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

4.3 Cosmic-Ray Sources and Transport

If the cosmic rays in our galaxy have a total energy ~ 10⁵⁵ erg and an average age ~ 2 x 10⁷ yr, their sources must accelerate cosmic rays at an average power level ~ 2 x 10⁴⁰ erg s^-1. Type II and Type Ib supernova remnants of short-lived M 8 M (Kennicutt 1984) stars are the leading accelerator candidates because they produce sufficient mechanical energy in shocks and are the strongest nonthermal sources in the Galaxy (Ginzburg & Syrovatskii 1964). Type Ia supernova remnants, arising from an older stellar population, are less important accelerators of cosmic rays in normal galaxies. It is now clear that Type Ia supernovae are much less common in late-type galaxies (van den Bergh & Tammann 1991); and many occur far from the equatorial plane of their parent galaxy, where the ambient interstellar density is lower. Type Ia SNRs might contribute to weak radio sources in galaxies with very low current star-formation rates.

But discrete supernova remnants themselves emit only a small fraction of the integrated nonthermal flux from M31 (Pooley 1969) and other nearby galaxies (Ilovaisky & Lequeux 1972, Biermann 1976). Most of the nonthermal emission is so smoothed by cosmic-ray transport that the spatial distribution of its sources cannot be deduced in detail. Lequeux (1971) found that the global spatial distributions of young stars and nonthermal continuum are correlated in the disks of galaxies, and he proposed that supernova remnants accelerate most of the cosmic rays observed throughout the disks. Van der Kruit et al. (1977) countered that the radial distribution of nonthermal continuum in NGC 6946 more closely matches the distribution of optical light produced by the older disk stellar population, which they suggested as the cosmic-ray source. Now that radio maps of many normal galaxy disks are available it is clear that the nonthermal radio scale lengths are usually greater than both the optical scale lengths of the older disk stars and the FIR scale lengths tracing very young stars (Bicay & Helou 1990). This is probably because cosmic-ray propagation expands the volume occupied by cosmic ray electrons. Therefore, radial scale lengths cannot directly be used to distinguish between younger and older stellar populations. Duric et al. (1986) observed that the nonthermal emission in NGC 3310 is locally more closely correlated with the (spiral) arms than with H II regions or other tracers of recent star formation, and Duric (1986) proposed spiral shocks as significant accelerators of cosmic rays in normal galaxies with high shock speeds. However, the gas containing cosmic rays may not be shocked (Section 4.1). Also, Giuricin et al. (1989) and Urbanik et al. (1989) found no correlation of radio brightness or the radio/blue ratio with spiral arm prominence in samples of normal galaxies. Harwit et al. (1987) suggested that violent face-on collisions between the molecular disks of galaxies accelerate the relativistic electrons in ultraluminous starbursts. Such sources would be very short lived and probably less compact than observed (Condon et al. 1991c).

The nonthermal radio luminosities of normal galaxies are correlated to different degrees with luminosities in most other wavebands, and these luminosity correlations have been used to support different stellar populations as sources of cosmic rays. Hummel (1981) once favored the old disk population because the radio and optical luminosities of normal galaxies are correlated while the disk radio brightness is not clearly correlated with (B - V) color (but see Kennicutt 1983b) or arm prominence. The radio/blue luminosity correlation is however quite broad and nonlinear (Condon 1989) since the most intense star formation is hidden behind dusty molecular clouds. Klein (1982) did find a correlation of radio brightness with optical color for blue compact galaxies and so favored a younger stellar population. Kennicutt (1983b) noted that the predominantly nonthermal 1.4 GHz flux densities of normal galaxies are correlated with their H fluxes and concluded that the relativistic electrons responsible for the nonthermal radio emission are accelerated by the population of massive (M 10 M) short-lived ionizing stars rather than by the old disk population. The X-ray luminosities of normal galaxies are better correlated with blue than with radio luminosities, so Fabbiano & Trinchieri (1985) suggested that low-mass X-ray binaries (older disk stars) accelerate most of the cosmic rays. The X-ray luminosities of starburst nuclei are also correlated with Br luminosities, a tracer of massive stars (Ward 1988). The best correlation with nonthermal radio luminosity is the one with FIR luminosity described in Section 5; it favors a very young stellar population (cf de Jong et al. 1985). Hummel et al. (1988a) stress the correlation of radio surface brightness with FIR dust color temperature as evidence for radio emission from young stars. A sophisticated five-band (radio, FIR, near infrared, blue, and X-ray) study of luminosity correlations in spirals led Fabbiano et al. (1988) to conclude that the radio emission from starbursts must originate in the young stellar population but no clear conclusion can be drawn from the luminosity correlations in less active spiral galaxies. Since there is no end to correlations with radio luminosities, this is probably the most that can be said with confidence.

