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

2. Ralf Klessen: PPV, Oct. 24, 2005 Overview concept of gravoturbulent star formation three „steps“ of star formation: 1. formation of molecular clouds in the disk of our galaxy 2. formation of protostellar cores 3. formation of stars: protostellar collapse and the stellar mass spectrum summary properties of molecular cloud turbulence intermezzo: properties of molecular cloud turbulence

3. Ralf Klessen: PPV, Oct. 24, 2005 the idea

4. Ralf Klessen: PPV, Oct. 24, 2005 Gravoturbulent star formation Idea: Dual role Dual role of turbulence: stability on large scales initiating collapse on small scales Star formation is controlled by interplay between gravity and supersonic turbulence! 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. Ralf Klessen: PPV, Oct. 24, 2005 Gravoturbulent star formation Idea:Validity: Star formation is controlled by interplay between gravity and supersonic turbulence! 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. Ralf Klessen: PPV, Oct. 24, 2005 Competing approaches in SF theory: quasistatic theories: magnetically mediated star formation dynamical theories: turbulent controll of star formation Shu, Adams, & Lizano (1987, ARAA) Larson (2003, Prog. Rep. Phys.) Mac Low & Klessen (2004, RMP, 76, 125) Elmegreen & Scalo (2004, ARAA) Scalo & Elmegreen (2004, ARAA)

7. Ralf Klessen: PPV, Oct. 24, 2005 Gravoturbulent star formation interstellar gas is highly inhomogeneous thermal instability gravitational instability turbulent compression turbulent compression (in shocks  /   M 2 ; in atomic gas: M ≈ 1...3) molecular clouds cold molecular clouds can form rapidly in high-density regions at stagnation points of convergent large-scale flows phase transition atomic  molecular chemical phase transition: atomic  molecular modulateddynamics process is modulated by large-scale dynamics in the galaxy cold clouds: turbulence gravity GRAVOTUBULENT FRAGMENTATION inside cold clouds: turbulence is highly supersonic ( M ≈ 1...20)  turbulence creates large density contrast, gravity selects for collapse  GRAVOTUBULENT FRAGMENTATION turbulent cascade:within stars star clusters 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) space density

8. Ralf Klessen: PPV, Oct. 24, 2005 cloud formation

9. Ralf Klessen: PPV, Oct. 24, 2005 Mach 3 colliding flow Vishniac instability + thermal instability compressed sheet breaks up and builds up cold, high-density „blobs“ of gas molecular cloud formation --> molecular cloud formation cold cloud motions correspond to supersonic turbulence Molecular cloud formation convergent large-scale flows... in convergent large-scale flows turbulent cascade... setting up the turbulent cascade (e.g. Koyama & Inutsuka 2002, Heitsch et al., 2005, Vazquez-Semadeni et al. 2004; also posters 8577, 8302)

10. Ralf Klessen: PPV, Oct. 24, 2005 Correlation with large-scale perturbations density/temperature fluctuations density/temperature fluctuations in warm atomar ISM are caused by thermal/gravitational instability and/or supersonic turbulence denseform H 2 some fluctuations are dense enough to form H 2 within “reasonable time”  molecular cloud external perturbuations increase external perturbuations (i.e. potential changes) increase likelihood space density space density (e.g. off arm) (e.g. on arm) (poster 8170: Dobbs & Bonnell) (poster 8577: Glover & Mac Low)

11. Ralf Klessen: PPV, Oct. 24, 2005 Star formation on global scales probability distribution function of the density (  -pdf) mass weighted  - pdf, each shifted by  log N = 1 varying rms Mach numbers: M1 > M2 > M3 > M4 > 0 (from Klessen, 2001; also Gazol et al. 2005, Mac Low et al. 2005)

