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Depolarization canals in Milky Way radio maps. Anvar Shukurov and Andrew Fletcher School of Mathematics and Statistics, Newcastle, U.K. Outline. Observational properties Origin: Differential Faraday rotation Gradients of Faraday rotation across the beam Physics extracted from canals. - PowerPoint PPT Presentation
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Polarization 2005, Orsay, 13/09/2005
Depolarization canalsin Milky Way radio maps
Anvar Shukurovand
Andrew Fletcher
School of Mathematics and Statistics, Newcastle, U.K.
Outline
• Observational properties
• Origin:Differential Faraday rotationGradients of Faraday rotation across the
beam
• Physics extracted from canals
Gaensler et al., ApJ, 549, 959, 2001. ATCA, = 1.38 GHz ( = 21.7 cm), W = 90” 70”.
Narrow, elongated regions of zero polarized intensity
Abrupt change in by /2 across a canal
Haverkorn et al. 2000
PI
Gaensler et al., ApJ, 549, 959, 2001
Position and appearance depend on the wavelength
Haverkorn et al., AA, 403, 1031, 2003Westerbork, = 341-375 MHz, W = 5’
No counterparts in total emission
Uya
nike
r et
al.,
A&
A S
uppl
, 13
8, 3
1, 1
999.
Eff
elsb
erg,
1.4
GH
z, W
= 9
.35’
No counterparts in I propagation effects
Sensitivity to Faraday depolarization
Potentially rich source of information on ISM
Complex polarization ( // l.o.s.)
Fractional polarization p, polarization angle and Faraday rotation measure RM:
Potential Faraday rotation:
Magneto-ionic layer +synchrotron emission,uniform along the l.o.s.,varying across the sky, = 0
Differential Faraday rotation produces canals
Uniform slab, thickness 2h, R = 2KnBzh, F = R2:
There exists a reference frame in the sky plane where Q (or U) changes sign across a canal produced by DFR, whereas U (or Q) does not.
Faraday screen: magneto-ionic layer in front of emitting layer,
both uniform along the l.o.s., F = R2 varies across the sky
Variation of F across the beam produces canals
• Discontinuity in F(x), F = /2 canals, = /2
• Continuous variation, F=/2 no canals, = /2
• Canals with a /2 jump in can only be produced by discontinuities in F and RM: x/D < 0.2
F
D = FWHM of a Gaussian beam
F = 2
x x
F
Continuous variation, F = canals, but with =
We predict canals, produced in a Faraday screen, without any variation in across them (i.e., with F = n).
Moreover, canals can occur with any F, if
(1) F = DF = n and (2) F(x) is continuous
Simple model of a Faraday screen
Both Q and U change sign across a canal produced in a Faraday screen.
Implications: DFR canals
• Canals: |F| = n |RM| = n/(22)
Canals are contours of RM(x)
• RM(x): Gaussian random function, S/N > 1
• What is the mean separation of contours of a (Gaussian) random function?
The problem of overshoots
• Consider a random function F(x).
• What is the mean separation of positions xi such that F(xi) = F0 (= const) ?
x
F
F0
§9 in A. Sveshnikov, Applied Methods of the Theory of Random Functions, Pergamon, 1966
f (F) = the probability density of F;f (F, F' ) = the joint probability density of F and
F' = dF/dx;
Great simplification: Gaussian random functions(and RM a GRF!)
F(x) and F'(x) are independent,
Mean separation of canals (Shukurov & Berkhuijsen MN 2003)
lT 0.6 pc at L = 1 kpc Re(RM) = (l0/lT)2 104105
Canals in Faraday screens: tracer of shock fronts
Observations: Haverkorn et al., AA, 403, 1031, 2003
Simulations: Haverkorn & Heitsch, AA, 421, 1011, 2004
Canals in Faraday screen: F=R2=(n +1/2)Haverkorn et al. (2003):
R = 2.1 rad/m2 (= 85 cm)
Shock front, 1D compression:
n2/n1 = , B2/B1 = , R2/R1 = 2,
R = (2-1)R1 1.3
(M = shock’s Mach number)
Distribution function of shocks(Bykov & Toptygin, Ap&SS 138, 341, 1987)
PDF of time intervals between passages of M-shocks:
Mean separation of shocks M > M0 in the sky plane:
Mean separation of shocks,Haverkorn et al. (2003)
M0 = 1.2, Depth = 600 pc,
cs = 10 km/s, fcl = 0.25
L 90' (= 20 pc)
(within a factor of 2 of what’s observed)
Smaller larger M0 larger L
Conclusions• The nature of depolarization canals seems to be
understood.
• They are sensitive to important physical parameters of the ISM (autocorrelation function of RM or Mach number of shocks).
• New tool for the studies of ISM turbulence: contour statistics
(contours of RM, I, PI, ….)
Details in: Fletcher & Shukurov, astro-ph/0510XXXX