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

1. Observations of turbulencein the magneto-ionized ISMon 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. The Southern Galactic Plane Survey Bryan Gaensler CfA  U of Sydney Naomi McClure-Griffiths ATNF, Sydney Anne Green U of Sydney Jo-Anne Brown U of Calgary John Dickey U of Tasmania

5. The Southern Galactic Plane Survey • 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

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

7. Cordes & Lazio 2001 electron density arms

8. Cordes & Lazio 2001 electron density arms

9. saturation: outer scale of fluctuations Haverkorn et al 2006 RM fluctuations in spiral arms: outer scale < ~10 pc: H II region dominated? RM fluctuations in interarm regions: outer scale ≈ 110 pc RM fluctuations in interarm regions: slope m = 0.3 - 0.7 Structure function DRM() = < (RM(x) - RM(x+))2 >x log(D) powerlaw fluctuations  log(

10. Shallow structure functions? Observed m = 0.3 - 0.7 Kolmogorov: 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. Bran10 G 2 G dl 1000 pc 6 kpc rout 6 pc 80 pc ne 0.1 0.1 cm-3m 5/3 5/3 • Superposition of two structure functions? DRM = 2 RM2 (r/rout)m spiral arm interarm Bran 4G 2 G dl 500 pc 6 kpc ne 0.1 cm-3 0.1 cm-3 rout 6 pc 80 pc m 5/3 5/3

13. 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. n = 2/3: 2D DRM (rad2 m-4) n = 5/3: 3D Kolmogorov  (degrees) • Two-dimensional turbulence (n = 2/3) ?  Minter & Spangler 1996

16. amplitude? scale?

17. <|p/p0|2> = 1 - 4 RM24 2m/2 (rsrc/rout)m(1+m/2)) (Tribble 1991) where structure function DRM(r)  2 RM2 (r/rout)m for r < rout Depolarization of point sources Polarization degree: parm = 0.015, 0.033 pinterarm = 0.055, 0.037 whereas phigh b = 0.104

18. DRM spiral arms 2RM2 log rout rout = 5 - 8 pc in Carina and Crux arm ≈ 0.1° <|p/p0|2> = 1 - 4 RM24 2m/2 (rsrc/rout)m(1+m/2))) m = 5/3 p0 = 0.104 rsrc = 6 arcsec

19. routdep ≈ 2 pc at 3 kpc for each interarm region interarms DRM 2(RMobs)2 2(RMdep)2 routdep routobs log <|p/p0|2> = 1 - 4 (RMdep)24 2m/2 (rsrc/routdep)m(1+m/2)) m = 5/3 p0 = 0.104 rsrc = 6 arcsec

20. DRM (rad2 m-4)  (degrees) Minter & Spangler 1996 DRM() = {251[(n02 CB2 + B//2 Cn2] + 23 Cn2 CB2 l02/3}L8/35/3 Good fit for parameters for Kolmogorov turbulence: Breg ≈ 0.8 G CB2 ≈2.2 10-13 G2 m-2/3 Bran ≈ 1 G n0 ≈ 0.26 cm-3 l0 ≈ 3.6 pc at D = 2.9 kpc

21. Interarm regions: Breg = 3 G n0 = 0.1 cm-3 l0 = 2 pc at D = 3 kpc CB2 ≈60, 100, 60 x 10-13 Bran ≈ 5.2, 6.7, 5.2 G Spiral arms: Breg = 1.5 G n0 = 0.1 cm-3 l0 = 6 pc at D = 3 kpc CB2 ≈ 90, 40 x10-13 Bran ≈ 6.4, 4.3 G

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

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

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

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

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