Origin of Galactic and Extragalactic Magnetic Fields

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A variety of observations suggest that magnetic fields are present in all galaxies and galaxy clusters. These fields are characterized by a modest strength (10^{-7}-10^{-5} G) and huge spatial scale (~Mpc). It is generally assumed that magnetic fields in s

Origin of Galactic and Extragalactic Magnetic FieldsLawrence M. WidrowDepartment of Physics, Queen’s University, Kingston, Ontario, Canada K7L 3N6A variety of observations suggest that magnetic elds are present in all galaxies and galaxy clusters. These elds are characterized by a modest strength (10 7 10 5 G) and huge spatial scale (< ～ 1 Mpc). It is generally assumed that magnetic elds in spiral galaxies arise from the combined action of di erential rotation and helical turbulence, a process known as the αω-dynamo. However fundamental questions concerning the nature of the dynamo as well as the origin of the seed elds necessary to prime it remain unclear. Moreover, the standard αω-dynamo does not explain the existence of magnetic elds in elliptical galaxies and clusters. The author summarizes what is known observationally about magnetic elds in galaxies, clusters, superclusters, and beyond. He then reviews the standard dynamo paradigm, the challenges that have been leveled against it, and several alternative scenarios. He concludes with a discussion of astrophysical and early Universe candidates for seed elds.arXiv:astro-ph/0207240v1 11 Jul 2002ContentsI. INTRODUCTION II. Preliminaries A. Magnetohydrodynamics and Plasma Physics B. Cosmology III. Observations of Cosmic Magnetic Fields A. Observational Methods 1. Synchrotron Emission 2. Faraday rotation 3. Zeeman Splitting 4. Polarization of Optical Starlight B. Spiral Galaxies 1. Field Strength 2. Global Structure of the Magnetic Field in Spirals 3. Connection with Spiral Structure 4. Halo Fields 5. Far Infrared-Radio Continuum Correlation C. Elliptical and Irregular Galaxies D. Galaxy Clusters E. Extracluster Fields F. Galactic Magnetic Fields at Intermediate Redshifts G. Cosmological Magnetic Fields 1. Faraday Rotation due to a Cosmological Field 2. Evolution of Magnetic Fields in the Early Universe 3. Limits from CMB Anisotropy Measurements 4. Constraints from Big Bang Nucleosynthesis 5. Intergalactic Magnetic Fields and High Energy Cosmic Rays IV. Galactic and Extragalactic Dynamos A. Primordial Field Hypothesis B. Mean-Field Dynamo Theory C. Disk Dynamos D. Growth Rate for the Galactic Magnetic Field E. Criticisms of Mean-Field Dynamo Theory F. Numerical Simulations of Disk Dynamos G. Diversity in Galactic Magnetic Fields H. Variations on the Dynamo Theme 1. Parker Instability 2. Magnetorotational Instability 3. Cross-Helicity Dynamo I. Dynamos in Irregular and Elliptical Galaxies and Galaxy Clusters 1. Elliptical Galaxies 2. Clusters V. Seed Fields 2 3 3 6 6 7 7 8 9 10 10 10 11 12 14 15 15 16 17 18 18 19 22 22 23 24 25 25 27 29 32 32 34 36 37 37 38 38 39 40 40 412A. Minimum Seed Field for the Galactic Dynamo B. Astrophysical Mechanisms 1. Seed Fields from Radiation-Era Vorticity 2. Biermann Battery E ect 3. Galactic Magnetic Fields from Stars 4. Active Galactic Nuclei C. Seed Fields from Early Universe Physics 1. Post-in ation Scenario

s 2. In ation-Produced Magnetic Fields VI. Summary and Conclusions Acknowledgments References 41 43 44 45 47 48 49 50 52 53 54 55I. INTRODUCTIONThe origin of galactic and extragalactic magnetic elds is one of the most fascinating and challenging problems in modern astrophysics. Magnetic elds are detected in galaxies of all types and in galaxy clusters whenever the appropriate observations are made. In addition there is mounting evidence that they exist in galaxies at cosmological redshifts. It is generally assumed that the large-scale magnetic elds observed in disk galaxies are ampli ed and maintained by an αω-dynamo wherein new eld is regenerated continuously by the combined action of di erential rotation and helical turbulence. By contrast, the magnetic elds in non-rotating or slowly rotating systems such as elliptical galaxies and clusters appear to have a characteristic coherence scale much smaller than the size of the system itself. These elds may be generated by a local, turbulent dynamo where, in the absence of rapid rotation, the eld does not organize on large scales. In and of itself, the dynamo paradigm must be considered incomplete since it does not explain the origin of the initial elds that act as seeds for subsequent dynamo action. Moreover, the timescale for eld ampli cation in the standard αω-dynamo may be too long to explain the elds observed in very young galaxies. It is doubtful that magnetic elds have ever played a primary role in shaping the large-scale properties of galaxies and clusters. In present-day spirals, for example, the energy in the magnetic eld is small as compared to the rotation energy in the disk. To be sure, magnetic elds are an important component of the interstellar medium (ISM) having an energy density that is comparable to the energy density in cosmic rays and in the turbulent motions of the interstellar gas. In addition, magnetic elds can remove angular momentum from protostellar clouds allowing star formation to proceed. Thus, magnetic elds can play a supporting role in the formation and evolution of galaxies and clusters but are probably not essential to our understanding of large-scale structure in the Universe. The converse is not true: An understanding of structure formation is paramount to the problem of galactic and extragalactic magnetic elds. Magnetic elds can be created in active galactic nuclei (AGN), in the rst generation of stars, in the shocks that arise during the collapse of protogalaxies, and in the early Universe. In each case, one must understand how the elds evolve during the epoch of structure formation to see if they are suitable as seeds for dynamo action. For example, magnetic elds will be ampli ed during structure formation by the stretching and compression of eld lines that occur during the gravitational collapse of protogalactic gas clouds. In spiral galaxies, for example, these processes occur prio