12. Ralf Klessen: PPV, Oct. 24, 2005 Star formation on global scales H 2 formation rate: mass weighted  - pdf, each shifted by  log N = 1 (rate from Hollenback, Werner, & Salpeter 1971, see also poster 8577) for n H  100 cm -3, H 2 forms within 10Myr, this is about the lifetime of typical MC’s. in turbulent gas, the H 2 fraction can become very high on short timescale (for models with coupling between cloud dynamics and time-dependent chemistry, see Glover & Mac Low 2005)

13. Ralf Klessen: PPV, Oct. 24, 2005 Correlation between H 2 and H I (Deul & van der Hulst 1987, Blitz et al. 2004) Compare H 2 - H I in M33: H 2 : BIMA-SONG Survey, see Blitz et al. H I : Observations with Westerbork Radio T. H 2 clouds are seen in regions of high H I density (in spiral arms and filaments)

14. Ralf Klessen: PPV, Oct. 24, 2005 turbulence

15. Ralf Klessen: PPV, Oct. 24, 2005 Properties of turbulence high laminar flows turn turbulent at high Reynolds numbers V = typical velocity on scale L, = viscosity, Re > 1000 anisotropic 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. Ralf Klessen: PPV, Oct. 24, 2005 Vortex Formation Vortices are streched and folded in three dimensions Porter et al. ASCI, 1997

17. Ralf Klessen: PPV, Oct. 24, 2005 Turbulent cascade log E log k k -5/3 L -1 η K -1 transfer energy input scale energy dissipation scale inertial range: scale-free behavior of turbulence „size“ of inertial range: Kolmogorov (1941) theory incompressible turbulence

18. Ralf Klessen: PPV, Oct. 24, 2005 Turbulent cascade log E log k k -2 L -1 η K -1 transfer energy input scale energy dissipation scale inertial range: scale-free behavior of turbulence „size“ of inertial range: Shock-dominated turbulence

19. Ralf Klessen: PPV, Oct. 24, 2005 molecular clouds  rms ≈ several km/s M rms > 10 L > 10 pc Turbulent cascade in ISM log E log k L -1 η K -1 energy source & scale NOT known (supernovae, winds, spiral density waves?) dissipation scale not known (ambipolar diffusion, molecular diffusion?) supersonic subsonic sonic scale massive cloud cores  rms ≈ few km/s M rms ≈ 5 L ≈ 1 pc dense protostellar cores  rms << 1 km/s M rms ≤ 1 L ≈ 0.1 pc

20. Ralf Klessen: PPV, Oct. 24, 2005 Density structure of MC’s (Motte, André, & Neri 1998) molecular clouds are highly inhomogeneous stars form in the densest and coldest parts of the cloud  -Ophiuchus cloud seen in dust emission let‘s focus on a cloud core like this one

21. Ralf Klessen: PPV, Oct. 24, 2005 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  /  ≈ M 2 M ≈ 10  /  ≈ 100 Turbulence is supersonic! --> produces strong density contrasts:  /  ≈ M 2 --> 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 --> core breaks up and forms a cluster of stars

22. Ralf Klessen: PPV, Oct. 24, 2005 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. Ralf Klessen: PPV, Oct. 24, 2005 Formation and evolution of cores stagnation pointsconvergent turbulent flows protostellar cloud cores form at the stagnation points of convergent turbulent flows collapse and star formation if M > M Jeans  -1/2 T 3/2 : collapse and star formation reexpansion after external compression fades away if M < M Jeans  -1/2 T 3/2 : reexpansion after external compression fades away typical timescales: t ≈ 10 4... 10 5 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. Ralf Klessen: PPV, Oct. 24, 2005 What happens to distribution of cloud cores? Two exteme cases:  =E kin /|E pot | >1 loose cluster of low-mass stars (1) turbulence dominates energy budget:  =E kin /|E pot | >1 --> individual cores do not interact --> collapse of individual cores dominates stellar mass growth --> loose cluster of low-mass stars  =E kin /|E pot | global contraction --> core do interact while collapsing --> competition influences mass growth --> dense cluster with high-mass stars Formation and evolution of cores

