Annu. Rev. Astron. Astrophys. 1992. 30: 575-611
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3.2 Isolating the Thermal Emission

In principle, the relatively flat-spectrum ( 0.1) thermal radio emission should be distinguishable from the steeper-spectrum ( ~ 0.8) nonthermal emission via total flux densities or maps obtained at two or more frequencies. In practice, most normal galaxies are not bright enough to be detected at frequencies much higher than ~ 10 GHz ( ~ 3 cm), so the observed thermal fractions ST / S, where S is the total flux density, are small and most measured ST are uncertain by a factor of two. Other indicators available for large samples of galaxies (e.g. H and FIR fluxes) suggest that the rms scatter in ST / S from galaxy to galaxy is not more than a factor of two (Kennicutt 1983b), except possibly for dwarf galaxies. Thus, the average < ST / S > ratio obtained from these samples is likely a better estimate of individual ST / S than the poorly observed values for many normal galaxies.

Klein & Emerson (1981) first succeeded in measuring good 10.7-GHz integrated flux densities for a small sample of nearby spiral galaxies with the Effelsberg 100-m telescope. The steepest power-law fit to flux densities measured at several lower frequencies was extrapolated to 10.7 GHz and subtracted from the observed flux density of each galaxy to remove the dominant nonthermal contribution, thereby determining ST. They detected no significant evidence for spectral flattening due to a thermal component emerging at 10.7 GHz and set upper limits ST / S 0.4 to the thermal fractions at 10.7 GHz. Likewise, Gioia et al. (1982) did not find flattening at 10.7 GHz in a larger sample of normal spiral galaxies with known 408 MHz and 4.9 GHz flux densities. They assumed a nonthermal spectral index = 0.8, subtracted the nonthermal component to obtain ST, and also concluded ST / S 0.4 at 10.7 GHz for most galaxies. Israel & van der Hulst (1983) claimed a marginal statistical detection, < ST / S ~ 0.3 > at 10.7 GHz, in a large sample of galaxies observed with the OVRO 130-ft telescope.

If integrated flux densities at only three or four frequencies are used to fit the (unknown) nonthermal spectral index and the thermal fraction simultaneously, the resulting nonthermal spectral index and thermal fraction are strongly correlated. Consequently, the actual errors in these quantities may be much larger than the formal uncertainties estimated by 2 tests. The (nonthermally dominated) low-frequency spectral indices of most spiral galaxies actually fall within a fairly narrow range: < > = 0.74, 0.12 in the Gioia et al. (1982) sample, and < > = 0.75, = 0.10 (Condon 1983). Individual values of ST derived from fits implying nonthermal spectral indices outside the range 0.6 1.0 (cf Duric et al. 1988, Skillman & Klein 1988, Klein et al. 1991) may be affected by this correlation.

The thermal fraction is controversial even in the brightest and best-observed normal galaxies such as M82 (Figure 1) because the nonthermal component may not have a straight spectrum. By assuming a straight nonthermal spectrum for M82, Klein et al. (1988) calculated a thermal flux density ST = 0.15 Jy at = 32 GHz and deduced an ionization rate of only Nuv ~ 2 x 1053 s-1. Using practically the same data but assuming that the nonthermal spectrum steepens at high frequencies, Carlstrom & Kronberg (1991) obtained ST = 0.5 Jy at = 92 GHz and estimated Nuv ~ 9 x 1053 s-1. The difficulty of distinguishing nonthermal spectral bends from different thermal fractions is illustrated by the calculated spectra in Figure 6 shown later (see Section 4.1). In the case of M82, Nuv can be estimated independently from the H53 radio recombination-line flux. This high-frequency (43 GHz) line is dominated by spontaneous emission and is unaffected by dust extinction. It indicates Nuv ~ 1054 s-1 (Puxley et al. 1989), in better agreement with a bent nonthermal spectrum and large thermal fraction at 92 GHz. The prototypical ultraluminous FIR galaxy Arp 220 may be similar. A power-law extrapolation of its low-frequency nonthermal spectrum yields ST / S < 0.3 at = 110 GHz, leading Scoville et al. (1991) to favor a monster in an AGN as the energy source rather than a starburst whose initial mass function (IMF) would have to be truncated above 25 M to produce the low observed Nuv / LFIR ratio. However, a normal IMF starburst would be consistent with the data if the high-frequency nonthermal spectrum of Arp 220 steepens and the thermal flux is a factor of two larger.

