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Galactic dynamo action from small to large scales
Anvar Shukurov
School of Mathematics & Statistics


Outline
1. Large-scale magnetic structures in spiral galaxies 2. Meso-scale magnetic structures: reversals, magnetic arms, etc. 3. Small-scale magnetic structures in the ISM: intermittency, magnetic filaments and ribbons


1. Large-scale magnetic structures in spiral galaxies
Azimuthal structure Vertical structure Radial structure

Further details in, e.g., A. Shukurov, Introduction to galactic dynamos. In: Mathematical Aspects of Natural Dynamos, eds E. Dormy & A. M. Soward, Chapman & Hall/CRC, 2007, pp. 313--359 (astro-ph/0411739).


1.1. Azimuthal structure
Observed: predominance of axisymmetric structures, azimuthal Fourier mode m = 0. Prediction of dynamo theory: m = 0 dominates (strong differential rotation). Distortions: m = 2 (spiral arms), m = 1 (overall asymmetries), ... ... ...
M5 1 m = 0+2

Fletcher et al. 2010: fitting polarization angles, = 3, 6, 20 cm


This disc, h/r



1, dynamo modes:

Br l - |d ln /d ln r |1/2 . B h Magnetic pitch angle: Br p = arctan -(10--20 ), as observed. B Vertical magnetic field: Bz (h/r)1/2 < 0.3, on average. B Bz 0.3 µG near the Sun (Mao et al. 2010). Bz Br , B near reversals and at h r .
h 0.5-1 kpc, r 10 kpc, l 0.1 kpc (turbulent scale)


1.2. Vertical structure
Quadrupolar symmetry in the main part of the disc: B(z) = B(-z), Br(z) = Br(-z), Bz(z) = -Bz(-z) . Dynamo theory: faster decay of dipolar modes predominance of quadrupolar symmetry. Distortions (e.g., north-south asymmetry in the Milky Way). Confirmed observationally for the Solar vicinity of the Milky Way.
Quadrupolar symmetry

Dipolar symmetry


-dynamo in a thin disc embedded in a poorly conducting halo, with random seed field (A. Brandenburg, from Beck et al., Ann. Rev. Astron. Astrophys. 1996)

t = 8 . 1 Gy r


Axisymmetric field structure near a reversal

Br Bz < B or Br , B Bz


Simple analytical solution for -dynamo in a thin disc in vacuum
(Shukurov & Sokoloff 2008, Dynamos, Elsevier, p. 251)

Bz 0. Accuracy better than 10% in galactic discs

+ radial dependence: B = Q(r)B (z ; r)
l R 3 , v h2 d R 3 r , lv dr

(flared disc)

d h2 D = R R 9r . 2 dr v

v 10 km/s (turbulent velocity), C0 = arbitrary constant


Further details in: Anvar Shukurov and Dmitry Sokoloff, Astrophysical dynamos. In: Ph. Cardin, L.F. Cugliandolo, editors, Les Houches, Session LXXXVIII, 2007, Dynamos. Elsevier, 2008, p. 251--299.


1.3. Radial structure
Large-scale dynamo controlled by magnetic helicity conservation (Shukurov et al., MNRAS, 2006): differential rotation, (r, z), helicity of interstellar turbulence, l2/h 0.5 km/s, gas outflow from the disc, RU = Uzh/ 0.2-2.
Uz = mass-averaged outflow velocity, Uz = Vzhot/ 0.1-1 km/s, lv 1026 cm2/s turbulent magnetic diffusivity.


Sur, Shukurov & Subramanian, MNRAS, 2007: Magnetic field evolution in a galactic disc with helicity advection by the galactic fountain or wind


Steady-state large-scale magnetic field due to helicity advection: 8 B RU (D/D C
2 crit

(Sur et al., MNRAS 2007)

- 1)v 2 (1µG)2 ,

C = 2(h/l)2 50, D ( h/v )2 10, the dynamo numb er near the Sun, Dcrit 8, critical dynamo numb er Dep endence of B on SFR, disc-halo connection, winds, galactic evolution, etc.
2 hot Vz

= S , S = SFR



BS

1/4

(IF all other relevant parameters are indep endent of SFR)


2. Meso-scale magnetic structures

Further details in: A. Shukurov, Mesoscale Magnetic Structures in Spiral Galaxies, in: Cosmic Magnetic Fields, eds. R. Wielebinski & R. Beck, Lect. Notes Phys. 664, Springer, 2005, pp. 113-135.


