Observations of turbulencein the magneto-ionized ISM

on subparsec scales

Marijke Haverkorn

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?

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

Bryan GaenslerCfA U of Sydney

Naomi McClure-GriffithsATNF, Sydney

John DickeyU of Tasmania

Anne GreenU of Sydney

The Southern Galactic Plane Survey

Jo-Anne BrownU of Calgary

• 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

Polarized extragalactic sources in the SGPS

pulsarpolarized extragalactic point source

Brown et al 2006

“Small”-scale structure: scale of RM fluctuationsLarge-scale structure: magnetic field strength and reversals

Cordes & Lazio 2001 electron density arms

Cordes & Lazio 2001 electron density arms

log(

log

(D) saturation:

outer scale of fluctuations

powerlawfluctuations

Structure function DRM() = < (RM(x) - RM(x+))2 >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

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) ?

• Superposition of two structure functions?

DRM = 2 RM2 (r/rout)m

spiral arm interarmBran 4G 2 Gdl 500 pc 6 kpcne 0.1 cm-3 0.1 cm-3

rout 6 pc 80 pcm 5/3 5/3

Bran 10 G 2 Gdl 1000 pc 6 kpcrout 6 pc 80 pcne 0.1 0.1 cm-3

m 5/3 5/3

• Superposition of two structure functions?

• Superposition of two structure functions?

• Discrete structures within a turbulent medium?

Small scales: ‘Kolmogorov’ turbulence

Large scales: ‘Kolmogorov’ turbulence + noise contribution from discrete sources = flatter structure function

• Two-dimensional turbulence (n = 2/3) ?

D

RM

(ra

d2 m-4)

(degrees)Minter & Spangler 1996

n = 5/3: 3D Kolmogorov

n = 2/3: 2D

scale?

amplitude?

Depolarization of point sources

<|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

Polarization degree:

parm = 0.015, 0.033pinterarm = 0.055, 0.037

whereas phigh b = 0.104

<|p/p0|2> = 1 - 4 RM2 4 2m/2 (rsrc/rout)m (1+m/2)))

m = 5/3p0 = 0.104rsrc = 6 arcsec

DRM

log

spiral arms

rout

2RM2

rout = 5 - 8 pc in Carina and Crux arm ≈ 0.1°

DRM

log

interarms

routobsrout

dep

2(RMobs)2

2(RMdep)2

<|p/p0|2> = 1 - 4 (RMdep)2 4 2m/2 (rsrc/rout

dep)m (1+m/2))

routdep ≈ 2 pc at 3 kpc

for each interarm region

m = 5/3p0 = 0.104rsrc = 6 arcsec

Minter & Spangler 1996

DRM() = {251[(n02 CB

2 + B//2 Cn

2] + 23 Cn2 CB

2 l02/3}L8/3 5/3

Good fit for parameters for Kolmogorov turbulence:Breg ≈ 0.8 G CB

2 ≈ 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

DR

M (

rad2 m

-4)

(degrees)

Interarm regions:Breg = 3 G n0 = 0.1 cm-3 l0 = 2 pc at D = 3 kpcCB

2 ≈ 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 kpcCB

2 ≈ 90, 40 x10-13

Bran ≈ 6.4, 4.3 G

Other observations?

Clegg et al 1992

• extragalactic sources in the Galactic plane

extragalactic sources at theNorth Galactic pole (Simonetti et al. 1984)

Possible slope turnover in the plane, not at the NGPOuter scale < 3.1º ≈ 150 pc at 3 kpc

n = 2/3

n = 5/3

n = 5/3

Perseus arm: Canadian Galactic Plane Survey

n = 2/3 rout ≈ 80 pc at D = 2 kpc

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?

Simonetti et al. 1984

“Region A”

180° < l < 220° 10° < b < 50°outer scale rout < 4°(200 pc at 3 kpc)

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

More two-dimensional turbulence?

Brown & Taylor 2001

RM/RM independent of longitude:RM fluctuations aligned with regular magnetic field