1. Theories of Massive Star Formation Ian A. Bonnell University of St Andrews

2. Two Issues How do massive stars form? How do massive stars form? Problem of accretion versus radiation pressure Problem of accretion versus radiation pressure Once M > 10-40 M o Once M > 10-40 M o e.g. Wolfire & Casinelli 1986; Edgar & Clarke 2003 e.g. Wolfire & Casinelli 1986; Edgar & Clarke 2003 c.f. Mark Krumholz’s talk c.f. Mark Krumholz’s talk Why do massive stars form? Why do massive stars form? Why are some stars 100 x M star ? Why are some stars 100 x M star ? Where does the star’s mass come from ? Where does the star’s mass come from ? Monolithic collapse versus competitive accretion Monolithic collapse versus competitive accretion

3. Radiation Pressure: Solutions I) Radiation beaming and disc accretion I) Radiation beaming and disc accretion III) Stellar mergers n ~ 10 8 stars pc -3 III) Stellar mergers n ~ 10 8 stars pc -3 Binary mergers n ~ 10 6 stars pc -3 Binary mergers n ~ 10 6 stars pc -3 Many O stars in close binaries Many O stars in close binaries Yorke & Sonnhalter 2002 Krumholz et al 2005 Bonnell et al. 1998; Bonnell & Bate 2002; Bally & Zinnecker 2005 II) Rayleigh-Taylor instabilities accretion in high optical depth filaments accretion in high optical depth filaments Bonnell & Bate 2005

4. Possible Models Monolithic Collapse Monolithic Collapse 1 core 1 massive star 1 core 1 massive star Pressure induced, in centre of cluster Pressure induced, in centre of cluster Slow, quasistatic Slow, quasistatic Question: Do initial conditions exist? Fragment? Question: Do initial conditions exist? Fragment? Competitive Accretion Competitive Accretion Fragmentation: thermal Jeans mass : 1 M o Fragmentation: thermal Jeans mass : 1 M o Multiple cores Multiple cores Accretion from shared reservoir Accretion from shared reservoir Dynamical, gravity driven Dynamical, gravity driven Question: Does it work? Question: Does it work? Need predictions/tests Need predictions/tests Occam’s Razor: simplest solution best Occam’s Razor: simplest solution best McKee & Tan 2004 Zinnecker 1982; Bonnell et al 1997, 2001, 2004

5. Massive Star formation: context Need to understand in context of low mass star formation Need to understand in context of low mass star formation ~All massive stars form in clusters ~All massive stars form in clusters Full IMF Full IMF Mass segregated Mass segregated Massive stars in centre Massive stars in centre Too young for dynamical 2-body relaxation Too young for dynamical 2-body relaxation In Binaries In Binaries With close massive companions With close massive companions Trapezium like systems Trapezium like systems M. McCaughrean

6. Stellar clusters and massive star formation Observed relation of M max and M clus, stellar density Observed relation of M max and M clus, stellar density Causal ? Causal ? Not random sampling of IMF? Not random sampling of IMF? Weidner & Kroupa 2005 Weidner & Kroupa 2005 Testi et al. 1997

7. Stellar clusters and massive star formation Observed relation of M max and M clus, stellar density Observed relation of M max and M clus, stellar density Causal ? Causal ? Not random sampling of IMF? Not random sampling of IMF? Weidner & Kroupa 2005 Weidner & Kroupa 2005 Weidner & Kroupa 2005

8. Turbulence Clump formation in shock layers Clump formation in shock layers Structures part of larger scale flow Structures part of larger scale flow Come and go Come and go Generate dist n of clump masses Generate dist n of clump masses Higher masses Higher masses Weaker shocks Weaker shocks Padoan & Nordlund 2002 Density, width of shock: Density, width of shock: Clump masses Clump masses Ballesteros-Paredes et al 2006 Inverse mass segregation Inverse mass segregation Higher-mass clumps most separated Higher-mass clumps most separated Elmegreen 1991; Padoan et al 1997

9. Turbulence and massive star formation Upper-mass IMF too steep? (Ballesteros-Paredes et.al. 2006) Upper-mass IMF too steep? (Ballesteros-Paredes et.al. 2006) Worse with fragmentation Worse with fragmentation Star formation sets in at Jeans mass Star formation sets in at Jeans mass Turbulence crucial for structure formation Turbulence crucial for structure formation Seeds for gravitational fragmentation Seeds for gravitational fragmentation Ballesteros-Paredes et al 2006 Clark & Bonnell 2006

10. Turbulent cores fragment Centrally condensed turbulent core Centrally condensed turbulent core Fragments on dynamical timescale Fragments on dynamical timescale How do such cores form ? How do such cores form ? Take many T dyn Take many T dyn Dobbs et al 2005

11. The Formation of a stellar cluster Forms full IMF Hierarchical : Filaments fragment Forms small-N clusters Grow and merge 10 3 M sun in 1 pc M Jeans = M sun

12. Stellar Properties Forms 419 stars in 2.5 t ff (5 x 10 5 years) ~ 10 final t dyn M max ~30 M o M acc ~ 10 -4 M o /yr M acc ~ 10 -4 M o /yr M med ~ 0.5 M o Stellar mass

