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

2. 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?

3. 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

4. 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

5. 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

6. 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

7. Cordes & Lazio 2001 electron density arms

9.  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

10. 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) ?

11. Superposition of two structure functions?

12. 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?

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

15. 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

16. scale? amplitude?

17. 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

18. = 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°

19. 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

20. 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)

21. 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

22. 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

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

24. 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?

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

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

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