Molecular Cloud Turbulence and Star Formation

1. Molecular Cloud Turbulence and Star Formation Javier Ballesteros-Paredes1, Ralf Klessen2, Mordecai-Mark Mac Low3, Enrique Vazquez-Semadeni1 1UNAM Morelia, Mexico, 2AIP, Potsdam, Germany, 3AMNH New York, USA Protostars & Planets V: Oct. 24, 2005

2. Overview • concept of gravoturbulent star formation • three „steps“ of star formation: • formation of molecular clouds in the disk of our galaxy • formation of protostellar cores • formation of stars: protostellar collapse and the stellar mass spectrum • summary intermezzo: properties of molecular cloud turbulence

3. the idea

4. Gravoturbulent star formation • Idea: • Dual role of turbulence: • stability on large scales • initiating collapse on small scales Star formation is controlled by interplay between gravity and supersonic turbulence! (e.g., Larson, 2003, Rep. Prog. Phys, 66, 1651; or Mac Low & Klessen, 2004, Rev. Mod. Phys., 76, 125)

5. Gravoturbulent star formation • Idea: • Validity: Star formation is controlled by interplay between gravity and supersonic turbulence! This hold on all scales and applies to build-up of stars and star clusters within molecular clouds as well as to the formation of molecular clouds in galactic disk. (e.g., Larson, 2003, Rep. Prog. Phys, 66, 1651; or Mac Low & Klessen, 2004, Rev. Mod. Phys., 76, 125)

6. Competing approaches in SF theory: quasistatic theories: magnetically mediatedstar formation Shu, Adams, & Lizano (1987, ARAA) dynamical theories: turbulent controll of starformation Larson (2003, Prog. Rep. Phys.) Mac Low & Klessen (2004, RMP, 76, 125) Elmegreen & Scalo (2004, ARAA) Scalo & Elmegreen (2004, ARAA)

7. density space Gravoturbulent star formation • interstellar gas is highly inhomogeneous • thermal instability • gravitational instability • turbulent compression (in shocks /  M2; in atomic gas: M ≈ 1...3) • cold molecular clouds can form rapidly in high-density regions at stagnation points of convergent large-scale flows • chemical phase transition: atomic  molecular • process is modulated by large-scale dynamics in the galaxy • inside cold clouds: turbulence is highly supersonic (M ≈ 1...20) turbulence creates large density contrast, gravity selects for collapse  GRAVOTUBULENT FRAGMENTATION • turbulent cascade: local compression within a cloud provokes collapse  formation of individual stars and star clusters (e.g. Mac Low & Klessen, 2004, Rev. Mod. Phys., 76, 125-194)

8. cloud formation

9. Molecular cloud formation ... in convergent large-scale flows ... setting up the turbulent cascade Mach 3 colliding flow Vishniac instability + thermal instability compressed sheetbreaks up and builds up cold, high-density „blobs“ of gas --> molecular cloud formation cold cloud motions correspond to supersonic turbulence (e.g. Koyama & Inutsuka 2002, Heitsch et al., 2005, Vazquez-Semadeni et al. 2004; also posters 8577, 8302)

10. density space density space Correlation with large-scale perturbations (e.g. off arm) density/temperature fluctuations in warm atomar ISM are caused by thermal/gravitational instability and/or supersonic turbulence some fluctuations are dense enough to form H2 within “reasonable time” • molecular cloud external perturbuations (i.e. potential changes) increase likelihood (e.g. on arm) (poster 8577: Glover & Mac Low) (poster 8170: Dobbs & Bonnell)

11. Star formation on global scales probability distribution function of the density (-pdf) varying rms Mach numbers: M1 > M2 > M3 > M4 > 0 mass weighted -pdf, each shifted by logN=1 (from Klessen, 2001; also Gazol et al. 2005, Mac Low et al. 2005)

12. Star formation on global scales H2 formation rate: for nH 100 cm-3, H2 forms within 10Myr, this is about the lifetime of typical MC’s. in turbulent gas, the H2 fraction can become very high on short timescale (for models with coupling between cloud dynamics and time-dependent chemistry, see Glover & Mac Low 2005) mass weighted -pdf, each shifted by logN=1 (rate from Hollenback, Werner, & Salpeter 1971, see also poster 8577)

13. Correlation between H2 and HI Compare H2 - HI in M33: H2: BIMA-SONG Survey, see Blitz et al. HI: Observations with Westerbork Radio T. H2 clouds are seen in regions of high HI density (in spiral arms and filaments) (Deul & van der Hulst 1987, Blitz et al. 2004)

14. turbulence

15. Properties of turbulence • laminar flows turn turbulentat highReynolds numbers V= typical velocity on scale L,  = viscosity, Re > 1000 • vortex streching --> turbulence is intrinsically anisotropic(only on large scales you may get homogeneity & isotropy in a statistical sense; see Landau & Lifschitz, Chandrasekhar, Taylor, etc.)(ISM turbulence: shocks & B-field cause additional inhomogeneity)

16. Vortex Formation Porter et al. ASCI, 1997 Vortices are streched and folded in three dimensions

17. Turbulent cascade inertial range: scale-free behavior of turbulence log E k -5/3 „size“ of inertial range: Kolmogorov (1941) theoryincompressible turbulence transfer log k ηK-1 L-1 energy input scale energy dissipation scale

18. Turbulent cascade inertial range: scale-free behavior of turbulence log E k -2 „size“ of inertial range: Shock-dominated turbulence transfer log k ηK-1 L-1 energy input scale energy dissipation scale

19. sonic scale dense protostellar cores molecular clouds massive cloud cores supersonic subsonic rms ≈ several km/s Mrms > 10 L > 10 pc rms ≈ few km/s Mrms ≈ 5 L ≈ 1 pc rms << 1 km/s Mrms ≤ 1 L ≈ 0.1 pc Turbulent cascade in ISM log E ηK-1 L-1 log k energy source & scale NOT known(supernovae, winds, spiral density waves?) dissipation scale not known (ambipolar diffusion, molecular diffusion?)

