The Spectral Correlation Function

1. The Spectral Correlation Function Principal Collaborators Héctor Arce, Caltech Javier Ballesteros-Paredes, UNAM Sungeun Kim, CfA Paolo Padoan, JPL/Caltech Erik Rosolowsky, UC Berkeley Enrique Vazquez-Semadeni, UNAM Jonathan Williams, U. Florida David Wilner, CfA Alyssa A. Goodman Harvard-Smithsonian Center for Astrophysics (currently on sabbatical at the Yale Astronomy Department) cfa-www.harvard.edu/~agoodman

3. Radio Spectral-line Observations of Interstellar Clouds BUT remember: Making this kind of map always loses 1 dimension.

4. Velocity as a "Fourth" Dimension Loss of 1 dimension No loss of information

5. 1950 1960 1970 1980 1990 2000 8 10 4 10 7 10 N 6 channels, 10 channels 3 10 *N N 5 10 channels pixels S/N in 1 hour, 2 10 4 10 (S/N)*N N 3 10 1 N 10 pixels pixels 2 10 0 10 1950 1960 1970 1980 1990 2000 Year The Superstore: Learning More from “Too Much Data” Product S/N

6. A Free Sample Data: Hartmann & Burton 1999; Figure: Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2002

7. The “Good” Old Days • Low Observational Resolution • Models of spherical, Smooth, Long-lasting “Cloud” Structures And more “structure” came from fragmentation

8. The New Age High(er) Observational Resolution (at many l’s) Highly irregular structures, many of which are “transient” on long time scales

9. So, are numerical simulations physically illuminating in this New Age? If so, in what way(s)? How might simulations be improved (i.e. to better match observations)?

10. Numerical MHD: The State of the Art 25 Years Ago • Two-dimensional “CEL” code • 10’s of hours of CPU time • Only possible to run 1 case • Grid size ~96 x 188 (~1282) • No magnetic fields • No gravity • Heating & coolingtreated • R-T and K-H Instabilities traced well Star-formation “triggered” by a spiral-density wave shock. (Woodward 1976)

11. Woodward’s Conclusions (1976)

12. [ ] T / 10 K b = [ ] 2 -3 [ ] n B m / 100 cm / 1 . 4 G H 2 MHD Simulations Today b=0.01 b=1 • Driven Turbulence; M K; no gravity • Colors: log density • Computational volume: 2563 • Dark blue lines: B-field • Red : isosurface of passive contaminant after saturation Stone, Gammie & Ostriker 1999

13. Figure based on work of Padoan, Nordlund, Juvela, et al. Excerpt from realization used in Padoan & Goodman 2002. (Synthetic)Spectral Line Maps from MHD Simulations

14. Target Spectrum Comparison Spectra Comparison Spectra The Spectral Correlation Function (SCF) Measures Similarity of Comparison Spectra to Target Figure from Falgarone et al. 1994

15. SCF, v.1.0(Rosolowsky, Goodman, Wilner & Williams 1999) etc. Figure from Falgarone et al. 1994

16. greyscale: TA=0.04 to 0. 3 K Antenna Temperature Map Application of the SCF(v.1.0) “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

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

18. 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

19. 1.0 Increasing Similarity of Spectra to Neighbors 0.8 0.6 Rosette C 18O Rosette 13CO Increasing Similarity of ALL Spectra in Map 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) G,O,S MHD +grav 0.2 HCl2 C 18O Peaks L134A 12CO(2-1). MacLow et al. MHD HLC Falgarone et al pure HD. 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 Preliminary SCF (v.1.0) Comparisons Change in Mean SCF with Randomization Mean SCF Value

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

21. v.2.0: Scale-Dependence of the SCF Scale Spectral Correlation Each plotted point is “mean” of distribution for that spatial lag. Example for “Simulated Data” Padoan, Rosolowsky & Goodman 2001

22. “Equipartition” Models “Stochastic” Models How Well Do Numerical Models Match Reality, Now? “Reality” Power-Law Slope of SCF vs. Lag Scaled “Superalfvenic” Models Padoan & Goodman 2002 Magnitude of Spectral Correlation at 1 pc

23. The Spectral Correlation Function Goal: • To improve simulations enough so that they “match” observations empirically, then use the matching simulations to “experiment” with ISM conditions. • Status: • Molecular cloud simulations ~rule out equipartition field(Padoan & Goodman 2002) • LMC scale height mapped(Padoan, Kim, Goodman & Stavely-Smith 2001) • Atomic ISM simulations much improved(Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2002) • Plans: • Ultimately include continuum (dust) data in comparisons. Higher-resolution simulations optimized to match existing observations, will allow extrapolation into presently unobservable regimes.

24. 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

25. The Behavior of the Atomic ISM Data: Hartmann & Burton 1999; Figure: Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2001

26. Insights into Atomic ISM from SCF (v.1.0) Comparison with simulations of Vazquez-Semadeni & 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 2002.

27. Revealing Shortcomings of a Simulation “Thermally Broadened,” very high T Velocity histogram, 16 bins Velocity histogram, 64 bins Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2002

28. Insights into Atomic ISM from SCF (v.1.0) From v-histograms, 64 bins

29. Insights into Atomic ISM from SCF (v.1.0) Thermally Broadened, very high T

30. Insights into Atomic ISM from SCF (v.1.0) Thermally Broadened, equivalent of much lower T--best match!

31. A Success of the SCF Sample spectra after velocity scale expanded x6 (to mimic lower temperature, and give more importance to “turbulence” in determining line shape) Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2002

32. The Spectral Correlation Function Goal: • To improve simulations enough so that they “match” observations empirically, then use the matching simulations to “experiment” with ISM conditions. • Status: • Molecular cloud simulations ~rule out equipartition field(Padoan & Goodman 2002) • LMC scale height mapped(Padoan, Kim, Goodman & Stavely-Smith 2001) • Atomic ISM simulations much improved(Ballesteros-Paredes, Vazquez-Semadeni & Goodman 2002) • Plans: • Ultimately include continuum (dust) data in comparisons. Higher-resolution simulations optimized to match existing observations, will allow extrapolation into presently unobservable regimes.

33. Magnetohydrodynamic Waves Inward Motions Outflows MHD Turbulence Thermal Motions Star Formation “Now” SNe/GRB H II Regions