Enrique Vázquez-Semadeni Centro de Radioastronomía y Astrofísica, UNAM, México

1. Formation and Evolution of Cores in Globally Collapsing Environments Enrique Vázquez-Semadeni Centro de Radioastronomía y Astrofísica, UNAM, México

2. Collaborators: CRyA UNAM: Javier Ballesteros-Paredes Pedro Colín Gilberto Gómez Postdoc: Robert Loughnane* Grad students: Raúl Naranjo-Romero* Manuel Zamora-Avilés * at this conference

3. Outline: • The case for globally collapsing molecular clouds (MCs). • Formation of filaments and clumps in collapsing MCs. • Idealized, spherically symmetric simulations. • Interpretation revisiting basic theory. • Preliminary synthetic observations of the clumps. • From the simple to the complex.

4. CLOUD FORMATION AND GLOBAL COLLAPSE

5. WNM n, T, P, -v1 WNM n, T, P, v1 • When a dense cold cloud forms by phase transition triggered by a compression in the warm atomic gas, it “automatically” (Vishniac 1994; Walder & Folini 1998, 2000; Koyama & Inutsuka 2002, 2004; Audit & Hennebelle 2005; Heitsch et al. 2005, 2006; Vázquez-Semadeni et al. 2006). • acquires mass (a cloud’s mass is not constant); • cools down (by a transition to the cold atomic phase) • acquires turbulence (through TI, NTSI, KHI?) • The compression may be driven by global turbulence, larger-scale (kpc) instabilities, etc. CNM

6. May cold clouds be globally collapsing? • Because they form out of a transition from the warm/diffuse to the cold/dense phase, they quickly become Jeans-unstable. (If the colliding flows were not already driven by larger-scale gravitational instability.) r 102r, T  10-2 T  Jeans mass, ~ r-1/2 T3/2, decreases by ~ 104 upon warm-cold transition.

7. Converging inflow setup Lbox Rinf Linflow • Run with Gadget 2 SPH code; 2.6x107 SPH particles: • L = 256 pc • <n> = 1 cm-3 • vinflow ~ 7 km s-1 • Tini = 5000 K • Rcyl = 32 pc (Gómez & Vázquez-Semadeni 2014, ApJ, in press., arXiv:1308.6298)

8. Gómez & VS 2014, (ApJ in press, arXiv:1308.6298)

9. Because the cloud contains many Jeans masses, its collapse is nearly pressureless. • Collapse proceeds fastest along shortest dimension (Lin+65): • Spheroids  Sheets  Filaments • Because collapse of filaments is slower than that of spheres (Toalá+12; Pon+12), spheroidal fluctuations within a filament collapse earlier than rest of the filament. •  Rest of filament “rains down” onto star-forming clump

10. Case-study of filaments formed in simulation: • Filaments are flow features(not equilibrium objects) where accretion changes from being ~2D to ~1D. • “River-like” features, flowing towards the gravitational potential trough (the core). cm-2 2 km s-1 Gómez & VS 2014, ApJ, in press (arXiv:1308.6298).

11.  Nonthermal motions dominated by infall at all scales in MCs? • Turbulence is only a background, • Not a support mechanism. • Albeit highly non-isotropic, multi-scale infall (Vázquez-Semadeni+09, ApJ, 707, 1023) • Small-scale, low-mass, high-density structures collapse first. • Large-scale, massive, lower-density structures collapse later. • Hierarchical gravitational collapse. • A multi-scale and anisotropic version of non-homologous, inside-out collapse (Shu 1977)

12. SPHERICAL COLLAPSE AND THEORY REVISITED

13. Highly idealized simulations: (Naranjo-Romero, VS & Loughnane, in prep.) • Spherical collapse(Larson 1969). • Collapsing gaussian fluctuation embedded in gravitationally unstable background(see also Mohammadpour & Stahler 2013): • <n> = 1000 cm-3 • Zero initial velocity • Box size: ~ 3 LJ (2.1 pc) • Fluctuation size: ~ 1 LJ (0.7 pc) • Fluctuation amplitude: rcl/rbg ~ 2 • Resolution: 5123 • Periodic boundaries t measured in units of global free-fall time, tff ~ 1 Myr.

14. = M(r)/MJ(r) 0.7 pc

15. = M(r)/MJ(r) 0.7 pc

16. = M(r)/MJ(r) 0.7 pc

17. = M(r)/MJ(r) 0.7 pc

18. = M(r)/MJ(r) 0.7 pc

19. = M(r)/MJ(r) 0.7 pc

20. Some points to note (Whitworth & Summers 1985): • At early times, the core has the profiles • r ~ cst. • |u| ~ r (linear, subsonic) • At intermediate times, two sonic points (v=cs) appear and the core develops the profiles (rs = inner sonic point): • Immediately before the formation of the singularity (the protostar), the core develops the profiles • r ~ r-2 • |u| ~ cst. Bonnor-Ebert like Singular isothermal sphere (SIS)-like, but with uniform infall speed.

21. Immediately before protostar formation: = M(r)/MJ(r) r ~ r-2 u ~ cst. 0.7 pc

22. So, SIS-like profile is approached at time of protostar formation, • Despite previous criticisms (Whitworth+96; Vázquez-Semadeni+05): • Static SIS is an unstable equilibrium, but... • ... with uniform infall velocity, it is the approached stage at singularity formation. • Also, supersonic velocities develop only during the last ~ 17% of the evolution. •  Most prestellar cores will appear subsonic.

