MHD Turbulence in Interstellar Medium by ewghwehws

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									Intermittency of MHD
     Turbulence
                 A. Lazarian
                   UW-Madison:
Astronomy and Center for Magnetic Self-Organization in
           Laboratory and Astrophysical Plasmas

             Special thanks to:
               A. Beresnyak (UW-Madison)
               A. Esquivel (UW-Madison)
               G. Kowal (Kracow, Poland)
                J. Cho (Chungnam, Korea)
               E. Vishniac (Johns Hopkins)
  Da Vinci’s view


                      Chaotic
                      Order!
                      Vortices
                       inside
                        flow



Turbulence = S eddies !
   Experimental insight

                                            Eddies
                                            inside
                                            eddies


                            Re ~ 15,000

Stochasticity depends on   Reynolds number Re = VL/n
Astrophysical relevance
   Re ~VL/n ~1010 >> 1
   n ~ rLvth, vth < V, rL<< L
 Is dissipation smooth?

• Kolmogorov theory-- yes it is smooth.
• Laboratory data shows intermittency.
• She & Leveque 95 proposed scaling for
  hydro turbulence.
• Politano & Pouquet 95 proposed scaling for
  MHD turbulence.
      Why do we care?

• Intermittent dissipation changes interstellar
  heating, allows funny chemistry as
  discussed for years by Falgarone’s group.
• Exciting effects for different astro problems.
• Gives insights into the very nature of
  turbulent cascade and its evolution.
She-Leveque and Politano-
     Pouquet models
     Scaling
No intermittency                            Kolmogorov model

Filaments                                      She-Leveque model

           Above is hydro. What about MHD?
General:                                              Politano-Pouquet
                                                      model for

where tcas~lx, zl~l1/g, C =3- (dimension of dissipation structure)
 For IK theory g=4, x=1/2, C=1 for sheet-like dissipation structures
 But does not account for anisotropy!
    Scale-dependent Anisotropy




                        B0




                       Cho, Lazarian
Magnetic               & Vishniac 03
 field     B0     B0
     Confusing results

• Pioneering study by Muller & Biscamp 00
  got C=3-2=1 for z in incompressible MHD
• Cho, Lazarian & Vishniac 02 got C=2 for
  velocity in incompressible MHD accounting
  for anisotropy
• Boldyrev 02 assumed C=1 and Padoan et al.
  03 got C=1 for velocity in supersonic
  compressible MHD and C=2 in subsonic
  case
Scaling in system of local B
                              Local system of reference is related to
                              local magnetic field




Cho, Lazarian & Vishniac 02


In local system of reference Alfvenic
 turbulence exhibits C=1 for velocities,
 equivalent to She-Leveque
        Scalings of velocity and
             magnetic field
Local system of reference              Global system of reference



                              MA~0.7

                            Incompressible




                   Cho, Lazarian & Vishniac 03
    Scaling is different for V and B!!!

    Scaling is different for local and global reference system.

    Scaling of z in global system corresponds to MB 00

    Scaling of v in local system corresponds to CLV 02
        Compressible and
      incompressible MHD
                                Compressible simulations for
                                Mach ~ 0.7, mean B~0




  Cho, Lazarian & Vishniac 03

   Elsasser variables Z scale closer to MB, while
   velocities indeed show C=2 in accordance with
   Padoan et al. 03.
However it is clear that MHD turbulence is
more complex than hydro. Caution is needed!
MHD modes (for Pmag > Pgas)
                 B
                      Alfven mode (v=VA cosq)
                          incompressible;
                          restoring force=mag. tension
        B
    k                 slow mode (v=cs cosq)
                          restoring force = Pgas


            B
                      fast mode (v=VA)
k                         restoring force = Pmag + Pgas

                Theoretical discussion in Lithwick & Goldreich 01
                                          Cho & Lazarian 02
                    Basis