r to disk formation and can amplify a primordial seed eld by several orders of magnitude. In principle, one should be able to follow the evolution of magnetic elds from their creation as seed elds through to the dynamo phase characteristic of mature galaxies. Until recently, theories of structure formation did not possess the sophistication necessary for such a program. Rather, it had been common practice to treat dynamo action and the creation of seed elds as distinct aspects of a single problem. Recent advances in observational and theoretical cosmology have greatly improved our understanding of structure formation. Ultra-deep observations, for example, have provided snapshots of disk galaxies in an embryonic state while numerical simulations have enabled researchers to follow an inpidual galaxy from linear perturbation to a fully-evolved disk-halo system. With these advances, a more complete understanding of astrophysical magnetic elds may soon be possible. This review brings together observational and theoretical results from the study of galactic and extragalactic magnetic elds, the pieces of a puzzle, if you like, which, once fully assembled, will provide a coherent picture of cosmic magnetic elds. An outline of the review is as follows: In Section II we summarize useful results from magnetohydrodynamics and cosmology. Observations of galactic and extragalactic magnetic elds are described in Section III. We begin with a review of four common methods used to detect magnetic elds; syncrotron emission, Faraday rotation, Zeeman splitting, and optical polarization of starlight (Section III.A). The magnetic elds in spiral galaxies, ellipticals, and galaxy clusters are reviewed in Sections III.B-III.D while observations of magnetic elds3 in objects at cosmological redshifts are described in Section III.E. The latter are essential to our understanding of the origin of galactic elds since they constrain the time available for dynamo action. Section III concludes with a discussion of observational limits on the properties of cosmological magnetic elds. Magnetic dynamos are discussed in Section IV. We rst review the primordial eld hypothesis wherein large scale magnetic elds, created in an epoch prior to galaxy formation, are swept up by the material that forms the galaxy and ampli ed by di erential rotation. The model has serious aws but is nevertheless instructive for the discussion that follows. Mean- eld dynamo theory is reviewed in Section IV.B. The equations for a disk dynamo are presented in Section IV.C and a simple estimate for the ampli cation rate in galaxies is given in Section IV.D. The standard mean- eld treatment fails to take into account backreaction of small-scale magnetic elds on the turbulent motions of the uid. Backreaction is a potentially fatal problem for the dynamo hypothesis for if magnetic elds inhibit turbulence, the dynamo will shut down. These issu

es are discussed in Section IV.E. Galactic magnetic elds, like galaxies themselves, display a remarkable variety of structure and thus an understanding of galactic dynamos has required full three-dimensional simulations. Techniques for performing numerical simulations are reviewed in Section IV.F and their application to the problem of persity in galactic magnetic elds is discussed in Section IV.G. In Section IV.H we turn to alternatives to the αω-dynamo. These models were constructed to address various di culties with the standard scenario. Section IV ends with a brief discussion of the generation of magnetic elds in elliptical galaxies and galaxy clusters. The question of seed elds has prompted a perse and imaginative array of proposals. The requirements for seed elds are derived in Section V.A. Section V.B describes astrophysical candidates for seed elds while more speculative mechanisms that operate in the exotic environment of the early Universe are discussed in Section V.C. The literature on galactic and extragalactic magnetic elds is extensive. Reviews include the excellent text by Ruzmaikin, Sokolo , & Shukurov (1988a) as well as articles by Rees (1987), Kronberg (1994), and Zweibel & Heiles (1997). The reader interested in magnetohydrodynamics and dynamo theory is referred to the classic texts by Mo att (1978), Parker (1979), and Krause & R¨dler (1980) as well as “The Almighty Chance” by Zel’dovich, Ruzmaikin, a & Sokolo (1990). A survey of observational results from the Galaxy to cosmological scales can be found in Vall´e e (1997). The structure of galactic magnetic elds and galactic dynamo models are discussed in Sofue, Fujimoto & Wielebinski (1986), Krause & Wielebinski (1991), Beck et al. (1996), and Beck (2000) as well as the review articles and texts cited above.II. PRELIMINARIES A. Magnetohydrodynamics and Plasma PhysicsMagnetohydrodynamics (MHD) and plasma physics describe the interaction between electromagnetic elds and conducting uids (see, for example, Jackson 1975; Mo att 1978; Parker 1979; Freidberg 1987; Sturrock 1994). MHD is an approximation that holds when charge separation e ects are negligible. Matter is described as a single conducting uid characterized by a density eld ρ(x, t), velocity eld V(x, t), pressure p(x, t), and current density J(x, t). The simple form of Ohm’s law is valid while the displacement current in Amp`re’s Law is ignored. In Gaussian units, the e relevant Maxwell equations take the form ·B=0 1 B =0 c t 4π J c (1) ×E+(2) ×B= and Ohm’s law is given by(3)J′ = σE′(4)where σ is the conductivity and “primed” quantities refer to the rest frame of the uid. Most astrophysical uids are electrically neutral and nonrelativistic so that J′ = J and E′ = E + (V × B) /c. Eq. (4) becomes4J=σ E+V×B c(5)which, when combined with Eqs. (2) and (3), yields the ideal MHD equation:

B = × (V × B) + η 2 B . t In deriving this equation, the molecular di usion coe cient, η ≡ c2 /4πσ, is assumed to be constant in space. In the limit of in nite conductivity, magnetic di usion is ignored and the MHD equation becomes B = × (V × B) t or equivalently dB = (B · ) V B ( · V) dt (8) (7) (6)where d/dt = / t + V · is the convective derivative. The interpretation of this equation is that the ux through any loop moving with the uid is constant (see, for example, Jackson 1975; Mo att 1978; Parker 1979), i.e., magnetic eld lines are frozen into the uid. Using index notation we have Vj Vi dBi Bi = Bj dt xj xj 1 Vk Vi δij = Bj xj 3 xk 2 Vj Bi 3 xj(9)where a sum over repeated indices is implied. This equation, together with the continuity equation dρ = ρ · V , dt gives 2 Bi dρ dBi = + Bj σij dt 3 ρ dt (11) (10)1 where σij = j Vi 3 δij k Vk (see, for example, Gnedin, Ferrara, & Zweibel 2000). The appearance of convective derivatives in Eq. (11) suggests a Lagrangian description in which the eld strength and uid density are calculated along the orbits of the uid elements. The rst term on the right-hand side of Eq. (11) describes the adiabatic compression or expansion of magnetic eld that occurs when ·V = 0. Consider, for example, a region of uniform density ρ and volume V that is undergoing homogeneous collapse or expansion so that σij = 0 and · V = C where C = C(t) is a function of time but not position. Eq. (11) implies that B ∝ ρ2/3 ∝ V 2/3 . Thus, magnetic elds in a system that is undergoing gravitational collapse are ampli ed while cosmological elds in an expanding universe are diluted. The second term in Eq. (11) describes the stretching of magnetic eld lines that occurs in ows with shear and vorticity. As an illustrative example, consider an initial magnetic eld B = B0 x subject to a velocity eld with Vy / x = constant. Over a time t, B developes a component in the y-direction and its strength increases by a factor1 + (t Vy / x) . Combining Eq. (8) and (10) yields the following alternative form for the MHD equation: d dt B ρ B · V . ρ21/2=(12)5 The formal solution of this equation is Bj (ξ, 0) xi Bi (x, t) = ρ (x, t) ρ (ξ, 0) ξj where ξ is the Lagrangian coordinate for the uid:t(13)xi (t) = ξi +0Vi (s)ds .(14)It follows that if a “material curve” coincides with a magnetic eld line at some initial time then, in the limit η = 0, it will coincide with the same eld line for all subsequent times. Thus, the evolution of a magnetic eld line can be determined by following the motion of a material curve (in practice, traced out by test particles) as it is carried along by the uid. The equation of motion for the uid is given by V 1 1 + (V · ) V = p

