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Studies of Velocity Fluctuations: Keep Theorists Honest!

Studies of Velocity Fluctuations: Keep Theorists Honest!. Lazarian A. UW-Madison, Astronomy and Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas Collaboration with Pogosyan D. (Univ. of Alberta) Chepurnov A. (UW-Madison) Beresnyak A. (UW-Madison).

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Studies of Velocity Fluctuations: Keep Theorists Honest!

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  1. Studies of Velocity Fluctuations: Keep Theorists Honest! Lazarian A. UW-Madison, Astronomy and Center for Magnetic Self-Organization in Laboratory and Astrophysical Plasmas Collaboration with Pogosyan D. (Univ. of Alberta) Chepurnov A. (UW-Madison) Beresnyak A. (UW-Madison)

  2. What I am going to say • Critical remarks: “What is our future?” • Possible models of TSAS • New quantitative techniques to study velocity spectra.

  3. Chaotic order and Re number • For turbulence Reynolds number Re = VL/n > 10~100 * inertialvs. viscosityterm Re ~ 15,000 Da Vinci’s view Re=40 Re=10000

  4. Challenge: Turbulent ISM Re ~VL/n ~1010 >> 1 n ~ rLvth, vth < V, rL<< L Numerics will not get to such Re in foreseeable future. Flows in ISM and computers are and will be different! Pc scales Computational efforts scale as Re4!!! Currently max Re of order <104 Is there any hope for progress?

  5. 0 max Is Visual Correspondence Enough? NSF reviewer:”The proposed work is in danger of being criticized for studying artificial situations that isolate particular physical concepts” Emission Nebulae Synthetic observations M=10 MHD 5123 Beresnyak, Lazarian & Cho 05

  6. correlations C~<(v1-v2)2> ~ rm m=2/3 for Kolmogorov model <…> is averaging Revealing Order: Turbulence Spectra and Correlations v( r ), r( r ), … Fourier analysis of correlations Spectrum : E(k) ~ k-n = + + …. E(k) k-n n=5/3 for Kolmogorov model Dk

  7. A Rare Quantitative Example Armstrong, Rickett & Spangler(1995) We shall deal with relatively large scales using a velocity info Slope ~ -5/3 Electron density fluctuations trace of turbulence only at small scales. No reliable info for large scales Electron density spectrum “Big power law in the sky” is cited a lot because there are no other good examples pc AU

  8. Shallow Density in Supersonic MHD Turbulence Fluctuation of density at scale k Density contours for > 25 mean density Spectrum gets flat at M=10, thus the fluctuations grow as scale gets smaller  M=10 E(k) v Beresnyak, Lazarian & Cho 05 log  MHD 5123 A possible way to create TSAS k

  9. Density filaments MHD Turbulence in Partially Ionized Gas: New Regime B For partially ionized gas viscosity is important while resistivity is not. Long filaments of density Cho & Lazarian 03 MHD turbulence does not stop at the viscous scale in partially ionized gas but creates a magnetic cascade up to decoupling scale Lazarian, Vishniac & Cho 04 ~0.3pc in WNM Length of filaments is large scale, may be related to TSAS Cho, Lazarian Vishniac 02 E(k) Resistive scale is not L/Rm, but L/Rm1/2 k Beresnyak & Lazarian 06

  10. Formation of Density Structures in Viscous Turbulent Flow Magnetic field in viscous fluid compresses density Projected density: MHD simulations 5123 Small scale slowly evolving structures overheating of ISM is not a problem Beresnyak & Lazarian 06

  11. Generation of Slab Alfvenic Turbulence by Cosmic Rays How do cosmic rays modify compressible MHD turbulence? Turbulent compressions of magnetic field creates compressions of cosmic rays and those create waves at Larmor radius rL ( model by Lazarian & Beresnyak 06) Instability growth Predicted spectra of slab-type Alfven modes: k-1.18 and k-1.45

