Measuring Turbulent Motions: from Galaxies to GMCs to Star-Forming Cores

1. Measuring Turbulent Motions: from Galaxies toGMCs to Star-Forming Cores Collaborators Héctor Arce, CfA Joe Barranco, UC Berkeley Javier Ballesteros-Paredes, AMNH Paola Caselli, Arcetri Bruce Draine, Princeton Mika Juvela, Helsinki Sungeun Kim, CfA Kishore Kuchibhotla, MIT Aake Nordlund, Copenhagen Paolo Padoan, CfA Örnólfur Einar Rögnvaldsson, Copenhagen Erik Rosolowsky, UC Berkeley Enrique Vazquez-Semadeni, UNAM Jonathan Williams, U. Florida David Wilner, CfA Alyssa A. Goodman Harvard-Smithsonian Center for Astrophysics

2. What did Alyssa Goodman say about “Measuring Turbulent Motions” in Santa Cruz? The Spectral Correlation Function (SCF) • Can discriminate amongst observed and simulated spectral-line maps other statistical measures find identical (Rosolowsky, Goodman, Wilner & Williams 1999, ApJ, 524, 887). • Exhibits power-law behavior as a function of scale, theindex of which seems to be excellent diagnosticof the nature ofturbulence(Padoan, Rosolowsly & Goodman 2001, ApJ, 547, 862 ). • Can map the scale height of a mostly face-on galaxy (the LMC; Padoan, Kim, Goodman & Stavely-Smith 2001, ApJ, 555, 33). • Should have its greatest use in the fine-tuning of simulations(e.g. Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001, preprint). • Should be able to find “coherent cores”(see Goodman, Barranco, Wilner & Heyer 1998, ApJ, 504, 223). MHD simulations already show a “turbulent shock origin of cores” (Padoan, Juvela, Goodman & Nordlund 2001, ApJ, 553, 227), as well as “accidental” infall profiles(Padoan et al. 2001, in prep). Outflows • Are definitely highly episodic, and their episodic nature can explain steep observed mass-velocity relations (Arce & Goodman 2001, ApJL, 551, L171; Arce & Goodman 2001, ApJ, 554, 132). Influence of episodicity on “driving” turbulence still needs to be understood. Provacative Suggestion • The central source of the outflow in PVCeph might be moving at ~10 km s-1(Arce & Goodman 2001, in prep.). cfa-www.harvard.edu/~agoodman July 15, 2001

3. Target Spectrum Comparison Spectra Comparison Spectra What is the Spectral Correlation Function? Measures Similarity of Comparison Spectra to Target Figure from Falgarone et al. 1994

4. SCF, v.1.0(Rosolowsky et al. 1999) etc. Figure from Falgarone et al. 1994

5. greyscale: TA=0.04 to 0. 3 K Antenna Temperature Map Application of the SCF “Normalized” SCF Map Data shown: C18O map of Rosette, courtesy M. Heyer et al. Results:Padoan, Rosolowsky & Goodman 2001. greyscale: while=low correlation; black=high

6. Normalized C18O Data for Rosette Molecular Cloud Randomized Positions Original Data SCF Distributions

7. Unbound High-Latitude Cloud Self-Gravitating, Star-Forming Region Observations Simulations No gravity, No B field No gravity,Yes B field Yes gravity, Yes B field Insights from SCF v.1.0Rosolowsky, Goodman, Williams & Wilner 1999 Lag & scaling adjustable Only lag adjustable Only scaling adjustable No adjustments

8. 1.0 0.8 0.6 Rosette C 18O Rosette 13CO Rosette 13CO Peaks SNR 0.4 HCl2 C 18O H I Survey L134A 13CO(1-0) Rosette C 18O Peaks Pol. 13CO(1-0) L1512 12CO(2-1) 0.2 HCl2 C 18O Peaks L134A 12CO(2-1). HLC 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Which of these is not like the others? Increasing Similarity of Spectra to Neighbors Increasing Similarity of ALL Spectra in Map Change in Mean SCF with Randomization G,O,S MacLow et al. Falgarone et al. Mean SCF Value

9. The Spectral Correlation Function as a Function of Spatial Scale (v.2.0; Padoan et al. 2001) Figure from Falgarone et al. 1994

10. v.2.0: Scale-Dependence of the SCF Example for “Simulated Data” Padoan, Rosolowsky & Goodman 2001

11. Galactic Scale Heights from the SCF (v.2.0) HI map of the LMC from ATCA & Parkes Multi-Beam, courtesy Stavely-Smith, Kim, et al. Padoan, Kim, Goodman & Stavely-Smith 2001

12. “Fine-tuning Simulations with the SCF” Data: Hartmann & Burton 1999; Figure: Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001

13. An Example of Fine-tuning SCF v.1.0 for NCP Loop Comparison with simulations of Vazquez-Semadeni, Ballesteros-Paredes & collaborators shows: • “Thermal Broadening” of H I Line Profiles can hide much of the true(?) velocity structure • SCF v.1.0 good at picking out shock-like structure in H I maps (also gives low correlation tail) See Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001.

