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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

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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

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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

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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)