Depolarization Canals and Interstellar Turbulence

Recent radio polarization observations have revealed a plethora of unexpected features in the polarized Galactic radio background that arise from propagation effects in the random (turbulent) interstellar medium. The canals are especially striking among them, a random network of very dark, narrow regions clearly visible in many directions against a bright polarized Galactic synchrotron background. There are no obvious physical structures in the ISM that may have caused the canals, and so they have been called Faraday ghosts. They evidently carry information about interstellar turbulence but only now is it becoming clear how this information can be extracted. Two theories for the origin of the canals have been proposed; both attribute the canals to Faraday rotation, but one invokes strong gradients in Faraday rotation in the sky plane (specifically, in a foreground Faraday screen) and the other only relies on line-of-sight effects (differential Faraday rotation). In this review we discuss the physical nature of the canals and how they can be used to explore statistical properties of interstellar turbulence. This opens studies of magnetized interstellar turbulence to new methods of analysis, such as contour statistics and related techniques of computational geometry and topology. In particular, we can hope to measure such elusive quantities as the Taylor microscale and the effective magnetic Reynolds number of interstellar MHD turbulence. 1 The promise and pitfalls of radio polarization High-resolution maps of the Milky Way synchrotron emission show a complex, irregular system of polarized and depolarized structures (Wieringa et al. 1993, Uyanıker et al. 1998b, Duncan et al. 1999, Gray et al. 1999, Haverkorn et al. 2000, Gaensler et al. 2001, Wolleben et al. 2006). Many polarized structures can be attributed to objects in the interstellar medium (ISM), such as supernova remnants and shock fronts. These objects are usually bright in total intensity as well. 1 School of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne, NE1 7RU, U.K; e-mail: [email protected] (AF) and [email protected] (AS) c © EDP Sciences 2008 DOI: (will be inserted later) 2 Title : will be set by the publisher Fig. 1: A 24◦× 9 section of the 1.4GHz Effelsberg Medium Latitude Survey centred at (l, b) = (162, 0) (Reich et al. 2004). Top: total intensity, with large-scale structure added from Dwingeloo data. Middle: polarized intensity, also including the Dwingeloo large-scale structure. Bottom: polarized intensity observed with the Effelsberg telescope with large scale structure missing. Note the strong difference between the (preliminary) absolutely calibrated polarized intensity map (middle) and the map with artificial base-levels (bottom). However extended, diffuse polarized emission is also rich in structure which most plausibly arises from propagation effects as the radiation passes through the ranA. Fletcher & A. Shukurov: Depolarization canals 3 dom ISM. As illustrated in Fig. 1, much of this structure is not mirrored in the total synchrotron intensity so the structure in polarization is not primarily caused by variations in emissivity. At low frequencies, the cloudy appearance of polarized intensity maps differs between adjacent, narrow frequency bands (Haverkorn et al. 2003) strongly suggesting that the polarization varies with wavelength and so a connection with Faraday rotation is plausible. Random fluctuations in the magnetized ISM — caused by its turbulent flows, for example — leave their fingerprint in the random appearance of polarized intensity maps. If a connection can be established between measurable properties of the radio maps to the physics of the ISM, a powerful new source of information about the dynamic state of the interstellar plasma will become available, particularly its little studied magnetic properties. Similarly, a reliable separation of the Milky Way synchrotron polarized foreground from cosmological signals, either through the creation of templates from low-frequency data or through statistical analysis, requires a thorough understanding of the origins of structure in the diffuse polarized emission. In the context of cosmological studies, the effects of the ISM on the polarized emission propagating through it are especially important. One of the most striking features of the maps is the twisting network of narrow, dark canals running through regions of bright polarized intensity, clearly visible in Fig. 1 at 1.4GHz and common in other maps at this frequency (Uyanıker et al. 1998b, Gaensler et al. 2001) and longer wavelengths (Haverkorn et al. 2000). The observed canals have the following properties: 1. the observed polarized intensity falls to zero, because the polarization angle changes by 90 across the canal; 2. a canal is one telescope