13. Where does the mass come from? 1.Initial fragment 2.Envelope till next forming star 3.Outside : competitive accretion

14. Origin of stellar masses Fragmentation mass Fragmentation mass ~ Jeans Mass ~ Jeans Mass Clump mass Clump mass Accretion from outside stellar cluster Accretion from outside stellar cluster  = -1 mass limit Massive stars form due to accretion from large-scale reservoir Bonnell, Vine & Bate (2004)

15. Competitive accretion Accretion rates Accretion rates Cluster potential Gas inflow All local variables Global Cloud  2 10 -19 g/cm 3 v 2 km/s M * 0.1 M sun 10 -9 M sun /yr Competitve accretion doesn’t work ? Krumholz et al 2005

16. Competitive accretion Accretion rates Accretion rates Cluster potential Gas inflow All local variables Global CloudLocal Cluster Core  2 10 -19 g/cm 3 10 -17 g/cm 3 v 2 km/s 0.5 km/s M * 0.1 M sun 0.5 M sun 10 -9 M sun /yr 10 -4 M sun /yr Large range in possible full IMF

17. Competitive accretion Gas inflow due to cluster potential Gas inflow due to cluster potential to cluster centre to cluster centre Higher gas density Higher gas density Initially low relative velocities Initially low relative velocities Turbulence locally small Turbulence locally small Small-N clusters Small-N clusters Stars in centre accrete more Stars in centre accrete more Higher accretion rates Higher accretion rates massive stars massive stars Cluster potential Gas inflow All local variables

18. Massive star formation in a stellar cluster Bonnell, Bate & Vine 2003Bonnell, Vine & Bate 2004 Gas that forms most massive starFormation of a stellar cluster

19. Accretion starts in small-N clusters Accretion starts in small-N clusters Low velocity dispersion Low velocity dispersion Short accretion timescale Short accretion timescale Attain ~higher masses before v disp high Attain ~higher masses before v disp high Form massive stars in few 10 5 years Form massive stars in few 10 5 years Bonnell & Bate 2006

20. Observables: Kinematics Line of sight velocities large due to projection effects Line of sight velocities large due to projection effects Multiple clumps, extended gas structures Multiple clumps, extended gas structures Bonnell & Bate 2006

21. Accretion and Mass Segregation Stellar masses colour coded Mass segregated clusters Bonnell, Larson & Zinnecker 2006 10 3 M sun in 1 pc Accretion forms massive star in centre of each sub-cluster

22. Link to Cluster Formation Massive star grows by accreting gas that falls into cluster Massive star grows by accreting gas that falls into cluster Gas is accompanied by low-mass stars Gas is accompanied by low-mass stars Forms cluster around massive star. Forms cluster around massive star.

23. Link to Cluster Formation

24. Accretion and massive binaries Stars form with low-mass and well separated Stars form with low-mass and well separated Form binary system due to 3-body (and gas) capture Form binary system due to 3-body (and gas) capture Accretion Accretion Increases masses Increases masses Decreases separation Decreases separation Stellar interactions harden binary Stellar interactions harden binary Forms close massive binaries Forms close massive binaries Evolve Bonnell & Bate 2005

25. Final Binary Properties R binary and M binary R binary and M binary < 1 to 1000 AU < 1 to 1000 AU R peri and M star R peri and M star <0.01 to 100 AU <0.01 to 100 AU More massive stars in closer binaries More massive stars in closer binaries Periastron separation < R * Periastron separation < R * Binary mergers likely Binary mergers likely Radius of star

26. Binary Mergers Stellar mergers Separation of binary system Distance to next closest (3 rd ) star Mass of most massive star Binary hardens due to accretion and interactions with 3rd star Interactions can force mergers Bonnell & Bate 2002

27. Discs around massive stars Disc formation Due to angular momentum in accreting gas Scale ~ 1000s AU Disc is disturbed, semi-transient structure Forms/Reforms on T dyn Bonnell, & Bate 2005

28. Discs and Outflows Circumstellar structure Circumstellar structure Collimated winds Collimated winds edge-on

29. Feedback from OB stars Ionisation from massive stars Ionisation from massive stars Collimated by circumstellar structure Collimated by circumstellar structure HII region one-sided HII region one-sided Accretion continues relatively unimpeded Accretion continues relatively unimpeded Dale et al. 2005

30. Feedback and Accretion Accretion largely unimpeded by feedback Accretion largely unimpeded by feedback Dale et al 2005; Krumholz etal 2005 Dale et al 2005; Krumholz etal 2005 Escapes along preferential directions Escapes along preferential directions Dale et al 2005

31. Feedback and Cloud Support Unlikely to support cluster over many t dyn Unlikely to support cluster over many t dyn t feedback ≤ t dyn t feedback ≤ t dyn Cluster cannot adapt to energy source Cluster cannot adapt to energy source Feedback will Feedback will 1. Do little 2. Remove gas (destroy system) e.g. Li & Nakamura feedback simulation ~ to our non feedback runs e.g. Li & Nakamura feedback simulation ~ to our non feedback runs