Φ + (J × B) + ν 2 V t ρ cρ(15)where ν is the viscosity coe cient and Φ the gravitational potential. In many situations, the elds are weak and the Lorentz term in Eq. (15) can be ignored. This is the kinematic regime. In the limit that the pressure term is also negligible, the vorticity ζ ≡ × V obeys an equation that is similar, in form, to Eq. (6): ζ = × (V × ζ) + ν 2 ζ . t Moreover, if viscosity is negligible, then ζ satis es the Cauchy equation (Mo att 1978): ζj (ξ, 0) xi ζi (x, t) . = ρ (x, t) ρ (ξ, 0) ξj (16)(17)However, Eq. (17) is not a solution of the vorticity equation so much as a restatement of Eq. (16) since x/ ξ is determined from the velocity eld which, in turn, depends on x. By contrast, in the kinematic regime and in the absence of magnetic di usion, Eq. (13) provides an explicit solution of Eq. (11). The magnetic energy density associated with a eld of strength B is B = B 2 /8π. For reference, we note that the energy density of a 1 G eld is 0.040 erg cm 3 . A magnetic eld that is in equipartition with a uid of density ρ 1/2 and rms velocity v has a eld strength B Beq ≡ 4πρv 2 . In a uid in which magnetic and kinetic energies are comparable, hydromagnetic waves propagate at speeds close to the so-called Alfv´n speed, vA ≡ B 2 /4πρ e . It is often useful to isolate the contribution to the magnetic eld associated with a particular length scale L. Following Rees & Reinhardt (1972) we write B2 8π B(L)2 dL 8π L1/2=V(18)where B 2 /8π is the magnetic eld energy density averaged over some large volume V. B(L) is roughly the 1/2 component of the eld with characteristic scale between L and 2L. Formally, B(L) = k 3 /2π 2 V Bk where 3 Bk ≡ d x exp (ik · x)B(x) is the Fourier component of B associated with the wavenumber k = 2π/L. In the MHD limit, magnetic elds are distorted and ampli ed (or diluted) but no net ux is created. A corollary of this statement is that if at any time B is zero everywhere, it must be zero at all times. This conclusion follows directly from the assumption that charge separation e ects are negligible. When this assumption breaks down, currents driven by non-electromagnetic forces can create magnetic elds even if B is initially zero.6B. CosmologyOccasionally, we will make reference to speci c cosmological models. A common assumption of these models is that on large scales, the Universe is approximately homogeneous and isotropic. Spacetime can then be described by the Robertson-Walker metric: ds2 = c2 dt2 a2 (t)dr2 (19)where a(t) is the scale factor and dr is the three-dimensional line element which encodes the spatial curvature of the model ( at, open, or closed). For convenience, we set a(t0 ) = 1 where t0 is the present age of the Universe. The evolution of a is described by the Friedmann equation (see, for example, Kolb & Turner 1990) 1 da a dt

k 8πG ( r + m + Λ ) 2 = 3 a2H(t)2 =(20)where r , m , and Λ are the energy densities in relativistic particles, nonrelativistic particles, and vacuum energy respectively, k = 0, ±1 parametrizes the spatial curvature, and H is the Hubble parameter. Eq. (20) can be recast as 1 da = H0 a dt r m (1 r m Λ ) + 3 + Λ + a4 a a21/2(21)where H0 ≡ H(t0 ) is the Hubble constant and is the present-day energy density in units of the critical density c ≡ 3H 2 /8πG, i.e., m ≡ m / c , etc.. Recent measurements of the angular anisotropy spectrum of the CMB indicate that the Universe is spatially at or very nearly so (Balbi et al. 2000; Melchiorvi et al. 2000; Pryke et al. 2001). If these results are combined with dynamical estimates of the density of clustering matter (i.e., dark matter plus baryonic matter) and with data on Type Ia supernova, a picture emerges of a universe with zero spatial curvature, m 0.15 0.4, and Λ = 1 m (see, for example, Bahcall et al. 1999). In addition, the Hubble constant has now been determined to an accuracy of ～ 10%: The published value from the Hubble Space Telescope Key Project is 71 ± 6 km s 1 Mpc 1 (Mould, et al. 2000).III. OBSERVATIONS OF COSMIC MAGNETIC FIELDSObservations of galactic and extragalactic magnetic elds can be summarized as follows: Magnetic elds with strength ～ 10µG are found in spiral galaxies whenever the pertinent observations are made. These elds invariably include a large-scale component whose coherence length is comparable to the size of the visible disk. There are also small-scale tangled elds with energy densities approximately equal to that of the coherent component. The magnetic eld of a spiral galaxy often exhibits patterns or symmetries with respect to both the galaxy’s spin axis and equatorial plane. Magnetic elds are ubiquitous in elliptical galaxies, though in contrast with the elds found in spirals, they appear to be random with a coherence length much smaller than the galactic scale. Magnetic elds have also been observed in barred and irregular galaxies. Microgauss magnetic elds have been observed in the intracluster medium of a number of rich clusters. The coherence length of these elds is comparable to the scale of the cluster galaxies. There is compelling evidence for galactic-scale magnetic elds in a redshift z 0.4 spiral. In addition, microgauss elds have been detected in radio galaxies at z > 2. Magnetic elds may also exist in damped Lyα systems at ～ cosmological redshifts.7 There are no detections of purely cosmological elds (i.e., elds not associated with gravitationally bound or collapsing structures). Constraints on cosmological magnetic elds have been derived by considering their e ect on big bang nucleosynthesis, the cosmic microwave background, and polarized radiation from extragalact