The distribution of the ratio S / F(H) provides an independent constraint on the average thermal fraction of normal disk galaxies. Kennicutt (1983b) found a strong correlation between S1.4 GHz and F(H) even though the total flux densities are completely dominated by nonthermal emission at 1.4 GHz. The observed average < S1.4 GHz / F(H) > corrected for extinction indicates that normal disk galaxies have an average thermal fraction < ST / S > ~ 0.1 at = 1.4 GHz, and the scatter about this average is approximately a factor of two. The FIR/radio correlation can also be used to estimate the average thermal fraction for normal galaxies (Condon & Yin 1990). Discrete Galactic IRAS sources coincide with thermal radio sources in luminous H II regions, not supernova remnants or other nonthermal radio sources (Haslam & Osborne 1987). The average FIR/radio flux density ratio of these thermal radio sources is about a factor of ten higher than the average FIR/radio ratio of normal galaxies at ~ 1.4 GHz, suggesting a fairly good upper limit < ST / S > 0.1 at = 1.4 GHz. Thus, at frequencies sufficiently high to make the free-free opacity small, the approximation (Condon & Yin 1990)

where ~ 0.8 is a typical nonthermal spectral index, probably yields a better estimate of the global thermal fraction than do existing radio spectra for most galaxies.

Spatial isolation of the brightest H II regions in radio maps is easier to achieve than global spectral separation of the thermal and nonthermal components. The radio emission from H II regions is much clumpier than the rather smooth synchrotron disk and spiral arms, so their derived distribution is fairly insensitive to the assumed nonthermal spectral index of the subtracted smooth background (Klein et al. 1982). The Effelsberg 100-m telescope has been used to separate the thermal and nonthermal components in maps of M33 (Buczilowski 1988), M81 (Beck et al. 1985), M101 (Gräve et al. 1990), and NGC 6946 (Klein et al. 1982). Multifrequency single-dish maps of the Large Magellanic Cloud (Klein et al. 1989) show the relatively large contribution from H II regions typical of dwarf irregular galaxies. Most of the moderately compact (D 20 pc) radio sources seen in high-resolution maps of nearby spiral disks are H II regions; see the maps of M31 (Braun 1990), M51 (van der Hulst et al. 1988), and NGC 4736 (Duric & Dittmar 1988).

Scaled arrays of the VLA can map the brightest sources in normal galaxies with similar (u, v)-plane coverage and high resolution at three frequencies — 1.5, 5, and 15 GHz. Fits for the nonthermal spectral index and the thermal flux density at each resolution element in the map yield separate maps of the thermal emission, the nonthermal emission, and the nonthermal spectral index. Duric et al. (1986) mapped NGC 3310 in this way with 4".5 FWHM resolution. They deduced a thermal fraction ST / S ~ 0.1 at = 1.5 GHz and obtained an impressive correlation of the thermal radio brightness and H brightness distributions. The large reported spectral-index gradient (from ~ 0.3 near the center to ~ 1.5 at the edge) of the smoother nonthermal disk is more sensitive to errors introduced by limited (u,v) coverage, primary-beam corrections, etc. The total flux density integrated over any large-scale interferometer map is actually zero, and every source is surrounded by a negative bowl that depresses the bowl-shaped positive emission from a disk. The negative bowl is wide and shallow if short baselines are present, and it may be largely removed by the CLEAN deconvolution algorithm (Cornwell & Braun 1989). Even so, observers can miss a lot of extended flux without realizing it, as Hummel & Gräve (1990) have pointed out in their paper containing excellent multifrequency maps of IC 342 made with the 100-m telescope and the VLA. Other spectral maps combining single-dish and interferometer data include those of M51 (Tilanus et al. 1988) and M83 (Sukumar et al. 1987).

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