25. Ralf Klessen: PPV, Oct. 24, 2005 turbulence creates a hierarchy of clumps

26. Ralf Klessen: PPV, Oct. 24, 2005 as turbulence decays locally, contraction sets in

27. Ralf Klessen: PPV, Oct. 24, 2005 as turbulence decays locally, contraction sets in

28. Ralf Klessen: PPV, Oct. 24, 2005 while region contracts, individual clumps collapse to form stars

29. Ralf Klessen: PPV, Oct. 24, 2005 while region contracts, individual clumps collapse to form stars

30. Ralf Klessen: PPV, Oct. 24, 2005 individual clumps collapse to form stars

31. Ralf Klessen: PPV, Oct. 24, 2005 individual clumps collapse to form stars

32. Ralf Klessen: PPV, Oct. 24, 2005 dense clusters in dense clusters, clumps may merge while collapsing --> then contain multiple protostars

33. Ralf Klessen: PPV, Oct. 24, 2005 dense clusters in dense clusters, clumps may merge while collapsing --> then contain multiple protostars

34. Ralf Klessen: PPV, Oct. 24, 2005 dense clusters in dense clusters, clumps may merge while collapsing --> then contain multiple protostars

35. Ralf Klessen: PPV, Oct. 24, 2005 dense clusters in dense clusters, competitive mass growth becomes important

36. Ralf Klessen: PPV, Oct. 24, 2005 dense clusters in dense clusters, competitive mass growth becomes important

37. Ralf Klessen: PPV, Oct. 24, 2005 dense clusters in dense clusters, N-body effects influence mass growth

38. Ralf Klessen: PPV, Oct. 24, 2005 low-mass objects may become ejected --> accretion stops

39. Ralf Klessen: PPV, Oct. 24, 2005 feedback terminates star formation

40. Ralf Klessen: PPV, Oct. 24, 2005 star cluster result: star cluster, possibly with H II region

41. Ralf Klessen: PPV, Oct. 24, 2005 some specific predictions

42. Ralf Klessen: PPV, Oct. 24, 2005 predictions

43. Ralf Klessen: PPV, Oct. 24, 2005 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: T bol -L bol evolution

44. Ralf Klessen: PPV, Oct. 24, 2005 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)

45. Ralf Klessen: PPV, Oct. 24, 2005 example 1

46. Ralf Klessen: PPV, Oct. 24, 2005 SPH model with 1.6x10 6 particles large-scale driven turbulence Transient cloud structure Mach number M = 6 periodic boundaries physical scaling: “Taurus” Gravoturbulent fragmentation of turbulent self-gravitating clouds xy projection xz projection yz projection

47. Ralf Klessen: PPV, Oct. 24, 2005 Gravoturbulent fragmentation Gravoturbulent fragmen- tation in molecular clouds: SPH model with 1.6x10 6 particles large-scale driven turbulence Mach number M = 6 periodic boundaries physical scaling: “Taurus”:  density n(H 2 )  10 2 cm -3  L = 6 pc, M = 5000 M 

48. Ralf Klessen: PPV, Oct. 24, 2005 Taurus cloud Taurus Star- forming filaments in the Taurus molecular cloud (from Hartmann 2002, ApJ) 20pc ~4pc

49. Ralf Klessen: PPV, Oct. 24, 2005 example 2

50. Ralf Klessen: PPV, Oct. 24, 2005 Quiescent & coherent cores column density map (contours column density) map of linewidth (contours column density) correlation between linewidth and column density (from Klessen et al. 2005, ApJ, 620, 768 - 794; also poster 8415) (e.g. Goodman et al. 1998; Barranco & Goodman 1998 Caselli et al. 2002; Tafalla et al. 2004)