                              Cho & Lazarian 02
• Decomposition over basis in Fourier space:
xs ~ [(1-D1/2+b/2)/(1+D1/2-b/2)](k^/k||)2 k|| + k^
 xf ~ k|| + [(1-D1/2-b/2)/(1+D1/2+b/2)](k||/k^)2 k^
     xA ~ k|| x k^      *D=(1+b/2)2-2b cosq
                         From Cho & Lazarian 02, 03


 Generation of compressible components by Alfven
 modes is marginal.
Fast decay of MHD turbulence is not
 due to compressibility!!!
  Generation of Compressible
            Mode
Normalized
Compres
energy                                  • Generalize scaling of
                  predicted
                                          compressive mode
                                          generation from hydro
                                          (Zank &Matthaeus93).
                                        • For MHD total Mach
                    (M2total VA/dV)-1     number is appropriate.
                       X                • Energy diffuses from
                                          GS95 cone
             Cho & Lazarian 02

    Predicted scaling for Mtotal<1 is       M2total VA/dV
Alfven ~k-5/3         slow ~k-5/3          fast ~k-3/2


                    Spectr
                    a


anisotropic (GS)       anisotropic (GS)     isotropic


                   Correlation
                   functions


        M=2         Magnetically          Cho & Lazarian 02
                How good is our
                decomposition?
                                         Decomposition: dashed lines
 Anistoropy
obtained without
decomposition                            M=7                                M=2.3




                                                 Cho & Lazarian 03

   • Our decomposition into modes is
     statistical
   • Testing of it for slow modes is
     successful
  For low beta plasma velocity of slow modes are nearly parallel to the local magnetic field.
  Therefore correlation functions calculated in the local reference frame can be used.
Intermittency Alfven, slow and
  fast modes: M<1 and M>>1
   Alfven                          slow                       fast

                         M~0.7
                        MA~0.7



                            2563

     Alfven
    Alfven                         slow                       fast

                           M~7
                         MA~0.7




  Alfven is pretty much the same, Slow is affected; fast is unclear
                   Kowal & Lazarian 05
 Local Frame Results

M~0.7




M~7




        Kowal & Lazarian 05
      Solenoidal & Potential

solenoidal   potential     M~0.7, Alfvenic



                           M~2.5, SuperAlfvenic
                                             MA~8

                           Decoupled only at small scales!
                           Caution is needed!




                            M~7, Alfvenic

                         Kowal & Lazarian 2005
Correlation contours of Density


       M~0.7           M~7
                       M=7
       M=2                              Flat density



                        Lazarian & Beresnyak 04




Density anisotropy depends Mach number!
Spectrum of density is flat for high M.
Logarithm of density at Mach=7

        before                     after




  • At high Mach number density is isotropic due to
    dominance of high peaks due to driving
  • Filtering of high peaks reveals GS pattern

         Beresnyak, Lazarian & Cho 05
Scaling of Density
                    Testing of predictions in Boldyrev 02

     log
           M~10

            5123




           M~3
           5123




                    Log of density scales
            M~0.7
                    similar to velocity
            2563

           Kowal & Lazarian 05
B                   Viscosity is important
                    while resistivity is not.

                        Viscous magnetized
                        fluid
                     Does viscous damping scale
                     is the scale at which MHD
                     turbulence ends?




    ~0.3pc in WNM
         Viscosity Damped
   Turbulence: New Regime of
    E(k)~k
           MHD Turbulence
                -1   intermittent



          Expected:
    k-1 for magnetic field
    k-4 for kinetic energy




Cho, Lazarian & Vishniac 02,   Numerical testing confirms that
                               magnetic turbulence does not die!!!
Scale-Dependent Intermittency

                                             Predicted in
                                         Lazarian, Vishniac & Cho 04
      Large scales perp. B


                                              -filling factor of high
                                                intensity magnetic
                                                       field

                                          Magnetic field gets more
       Small scales perp. B               intermittent as scale
                                          gets smaller




