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The formation of stars and planets . Day 2, Topic 1: Giant Molecular Clouds and Gravitational Stability Lecture by: C.P. Dullemond. Giant Molecular Clouds. Typical characteristics of GMCs: Mass = 10 4 ...10 6 M  Distance to nearest GMC = 140 pc (Taurus) Typical size = 5..100 pc

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the formation of stars and planets

The formation of stars and planets

Day 2, Topic 1:

Giant Molecular Clouds


Gravitational Stability

Lecture by: C.P. Dullemond

giant molecular clouds
Giant Molecular Clouds
  • Typical characteristics of GMCs:
    • Mass = 104...106 M
    • Distance to nearest GMC = 140 pc (Taurus)
    • Typical size = 5..100 pc
    • Size on the sky of near GMCs = 5..20 x full moon
    • Average temperature (in cold parts)= 20...30 K
    • Typical density = 103...106 molec/cm3
    • Typical (estimated) life time = ~107 year
    • Star formation efficiency = ~1%..10%
giant molecular clouds3
Giant Molecular Clouds
  • Composition of material:
    • 99% gas, 1% solid sub-micron particles (‘dust’) (by mass)
    • Gas: 0.9 H2/H, 0.1 He, 10-4 CO, 10-5 other molecules (by number)
    • Dust: Mostly silicates + carbonaceous (< m in size)
  • Properties of the gas:
    • Gas mostly in molecular form: hydrogen in H2, carbon in CO, oxygen in O (O2?), nitrogen in N2(?).
    • At the edges of molecular clouds: transition to atomic species. “Photo-Dissociation Regions” (PDRs).
    • H2 cannot be easily observed. Therefore CO often used as tracer.
giant molecular clouds4
Giant Molecular Clouds
  • Taurus (dist ≈ 140 pc, size ≈ 30 pc, mass ≈104 M): Only low mass stars (~105), quiet slow star formation, mostly isolated star formation.
  • Ophiuchus (dist ≈ 140 pc, size ≈ 6 pc, mass ≈ 104 M): Low mass stars (~78), strongly clustered in western core (stellar density 50 stars/pc), high star formation efficiency
  • Orion (dist ≈ 400 pc, size ≈ 60 pc, mass ≈ 106 M): Cluster of O-stars at center, strongly ionized GMC, O-stars strongly affect the low-mass star formation
  • Chamaeleon...
  • Serpens...

Nearby well-studied GMCs:

orion gmc

Orion Nebula (part of Orion GMC)

Orion GMC

From: CfA Harvard, Millimeter Wave Group

giant molecular clouds6

fractal dimension

Giant Molecular Clouds

Structure of GMCs: two descriptions

  • Clump picture: hierarchical structure
    • Clouds (≥ 10 pc)
    • Clumps (~1 pc)
      • Precursors of stellar clusters
    • Cores (~0.1 pc)
      • High density regions which form individual stars or binaries
  • Fractal picture: clouds are scale-free
clump mass spectrum

Most of mass in massive clumps

Clump mass spectrum

Orion B: First GMC systematically surveyed for dense gas and embedded YSOs by E. Lada 1990

Survey of gas clumps

Clumps in range M = 8..500 M

core mass spectrum

Deep 1.3 mm continuum map of  Ophiuchi (140 pc) at 0.01 pc (=2000 AU) resolution. Motte et al. 1998

Core mass spectrum

Most clumps don’t form stars. But if they do, they form many.

Core mass spectrum is more interesting for predicting the stellar masses of the newborn stars.

core mass spectrum9

for M < 0.5 M

for M > 0.5 M

Core mass spectrum

Result of survey:

Motte et al. 1998

core mass spectrum10

Salpeter (1955) IMF:

Core mass spectrum

Similar to stellar IMF (Initial Mass Function)

Stellar IMF:

Meyer et al. PP IV

jeans mass

Continuity equation:

Euler equation:

Poisson’s equation:

Jeans mass
  • Given a homogeneous medium of density 0
  • Do linear perturbation analysis to see if there exist unstable wave modes:
jeans mass13

Try a plane wave:

Obtain dispersion relation:

Jeans mass

Equation to solve:

jeans mass14

For  larger than:

Jeans mass

Jean’s length

the wave grows exponentially.