ic sources. These points will be discussed in detail. Before doing so, we describe the four most common methods used to study astrophysical magnetic elds. A more thorough discussion of observational techniques can be found in various references including Ruzmaikin, Shukurov, and Sokolo (1988a).A. Observational Methods 1. Synchrotron EmissionSynchroton emission, the radiation produced by relativistic electrons spiralling along magnetic eld lines, is used to study magnetic elds in astrophysical sources ranging from pulsars to superclusters. The total synchrotron emission from a source provides one of the two primary estimates for the strength of magnetic elds in galaxies and clusters while the degree of polarization is an important indicator of the eld’s uniformity and structure. For a single electron in a magnetic eld B, the emissivity as a function of frequency ν and electron energy E is ν νc1/3J(ν, E) ∝ B⊥fν νc2(22)where B⊥ is the component of the magnetic eld perpendicular to the line of sight, νc ≡ νL E/mc2 is the so-called critical frequency, νL = (eB⊥ /2πmc) is the Larmor frequency, and f (x) is a cut-o function which approaches unity for x → 0 and vanishes rapidly for x 1. The total synchrotron emission from a given source depends on the energy distribution of electrons, ne (E). A commonly used class of models is based on a power-law distribution E E0 γne (E)dE = ne0dE(23)assumed to be valid over some range in energy. The exponent γ is called the spectral index while the constant ne0 ≡ ne (E0 ) sets the normalization of the distribution. A spectral index γ 2.6 3.0 is typical for spiral galaxies. The synchrotron emissivity is jν ≡ J(ν, E)ne (E)dE. Eq. (22) shows that synchrotron emission at frequency ν is 1/2 dominated by electrons with energy E me c2 (ν/νL ) , i.e., ν νc , so that to a good approximation, we can write J(ν, E) ∝ B⊥ νc δ (ν νc ). For the power-law distribution Eq. (23) we nd jν ∝ ne0 ν (1 γ)/2 B⊥(1+γ)/2.(24)Alternatively, we can write the distribution of electrons as a function of νc : n(νc ) ≡ ne (E)dE/dνc ∝ jνc /νc B⊥ . (See Leahy 1991 for a more detailed discussion). The energy density in relativistic electrons is re = n(E)EdE. Thus, the synchrotron emission spectrum can be related to the energy density in relativistic electrons re and the strength of the magnetic eld (Burbidge 1956; Pacholczyk 1970; Leahy 1991). It is standard practice to write the total kinetic energy in particles as k = (1 + k) re where k ～ 100 is a constant (see, for example, Ginzberg & Syrovatskii 1964; Cesarsky 1980). The total energy (kinetic plus eld) is therefore tot = (1 + k) re + B . One can estimate the magnetic eld strength either by assuming equipartition ((1 + k) re = B ) or by minimizing tot with respect to B. The standard calculation of re uses a xed i

ntegration interval in frequency, νL ≤ ν ≤ νU :νU re =νLEn(νc )dνc ∝ B 3/2 Θ2 Sν (ν0 )(25)where Sν is the total ux density, Θ is the angular size of the source, and ν0 is a characteristic frequency between νL and νU . Assuming either equipartition or minimum energy, this expression leads to an estimate for B of the form8 Beq ∝ Sν Θ 4/7 . However Beck et al. (1996) and Beck (2000) pointed out that a xed frequency range corresponds to di erent ranges in energy for di erent values of the magnetic eld (see also Leahy (1991) and references therein). From (γ+1)/2 Eq. (24) we have ne0 ∝ j(ν)ν (γ 1)/2 B⊥ . Integrating over a xed energy interval gives re ∝ Θ2 Sν B (γ+1)/2 2/(γ+5) 4/(γ+5) which leads to a minimum energy estimate for B of the form Beq ∝ Sν Θ . Interactions between cosmic rays, supernova shock fronts, and magnetic elds can redistribute energy and therefore, at some level, the minimum energy condition will be violated. For this reason, the equipartition/minimum energy method for estimating the magnetic eld strength is under continous debate. Duric (1990) argued that discrepancies of more than a factor of 10 between the derived and true values for the magnetic eld require rather extreme conditions. Essentially, B/Beq sets the scale for the thickness of radio synchrotron halos. A eld as small as 0.1Beq requires higher particle energies to explain the synchrotron emission data. However, high energies imply large propagation lengths and hence an extended radio halo (scale height ～ 30 kpc) in con ict with observations of typical spiral galaxies. Conversely, a eld as large as 10Beq would con ne particles to a thin disk (～ 300 pc) again in con ict with observations. In the Galaxy, the validity of the equipartition assumption can be tested because we have direct measurements of the local cosmic-ray electron energy density and independent estimates of the local cosmic-ray proton density from di use continuum γ-rays. A combination of the radio synchrotron emission measurements with these results yields a eld strength in excellent agreement with the results of equipartition arguments (Beck 2002). While synchroton radiation from a single electron is elliptically polarized, the emission from an ensemble of electrons is only partially polarized. The polarization degree p is de ned as the ratio of the intensity of linearly polarized radiation to the total intensity. For a regular magnetic eld and power-law electron distribution (Eq. (23)) p is xed by the spectral index γ. In particular, if the source is optically thin with respect to synchrotron emission (a good assumption for galaxies and clusters), γ+1 γ + 7/32/7p = pH ≡(26)(Ginzburg & Syrovatskii 1964; Ruzmaikin, Shukurov, & Sokolo 1988a). For values of γ appropriate to spiral galaxies, this implies a polarization degree in the range p = 0.72 0.74. The obs