  12. y x V PPV cube Velocity Statistics VCA and VCS: Keeping Theorists Honest 2 new techniques to recover turbulent velocity spectra VCA and VCS Velocity slice Column density y Velocity Channel Analysis (VCA) relates spectra of velocity slices to spectra of turbulent velocity (Lazarian & Pogosyan 00, 04) z x Velocity Coordinate Spectrum (VCS) relates spectra of velocity along velocity coordinate to spectra of turbulent velocity (Lazarian & Pogosyan 00, 06) 3d dimension is velocity Modified from A Goodman

  13. Mathematical Setting in Lazarian & Pogosyan 00 Density in PPV (xyv) Velocity distribution Correlation function in PPV where Real (xyz) density correlation Velocity correlation

  14. VCS: Predictions and TestingLazarian & Pogosyan 06, Chepurnov & Lazarian 06 Relation of VCS to the velocity spectral index VCS expression: S(v) observed line Synthetic observations change of VCS slope Velocity index High resolution Low resolution Not affected by phase fraction

  15. VCA/VCS Simulations (noisy part of P1 filtered out) - number of points over z, assuring absence of shot-noise

  16. VCS: Application to Real Data . VCS was tested with Arecibo GALFA data for both low and high resolution limits Resolution was decreased to test the theory Data handling by Chepunov & Lazarian 06 Temperature 100 K Data provided by Stanimirovic Theory predicts suppression by a factor exp (-aTkv^2). Correcting for it recovers the slope and gets the temperature of cold gas.

  17. Future Missions: Spectrum of Turbulence with Constellation X Studies of turbulence is possible with X-rays using new missions Hydra A Galaxy Cluster Constellation X will get turbulent spectra with VCS technique (Lazarian & Pogosyan 06) in 1 hour Chepurnov & Lazarian 06

  18. Synthetic mapstests “n” is the density spectral index, E~k2P, P~k-n , “m” is related to the velocity energy spectral index as m=-3+ , Ev~ k2Pv, Pv~k- Thin channels  Thick channels Velocity Channel Analysis(Lazarian & Pogosyan 00) (d~rm) Velocity structure function Spectrum intensity channels Ps~ K-g Application of VCA to SMC Spectra shallow than Kolmogorov were obtained for velocity in Stanimirovic & Lazarian 01

  19. VCS and VCS: Prospects Absorption lines can be used to study turbulence (extragalactic objects, Lyman alpha, supernovae remnants). Emission and absorption studies can be combined to get both density and velocity statistics for unresolved objects spectrum compression factor = 8 VCS from a single absorption line In addition: To increase velocity coverage use heavy species. Possible to separate thermal and non-thermal contributions to line width. Measure cold gas temperature. Emission lines with self-absorption LP 04, 06 (applications: HI, CO2 etc.) New asymptotics predicted, e.g. K-3 Use of entire 3D PPV cubes is promising!

  20. rs = antennae temperature at frequency n (depends on both velocity and density) rs n VCS and VCA versus Centroids Definition: Centroids are OK to reveal anisotropy due to magnetic field (Lazarian et al.01), distinguish between subAlfvenic and superAlfvenic turbulence. Centroids may not be good to study M>1 turbulence (Esquivel & Lazarian 05). From Esquivel & Lazarian 05 Necessary criterion for centroids to reflect velocities is found in Lazarian & Esquivel 03

  21. Summary Turbulence is a basic property of ISM. • Computers may mislead us unless we understand the underlying physics. • Observers should keep theorists in check. • VCS is a new promising technique. • The wealth of surveys can be used to study ISM (identify sources and sinks of energy) and test theories of turbulent ISM.

  22. Compressible Extension of GS95 MHD Turbulence Model Magnetic field and velocity in Cho & Lazarian 02 1.GS95 scaling for Alfven and slow modes: Elongated Alfven eddies New computations: Beresnyak & Lazarian 06 2.Isotropic acoustic-type fast modes: Fast modes are isotropic

  23. Does GS95 Model Require Improvements? Incompressible turbulence shows spectrum flatter than the GS95 model predicts. Why? Maron & Goldreich 01 Boldyrev 05, 06, poster Galtier et al. 05 Different explanations Polarization intermittency in Beresnyak & Lazarian 06 causes some flattening V and B show different anisotropies and scalings

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