Annu. Rev. Astron. Astrophys. 1992. 30: 575-611
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6. RADIO EMISSION AND STAR FORMATION

6.1 Nonthermal Luminosity and the Supernova Rate

The lifetimes of the massive stars responsible for most of the radio emission from normal galaxies are much shorter than a Hubble time, so the current radio luminosity is proportional to the recent star-formation rate. Biermann (1976) first included thermal and nonthermal radio flux measurements in quantitative galaxy models because they had ``attained a precision which is comparable to or in some cases clearly better than the precision of optical measurements.'' This pioneering work compared (B - V) colors with blue/radio flux ratios. Biermann assumed a time-independent power-law IMF (M) M-, with slope = 2.35 and upper mass limit MU. All stars with M MSN ~ 6.7 M were presumed to produce radio-emitting supernova remnants, so the radio supernova rate is

His flux-time integral for each supernova remnant – 0.1 Jy yr at = 5 GHz when seen from a distance d = 20 Mpc – is an extrapolation of the observed (Clark & Caswell 1976) surface brightness-diameter ( - D) relation for Galactic supernova remnants. Biermann noted that the lower mass limit MSN for radio supernovae is more critical than MU MSN because the steep IMF slope implies that most radio supernova progenitors have masses just above MSN. The resulting models could be made to agree with the observed blue/radio ratios only if the assumed nonthermal radio energy per supernova were increased by a factor of ten.

A very clear derivation of the relation between the supernova rate and the nonthermal radio luminosity implied by the - D relation was given by Ulvestad (1982). The 408 MHz data indicate (W m-2 Hz-1 sr-1) ~ 10-15 [D(pc)]-3 and D(pc) ~ 0.43 E501/5[n(cm-3)]-1/5[t(yr)]2/5, where E50 is the explosion energy in units of 1050 ergs, n is the ambient particle density, and t is the time since the supernova explosion (Clark & Caswell 1976). If the supernova remnant is a radio source only during its adiabatic lifetime (yr) ~ 2 x 104 E504/17 [n(cm-3)]-9/17, then

at 408 MHz. Ulvestad (1982) used a relation similar to Equation 17 to derive SN from the observed radio luminosities of Seyfert galaxies. He scaled the infrared/optical luminosities from the classic Rieke et al. (1980) model D for M82 with SN and found them to exceed the observed values by at least a factor of ten. This prompted his suggestion that the radio sources in most Seyfert galaxies are powered by AGNs instead of stars.

Gehrz et al. (1983) constructed a steady-state model for the compact starbursts in NGC 3690 that unified features of the earlier models, and they used the FIR luminosity as the best estimate of the bolometric luminosity of a starburst. Gehrz et al. (1983) compared H, FIR, and radio continuum luminosities of NGC 3690 with starburst models parameterized by different IMF slopes and mass limits ML, MU. They also found it difficult to reconcile the high supernova rate needed to explain the nonthermal radio emission with the observed FIR and H luminosities. Their successful models have a very steep ( = 3.5) and severely truncated (MU ~ 25 M) IMF, plus a low MSN ~ 6 M. Such models favor SN while minimizing the bolometric luminosity and Nuv. They cannot be applied to all galaxies since the discovery of Wolf-Rayet stars in some FIR luminous galaxies (Armus et al. 1988) proves that the IMF does extend beyond 25 M in galaxies obeying the ubiquitous FIR/radio correlation.

These and related difficulties are unavoidable if the SNRs themselves are required to provide all of the nonthermal radio emission from normal galaxies. Heckman et al. (1983) argued that monsters in AGNs, not starbursts, power strong nuclear sources in spiral galaxies since the average radio spectral index < > ~ 0.45 of Galactic SNRs is significantly less than the average spectral index < > ~ 0.75 of spiral galaxies. Jenkins (1984) could not reconcile the high supernova rate required to explain the nonthermal radio luminosity of the normal spiral galaxy NGC 5953 with its H and bolometric luminosities, concluding that ``no explanation can be found for the radio emission.'' Kronberg & Biermann (1981) found excessive consumption of H I mass by the starburst nucleus of NGC 2146. For the LN ~ 6 x 1021 W Hz-1 nonthermal luminosity of our galaxy at 408 MHz (Berkhuijsen 1984), Equation 17 implies an excessive radio supernova rate SN ~ 0.4 yr-1. This is much higher than the Type II supernova rate SN ~ 0.023 yr-1 estimated by Tammann (1982) or the Galactic pulsar birthrate 0.01-0.03 yr-1 (Lyne et al. 1985). Even the radio counts of young Galactic SNRs suggest a radio supernova rate SN ~ 0.013 yr-1 (Caswell & Lerche 1979), albeit with large uncertainty (Green 1984). Supernova remnants may accelerate the relativistic electrons producing the nonthermal radio emission in spiral galaxies, but > 90% of this emission must be produced long after the individual supernova remnants have faded out and the electrons have diffused throughout the galaxy – an old (Pooley 1969, Ilovaisky & Lequeux 1972) but often overlooked result. Therefore, Condon & Yin (1990) dropped Equation 17 in favor of the observed Galactic relation between LN and SN, which implies

Equation 18 probably applies to most normal galaxies, since significant variations in the ratio LN / SN from galaxy to galaxy would violate the observed FIR/radio correlation. Also, Völk et al. (1989) have argued that the cosmic-ray energy production per supernova is the same in the starburst galaxy M82 as in our galaxy.

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