2.1. Axisymmetric reversals
Poezd at al. (1993): thin-disc dynamo, random seed field: numerous reversals, nonlinear effects can preserve some of them for a long time in the Milky Way, but not in M31. Positions of reversals:
t = 8.1 Gyr t = 9.6 Gyr =0

t =0

t = 0.55 Gyr

t = 2.2 Gyr

t = 5.3 Gyr


Localised reversals?
Bykov et al . (1997): long-lived region of reversed magnetic field near the corotation radius. Rotation curve and spiral structure of M51


Observational picture
· The only firmly established reversal of the largescale magnetic field is the Sagittarius-arm one
(Simard-Normandin & Kronberg, Nature 1979).

· All models with more reversals do not meet even basic statstical criteria. Likewise, it is not possible to decide what is the global azimuthal symmetry (ASS vs BSS) (Men et al. A&A, 819, 2008; Farrar et al. 2009). · Nature of the problems: deriving B from 0LneB// ds, need for a VERY careful statistical treatment


Deducing the global structure from noisy data


Multiple reversals?

RM(L) = 0 ne B dl

L


Random magnetic field:

RM

= K ne b(2dL)

1 /2

55 rad m

-2

ne 0.03 cm

-3

d b ( ) 5 µG 100 pc

1/2

L ) ( 1 kp c

1/2

± ±2

RM

RM


3. Small-scale magnetic structures in the multi-phase ISM
Interstellar magnetic field random vector field.



a quasi-homogeneous Gaussian

Interstellar shocks, multi-phase structure, ... A quasi-homogeneous, weaker magnetic background from the tangling of the large-scale magnetic field by turbulence.
Further details in: A. Shukurov & D. Sokoloff, Astrophysical dynamos. In: Ph. Cardin, L.F. Cugliandolo, editors, Les Houches, Session LXXXVIII, 2007, Dynamos. Elsevier, 2008, p. 251-- 299. A. Shukurov, Introduction to galactic dynamos. In: Mathematical Aspects of Natural Dynamos, eds E. Dormy & A. M. Soward, Chapman & Hall/CRC, 2007, pp. 313--359 (astro-ph/0411739).


More importantly: fluctuation dynamo produces intermittent magnetic fields even in a homogeneous medium Magnetic filaments (+ ribbons & sheets?), B = 0
B
max

Beq = (4)1/2v 5 µG.
2 max

Length l 50-100 pc. Low volume filling factor, B2 0.1 B .
1/2

Kinematic stage: magnetic energy max at l = l Rm- Nonlinear, statistically steady state: controversial
o o

.

folds at l = l Rm-1/2 10-7 pc (???) (Schekochihin et al. 2004) or thicker structures l,cr = l Rm,cr-1/2 10 pc (Subramanian 1999).


Haugen et al., PRE 2004
(1024)3

Simulations of the fluctuation dynamo: magnetic isosurfaces, B2 = const

(128) (256)
3

3

Wilkin et al., PRL 2007

Schekochihin et al., ApJ 2004


Implications Power spectrum & structure/correlation function are not suitable tools to describe intermittent magnetic fields
(intense flux ropes separated by extended regions with relatively weak magnetic field).

Magnetic field estimates from synchrotron intensity can be strongly affected (underestimated random magnetic field). Cosmic ray propagation can be strongly affected by magnetic intermittency. No models available of cosmic ray propagation in such magnetic fields. Locally anisotropic magnetic fields are less efficient in cosmic ray scattering (> 102-103 GeV) (Chandran 2000).