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Depolarization canals in Milky Way radio maps

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.

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Depolarization canals in Milky Way radio maps

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  1. Depolarization canalsin Milky Way radio maps Anvar Shukurov and Andrew Fletcher School of Mathematics and Statistics, Newcastle, U.K.

  2. Outline • Observational properties • Origin: • Differential Faraday rotation • Gradients of Faraday rotation across the beam • Physics extracted from canals

  3. Narrow, elongated regions of zero polarized intensity Gaensler et al., ApJ, 549, 959, 2001. ATCA,  = 1.38 GHz ( = 21.7 cm), W = 90” 70”.

  4. Abrupt change in  by /2 across a canal • PI Gaensler et al., ApJ, 549, 959, 2001   Haverkorn et al. 2000

  5. Position and appearance depend on the wavelength Haverkorn et al., AA, 403, 1031, 2003 Westerbork,  = 341-375 MHz, W = 5’

  6. No counterparts in total emission Uyaniker et al., A&A Suppl, 138, 31, 1999. Effelsberg, 1.4 GHz, W = 9.35’

  7. No counterparts in I propagation effects Sensitivity to   Faraday depolarization Potentially rich source of information on ISM

  8. Complex polarization ( // l.o.s.)

  9. Fractional polarization p, polarization angle  and Faraday rotation measure RM: Potential Faraday rotation:

  10. Differential Faraday rotation produces canals Magneto-ionic layer + synchrotron emission, uniform along the l.o.s., varying across the sky,  = 0 

  11. 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.

  12. Variation of F across the beam produces canals • Discontinuity in F(x), F = /2  canals, =/2 • Continuous variation, F=/2 no canals,  = /2 Faraday screen: magneto-ionic layer in front of emitting layer, both uniform along the l.o.s., F = R2 varies across the sky

  13. F x x F • Canals with a /2 jump in  can only be produced by discontinuities in F and RM: x/D < 0.2 D = FWHM of a Gaussian beam F = R2

  14. 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

  15. Simple model of a Faraday screen Both Q and U change sign across a canal produced in a Faraday screen.

  16. 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?

  17. 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

  18. f (F) = the probability density of F; • f (F, F' ) = the joint probability density of F and F' = dF/dx;

  19. Great simplification: Gaussian random functions(and RM a GRF!) F(x) and F'(x) are independent,

  20. Mean separation of canals (Shukurov & Berkhuijsen MN 2003) lT  0.6 pc at L = 1 kpc  Re(RM) = (l0/lT)2  104105

  21. Canals in Faraday screens: tracer of shock fronts Observations: Haverkorn et al., AA, 403, 1031, 2003 Simulations: Haverkorn & Heitsch, AA, 421, 1011, 2004

  22. 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)

  23. 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:

  24. 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largerM0 larger L

  25. 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

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