depolarization canals in milky way radio maps
DESCRIPTION
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 PresentationTRANSCRIPT
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