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)

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

Chaotic order and Re number For turbulence Reynolds number Re = VL/ > 10~100 Re ~ 15,000 * inertial vs. viscosity term Da Vinci’s view Re=40Re=10000

Challenge: Turbulent ISM Re ~VL/ ~10 10 >> 1 ~ r L v th, v th < V, r L << L Is there any hope for progress? Pc scales Numerics will not get to such Re in foreseeable future. Flows in ISM and computers are and will be different! Computational efforts scale as Re 4 !!! Currently max Re of order <10 4

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

Revealing Order: Turbulence Spectra and Correlations Spectrum : E(k) ~ k -n kk E(k) = + + …. v( r ),  r , … Fourier analysis of correlations k -n n=5/3 for Kolmogorov model correlations C~ ~ r m m=2/3 for Kolmogorov model is averaging

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

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

For partially ionized gas viscosity is important while resistivity is not. B ~0.3pc in WNM MHD Turbulence in Partially Ionized Gas: New Regime 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 Resistive scale is not L/Rm, but L/Rm 1/2 Beresnyak & Lazarian 06 Density filaments Length of filaments is large scale, may be related to TSAS Cho, Lazarian Vishniac 02 Long filaments of density Cho & Lazarian 03 E(k) k

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

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 r L ( model by Lazarian & Beresnyak 06) Instability growth Predicted spectra of slab-type Alfven modes: k and k -1.45

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

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

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

VCA (spatial spectrum, N y =N z =32768) VCS (spectrum over v, N z =32768)  u = 4.0 needed N z :  u =3.67 needed N z : number of points over z, assuring absence of shot-noise (noisy part of P 1 filtered out) VCA/VCS Simulations

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

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

Velocity Channel Analysis (Lazarian & Pogosyan 00) “Shallow” density n>-3 “Steep” density n<-3 “Thin” channels “Thick” channels Thin channels Thick channels Synthetic maps tests (d~r m   P s ~ K-  “n” is the density spectral index, E~k 2 P, P~k -n, “m” is related to the velocity energy spectral index as m=-3+ , E v ~ k 2 P v, P v ~k -  Velocity structure function Spectrum intensity channels Application of VCA to SMC Spectra shallow than Kolmogorov were obtained for velocity in Stanimirovic & Lazarian 01

VCS and VCS: Prospects spectrum compression factor = 8 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 To increase velocity coverage use heavy species. Possible to separate thermal and non-thermal contributions to line width. Measure cold gas temperature. In addition: Emission lines with self-absorption LP 04, 06 (applications: HI, CO 2 etc.) New asymptotics predicted, e.g. K -3 Use of entire 3D PPV cubes is promising! VCS from a single absorption line

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

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.

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

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