erved values — p = 0.1 0.2 for the typical spiral — are much smaller. There are various e ects which can lead to the depolarization of the synchrotron emission observed in spiral galaxies. These e ects include the presence of a uctuating component to the magnetic eld, inhomogeneities in the magneto-ionic medium and relativistic electron density, Faraday depolarization (see below) and beam-smearing (see, for example, Sokolo et al. 1998). Heuristic arguments by Burn (1966) suggest that for the rst of these e ects, the polarization degree is reduced by a factor equal to the ratio of the energy density of the regular eld B to the energy density of the total eld: B p = pH 2 . B2(27)(This expression is useful only in a statistical sense since one does not know a priori the direction of the regular eld.) Thus, perhaps only ～ 25% of the total magnetic eld energy in a typical spiral is associated with the large-scale component. Of course, the ratio B/B would be higher if other depolarization e ects were important.2. Faraday rotationElectromagnetic waves, propagating through a region of both magnetic eld and free electrons, experience Faraday rotation wherein left and right-circular polarization states travel with di erent phase velocities. For linearly polarized radiation, this results in a rotation with time (or equivalently path length) of the electric eld vector by an angle e3 λ2 2πm2 c4 els =ne (l)B (l)dl + 00(28)where me is the mass of the electron, λ is the wavelength of the radiation, 0 is the initial polarization angle, and B is the line-of-sight component of the magnetic eld. Here, ne (l) is the density of thermal electrons along the line of sight from the source (l = ls ) to the observer (l = 0). is usually written in terms of the rotation measure, RM:9 = (RM ) λ2 + 0 where e3 2πm2 c4 e rad m2ls(29)RM ≡ne (l)B (l)dl0 ls 0 810ne cm 3B µGdl kpc(30)In general, the polarization angle must be measured at three or more wavelengths in order to determine RM accurately and remove the ≡ ± nπ degeneracy. By convention, RM is positive (negative) for a magnetic eld directed toward (away from) the observer. The Faraday rotation angle includes contributions from all magnetized regions along the line of sight to the source. Following Kronberg & Perry (1982) we decompose RM into three basic components: RM = RMg + RMs + RMig (31)where RMg , RMs , and RMig are respectively the contributions to the rotation measure due to the Galaxy, the source itself, and the intergalactic medium. Faraday rotation from an extended source leads to a decrease in the polarization: The combined signal from waves originating in di erent regions of the source will experience di erent amounts of Faraday rotation thus leading to a spread in polarization directions. Faraday depolarization can, in fact, be a useful measure of magnetic eld in the fore

ground of a source of polarized synchrotron emission.3. Zeeman SplittingIn vacuum, the electronic energy levels of an atom are independent of the direction of its angular momentum vector. A magnetic eld lifts this degeneracy by picking out a particular direction in space. If the total angular momentum of an atom is J (= spin S plus orbital angular momentum L) there will be 2j + 1 levels where j is the quantum number associated with J. The splitting between neighboring levels is E = gµB where g is the Lande factor which relates the angular momentum of an atom to its magnetic moment and µ = e¯ /2me c = 9.3 × 10 21 erg G 1 is the h Bohr magneton. This e ect, known as Zeeman splitting, is of historical importance as it was used by Hale (1908) to discover magnetic elds in sunspots, providing the rst known example of extraterrestrial magnetic elds. Zeeman splitting provides the most direct method available for observing astrophysical magnetic elds. Once E is measured, B can be determined without additional assumptions. Moreover, Zeeman splitting is sensitive to the regular magnetic eld at the source. By contrast, synchrotron emission and Faraday rotation probe the line-of-sight magnetic eld. Unfortunately, the Zeeman e ect is extremely di cult to observe. The line shift associated with the energy splitting is ν = 1.4g ν B µG Hz ν.(32)For the two most common spectral lines in Zeeman-e ect observations — the 21 cm line for neutral hydrogen and the 18 cm OH line for molecular clouds — ν/ν 10 9 g (B/µG). A shift of this amplitude is to be compared with Doppler broadening, ν/ν vT /c 6 × 10 7 (T /100 K)1/2 where vT and T are the mean thermal velocity and temperature of the atoms respectively. Therefore Zeeman splitting is more aptly described as abnormal broadening, i.e., a change in shape of a thermally broadened line. Positive detections have been restricted to regions of low temperature and high magnetic eld. Within the Galaxy, Zeeman e ect measurements have provided information on the magnetic eld in star forming regions and near the Galactic center. Of particular interest are studies of Zeeman splitting in water and OH masers. Reid & Silverstein (1990), for example, used observations of 17 OH masers to map the large-scale magnetic eld of the Galaxy. Their results are consistent with those found in radio observations and, as they stress, provide in10 situ measurements of the magnetic eld as opposed to the integrated eld along the line-of-sight. Measurements of Zeeman splitting of the 21 cm line have been carried out for a variety of objects. Kaz`s, Troland, & Crutcher (1991), e for example, report positive detections in High Velocity HI clouds as well as the active galaxy NGC 1275 in the Perseus cluster. However, Verschuur (1995) has challenged these results, suggesting that the claimed detections are spurious signals, the result of confusion be

tween the main beam of the telescope and its sidelobes. Thus, at present, there are no con rmed detections of Zeeman splitting in systems beyond the Galaxy.4. Polarization of Optical StarlightPolarized light from stars can reveal the presence of large-scale magnetic elds in our Galaxy and those nearby. The rst observations of polarized starlight were made by Hiltner (1949a,b) and Hall (1949). Hiltner was attempting to observe polarized radiation produced in the atmosphere of stars by studying eclipsing binary systems. He expected to nd time-variable polarization levels of 1-2%. Instead, he found polarization levels as high as 10% for some stars but not others. While the polarization degree for inpidual stars did not show the expected time-variability, polarization levels appeared to correlate with position in the sky. This observation led to the conjecture that a new property of the interstellar medium (ISM) had been discovered. Coincidentally, it was just at this time that Alfv´n (1949) and Fermi e (1949) were proposing the existence of a galactic magnetic eld as a means of con ning cosmic rays (See Trimble 1990 for a further discussion of the early history of this subject). A connection between polarized starlight and a galactic magnetic eld was made by Davis and Greenstein (1951) who suggested that elongated dust grains would have a preferred orientation in a magnetic eld: for prolate grains, one of the short axes would coincide with the direction of the magnetic eld. The grains, in turn, preferentially absorb light polarized along the long axis of the grain, i.e., perpendicular to the eld. The net result is that the transmitted radiation has a polarization direction parallel to the magnetic eld. Polarization of optical starlight has limited value as a probe of extragalactic magnetic elds for three reasons. First, there is at least one other e ect that can lead to polarization of starlight, namely anisotropic scattering in the ISM. Second, the starlight polarization e ect is self-obscuring since it depends on extinction. There is approximately one magnitude of visual extinction for each 3% of polarization (see, for example, Scarrott, Ward-Thompson, & WarrenSmith 1987). In other words, a 10% polarization e ect must go hand in hand with a factor of 20 reduction in luminosity. Finally, the precise mechanism by which dust grains are oriented in a magnetic eld is not well understood (see, for example, the review by Lazarian, Goodman, & Myers 1997). Polarized starlight does provide information that is complementary to what can be obtained from radio observations. The classic polarization study by Mathewson & Ford (1970) of 1800 stars in the Galaxy provides a vivid picture of a eld that is primarily in the Galactic plane, but with several prominent features rising above and below the plane. In addition, there are examples of galaxies where a spiral pattern of polarized optical radiation has been obs

