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Observations of turbulence in the magneto-ionized ISM on subparsec scales Marijke Haverkorn

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Conclusions Rotation measures of polarized extragalactic point sources in the Galactic plane show power law fluctuations on ~1 - 100 pc scales Spiral arms and interarms show different structure Spiral arms: outer scale < 10 pc; ~5 pc if ‘Kolmogorov’ turbulence on smaller scales Interarm regions: possibly the same outer scale (~5 pc) for ‘Kolmogorov’, but turnover in slope and additional structure until ~100 pc Halo: no turnover in slope: ‘Kolmogorov’ only up to ~ 100 pc scales?

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Outline Southern Galactic Plane Survey Structure functions: RM fluctuations in spiral arms and interarms How to explain these fluctuations? –turnover in spectrum: outer scale of structure – amplitude of spectrum: magnetic field

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Bryan Gaensler CfA U of Sydney Naomi McClure-Griffiths ATNF, Sydney John Dickey U of Tasmania Anne Green U of Sydney The Southern Galactic Plane Survey Jo-Anne Brown U of Calgary

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1.4 GHz/20 cm polarized continuum and H I 253° < l < 358°, |b| < 1.5° Australia Telescope Compact Array + Parkes 64m single dish Resolution 1, rms noise 1 mJy, velocity resolution 1 km/s The Southern Galactic Plane Survey

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Polarized extragalactic sources in the SGPS pulsar polarized extragalactic point source Brown et al 2006 “Small”-scale structure: scale of RM fluctuations Large-scale structure: magnetic field strength and reversals

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Cordes & Lazio 2001 electron density arms

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log( log(D) saturation: outer scale of fluctuations powerlaw fluctuations Structure function D RM ( ) = x RM fluctuations in spiral arms: outer scale < ~ 10 pc: H II region dominated? Haverkorn et al 2006 RM fluctuations in interarm regions: outer scale ≈ 110 pc RM fluctuations in interarm regions: slope m = 0.3 - 0.7

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Shallow structure functions? Observed m = 0.3 - 0.7Kolmogorov: n = 5/3 Superposition of two structure functions? Discrete structures within a turbulent medium? Two-dimensional turbulence (n = 2/3) ?

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Superposition of two structure functions?

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D RM = 2 RM 2 (r/r out ) m spiral arminterarm B ran 4 G 2 G dl500 pc6 kpc n e 0.1 cm -3 0.1 cm -3 r out 6 pc80 pc m5/35/3 B ran 10 G 2 G dl1000 pc6 kpc r out 6 pc80 pc n e 0.10.1 cm -3 m5/35/3 Superposition of two structure functions?

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Discrete structures within a turbulent medium? Small scales: ‘Kolmogorov’ turbulence Large scales: ‘Kolmogorov’ turbulence + noise contribution from discrete sources = flatter structure function

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Two-dimensional turbulence (n = 2/3) ? D RM (rad 2 m -4 ) (degrees) Minter & Spangler 1996 n = 5/3: 3D Kolmogorov n = 2/3: 2D

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scale? amplitude?

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Depolarization of point sources = 1 - 4 RM 2 4 2 m/2 (r src /r out ) m (1+m/2)) (Tribble 1991) where structure function D RM (r) 2 RM 2 (r/r out ) m for r < r out Polarization degree: p arm = 0.015, 0.033 p interarm = 0.055, 0.037 whereas p high b = 0.104

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= 1 - 4 RM 2 4 2 m/2 (r src /r out ) m (1+m/2))) m = 5/3 p 0 = 0.104 r src = 6 arcsec D RM log spiral arms r out 2 RM 2 r out = 5 - 8 pc in Carina and Crux arm ≈ 0.1°

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D RM log interarms r out obs r out dep 2( RM obs ) 2 2( RM dep ) 2 = 1 - 4 ( RM dep ) 2 4 2 m/2 (r src /r out dep ) m (1+m/2)) r out dep ≈ 2 pc at 3 kpc for each interarm region m = 5/3 p 0 = 0.104 r src = 6 arcsec

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Minter & Spangler 1996 D RM ( ) = {251[(n 0 2 C B 2 + B // 2 C n 2 ] + 23 C n 2 C B 2 l 0 2/3 }L 8/3 5/3 Good fit for parameters for Kolmogorov turbulence: B reg ≈ 0.8 G C B 2 ≈ 2.2 10 -13 G 2 m -2/3 B ran ≈ 1 G n 0 ≈ 0.26 cm -3 l 0 ≈ 3.6 pc at D = 2.9 kpc D RM (rad 2 m -4 ) (degrees)

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Interarm regions: B reg = 3 G n 0 = 0.1 cm -3 l 0 = 2 pc at D = 3 kpc C B 2 ≈ 60, 100, 60 x 10 -13 B ran ≈ 5.2, 6.7, 5.2 G Spiral arms: B reg = 1.5 G n 0 = 0.1 cm -3 l 0 = 6 pc at D = 3 kpc C B 2 ≈ 90, 40 x10 -13 B ran ≈ 6.4, 4.3 G

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Other observations? Clegg et al 1992 extragalactic sources in the Galactic plane extragalactic sources at the North Galactic pole (Simonetti et al. 1984) Possible slope turnover in the plane, not at the NGP Outer scale < 3.1º ≈ 150 pc at 3 kpc n = 2/3 n = 5/3

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Perseus arm: Canadian Galactic Plane Survey n = 2/3 r out ≈ 80 pc at D = 2 kpc

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Conclusions Rotation measures of polarized extragalactic point sources in the Galactic plane show power law fluctuations on ~1 - 100 pc scales Spiral arms and interarms show different structure Spiral arms: outer scale < 10 pc; ~5 pc if ‘Kolmogorov’ turbulence on smaller scales Interarm regions: possibly the same outer scale (~5 pc) for ‘Kolmogorov’, but turnover in slope and additional structure until ~100 pc Halo: no turnover in slope: ‘Kolmogorov’ only up to ~ 100 pc scales?

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Simonetti et al. 1984 “Region A” 180° < l < 220° 10° < b < 50° outer scale r out < 4° (200 pc at 3 kpc)

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Region A: possible ‘magnetic bubble’ at D > ~ 3 kpc, size 2 kpc (Vallee 84)

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More two-dimensional turbulence? Brown & Taylor 2001 RM /RM independent of longitude: RM fluctuations aligned with regular magnetic field

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