This is true for all waves (in all directions) with >J. This defines maximum stable mass: a sphere with diameter J:

Jean’s mass

problem of star formation efficiency

For interstellar medium (ISM):

Total amount of molecular gas in the Galaxy:

Expected star formation rate:

Observed star formation rate:

Problem of star formation efficiency

Gas in the galaxy should be wildly gravitationally unstable. It should convert all its mass into stars on a free-fall time scale:

Something slows star formation down...

magnetic field support

Replace Jeans mass with critical mass, defined as:

Magnetic field support

In presence of B-field, the stability analysis changes.

Magnetic fields can provide support against gravity.

magnetic field support17

Jeans mass decreases:

Magnetic field support

Consider an initially stable cloud. We now compress it. The density thereby increases, but the mass of the cloud stays constant.

If no magnetic fields: there will come a time when M>MJand the cloud will collapse.

But Mcr stays constant (magnetic flux freezing)

So if B-field is strong enough to support a cloud, no compression will cause it to collapse.

ambipolar diffusion

Friction between ions and neutrals:

The drift velocity is inversely proportional to the friction:

Ambipolar diffusion

But magnetic flux freezing is not perfect. Only the (few) electrons and ions are stuck to the field lines. The neutral molecules do not feel the B-field. They may slowly diffuse through the ‘fixed’ background of ions and electrons.

ambipolar diffusion19
Ambipolar diffusion

Slowly a cloud (supported by B-field) will expell the field, and contract, until it can no longer support itself, and will collapse.

Simulations: Lizano & Shu (1989)

See later...




hii regions
HII Regions

Strong UV flux from O star ionizes GMC.

Simple model: constant density, spherically symmetric.

HII region

(‘Strömgren sphere’)

O star

ionization heating recombination

Thermalization of electron to local gas temperature. This heats the gas to high temperatures

Ionization, heating, recombination...

Continuum (free electron)

Recombination to the ground state produces a photon that immediately ionizes another atom.

Excited states (bound electron)

Ground state

ionization heating recombination24

Thermalization of electron to local gas temperature. This heats the gas to very high temperatures

Ionization, heating, recombination...

Continuum (free electron)

Excited states (bound electron)

Ground state

str mgren sphere

Ionization balance:


Mean intensity of ionizing radiation:


The ionization balance then becomes:

Strömgren sphere

From: Osterbrock “Astrophysics of Gaseous Nebulae and AGN”

str mgren sphere26

Express NH0, Ne and Np as:

Approximate ionization cross section of atomic hydrogen:

Approximate recombination coefficient:

Strömgren sphere
str mgren sphere27

O6 star with T=40,000 K:

Strömgren sphere


Hydrogen density of 10 atoms / cm3

At r = 5 pc we get  = 4x10-4, i.e. nearly complete ionization!

Conclusion: Unless LN drops really low (or one is very far away from the star),  will be near 0, i.e. virtually complete ionization.

str mgren sphere28
Strömgren sphere

Effect of extinction:

Inside sphere: virtually complete ionization. Recombination rate per volume element is:

Need continuous re-ionization to compensate for recombination. This `eats away’ stellar photons (extinction):

str mgren sphere29
Strömgren sphere

Outer radius of Strömgren sphere: where all photons are used up, i.e. where LN(r)=0.

str mgren sphere30
Strömgren sphere

Abundance of neutral hydrogen :



Very sharp transition to neutral.


Ionized material inside the HII region is very hot (~104 K). Therefore pressure is about thousand times higher than in the neutral surrounding medium.

The sphere expands and drives a strong shock through the medium.

champagne flows blisters

Orion Nebula (rotated 90 deg)

Champagne flows (‘blisters’)

When shell reaches end of Molecular Cloud, it bursts out with high velocity outflow. Similarity to uncorking a bottle of champagne, hence the name “Champagne Flows”.