| Annu. Rev. Astron. Astrophys. 1992. 30:
575-611 Copyright © 1992 by . All rights reserved |
Estimates of the magnetic field strength B are usually derived from the
assumption of minimum total energy E = (Up +
Um) V, where Up is the
relativistic particle energy density, Um is the
magnetic energy density, and V is the source volume (Burbidge
1956). The total energy for a given synchrotron luminosity is minimized
when Um = 3 Up / 4. This is very
close to energy equipartition (Um =
Up) and also to pressure equality
(Pm = Pp)
since Pm = Um and
Pp = Up / 3 for ultrarelativistic
particles. The calculated minimum-energy field Bmin
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 Tb = SN c2 /
(2k
2
) is the observed nonthermal Rayleigh-Jeans brightness
temperature at frequency and
l is the depth of the source along the line-of-sight. Equivalently,
Tb 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
Tb ~ 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 (SN ~ 10 Jy at = 1 GHz from a 30" x 10" region perhaps
0.5 kpc thick) is Bmin ~ 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 Tb (the
thickness is simply inferred from the transverse dimensions of the
source), so the calculated values of Bmin 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 Bmin. Should B
Bmin
occur, (Pp / Pm) = (4 / 9)
(B / Bmin)-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 
Bmen 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 
ne
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.