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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