32. Triggering of star formation

33. Model Predictions Competitive accretion Competitive accretion Hierarchical fragmentation Hierarchical fragmentation Non-relaxed, structured systems (early) Non-relaxed, structured systems (early) M max function of M tot (IMF at all times) M max function of M tot (IMF at all times) Monolithic Collapse Monolithic Collapse Quasistatic Quasistatic Relaxed, no significant sub structure Relaxed, no significant sub structure Truncated IMFs (early) Truncated IMFs (early) Massive stars form last Massive stars form last

34. Conclusions Competitive accretion viable mechanism to form massive stars Competitive accretion viable mechanism to form massive stars Gravity driven: simplest solution Gravity driven: simplest solution Massive star formation linked to formation of stellar cluster Massive star formation linked to formation of stellar cluster Full IMFs Full IMFs Mass segregated clusters Mass segregated clusters Close binaries Close binaries

35. Observables: clump masses 3-D ‘real’ clumps 2-D projected clumps 3-D ‘real’ clumps 2-D projected clumps

36. Radiative driven implosion Some SF triggered Some SF triggered 2x # of stars 2x # of stars Some just revealed Some just revealed Can we tell which? Can we tell which? Not from end-result Not from end-result Need observable tests, predictions Need observable tests, predictions

37. Formation of OB Associations Globally unbound GMCsGlobally unbound GMCs Local dissipation of turbulenceLocal dissipation of turbulence Star formationStar formation SF involves ~10% of mass SF involves ~10% of mass Clark et al 2005

38. Need models in context of GMC 10 4 M sun in 10 pc Clustered and distributed SF Universal IMF Gravity, turbulence and thermal pressure

39. External Collimation of winds from massive stars Intrinsically spherical wind Intrinsically spherical wind SPH Particle injection SPH Particle injection Collimated by external density structure Collimated by external density structure From a previous simulation of massive star formation From a previous simulation of massive star formation Produces collimated outflow Produces collimated outflow

40. High surface density simulation  = 1.0 M sun pc -2 (10 6 M sun ) Size ~ 500 pc

41. Forming close binary systems Calculate real separations from spec. angular momentum and energy of binary Calculate real separations from spec. angular momentum and energy of binary Semi-major axis of 0.1 to 10 AU Semi-major axis of 0.1 to 10 AU Periastron separations of 1 AU Periastron separations of 1 AU But stellar radii are ~0.03 AU But stellar radii are ~0.03 AU collisions collisions

42. Binary Mergers Many binaries have r peri < r star Many binaries have r peri < r star Binary mergers Binary mergers Mergers > double star’s mass Mergers > double star’s mass Stellar density need not be so high Stellar density need not be so high Require encounters at R= r apastron >> r star Require encounters at R= r apastron >> r star For R=10 AU, For R=10 AU, need n ~ 10 6 stars/pc 3 need n ~ 10 6 stars/pc 3

43. Binary separation Red: M>8 M o

45. Modeling stellar mergers Little mass loss (Dale & Davies 2005, Davies et al 2005) Little mass loss (Dale & Davies 2005, Davies et al 2005) Rapid rotation Rapid rotation Energies 10 48 to 10 51 ergs Energies 10 48 to 10 51 ergs 1. Tidal capture from close flyby’s 2. Tidal shredding of lower-mass star Disc formation from debris Disc formation from debris Disc capture of next close passage Disc capture of next close passage Davies et al 2005 (Bally & Zinnecker 2005

46. Circumstellar structure and Outflows Circumstellar structure Circumstellar structure Collimated winds Collimated winds x-y x-z

49. Characteristic stellar mass What sets the characteristic stellar mass? What sets the characteristic stellar mass? Simulations show Masses ~ M J (Jeans Mass) Simulations show Masses ~ M J (Jeans Mass) What sets M J ? What sets M J ? Equation of state Equation of state line to dust cooling line to dust cooling T T T T Bonnell, Clarke & Bate 2006 (Larson 2005, Spaans & Silk 2000)

50. Formation of Molecular Clouds Spiral shocks forms GMCs 10% of gas in molecular clouds Forms spurs and feathering Size ~ 4 kpc Dobbs et al 2006

52. Spiral Triggering of star formation Follow gas flow through spiral arm Follow gas flow through spiral arm Form dense clouds Form dense clouds GMCs GMCs Onset of gravitational collapse and SF Onset of gravitational collapse and SF Efficiencies ~10 % Efficiencies ~10 % Bonnell et al 2006

53. Low surface density simulation  = 0.1 M sun pc -2 (10 5 M sun )

55. GMC Kinematics Convergent gas streams Convergent gas streams Clumpy gas Clumpy gas Broadens shock Broadens shock Post-shock velocity Post-shock velocity Mass loading in shock Mass loading in shock generates velocity dispersion generates velocity dispersion Velocity dispersion in plane of galaxy

56. Velocity dispersion in clumpy shocks - Gas through 1D sinusoidal potential. - Velocity dispersion flat and subsonic for uniform shock (---) - Clumpy shock  v ~ r 0.5 for clumpy shock (---) Dobbs & Bonnell 2006