Origin of Galactic and Extragalactic Magnetic Fields(3)

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

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

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

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 whe …… 此处隐藏：7306字，全部文档内容请下载后查看。喜欢就下载吧 ……