erved including NGC 6946 (Fendt, Beck, & Neininger 1998), M51 (Scarrott, Ward-Thompson, & Warren-Smith 1987), and NGC 1068 (Scarrott et al. 1991). The optical polarization map of M51, for example, suggests that its magnetic eld takes the form of an open spiral which extends from within 200 pc of the galactic center out to at least 5 kpc. Radio polarization data also indicates a spiral structure for the magnetic eld for this galaxy providing information on the magnetic con guration from 3 kpc to 15 kpc (Berkhuijsen et al. 1997). Nevertheless, it is sometimes di cult to reconcile the optical and radio data. Over much of the M51 disk, the data indicates that the same magnetic eld gives rise to radio synchrotron emission and to the alignment of dust grains (Davis-Greenstein mechanism). However in one quadrant of the galaxy, the direction of the derived eld lines di er by ～ 60 suggesting that either the magnetic elds responsible for the radio and optical polarization reside in di erent layers of the ISM or that the optical polarization is produced by a mechanism other than the alignment of dust grains by the magnetic eld.B. Spiral GalaxiesSpiral galaxies are a favorite laboratory for the study of cosmic magnetic elds. There now exist estimates for the magnetic eld strength in well over 100 spirals and, for a sizable subset of those galaxies, detailed studies of their magnetic structure and morphology.1. Field StrengthThe magnetic eld of the Galaxy has been studied through synchrotron emission, Faraday rotation, optical polarization, and Zeeman splitting. The latter provides a direct determination of the in situ magnetic eld at speci c sites in the Galaxy. Measurements of the 21-cm Zeeman e ect in Galactic HI regions reveal regular magnetic elds11 with B 2 10 µG, the higher values being found in dark clouds and HI shells (Heiles 1990 and references therein). Similar values for the Galactic eld have been obtained from Faraday rotation surveys of galactic and extragalactic sources (i.e., estimates of RMg ). Manchester (1974) has compiled RM data for 38 nearby pulsars and was able to extract the Galactic contribution. He concluded that the coherent component of the local magnetic eld is primarily toroidal with a strength B 2.2 ± 0.4 µG. Subsequent RM studies con rmed this result and provided information on the global structure of the Galactic magnetic eld (see for example Rand & Lyne 1994 and also Frick, Stepanov, Shukurov, & Sokolo (2001) who describe a new method for analysing RM data based on wavelets). Early estimates of the strength of the magnetic eld from synchrotron data were derived by Phillipps et al. (1981). Their analysis was based on a model for Galactic synchrotron emission in which the magnetic eld in the Galaxy is decomposed into regular and tangled components. An excellent t to the data was obtained when each component was assumed to have a va

lue of 3 µG. More recent estimates give ～ 4µG for the regular and ～ 6µG for the total local eld strength (Beck 2002). Magnetic elds in other galaxies are studied primarily through synchrotron and Faraday rotation observations. An interesting case is provided by M31. Polarized radio emission in this galaxy is con ned to a prominent ring ～ 10 kpc from the galaxy’s center. The equipartition eld strength in the ring is found to be ～ 4 µG for both regular and random components. Fitt & Alexander (1993) applied the minimum energy method to a sample of 146 late-type galaxies. The distribution of eld strengths across the sample was found to be relatively narrow with an average value of Beq 11 ± 4 µG (using k = 100), in agreement with earlier work by Hummel et al. (1988). The magnetic eld strength does not appear to depend strongly on galaxy type although early-type galaxies have a slightly higher mean. A few galaxies have anomalously strong magnetic elds. A favorite example is M82 where the eld strength, derived from radio continuum observations, is 50 µG (Klein, Wielebinski, & Morsi 1988). This galaxy is characterized by an extraordinarily high star formation rate.2. Global Structure of the Magnetic Field in SpiralsAnalysis of RM data as well as polarization maps of synchrotron emission can be used to determine the structure of magnetic elds in galaxies. It is common practice to classify the magnetic eld con gurations in disk galaxies according to their symmetry properties under rotations about the spin axis of the galaxy. The simplest examples are the axisymmetric and bisymmetric spiral patterns shown in Figure 1. In principle, an RM map can distinguish between the di erent possibilities (Tosa & Fujimoto 1978; Sofue, Fujimoto, & Wielebinski 1986). For example, one can plot RM as a function of the azimuthal angle φ at xed physical distance from the galactic center. The result will be a single (double) periodic distribution for a pure axisymmetric (bisymmetric) eld con guration. The RM-φ method has a number of weaknesses as outlined in Ruzmaikin, Sokolo , Shukurov, & Beck (1990) and Sokolo , Shukurov, & Krause (1992). In particular, the method has di culty disentangling a magnetic eld con guration that consists of a superposition of di erent modes. In addition, determination of the RM is plagued by the “nπ degeneracy” and therefore observations at a number of wavelengths is required. An alternative is to consider the polarization angle ψ as a function of φ. and model ψ(φ) as a Fourier series: ψ(φ) = n an cos (nφ) + bn sin (nφ). The coe cients an and bn then provide a picture of the azimuthal structure of the eld. Of course, if an estimate of the eld strength is desired, multiwavelength observations are again required (Ruzmaikin, Sokolo , Shukurov, & Beck 1990; Sokolo , Shukurov, & Krause 1992). In M31, both RM (φ) and ψ(φ) methods suggest strong

