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

3.3 Integrated Radio Spectra and Brightness Temperatures

If the thermal and nonthermal radio sources in a normal galaxy are coextensive, the total radio emissivity is everywhere proportional to the free-free absorption coefficient . The radio brightness-temperature spectrum of any such galaxy then follows from Equation 5; it is approximately

where is the average free-free optical depth along the line of sight and T_e ~ 10⁴ K is the electron temperature. A set of curves outlining the possible radio spectra of normal galaxies is shown in Figure 4. Inhomogeneities in real sources will produce spectral peaks somewhat broader than those plotted. In the limit [1 - exp(-)] -> 1 Equation 6 predicts that the maximum brightness temperatures of normal galaxies are T_e 10⁵ K for 1 GHz, as indicated by the upper-left envelope of the spectra in Figure 4. The spectrum of our galaxy at high latitudes turns over due to free-free absorption ( ~ 1) near = 0.003 GHz, and the observed brightness spectrum (Cane 1979) lies just above the lowest curve in Figure 4. The median face-on disk surface brightness of nearby spiral galaxies is < T_b > = 0.75 ± 0.25 K at = 1.4 GHz (Hummel 1981), so the brightness spectra of most normal galaxies fall between the two lowest curves (corresponding to = 1 between = 0.003 and 0.01 GHz) in Figure 4. Brighter radio sources have higher turnover frequencies. For example, the central component in the starburst galaxy M82 has a brightness S / ~ 30 mJy arcsec^-2 at ~ 1 GHz, the frequency at which ~ 1. The integrated spectrum of M82 (Figure 1) flattens but does not actually turn over below 1 GHz because this source is quite inhomogeneous and synchrotron emission from the surrounding halo (Seaquist & Odegard 1991) does not suffer significant free-free absorption.

Figure 4. Radio brightness spectra (continuous curves) of normal galaxies containing mixed thermal/nonthermal sources. Successive curves correspond to increasing the frequency ₁ at which the free-free optical depth is = 1: ₁ = 0.003, 0.01, 0.03, 0.1, 0.3, 1, and 3 GHz. Dotted lines of constant brightness temperature T_b (K) are alson shown. The brightness temperatures of normal galaxies do not exceed T_b ~ 10⁵ K at frequencies above ~ 1 GHz. Abscissa: frequency (GHz). Ordinate: brightness (mJy arcsec^-2).

The low-frequency spectra of many normal spiral galaxies with only moderate surface brightness (Israel & Mahoney 1990), including our own (Sironi 1974, Webster 1974), appear to flatten slightly in the range 0.1-1 GHz, much higher than the 0.01 GHz predicted by Equation 6 if T_e ~ 10⁴ K. Israel & Mahoney (1990) found that the difference between flux densities extrapolated from higher frequencies and their measured 57.5 MHz flux densities is greatest for highly inclined disks, so they proposed free-free absorption by very cool (T_e < 1000 K) ionized gas filling a fairly large fraction of the radio emitting volume to explain their low-frequency spectra. Hummel (1991a) reanalyzed the radio spectra, confirming a spectral break with median < > ~ 0.25 but questioning its inclination dependence. His interpretation is that there is little absorption at low frequencies, but the high-frequency nonthermal spectra steepen owing to the effects of propagation (convection or energy-dependent diffusion) on the relativistic electrons. However, Webster (1970) showed that the spectral steepening from this process is too gradual to explain the fairly sharp bend in the high-latitude spectrum of our own galaxy. Thus, the low-frequency spectral break in typical spiral galaxies is still not completely understood.

The brightest known radio sources in galaxies claimed to be ``normal'' are the compact starburst nuclei of ultraluminous IRAS sources. They have 8.44 GHz brightness temperatures approaching 10⁴ K and show spectral flattening above 1.49 GHz (Condon et al. 1991c, Sopp & Alexander 1991). For example, the strong compact source in IC 694 has a flat ( ~ 0.3) spectrum above 1.49 GHz, leading Gehrz et al. (1983) to conclude that it was synchrotron self-absorbed and hence much too bright (implied T_b > 10¹⁰ K) to be a starburst. However, an 8.44 GHz VLA map made with 0".25 resolution (Figure 5) shows that this source is extended and its peak brightness temperature is only T_b 10⁴ K. Therefore, a flat spectrum even at GHz frequencies is not sufficient to prove that a radio source is powered by an AGN. Flat-spectrum sources produced by monsters in Seyfert galaxies, classical radio galaxies quasars, etc. generally are synchrotron self-absorbed. Thus, high-resolution maps capable of separating sources with T_b 10⁵ K from those with T_b > 10¹⁰ K (cf Norris et al. 1990) should be able to distinguish between flat-spectrum starbursts and monsters. But it is not enough to show that T_b 10¹⁰ K at high frequencies ( ~ 15 GHz) to reject starbursts (cf Carral et al. 1990, Chapman et al. 1990); starburst galaxies much brighter than M82 do exist.

Figure 5. The nucleus of IC 694 is typical of the brightest and most compact sources found in ``normal'' galaxies. Its 8.44 GHz brightness temperature is only ~ 10⁴ K, so its relatively flat radio spectrum indicates free-free absorption by thermal electrons with temperature T_e ~ 10⁴ K, not synchrotron self-absorption by relativistic electrons with kinetic temperatures T_r > m_e c² / k ~ 10¹⁰ K. The logarithmic contours are separated by factors of 2^1/2 in brightness, and the lowest contour is 0.1 mJy beam^-1 ~ 28 K.