Growth of Magnetic Fields by Turbulent Motions and Characteristic Scales of MHD Turbulence

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1 Growth of Magnetic Fields by Turbulent Motions and Characteristic Scales of MHD Turbulence Jungyeon Cho Chungnam National University, Korea Cho, Vishniac, Beresnyak, Lazarian & Ryu 2009, ApJ Cho & Ryu, 2009, ApJ Lett (submitted) (+Ryu, Kang, Cho, & Das 2008, Science)

2 Distribution of Nearby Galaxies (2Micron All Sky Survey) Questions: σ RM =?

3 Galaxy clusters (~10 3 galaxies) Size ~ 1Mpc ~ a few x10 6 ly Total mass ~ M sun σ v ~ km/sec T ICM ~ K n ICM ~ cm -3 E turb /E th ~ (nm H σ v2 )/(nkt) < 1

4 ICM (intracluster medium) is turbulent Turbulence! 3C Abell 2634 σ v ~ km/sec

5 ICM is magnetized diffuse synchrotron emission Kim, Kronberg et al (1989): B ~ µg

6 Origin of cosmic seed magnetic fields is uncertain. Cosmological? Astrophysical? (e.g. Xu (+Li, Li) et al. 2009) In this talk, we assume this is the case.

7 Topic 1. Amplification of B fields in turbulence - How can MHD turbulence amplify B fields? Weak seed field (B 0 )

8 Stretching of field lines B 0 t=0: Fluid elements and field lines move together *Back reaction is negligible if E mag <E kin

9 Stretching Increase of E B (Suppose that the fluid is incompressible) A 1 B 1 B 2 A 2 B 1 A 1 =B 2 A 2 -B 2 =(A 1 /A 2 )B 1 > B 1 -B 2 /8π > B 1 /8π

10 Expectations Question: On what scale is stretching most active? (We assume that B 0 is very weak) Turbulence = Σ eddies!

11 Turbulence=Σ eddies! v l l Eddy turnover time ~ l/v l

12 Kolmogorov theory: incompressible V l 2 t cas t cas = l/v l hydrodynamic turbulence = const V 3 l l = const V l ~ l 1/3 l v

13 V l ~ l 1/3 Eddy turnover time: l/v l ~ l 2/3 Smaller eddies turn over faster. Stretching is most active on the smallest scale. In turbulence, smallest scale=dissipation scale

14 Expectations: Stretching on the dissipation scale will occur first B E(k) k Exponential growth (Batchelor 1950)

15 Expectations: E turb (k) E(k) What will happen when E turb ~ E mag on the dissipation scale? Exponential growth stage will end! Stretching scale gradually moves to larger scales. k

16 Results of simulations linear exponential Ryu (+Cho) et al (2008)

17 linear growth exponential growth Cho et al. (2009) * See also Schekochihin et al (2006); Cho & Vishniac (2000)

18 The growth rate seems to be universal Cho et al (2009)

19 Why linear? (from Schekochihin et al 2006) db 2 (t)/dt ~ b l2 /(l/v l ) ~ v l3 /l ~ ε ~ const E v (k) k~1/l E b (k) k

20 Conclusion for Topic 1 -Turbulence can amplify weak seed B fields -Two stages of amplification: exp. and linear -Simulations show that the growth rate of the linear stage seems to be universal.

21 Topic 2: Rotation measure=?

22 Cf) A model for B in LSS ( Ryu et al 2008) Observed strength of B: In clusters: ~ µg In filaments: ~10 ng (?) In voids:?

23 Using the turbulence model, we can estimate strengths of cosmic B fields Cosmological simulation Ryu et al (2003)

24 Turbulence in clusters and filaments Turbulence is strong in clusters velocity We measured strengths of turbulence using vorticity Turbulence is weak in filaments

25 Weak B 0 Strength of turbulence B

26 Ryu et al (2008) 0.1nG 10µG

27 -This model is consistent with observations -Turbulence in the ICM can amplify weak seed fields to ~µg level! (Even the case initial seed fields are localized [e.g. Xu et al. 2009], this should be true.)

28 initial B field~doughnut shape localized seed B uniform seed B Cho (+Yoo, Jang, Ryu) 2009 (in prep)

29 Topic 2: Rotation measure=?

30 Rotation measure polarized light magnetized plasma angle RM n e B dl

31

32 (For simplicity, let s assume n e =const.) RM 2π 2π Fourier transform of RM k =0 plane in Fourier space RM projected B k k k =0

33 k 2 average power of Fourier modes with k =k B k 1 k RM k 2 k 1 k =0 spectrum of RM E B (k)/k

34 σ RM2 =? Of course, we can calculate < (RM) 2 > directly. RM Another way of getting σ RM2?

35 Hint: How can we get <V 2 >? V 1) We can directly calculate <V 2 > in real space 2) We use the identity: <v 2 > = E v (k) dk

36 σ RM2 =? Of course, we can calculate < (RM) 2 > directly. RM Another way of getting σ RM2? σ RM2 = E RM (k) dk E B (k)/k dk

37 Therefore we have (σ RM ) 2 =<(RM) 2 > E B (k)/k dk More precisely, we have (σ RM ) 2 L B=µG L=pc n e =cm -3

38 Simulations 512 3

39 Λ int =L int /L outer scale filaments ICM Cho & Ryu 2009

40 Fitting formula: outer scale

41 B=µG L=pc n e =cm -3 *We used L outer scale ~ 100kpc, L~1Mpc, n e ~10-3 cm -3, for filaments to line-of-sights. *But there are uncertainties (cf. Xu et al 2006)

42 Conclusions -Turbulence can amplify weak seed B fields -Two stages of amplification: exp. and linear -We showed that the relevant length scale for RM is the integral scale L int. -We obtained estimates of σ RM for clusters and filaments

43 2π k k =0 Projected B Fourier modes with k =0 Energy spectrum E(k)/k