beam wide; 3. a canal passes through a region of significant polarized intensity; 4. the canal is not related to any obvious structure in the total intensity. Care in interpreting the observations is especially important in the case of polarized emission: interferometer observations miss emission at large scales (determined by their shortest baseline), and single-dish surveys often have arbitrarily set base-levels around their edges. Correcting for the missing large-scale structure involves adding a smoothly varying signal to the Stokes parameters. In the case of total intensity (Stokes I) the consequences are easily predictable. However, the Stokes parameters Q and U are not positive definite and therefore algebraic addition of a smooth component can create and/or remove zeros in either. Hence minima in polarized intensity (Q + U) can become maxima and vice versa. The effect of absolute calibration on the polarization angle Ψ = 1 2 arctan (U/Q) can be equally counter-intuitive. Reich et al. (2004) clearly identify and discuss these problems. The dramatic effect the missing data can have on the appearance of the polarization pattern can be seen by comparing the bottom two panels of Fig. 1. It is clear that unless statistical parameters can be identified that are independent of the Q and U intensity values, polarization surveys should be tied 4 Title : will be set by the publisher to an absolutely calibrated reference frame (Uyanıker et al. 1998a, Reich et al. 2004). The recent absolutely calibrated all-sky survey at 1.4GHz by Wolleben et al. (2006) will be a mine of useful information for polarization studies. Haverkorn et al. (2004) argue that if fluctuations in Faraday rotation measure are sufficiently strong and of a small scale, the resulting structure in Q and U can be of such a small scale that the missing short spacings will not cause a problem. In other words, Q and U may have no large scale structure; this can easily happen at metre wavelengths. Two theories accounting for the origin of the canals have been proposed: one invokes strong plane-of-sky gradients or discontinuities in Faraday rotation measure in a foreground screen between the emitting region and the observer (Haverkorn et al. 2000, 2004; Haverkorn & Heitsch 2004) and the other proposes differential Faraday rotation along the line-of-sight through the emitting layer (Beck 1999, Shukurov & Berkhuijsen 2003). In this review we summarize recent work on the interpretation of depolarized canals and provide a more detailed explanation of some analytic results than is available in the readily accessible literature. After introducing basic equations and defining our notation in Section 2, we describe the effects of differential Faraday rotation and Faraday screens, demonstrate how canals are formed by the two proposed mechanisms and discuss how observable quantities behave in the vicinity of a canal in each case. Then in Section 3 we turn to the interpretation of the properties of the canals in terms of the physical state of the ISM. In Section 3.1 the case of differential Faraday rotation is discussed in the context of the statistical properties of contours of a random field and we show how canals of this type can yield information about the smallest scales of ISM turbulence. Similar techniques can be applied to canals produced by Faraday screens, and more generally to contours of any randomly distributed observable quantity. Section 2.2 demonstrates that true discontinuities in Faraday rotation are required if a foreground screen is to produce canals similar to those observed. In the case that these discontinuities are shock fronts originating from supernovae, we show in Section 3.2 how the distance between canals is related to the separation of shock fronts. 2 The complex polarization, Stokes parameters and depolarization The complex polarization is commonly written as P = p0 ∫ V W (r)ǫ(r) exp [2iψ(r)] dV ∫ V W (r)ǫ(r) dV , (2.1) where p0 ≃ 0.7 is the maximum degree of polarization for synchrotron emission (a function of the spectral index), W is the beam profile around a given position in the sky, ǫ is the synchrotron emissivity, and ψ is the local polarization angle. The integrals are taken over the volume of the beam cylinder and r = (x, y, z) specifies a location with respect to the sky plane (x, y) and the line of sight, z. The modulus and argument of P are the observed degree of polarization p and A. Fletcher & A. Shukurov: Depolarization canals 5 polarization angle Ψ respectively, P = p exp (2iΨ). (2.2) When polarized radio emission propagates through magnetized and ionized ISM, the local polarization angle ψ undergoes Faraday rotation: ψ(r) = ψ0(r) + φ(r) , (2.3) where ψ0 is the intrinsic polarization angle (perpendicular to the magnetic field component transverse to the line of sight at the point of emission),