20. let‘s focus on a cloud core like this one Density structure of MC’s molecular clouds are highly inhomogeneous stars form in the densest and coldest parts of the cloud -Ophiuchus cloud seen in dust emission (Motte, André, & Neri 1998)

21. Evolution of cloud cores • Does core form single massive star or cluster with mass distribution? • Turbulent cascade „goes through“ cloud core--> NO scale separation possible --> NO effective sound speed • Turbulence is supersonic!--> produces strong density contrasts:/ ≈ M2--> with typical M ≈ 10 --> / ≈ 100! • many of the shock-generated fluctuations are Jeans unstable and go into collapse • --> core breaks up and forms a cluster of stars

22. Evolution of cloud cores indeed -Oph B1/2 contains several cores (“starless” cores are denoted by , cores with embedded protostars by ) (Motte, André, & Neri 1998)

23. Formation and evolution of cores • protostellar cloud cores form at the stagnation points of convergent turbulent flows • if M > MJeans-1/2 T3/2: collapse and star formation • if M < MJeans-1/2 T3/2: reexpansion after external compression fades away • typical timescales: t ≈ 104 ... 105 yr • because turbulent ambipolar diffusion time is short, this time estimate still holds for the presence of magnetic fields, in magnetically critical cores (e.g. Vazquez-Semadeni et al 2005) (e.g. Fatuzzo & Adams 2002, Heitsch et al. 2004)

24. Formation and evolution of cores What happens to distribution of cloud cores? Two exteme cases: (1) turbulence dominates energy budget: =Ekin/|Epot| >1--> individual cores do not interact --> collapse of individual cores dominates stellar mass growth--> loose cluster of low-mass stars (2) turbulence decays, i.e. gravity dominates: =Ekin/|Epot| <1--> global contraction--> core do interact while collapsing --> competition influences mass growth--> dense cluster with high-mass stars

25. turbulence creates a hierarchy of clumps

26. as turbulence decays locally, contraction sets in

27. as turbulence decays locally, contraction sets in

28. while region contracts, individual clumps collapse to form stars

29. while region contracts, individual clumps collapse to form stars

30. individual clumps collapse to form stars

31. individual clumps collapse to form stars

32. in dense clusters, clumps may merge while collapsing --> then contain multiple protostars

33. in dense clusters, clumps may merge while collapsing --> then contain multiple protostars

34. in dense clusters, clumps may merge while collapsing --> then contain multiple protostars

35. in dense clusters, competitive mass growth becomes important

36. in dense clusters, competitive mass growth becomes important

37. in dense clusters, N-body effects influence mass growth

38. low-mass objects maybecome ejected --> accretion stops

39. feedback terminates star formation

40. result: star cluster, possibly with HII region

41. predictions

42. Predictions • global properties (statistical properties) • SF efficiency and timescale • stellar mass function -- IMF • dynamics of young star clusters • description of self-gravitating turbulent systems (pdf's, -var.) • chemical mixing properties • local properties (properties of individual objects) • properties of individual clumps (e.g. shape, radial profile, lifetimes) • accretion history of individual protostars (dM/dt vs. t, j vs. t) • binary (proto)stars (eccentricity, mass ratio, etc.) • SED's of individual protostars • dynamic PMS tracks: Tbol-Lbol evolution

43. Examples and predictions example 1:transient structure of turbulent clouds example 2:quiescent and coherent appearence of molecular cloud cores example 3:speculations on the origin of the stellar mass spectrum (IMF)

44. example 1

45. Transient cloud structure Gravoturbulent fragmentation of turbulent self-gravitating clouds xz projection yz projection xy projection SPH model with 1.6x106 particles large-scale driven turbulence Mach number M = 6 periodic boundaries physical scaling: “Taurus”

46. Gravoturbulent fragmentation Gravoturbulent fragmen- tation in molecular clouds: SPH model with 1.6x106 particles large-scale driven turbulence Mach number M = 6 periodic boundaries physical scaling: “Taurus”: density n(H2)102cm-3L=6pc, M=5000M

47. Taurus cloud 20pc ~4pc ~4pc Star-forming filaments in the Taurus molecular cloud (from Hartmann 2002, ApJ)

48. example 2

49. Quiescent & coherent cores correlation between linewidth and columndensity (e.g. Goodman et al. 1998; Barranco & Goodman 1998 Caselli et al. 2002; Tafalla et al. 2004) map of linewidth (contours columndensity) (from Klessen et al. 2005, ApJ, 620, 768 - 794; also poster 8415) column density map (contours columndensity)

50. Quiescent & coherent cores correlation between linewidth and columndensity (e.g. Goodman et al. 1998; Barranco & Goodman 1998 Caselli et al. 2002; Tafalla et al. 2004) map of linewidth (contours columndensity) (from Klessen et al. 2005, ApJ, 620, 768 - 794; also poster 8415) column density map (contours columndensity)