1. The formation of stars and planets
Day 2, Topic 1:
Giant Molecular Clouds
and
Gravitational Stability
Lecture by: C.P. Dullemond

2. Giant Molecular Clouds
Typical characteristics of GMCs:
Mass = M
Distance to nearest GMC = 140 pc (Taurus)
Typical size = pc
Size on the sky of near GMCs = x full moon
Average temperature (in cold parts)= K
Typical density = molec/cm3
Typical (estimated) life time = ~107 year
Star formation efficiency = ~1%..10%

3. 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.

4. Giant Molecular Clouds
Nearby well-studied GMCs:
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...

5. Orion GMC Orion Nebula (part of Orion GMC)
From: CfA Harvard, Millimeter Wave Group

6. 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
fractal dimension

7. 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 = M
Most of mass in massive clumps

8. 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.
Deep 1.3 mm continuum map of  Ophiuchi (140 pc) at 0.01 pc (=2000 AU) resolution Motte et al. 1998

9. Core mass spectrum Result of survey: for M < 0.5 M
Motte et al. 1998

10. Core mass spectrum Similar to stellar IMF (Initial Mass Function)
Meyer et al. PP IV
Salpeter (1955) IMF:

11. Jeans mass Given a homogeneous medium of density 0
Do linear perturbation analysis to see if there exist unstable wave modes:
Continuity equation:
Euler equation:
Poisson’s equation:

12. Jeans mass
Take derivative to t:

13. Jeans mass Equation to solve: Try a plane wave:
Obtain dispersion relation:

14. Jeans mass For  larger than: 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

15. 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:
For interstellar medium (ISM):
Total amount of molecular gas in the Galaxy:
Expected star formation rate:
Observed star formation rate:
Something slows star formation down...

16. Magnetic field support
In presence of B-field, the stability analysis changes.
Magnetic fields can provide support against gravity.
Replace Jeans mass with critical mass, defined as:

17. Magnetic field support
Consider an initially stable cloud. We now compress it. The density thereby increases, but the mass of the cloud stays constant.
Jeans mass decreases:
If no magnetic fields: there will come a time when M>MJ and 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.

18. 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.
Friction between ions and neutrals:
The drift velocity is inversely proportional to the friction:

19. 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...

20. Gravoturbulent
Star Formation

21. Supersonic turbulence
Supersonic turbulence is alternative way to prevent GMCs to collapse
Problem: very quickly decays (each shock converts almost all energy in heat)
Possible solutions:
Energy input from
young stars
Ionization from
massive stars
McLow, Klessen, Burkert, Smith

22. Star formation in turbulent GMCs
Klessen & Burkert 1997

23. Star formation in turbulent GMCs
Klessen & Burkert 1997

24. Star formation in turbulent GMCs
Jappsen, Klessen

25. HII
Regions

26. Remember:

27. HII Regions Strong UV flux from O star ionizes GMC.
Simple model: constant density, spherically symmetric.
HII region
(‘Strömgren sphere’)
O star

28. Ionization, heating, recombination...
Thermalization of electron to local gas temperature. This heats the gas to high temperatures
Continuum (free electron)
Recombination to the ground state produces a photon that immediately ionizes another atom.
Excited states (bound electron)
Ground state

29. Ionization, heating, recombination...
Thermalization of electron to local gas temperature. This heats the gas to very high temperatures
Continuum (free electron)
Excited states (bound electron)
Ground state

30. Strömgren sphere Ionization balance:
From: Osterbrock “Astrophysics of Gaseous Nebulae and AGN”
Ionization balance: Å
Mean intensity of ionizing radiation:
Approximation:
The ionization balance then becomes:

31. Strömgren sphere Express NH0, Ne and Np as:
Approximate ionization cross section of atomic hydrogen:
Approximate recombination coefficient:

32. Strömgren sphere Example: O6 star with T=40,000 K:
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.

33. 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):

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

35. Strömgren sphere Abundance of neutral hydrogen : ionized neutral
Very sharp transition to neutral.

36. Expansion
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.

37. 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”.
Orion Nebula (rotated 90 deg)