51. Ralf Klessen: PPV, Oct. 24, 2005 Quiescent & coherent cores column density map (contours column density) map of linewidth (contours column density) correlation between linewidth and column density (from Klessen et al. 2005, ApJ, 620, 768 - 794; also poster 8415) (e.g. Goodman et al. 1998; Barranco & Goodman 1998 Caselli et al. 2002; Tafalla et al. 2004)

52. Ralf Klessen: PPV, Oct. 24, 2005 Quiescent & coherent cores column density map (contours column density) map of linewidth (contours column density) correlation between linewidth and column density (from Klessen et al. 2005, ApJ, 620, 768 - 794; also poster 8415) cores form at stagnation points of convergent large-scale flows --> often are bounded by ram pressure --> velocity dispersion highest at boundary (e.g. Goodman et al. 1998; Barranco & Goodman 1998 Caselli et al. 2002; Tafalla et al. 2004)

53. Ralf Klessen: PPV, Oct. 24, 2005 Quiescent & coherent cores 23% of our cores are quiescent quiescent (i.e. with  rms ≤ c s ) 48% of our cores are transonic transonic (i.e. with c s ≤  rms ≤ 2c s ) half of our cores are coherent coherent (i.e. with  rms independent of N) Statistics: large-scale turb. small-scale turb. (from Klessen et al. 2005, ApJ, 620, 768 - 794; also poster 8415)

54. Ralf Klessen: PPV, Oct. 24, 2005 Quiescent & coherent cores most cores have masses smaller than M vir (should reexpand once external compresseion fades) (from Klessen et al. 2005, ApJ, 620, 768 - 794; also poster 8415) some core have more mass than M vir (should collapse) (indeed all cores with protostars have M>M vir ) Statistics: M < M vir M > M vir

55. Ralf Klessen: PPV, Oct. 24, 2005 example 3

56. Ralf Klessen: PPV, Oct. 24, 2005 IMF distribution of stellar masses depends on turbulent initial conditions --> mass spectrum of prestellar cloud cores collapse and interaction of prestellar cores --> competitive accretion and N-body effects thermodynamic properties of gas --> balance between heating and cooling --> EOS (determines which cores go into collapse) (proto) stellar feedback terminates star formation ionizing radiation, bipolar outflows, winds, SN (e.g. Larson 2003, Prog. Rep. Phys.; Mac Low & Klessen, 2004, Rev. Mod. Phys, 76, 125 - 194)

57. Ralf Klessen: PPV, Oct. 24, 2005 Star cluster formation Most stars form in clusters  star formation = cluster formation cloud coresstar clusters How to get from cloud cores to star clusters? acquiremass How do the stars acquire mass? (e.g. Larson 2003, Prog. Rep. Phys.; Mac Low & Klessen, 2004, Rev. Mod. Phys, 76, 125 - 194)

58. Ralf Klessen: PPV, Oct. 24, 2005 Star cluster formation Trajectories of protostars in a nascent dense cluster created by gravoturbulent fragmentation (from Klessen & Burkert 2000, ApJS, 128, 287) in dense clusters protostellar interaction may be come important!

59. Ralf Klessen: PPV, Oct. 24, 2005 Star cluster formation Trajectories of protostars in a nascent dense cluster created by gravoturbulent fragmentation (from Klessen & Burkert 2000, ApJS, 128, 287) Most stars form in clusters  star formation = cluster formation

60. Ralf Klessen: PPV, Oct. 24, 2005 Mass accretion rates vary with time and are strongly influenced by the cluster environment. Accretion rates in clusters (Klessen 2001, ApJ, 550, L77; also Schmeja & Klessen, 2004, A&A, 419, 405)

61. Ralf Klessen: PPV, Oct. 24, 2005 Dependency on EOS EOS! degree of fragmentation depends on EOS! p   polytropic EOS: p    <1  <1: dense cluster of low-mass stars  >1:  >1: isolated high-mass stars (see Li, Klessen, & Mac Low 2003, ApJ, 592, 975; also Kawachi & Hanawa 1998, Larson 2003)