14. Revealing Shortcomings of a Simulation “Thermally Broadened,” very high therm/turb Velocity histogram, 16 bins Velocity histogram, 64 bins Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001

15. An Example of Fine-tuning H I Observations From v-histograms, 64 bins

16. An Example of Fine-tuning H I Observations Thermally Broadened, high therm/turb

17. An Example of Fine-tuning Reduce therm/turb x 6 --best match! H I Observations

18. The Fine-Tuned Simulation Sample spectra after velocity scale expanded x6 (to mimic lower ratio of thermal to turbulent pressure) Mean temperature should really be <<8000 K and/or Much more energy input to turbulence (e.g. real SNe) needed Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001

19. Recent SCF Comparisons

20. What have we learned, lately, from well-matched simulations? • Realistic core properties, and the IMF can be reproduced from “turbulent fragmentation.” (Padoan & Nordlund 2000; Padoan, Juvela, Goodman & Nordlund 2001) • Reduction in polarization near peaks of SCUBA maps caused by reduced polarization efficiency, not geometry. (Padoan, Goodman, Draine, Juvela, Nordlund & Rögnvaldsson 2001) • “Infall” can be faked, but not w/o non-LTE radiative transfer. (Padoan et al., in prep.)

21. Falling in Zero-g Simulations by Padoan et al. Pattern is similar to observations of extended infall by e.g. Lee, Myers & Tafalla 2001.

22. What about outflows, Mordecai?? • They’re highly episodic. • Much momentum and energy is deposited in the cloud (~1044 to 1045 erg, comparable or greater than cloud K.E.). • Some cloud features are all outflow. That’s how much gas is shoved around! See collected thesis papers of H. Arce. (Arce & Goodman 2001a,b,c,d).

23. L1448 Bachiller, Tafalla & Cernicharo 1994 Lada & Fich 1996 B5 Yu Billawala & Bally 1999 Bachiller et al. 1990 Sample outflow position-velocity diagrams

24. Outflow position-velocity diagrams Arce & Goodman 2001

25. Mass-Velocity Relations can be very steep, especially in “bursty- looking” sources… B5 Yu, Billawala, Bally, 1999

26. 0 10 10 A,B,C... for constant vmax a,b,c... for varying vmax Slope of Each Outburst = -2 as in Matzner & McKee 2000 (alphabetical=chronological) -1 10 a 8 1 -2 10 Mass [Msun] 6 Maximum Velocity, vmax -3 10 2 4 -4 10 d A C B 3 D E 4 -5 10 2 6 5 7 c e 8 b 2 3 4 5 6 7 8 2 3 4 5 6 7 8 2 2 4 6 8 10 0.1 1 10 Velocity [km s-1] Maximum Offset from Source, dmax Mass-Velocity Relations in Episodic Outflows: Steep Slopes result from Summed Bursts Power-law Slope of Sum = -2.7 (arbitrarily >2) Time history hard to reconstruct uniquely. Arce & Goodman 2001

27. “Giant” Herbig-Haro Flows:PV Ceph 1 pc Reipurth, Bally & Devine 1997

28. A New Proposal: Episodic ejections from precessing or wobblingmoving source Required motion of 0.25 pc (e.g. 2 km s-1 for 125,000 yr or 20 km s-1 for 12,500 yr) Arce & Goodman 2001

29. 67:55 H H 3 1 5 C H H 3 1 5 B 67:50 H H 3 1 5 A H H 4 1 5 HH 215P2 ) 0 HH 215P1 5 9 1 ( PV Cephei d 67:45 HH 315D H H 3 1 5 E 67:40 H H 3 1 5 F 20:46 20:45 ( 1 9 5 0 ) a PV Ceph 12CO (2-1) OTF Map from NRAO 12-m Red: 3.0 to 6.9 km s-1 Blue: -3.5 to 0.4 km s-1 Arce & Goodman 2001

30. Even leaves a trail? Arce & Goodman 2001