The formation of stars and planets

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 = 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%

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 • 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:

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

6. 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

7. 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

8. 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.

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

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

11. 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:

12. Take derivative to t: Jeans mass

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

14. 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

15. 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...

16. 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.

17. 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.

18. 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.

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. HII Regions

21. Remember:

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

23. 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

24. 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

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

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

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

28. 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):

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

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

31. 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.

32. 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”.