Transcript Presentation

Depolarization canals
in Milky Way radio maps
Anvar Shukurov
and
Andrew Fletcher
School of Mathematics and Statistics, Newcastle, U.K.
Polarization 2005,
Orsay, 13/09/2005
Outline
• Observational properties
• Origin:
Differential Faraday rotation
Gradients of Faraday rotation across the
beam
• Physics extracted from canals
Narrow, elongated regions of zero polarized intensity
Gaensler et al., ApJ, 549, 959, 2001. ATCA,  = 1.38 GHz ( = 21.7 cm), W = 90” 70”.
Abrupt change in  by /2 across a canal
 PI
Gaensler et al., ApJ,
549, 959, 2001

Haverkorn et al. 2000
Position and appearance depend on the wavelength
Haverkorn et al., AA, 403, 1031, 2003
Westerbork,  = 341-375 MHz, W = 5’
Uyaniker et al., A&A Suppl, 138, 31, 1999.
Effelsberg, 1.4 GHz, W = 9.35’
No counterparts in total emission
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:
Differential Faraday rotation produces canals

Magneto-ionic layer +
synchrotron emission,
uniform along the l.o.s.,
varying across the sky,
 = 0
Uniform slab,
thickness 2h, R = 2KnBzh, F = R2:
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.
Variation of F across the beam produces canals
Faraday screen: magneto-ionic layer in front of emitting layer,
both uniform along the l.o.s., F = R2 varies across the sky
• 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
F
x
x
D = FWHM of a
Gaussian beam
F = R2
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 = DF = 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/(22)
•  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) ?
§9 in A. Sveshnikov,
Applied Methods of
the Theory of
Random Functions,
Pergamon, 1966
F
F0
x
 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)
2
= (l0/lT)  104105
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=R2=(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,
cs = 10 km/s,
Depth = 600 pc,
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