Annu. Rev. Astron. Astrophys. 1992. 30: 575-611 Copyright © 1992 by Annual Reviews. All rights reserved

4.2 Magnetic Fields

Estimates of the magnetic field strength B are usually derived from the assumption of minimum total energy E = (U_p + U_m) V, where U_p is the relativistic particle energy density, U_m is the magnetic energy density, and V is the source volume (Burbidge 1956). The total energy for a given synchrotron luminosity is minimized when U_m = 3 U_p / 4. This is very close to energy equipartition (U_m = U_p) and also to pressure equality (P_m = P_p) since P_m = U_m and P_p = U_p / 3 for ultrarelativistic particles. The calculated minimum-energy field B_min depends weakly on the source geometry, the nonthermal spectral index , and the frequency range containing synchrotron radiation, usually taken to be 0.01-100 GHz. It also depends on the relativistic proton/electron abundance ratio , which is ~ 40 in our galaxy (Webber 1991). For a disk with ~ 0.75

where T_b = S_N c² / (2k²) is the observed nonthermal Rayleigh-Jeans brightness temperature at frequency and l is the depth of the source along the line-of-sight. Equivalently, T_b is the face-on brightness temperature and l ~ 2 kpc (cf Beuermann et al. 1985, Hummel 1990) is a typical radio disk thickness. The median face-on brightness temperature of spiral galaxies is T_b ~ 1 K at = 1.5 GHz, so most spiral disks are characterized by field strengths in the range 5-10 µG (Sofue et al. 1986, Hummel et al. 1988a). The minimum-energy field in the central region of M82 (S_N ~ 10 Jy at = 1 GHz from a 30" x 10" region perhaps 0.5 kpc thick) is B_min ~ 100 µG, and the field strengths in the brightest compact sources associated with normal galaxies approach 1000 µG (Condon et al. 1991c). Note that the only real observable in Equation 13 is T_b (the thickness is simply inferred from the transverse dimensions of the source), so the calculated values of B_min are little more than measures of synchrotron surface brightness. Yet there are good reasons to believe that the actual magnetic field strengths in the disks of normal galaxies are close to B_min. Should B B_min occur, (P_p / P_m) = (4 / 9) (B / B_min)^-7/2 would become large, the cosmic rays would inflate a bubble and be expelled from the disk (Parker 1965); the magnetic field is a very sensitive pressure regulator for relativistic particles. The fields and particles are confined to the plane only by the weight of the interstellar medium (Parker 1966), so B B_men is also unlikely.

The large-scale magnetic field structures of spiral galaxies can be obtained from multifrequency polarization maps (see Krause 1990 and Beck 1991 for recent reviews). The intrinsic degree of linear polarization for optically thin synchrotron radiation from a power-law distribution of relativistic electrons in a vacuum is = (3 + 3) / (3 + 7). The observed degree is reduced by Faraday depolarization and by variations in the magnetic field orientation within the beam (Segalovitz et al. 1976). Disk magnetic fields are generally more uniform in areas of low star formation (the outer disk and interarm regions) and more turbulent where the star-formation rate is high (spiral arms with large H II regions or molecular clouds, and near the nucleus) (Krause et al. 1989a, Sukumar & Allen 1989, Neininger et al. 1991). The intrinsic position angle of E is perpendicular to the projection of B onto the sky. The observed position angle must be corrected for Faraday rotation, which is approximately proportional to ² multiplied by the rotation measure RM n_e B_|| dl, where B_|| is the magnetic field component parallel to the line-of-sight. High-resolution maps made at two or more short ( 20 cm) wavelengths show that large-scale disk magnetic fields of spiral galaxies normally run almost parallel to the spiral arms. The field lines may spiral inward or outward, and this 180° ambiguity can be resolved in slightly inclined galaxies because the sign of the RM changes with the sign of the B_|| projection. Axisymmetric disk fields (always pointing either inward or outward) cause the RM sign to change once every 180° of galaxy azimuth: RM sign changes every 90° indicate bisymmetric fields alternating in direction. Axisymmetric fields have been observed in M31 (Beck 1982, Beck et al. 1989) and IC 342 (Krause et al. 1989b), bisymmetric fields in M51 (Horellou et al. 1990) and M81 (Krause et al. 1989a). However, the large-scale field structure does not always fit any simple axisymmetric or bisymmetric dynamo model (Harnett et al. 1989). The unexpectedly high RM and strong Faraday depolarization found in the southwest quadrant of the NGC 6946 disk suggest a large vertical component to the disk field ­ a galactic ``coronal hole'' (Beck 1991). Systematic variations of RM across the disk of M83 also reveal a significant vertical field that complicates the determination of its large-scale disk field structure (Neininger et al. 1991). Magnetic field structure above and below the disk can be measured by multifrequency polarization maps of edge-on spiral galaxies. The dominant field direction of NGC 891 appears to be parallel to the disk (Allen & Sukumar 1991), but the field lines in the extended radio halo of NGC 4631 (Hummel et al. 1991a) point radially outward.