ly that the regular magnetic eld in the outer parts of the galaxy (outside the synchroton emission ring) is described well by an axisymmetric eld. Inside the ring, the eld is more complicated and appears to have a signi cant admixture of either m = 1 or m = 2 modes (Ruzmaikin, Sokolo , Shukurov, & Beck 1990). These higher harmonics may be an indication that the dynamo is modulated by the two-arm spiral structure observed in this region of the galaxy. The polarized synchrotron emissivity along the ring may provide a further clue as to the structure of the magnetic eld. The emissivity is highly asymmetric — in general much stronger along the minor axis of the galaxy. Urbanik, Otmianowska-Mazur, & Beck (1994) suggested that this pattern in emission are better explained by a superposition of helical ux tubes that wind along the axis of the ring rather than a pure azimuthal eld. (For a further discussion of helical ux tubes in the context of the αω-dynamo see Donner & Brandenburg 1990). Field con gurations in disk galaxies can also be classi ed according to their symmetry properties with respect to re ections about the central plane of the galaxy. Symmetric, or even parity eld con gurations are labeled Sm where, as before, m is the azimuthal mode number. Antisymmetric or odd parity solutions are labelled Am. Thus as S0 eld con guration is axisymmetric (about the spin axis) and symmetric about the equatorial plane. An A0 con guration is also axisymmetric but is antisymmetric with respect to the equatorial plane. As shown in Figure 2, the poloidal component of a symmetric (antisymmetric) eld con guration has a quadruple (dipole) structure.12FIG. 1 Axisymmetric and bisymmetric eld con gurations for disk systems along with the corresponding RM vs. φ plots. Top panels show toroidal eld lines near the equatorial plane. Lower panels show RM as a function of azimuthal angle φ for observations at the circle (dotted line) in the corresponding top panel. Note that the pitch angle has the opposite sign for the two cases shown.The parity of a eld con guration in a spiral galaxy is extremely di cult to determine. Indeed, evidence in favor of one or the other type of symmetry has been weak at best and generally inconclusive (Krause & Beck 1998). One carefully studied galaxy is the Milky Way where the magnetic eld has been mapped from the RMs of galactic and extragalactic radio sources. An analysis by Han, Manchester, Berkhuijsen, & Beck (1997) of over 500 extragalactic objects suggests that the eld con guration in the inner regions of the Galaxy is antisymmetric about its midplane. On the other hand the analysis by Frick et al. (2001) indicates that the eld in the solar neighborhood is symmetric. Evidently, the parity of the eld con guration can change from one part of a galaxy to another. A second well-studied case is M31 where an analysis of the RM across its disk suggests

that the magnetic eld is symmetric about the equatorial plane, i.e., an even-parity axisymmetric (S0) con guration (Han, Beck, & Berkhuijsen 1998). Among S0-type galaxies, there is an additional question as to the direction of the magnetic eld, namely whether the eld is oriented inward toward the center of the galaxy or outward (Krause & Beck 1998). The two possibilities can be distinguished by comparing the sign of the RM (as a function of position on the disk) with velocity eld data. Krause & Beck (1998) point out that in four of ve galaxies where the eld is believed to be axisymmetric, those elds appear to be directed inward. This result is somewhat surprising given that a magnetic dynamo shows no preference for one type of orientation over the other. It would be premature to draw conclusions based on such a small sample. Nevertheless, if, as new data becomes available, a preference is found for inward over outward directed elds (or more realistically, a preference for galaxies that are in the same region of space to have the same orientation), it would reveal a preference in initial conditions and therefore speak directly to the question of seed elds.3. Connection with Spiral StructureOften, the spiral magnetic structures detected in disk galaxies appear to be closely associated with the material spiral arms. A possible connection between magnetic and optical spiral structure was rst noticed in observations of M83 (Sukumar & Allen 1989), IC 342 and M81 (Krause, Hummel, & Beck 1989a, 1989b). A particularly striking example of magnetic spiral structure is found in the galaxy NGC 6946, as shown in Figure 3 (Beck & Hoernes 1995; Frick et al. 2000). In each case, the map of linearly polarized synchrotron emission shows clear evidence for spiral magnetic structures across the galactic disk. The magnetic eld in IC 342 appears to be an inwardly-directed axisymmetric spiral while the eld in M81 is more suggestive of a bisymmetric con guration (Sofue, Takano, &13FIG. 2 Field lines for even (top panel) and odd (bottom panel) con gurations. Shown are cross-sections perpendicular to the equatorial plane and containing the symmetry axis of the galaxy (i.e., poloidal planes). The toroidal eld is indicated by an ‘x’ ( eld out of the page) or ‘dot’ ( eld into the page).Fujimoto 1980; Krause, Hummel, & Beck 1989a, 1989b; Krause 1990). In many cases, magnetic spiral arms are strongest in the regions between the optical spiral arms but otherwise share the properties (e.g., pitch angle) of their optical counterparts. These observations suggest that either the dynamo is more e cient in the interarm regions or that magnetic elds are disrupted in the material arms. For example, Mestel & Subramanian (1991, 1993) proposed that the α-e ect of the standard dynamo contains a non-axisymmetric contribution whose con guration is similar to that of the material spiral arms. The justi cation comes

from one version of spiral arm theory in which the material arm generates a spiral shock in the interstellar gas. The jump in vorticity in the shock may yield an enhanced αe ect with a spiral structure. Further theoretical ideas along these lines were developed by Shukurov (1998) and a variety of numerical simulations which purport to include nonaxisymmetric turbulence have been able to reproduce the magnetic spiral structures found in disk galaxies (Rohde & Elstner 1998; Rohde, Beck, & Elstner 1999; Elstner, Otmianowska-Mazur, von Linden, & Urbanik 2000). Along somewhat di erent lines, Fan & Lou (1996) attempted to explain spiral magnetic arms in terms of both slow and fast magnetohydrodynamic waves. Recently, Beck et al. (1999) discovered magnetic elds in the barred galaxy NGC 1097. Models of barred galaxies predict that gas in the region of the bar is channeled by shocks along highly non-circular orbits. The magnetic eld in the bar region appears to be aligned with theoretical streamlines suggesting that the eld is mostly frozen into the gas ow in contrast with what is expected for a dynamo-generated eld. The implication is that a dynamo is required to generate new eld but that inside the bar simple stretching by the gas ow is the dominant process (see Moss et al. 2001).14FIG. 3 Polarized synchrotron intensity (contours) and magnetic eld orientation of NGC 6946 (obtained by rotating E-vectors by 90 ) observed at λ6.2 cm with the VLA (12.5 arcsec synthesized beam) and combined with extended emission observed with the E elsberg 100 m telescope (2.5 arcmin resolution). The lengths of the vectors are proportional to the degree of polarization. (From Beck & Hoernes 1996.)4. Halo FieldsRadio observations of magnetic elds in edge-on spiral galaxies suggest that in most cases the dominant component of the magnetic eld is parallel to the disk plane (Dumke, Krause, Wielebinski, & Klein 1995). However, for at least some galaxies, magnetic elds are found to extend well away from the disk plane and have strong vertical components. Hummel, Beck, and Dahlem (1991) mapped two such galaxies, NGC 4631 and NGC 891, in linearly polarized radio emission and found elds with strength ～ 5 and ～ 8 µG respectively with scale heights ～ 5 10 kpc. The elds in these two galaxies have rather di erent characteristics: In NGC 4631 (Figure 4), numerous prominent radio spurs are found throughout the halo. In all cases where the magnetic eld can be determined, the eld follows these spurs (Golla & Hummel 1994). (Recent observations by T¨ llmann et al. (2000) revealed similar structures in the edge-on spiral NGC u 5775.) Moreover, the large-scale structure of the eld is consistent with that of a dipole con guration (anti-symmetric about the galactic plane) as in the bottom panel of Figure 2. The eld in NGC 891 is more disorganized, that is, only ordered in small regions with no global structur