           Cho, Lazarian & Vishniac 03
       Fraction of energy versus
                volume
                Scale-dependent intermittency
    Ordinary turbulence                     New regime




                          Cho, Lazarian & Vishniac 03

In viscosity-damped turbulence most of magnetic energy is in a small
 fraction of volume
       High moment scaling




                             Cho, Lazarian & Vishniac 03


                       The exponent is between 0.5 and 0

Using predictions for intermittent magnetic field from
Lazarian, Vishniac & Cho 04
Density in viscosity-dominated
            regime
    Incompressible                         compressible
     phys. diffusion




                             Cho & Lazarian 03


                 intermittency

    magnetic             magnetic                density



                       Cho, Lazarian & Vishniac 03
   Observational testing: Can we
     use Velocity Centroids?
      Definition: S ( x, y)   v  ( x, y, v )dv
                                        z   s         z         z

s = antennae temperature at
   frequency n (depends on                      s
                                                          n
   both velocity and density)

Structure function of centroids   S (X1 )  S (X 2 )2          
                                                                 v ( x1 ) 



Can be obtained from observational
data.
   Velocity High Moments?
Not yet available. Problem with tools

                            Centroids properly reflect velocity
                            only at Mach number M<3

                            Modification of centroids proposed
                            by Lazarian & Esquiel 03 may help




    Esquiel & Lazarian 05
              Genus analysis
• A 2D genus number    G2 (n )  (number of isolated high density regions )
  defined as:                  (number of isolated low density regions )


          For a Gaussian map the genus-threshold
          curve is symmetric around the mean:




             Work with A. Esquivel
                 Genus analysis
• A shift from the mean can                   SMC
  reveal “meatball” or
  “Swiss cheese” topology.
• Genus curve of the HI in
  the SMC and from MHD
  simulations are different
  although the spectra are                    MHD
  similar
• The SMC show a evident
  “Swiss cheese” topology,
  the simulations are more
  or less symmetric.

                              Lazarian, Pogosyan & Esquivel 2003
                  Summary
• Turbulence intermittency is astrophysically
  important.
• In low M local magnetic field system velocity
  intermittency is similar to hydro.
• Intermittency of B is larger than that of V.
• Intermittencies of Alfven, slow and fast modes are
  different (Alfven is most stable with Mach number).
• Log of density intermittency is similar to velocity.
• Viscosity-dominated regime demonstrates scale-
  dependent intermittency.
• Observational testing is possible and necessary.
Implications for CR Transport
                    Big difference!!!
                          10-7


     (Kolmogorov)



                                        Fast modes


                          10-10


                                  Yan & Lazarian 02

  Fast modes determine scattering!
Viscosity-Dominated Regime
     (Lazarian, Vishniac & Cho 04)

 • MHD turbulence does not vanish at the
   viscous damping scale. Magnetic energy
   cascades to smaller scales.
 • Magnetic intermittency increases with
   decrease of the scale.
 • Turbulence gets resurrected at ion
   decoupling scale.
Density, compressible and
  Alfven modes (5123)




              Cho & Lazarian 05
• It is easy to mix magnetic field
  lines: V^ ~ l^1/3     (E(k^)~k^-5/3)
  Kolmogorov in ^ direction              Basics of
• Coupling between || and ^:             Goldreich &
                                         Sridhar
l^         V^                            model (1995)
       ~                 l^2/3 ~ l||
l||        VA
Anisotropy is larger at small scales
What are the scattering rates for different ISM phases?
                        (Cont.)
             gyroresonance                          TTD




                 Solid line is analytical results
                 Symbols are numerical results
  (c) scattering frequency by gyroresonance vs. pitch angle cosine;
  (d) near 90o transit time damping should be taken into account.
Spectroscopic Observations
    and velocity statistics  Spectral Line Observations




               (slide composition by A. Goodman)

								
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