23. To what extent does spherical collapse explain observations? • BE-like density profile consistent with observations of prestellar cores (e.g., Alves+01; Andre+14). • Not indicative of hydrostatic equilibrium! • Central “quiescent” region is an intrinsic property of collapsing cores in prestellar (pre-singularity formation) stage. • u ~ r in central region. • Not a turbulence-dissipation region. • What do synthetic observations tell us? • Synthetic NH3 (1,1) observations. • Using MOLLIE radiative transfer code (Keto 1990). • Central 8 out of 18 hyperfine lines.

25. Profiles at t = 1.8 tff: Center r = ½ LJ r = ¾ LJ Raw profiles with zero nonthermal velocity

26. We note that: • No background turbulence. • Double peak actually more pronounced in outer parts. • At center, infall speeds smear out hyperfine lines. • Hard to distinguish infall signature from hyperfine lines.

27. We note that: • No background turbulence. • Double peak actually more pronounced in outer parts. • At center, infall speeds smear out hyperfine lines. • Hard to distinguish infall signature from hyperfine lines. Compare to Pineda+2010:

28. CORE COLLAPSE IN CLOUD FORMATION SIMULATIONS

29. More realistic simulations: (Loughnane, Zamora-Avilés & VS 2014, in prep.) • Colliding-flow simulations with magnetic field and stellar feedback • FLASH 2.5 AMR code. • Periodic boundaries • Box size: ~ 256 pc • <n> = 1 cm-3 • <T> ~ 5000 K • Maximum resolution: 0.002 pc ~ 400 AU • Look at one ~25-Msun core in its final prestellar stages.

31. t=10.6 Myr 1 pc

32. t=10.7 Myr 1 pc

33. t=10.7 Myr : beam 1 pc

34. Compare to Pineda+2010:

35. Similar behavior of line profile with distance from core center to that of Pineda+10, • ...although just part of a continuous collapse process, with no turbulence-supported hydrostatic stage, • nor a turbulence-dissipation stage at the center. • Although complex motions in envelope seem necessary to blur the hyperfine lines.

36. SUMMARY

37. Dense clouds... • evolve! • Growing in mass • are likely dominated by infall, not strong random turbulence. • have only moderately supersonic initial turbulence (atomic phase). • Strongly supersonic motions develop as a consequence of collapse. • Collapse • Is multi-scale, and • occurs inside-out at each scale. • Spherical cores initiating collapse in unstable environments: • Have Bonnor-Ebert-like profiles during prestellar phases, but finite infall speeds. • At formation of singularity (YSO), develop SIS-like profile (r ~ r-2), but with uniform infall speed. • 4. Synthetic observations of cores in more realistic cloud-formation simulations • Exhibit similar radial variation as Pineda+10. • Although not because of turbulence-dissipation process, but just ongoing collapse on top of chaotic background.

38. THE END

39. (Gómez & Vázquez-Semadeni 2014, ApJ, subm., arXiv:1308.6298)

40. Collision-driven turbulence is only moderately supersonic. • Strongly supersonic velocities typical of GMCs appear later, as a consequence of gravitational contraction. 4.2 Inflow weakens, collapse starts (11 Myr) SF starts (17.2 Myr)  Cannot rely on those highly supersonic motions to support the clouds. 2.8 1.4 ~ 0.5 km s-1 Turbulence driven by compression, through NTSI, TI and KHI. (Vázquez-Semadeni et al. 2007)

41. The same happens with grid codes: • AMR simulations with feedback (VS+2010, ApJ, 715, 1302) • density-weighted s • volume-weighted s • with feedback • without feedback

42. Filament and clump formation by gravitational contraction in dense gas

43. Because the cloud contains many Jeans masses, its collapse is nearly pressureless. • Collapse proceeds fastest along shortest dimension (Lin+65): • Spheroids  Sheets  Filaments • Because collapse of filaments is slower than that of spheres (Toalá+12; Pon+12), spheroidal fluctuations within a filament collapse earlier than rest of the filament. •  Rest of filament “rains down” onto star-forming clump

44. This mechanism contrasts with the standard picture that: • Cores form by supersonic turbulent compressions in the clouds. • Cores proceed to collapse once their internal turbulence dissipates. • Through a “transition to coherence” (Goodman+98; Pineda+10). Velocity dispersion Hyperfine separation Pineda+2010: B5 Core. Velocity dispersion derived from nonthermal component necessary to erase the peaks, assumed to be the NH3 (1,1) hyperfine lines.

45. Investigate the clump dynamics (Camacho+14, in prep.) • In terms of the “virial parameter” a(Bertoldi & McKee 1992):

46. GMCs and massive star-forming clumps are observed to lie near “equipartition line” in “extended Larson diagram”(Keto & Myers 1986; Heyer+2009): GMCs (Heyer +09) Massive clumps (Gibson+09) Virial equilibrium: a=1 Free-fall or equipartition a=2 Ballesteros-Paredes+11 Dobbs+14 (PPVI)

47. Although some clumps seem to have too large Ek. Unbound?? (Barnes+2011)

48. What do the clumps look like in the simulation? • Use a clump-finding algorithm for SPH data by Mata & Gómez: All particles in domain One clump above n = 104 cm-3 (Camacho+14, in prep.)

49. t = 20 Myr • “Raw” clumps tend to lie above equipartition line. Unbound??? How could this be, if the turbulence has decayed, and there’s no other energy source than gravity? (Camacho+14, in prep.)

50. Or are we missing mass? All clumps, adding stellar mass Only clumps with no stellar particles t = 20 Myr (Camacho+14, in prep.)