Radio supernovae are compact synchrotron sources that appear and disappear within a period of months to years following Type II or Type Ib supernovae; no radio emission has been detected from Type Ia supernovae (Weiler et al. 1986). The power source appears to be the supernova shock that propagates into the dense circumstellar wind (Chevalier 1982) or H II region (McKee 1988, Chevalier & Laing 1989) produced by the supergiant progenitor star before it exploded. Too few radio supernovae have been observed to establish radio supernova rates in galaxies. They do not appear to contribute a significant fraction of the average radio luminosities of normal galaxies, although a single radio supernova may have a radio luminosity L ~ 10²¹ h^-2 W Hz^-1 (Rupen et al. 1987) for a few years. Supernova remnants become radio sources about 50 yr after the explosion (Gull 1973) as Rayleigh-Taylor instabilities develop in the boundary between the shock and the ambient interstellar medium, and radio SNRs remain visible for hundreds or thousands of years. About 40 young SNRs are conspicuous in high-resolution maps of M82 at 5 GHz (Kronberg et al. 1985) and 8.4 GHz (Figure 7), and radio SNRs are just visible in NGC 253 (Antonucci & Ulvestad 1988) and NGC 3448 (Noreau & Kronberg 1987).

Figure 7. The compact sources visible in this 8.44 GHz VLA map (Z.-P. Huang, unpublished data) of the center of M82 are radio SNRs, the faintest of which are about as luminous as the Galactic SNR Cassiopeia A. The logarithmic contours are separated by factors of 2^1/2 in brightness, and the lowest contour is 0.5 mJy beam^-1.

SNRs account for < 10% of the radio luminosities of normal galaxies, but they can be used to estimate supernova rates. Shklovsky (1968) showed that an optically thin young radio SNR expanding adiabatically with constant speed and conserving magnetic flux will decay exponentially in luminosity. Its age t can be estimated from its radio half-life with the equation t ~ 2(2 + 1) / ln2, where is the spectral index. Kronberg & Sramek (1985) monitored 5 GHz flux densities of the ten strongest SNRs in M82 and found half-lives ~ 15 yr, which lead to average ages t ~ 10² yr. Thus, the radio supernova rate in M82 lies in the range 0.1-0.4 yr^-1 depending on whether or not the ten strongest SNRs are the ten youngest. VLBI measurements and lower limits for the angular diameters of SNRs in M82 yield a radio supernova rate _SN ~ 0.1 yr^-1 if their radii grow ~ 6 x 10³ km s^-1 (Bartel et al. 1987, Wilkinson & de Bruyn 1990).

Most cosmic rays escape their parent SNRs, filling the galaxy disk and halo. In diffusion models, cosmic-ray propagation is specified by an empirical energy-dependent diffusion coefficient D(E). For our galaxy D(E) ~ 10²⁹ cm² s^-1 if E < 1 GeV and D(E) ~ 10²⁹ (E / GeV)^1/2 cm² s^-1 if E > 1 GeV (Ginzburg et al. 1980). After time the cosmic rays diffuse a distance d ~ (D)^1/2. Taking E ~ 4 GeV for electrons radiating at = 1.49 GHz and ~ 2 x 10⁷ yr in the solar neighborhood indicates d ~ 3 kpc. This is sufficient to make the nonthermal radio disk smooth and increase its radial scale length significantly, although the synchrotron brightness scale length is shorter than the equipartition cosmic-ray or magnetic field scale lengths (cf Hummel & Gräve 1990, Hummel 1991b). Bright compact sources in galactic nuclei much smaller than 3 kpc are possible because their cosmic rays have short synchrotron and inverse-Compton lifetimes (Condon et al. 1991c). Simple diffusion spreads the cosmic rays from a point source into a Gaussian distribution, but Bicay & Helou (1990) found that convolving the FIR brightness distributions (taken to be the source brightness distributions) of nearby face-on spiral galaxies with Gaussians did not yield good fits to the observed radio brightness distributions. Alternatively, cosmic rays can stream at the Alfvén speed V_A 100 km s^-1 in the ionized interstellar medium and travel 2 kpc in 2 x 10⁷ yr. Cosmic rays may also diffuse into a static halo or convect away from the disk into a dynamic halo. The effects of cosmic ray propagation on the nonthermal radio emission from halos were studied in some detail by Lerche & Schlickeiser (1980, 1982). Energy-dependent diffusion and adiabatic losses from convection produce spectral bends of the form given by Equation 12 with asymptotic spectral-index changes ~ 1/4. The spectral bends are very gradual, however; realistic simulations show only small differences between the spectra of edge-on galaxies with static or dynamic halos (van der Walt 1990). The radio spectra of the best-observed halos in NGC 891 (Hummel et al. 1991b) and NGC 4631 (Hummel & Dettmar 1990) are consistent with convection. Other signs of convection or winds are synchrotron protrusions from edge-on disks (Condon 1983, Reuter et al. 1991, Seaquist & Odegard 1991) and ordered halo magnetic fields (Hummel & Dettmar 1990, Hummel et al. 1988b, 1991a). Observable distinctions between static and dynamic halos were recently reviewed by Bloemen(1991a).