Sternentstehung

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Sternentstehung
Ralf Klessen
Christian Fendt
Star Formation on Large Scales 2
Uni Potsdam, WS2002/03
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Intermezzo
Hydrodynamics and fluid instabilities
(See complementary handout)
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Fluid instabilities

• convective instability
• rotational instability (with B-field MRI)
• Rayleigh-Taylor instability
• Kelvin-Helmholtz instability
• thermal instability
• gravitational instability (Jeans instability)
• gravitational instability in shearing disks
  (Toomre instability)
• non-linear thin shell instability (Vishniac
  instability)
• magneto-rotational instability (Balbus-Hawley
  instability)
• Parker instability

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Fluid instabilities

• convective instability

Criterion dsgt0
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Fluid instabilities

• rotational instability

Rayleigh criterion
specific angular momentum
Instability if specific angular momentum j
decreases outward In astrophysics accretion
disks and galactic disks have radiallyincreasing
j ? should be hydrodynamically stable

• magneto-rotational instability

Magnetic field leads to instability in
differentially rotating disks.
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Fluid instabilities

• magneto-rotational instability

• magnetic fields reduce shear and thus help
  instability
• minimum B-field
• maximum B-field

Picture from Rainer Arlt
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Fluid instabilities

• Rayleigh-Taylor instability

• Kelvin-Helmholtz instability

Richardson criterion
Movies from ITSC webpage http//www.itsc.com
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Fluid instabilities

• non-linear thin sheet instability (NLRI,
  Vishniac instability)

• Linearly stable against bending and breathing
  modes
• Instability arises from the non-linear terms.
  (Vishniac 1994)

(from Vishniac 1994)
(from Walder Folini)
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Fluid instabilities

• thermal instability

Criterion
Lgt0 (cooling)
log T
Llt0 (heating)
L0
pconst
log ?
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Fluid instabilities

• gravitational instability (Jeans)

Criterion MgtMJ
With Jeans mass
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Stability of galactic disks

• 1D stability criterion for homogeneous gaseour
  disk (agains radial perturbations)
  Toomre criterion
• Collaboration between the isothermal pressure
  at small-scale and the rotation at
  large-scale against gravitational attraction.
  (Toomre 1964)
• Toomre criterion for gas stars (Jog
  Solomon 1984)
• in general cs, ?, and ? are functions of R (for
  flat rotation curve ?22?2)

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Stability of galactic disks

• Disks of both stars and gas are more unstable
  that disks with one single component only.
• Both contributions are comparable even for ?s/?g
  0.1 0.2. Due to the smaller velocity
  dispersion of gas (csltlt?)
• The relative contribution to the instability
  from gas compared to the stars grows with
  wavenumber k
• For low values of k (large ?), the stellar
  component dominates the
• instability at small scale, the gas
  dominates by its low dispersion.
• Maintaining the instability over a longer time
  requires gas, as gas dissipates. Stars alone
  are unstable only transiently, as the disk
  would heat up and become stable
  (self-regulation).
• What are typical values of Q?

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Stability of galactic disks

• Galactic disks appear marginally stable.
• Typical values cs6km/s, vc200km/s, ?s/?g
  0.1, for ?(R)1/R it follows Q 2.8cs/vc?.
  This gives Q 0.84?1.
• Q is often used to justify star formation law in
  galaxies (Kennicutt 1989) Gas is unstable if
  S gt S crit.
• Measured values for HI gas
• No local correlation

(from Kennicutt 1989)
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Star formation rate
For normal disks as for starburst galaxies, the
star formation rate appears to be proportional to
gas density But average on large-scale, the whole
disk Global Schmidt law, with a power n1.4
(Kennicutt 98) S SFR
S g 1.4 Another formulation works as well
S SFR S g O or S g/tdyn SFR
gas density/tff ? 1.5 or cloud-cloud
collisions in ? 2 (Scoville 00)
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Slope n1.4 Normal galaxies (filled
circles) starburst (squares) nuclei (open circles)
Slope n1
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Problems with the use of Qg

• Disks are self-regulated, on a dynamical
  time-scale
• if gas too cold and unstable, gravitational
  instabilities develop
• and heat the medium until marginal stability is
  reached
• Qg for stability might not be 1, but 2 or 3
  according to the stellar
• disk properties (Qs) or the thickness, etc..
• Difficult to measure the total gas, especially
  the CO/H2 conversion
• ratio not known within a factor 2
• Time delay for the feed-back?
• Instabilities formation of structures, or stars?