Depolarization canals in Milky Way radio maps

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