Origin of Galactic and Extragalactic Magnetic Fields(2)

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

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 diversity 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 diverse 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) becomes4J=σ E+V×B c(5)which, when combined with Eqs. (2) and (3), yields the ideal MHD equation:

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

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 …… 此处隐藏：7160字，全部文档内容请下载后查看。喜欢就下载吧 ……