62. Ralf Klessen: PPV, Oct. 24, 2005 Dependency on EOS (from Li, Klessen, & Mac Low 2003, ApJ, 592, 975)  =0.2  =1.0  =1.2 for  <1 fragmentation is enhanced  cluster of low-mass stars for  >1 it is suppressed  formation of isolated massive stars Ralf Klessen: UCB, 08/11/04

63. Ralf Klessen: PPV, Oct. 24, 2005 How does that work? (1) p       p 1/  (1) p       p 1/  (2) M jeans   3/2  (3  -4)/2 (2) M jeans   3/2  (3  -4)/2  <1: large  <1:  large density excursion for given pressure   M jeans  becomes small  number of fluctuations with M > M jeans is large  >1: small  >1:  small density excursion for given pressure   M jeans  is large  only few and massive clumps exceed M jeans

64. Ralf Klessen: PPV, Oct. 24, 2005 Implications EOS! degree of fragmentation depends on EOS! p   polytropic EOS: p    <1  <1: dense cluster of low-mass stars  >1:  >1: isolated high-mass stars (see Li, Klessen, & Mac Low 2003, ApJ, 592, 975; Kawachi & Hanawa 1998; Larson 2003; also Jappsen, Klessen, Larson, Li, Mac Low, 2005, 435, 611) implications for extreme environmental conditions - expect Pop III stars to be massive and form in isolation - expect IMF variations in warm & dusty starburst regions (Spaans & Silk 2005; Klessen, Spaans, & Jappsen 2005) Observational findings: isolated O stars in LMC (and M51)? (Lamers et al. 2002, Massey 2002; see however, de Witt et al. 2005 for Galaxy)

65. Ralf Klessen: PPV, Oct. 24, 2005 More realistic EOS chemical state balanceheatingcooling But EOS depends on chemical state, on balance between heating and cooling log density log temperature P    P   T   = 1+dlogT/dlo  n(H 2 ) crit ≈ 2.5  10 5 cm -3  crit ≈ 10 -18 g cm -3  = 1.1  = 0.7 (Larson 2005; Jappsen et al. 2005, A&A, 435, 611)

66. Ralf Klessen: PPV, Oct. 24, 2005 IMF in nearby molecular clouds (Jappsen et al. 2005, A&A, 435, 611) “Standard” IMF of single stars (e.g. Scalo 1998, Kroupa 2002) with  crit ≈ 2.5  10 5 cm -3 at SFE ≈ 50%

67. Ralf Klessen: PPV, Oct. 24, 2005 summary

68. Ralf Klessen: PPV, Oct. 24, 2005 Summary interstellar gas is highly inhomogeneous thermal instability gravitational instability turbulent compression turbulent compression (in shocks  /   M 2 ; in atomic gas: M ≈ 1...3) molecular clouds cold molecular clouds form rapidly in high-density regions phase transition atomic  molecular chemical phase transition: atomic  molecular modulateddynamics process is modulated by large-scale dynamics in the galaxy cold clouds: turbulencegravity GRAVOTUBULENT FRAGMENTATION inside cold clouds: turbulence is highly supersonic ( M ≈ 1...20)  turbulence creates density structure, gravity selects for collapse  GRAVOTUBULENT FRAGMENTATION turbulent cascade:within turbulent cascade: local compression within a cloud provokes collapse stars star clusters individual stars and star clusters form through sequence of highly stochastic events: collapse collapse of cloud cores in turbulent cloud (cores change during collapse) interaction competitive accretion plus mutual interaction during collapse (importance depends on ratio of potential energy to turbulent energy) (buzz word: competitive accretion)

69. Ralf Klessen: PPV, Oct. 24, 2005 Thanks!

70. Ralf Klessen: PPV, Oct. 24, 2005 (from Mc Low & Klessen, 2004, Rev. Mod. Phys., 76, 125 - 194) SF Flow Chart