e evident. Magnetic elds are but one component of the ISM found in the halos of spiral galaxies. Gas (which exists in many di erent phases), stars, cosmic rays, and interstellar dust, are also present. Moreover, the disk and halo couple as material ows out from the disk and into the halo only to eventually fall back completing a complex circulation of matter (see, for example, Dahlem 1997). At present, it is not clear whether halo elds are the result of dynamo action in the halo or alternatively, elds produced in the disk and carried into the halo by galactic winds or magnetic buoyancy (see Section IV.G).15FIG. 4 Total radio emission and B vectors of polarized emission of NGC 4631 at λ22 cm (VLA, 70′′ synthesized beam). The B vectors have been corrected for Faraday rotation; their length is proportional to the polarized intensity (From Krause & Beck, unpublished)5. Far Infrared-Radio Continuum CorrelationAn observation that may shed light on the origin and evolution of galactic magnetic elds is the correlation between galactic far infrared (FIR) emission and radio continuum emission. This correlation was rst discussed by Dickey & Salpeter (1984) and de Jong, Klein, Wielebinski, & Wunderlich (1985). It is valid for various types of galaxies including spirals, irregulars, and cluster galaxies and has been established for over four orders of magnitude in luminosity (see Niklas & Beck (1997) and references therein). The correlation is intriguing because the FIR and radio continuum emissions are so di erent. The former is thermal and presumably related to the star formation rate (SFR). The latter is mostly nonthermal and produced by relativistic electrons in a magnetic eld. Various proposals to explain this correlation have been proposed (For a review, see Niklas & Beck (1997).) Perhaps the most appealing explanation is that both the magnetic eld strength and the star formation rate depend strongly on the volume density of cool gas (Niklas & Beck 1997). Magnetic eld lines are anchored in gas clouds (Parker 1966) and therefore a high number density of clouds implies a high density of magnetic eld lines. Likewise, there are strong arguments in favor of a correlation between gas density and the SFR of the form SFR∝ ρn (Schmidt 1959). With an index n = 1.4 ± 0.3, taken from survey data of thermal radio emission (assumed to be an indicator of the SFR), where able to provide a self-consistent picture of the FIR and radio continuum correlation.C. Elliptical and Irregular GalaxiesMagnetic elds are ubiquitous in elliptical galaxies though they are di cult to observe because of the paucity of relativistic electrons. Nevertheless, their presence is revealed through observations of synchrotron emission. In16 addition, Faraday rotation has been observed in the polarized radio emission of background objects. One example is that of a gravitationally lensed quasar where the two quasar images have rotation

measures that di er by 100 rad m 2 (Green eld, Roberts, & Burke 1985). The conjecture is that light for one of the images passes through a giant cD elliptical galaxy whose magnetic eld is responsible for the observed Faraday rotation. A more detailed review of the observational literature can be found in Moss & Shukurov (1996). These authors stress that while the evidence for microgauss elds in ellipticals is strong, there are no positive detections of polarized synchrotron emission or any other manifestation of a regular magnetic eld. Thus, while the inferred eld strengths are comparable to those found in spiral galaxies, the coherence scale for these elds is much smaller than the scale of the galaxy itself. Recently, magnetic elds were observed in the dwarf irregular galaxy NGC 4449. The mass of this galaxy is an order of magnitude lower than that of the typical spiral and shows only weak signs of global rotation. Nevertheless, the regular magnetic eld is measured to be 6 8 µ G, comparable to that found in spirals (Chyzy et al. 2000). Large domains of non-zero Faraday rotation indicate that the regular eld is coherent on the scale of the galaxy. This eld appears to be composed of two distinct components. First, there is a magnetized ring 2.2 kpc in radius in which clear evidence for a regular spiral magnetic eld is found. This structure is reminiscent of the one found in M31. Second, there are radial “fans” – coherent magnetic structures that extend outward from the central star forming region. Both of these components may be explained by dynamo action though the latter may also be due to out ows from the galactic center which can stretch magnetic eld lines.D. Galaxy ClustersGalaxy clusters are the largest non-linear systems in the Universe. X-ray observations indicate that they are lled with a tenuous hot plasma while radio emission and RM data reveal the presence of magnetic elds. Clusters are therefore an ideal laboratory to test theories for the origin of extragalactic magnetic elds (see, for example, Kim, Tribble, & Kronberg 1991; Tribble 1993). Data from the Einstein, ROSAT, Chandra, and XMM-Newton observatories provide a detailed picture of rich galaxy clusters. The intracluster medium is lled with a plasma of temperature T 107 108 K that emits X-rays with energies ～ 1 10 keV. Rich clusters appear to be in approximate hydrostatic equilibrium with virial velocities ～ 1000 km s 1 (see, for example, Sarazin 1986). In some cluster cores, the cooling time for the plasma due to the observed X-ray emission is short relative to the dynamical time. As the gas cools, it is compressed and ows inward under the combined action of gravity and the thermal pressure of the hot outer gas (Fabian, Nulsen, & Canizares 1984). These cooling ows are found in elliptical galaxies and groups as well as clusters. The primary evidence for cooling ows comes from X-ray obse

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