4. Are losses significant?
The separation of thermal and non-thermal emission is based on two assumptions about the physical conditions in galaxies. One is the assumption of optically thin emission, and the second is that the synchrotron emission of a galaxy can be described by a single power-law in the frequency range from 400 MHz up to 10 GHz. Especially the second assumption is critical, because of the effects of loss processes on high-energy electrons. Hence, it is possible that the high-frequency radio spectrum of a galaxy is affected by synchrotron losses. In this case, the above described method of the separation would underestimate the thermal amount, and the derived non-thermal spectral indices would be too flat.
In order to check this an independent estimate of the thermal radio flux density is necessary. It is possible to calculate the thermal radio flux from the emission in the H recombination line and an assumed thermal electron temperature . The H emission in normal spiral galaxies is proportional to the free-free emission of thermal electrons in the HII regions. Using the equations of thermal free-free emission in an ionized gas one can compute the thermal radio flux density from the H flux in the following way (see e.g. Caplan & Deharveng 1986):
Using Eq. 2 it is possible to calculate the thermal radio flux density at every frequency for a galaxy with a given H flux. Kennicutt & Kent (1983) carried out an H survey of normal galaxies. For 29 galaxies from Table 1 H fluxes were available from this survey. For these galaxies we calculated thermal radio fluxes at those frequencies where radio flux densities are available, using Eq. 2. The assumed thermal electron temperature is K. The thermal fluxes were subtracted from the flux densities at the corresponding frequencies in the integrated spectra. We fitted power-laws to the residual spectra in order to obtain the non-thermal spectral index . The determination of and is less sensitive to observational errors than the derived thermal flux densities because the non-thermal spectral indices do not depend on just one data point.
Fig. 4 shows two representative examples. In the case of complete elimination of the thermal component by the subtraction of the residual spectrum will represent the pure synchrotron spectrum. The non-thermal spectral index from Table 1 and should be the same if loss processes have not significantly steepened the synchrotron spectrum. If energy losses are important the residual spectrum will show a steepening at shorter wavelengths, and should be larger than from Table 1.
Fig. 5 shows plotted versus . There exists a clear correlation between the two quantities. This confirms the results of Table 1 and, in particular the wings of the distribution of are not due to observational scatter. Hence, the values of range indeed from 0.5 to 1.2. On the other hand, generally tends to be smaller than . This can be interpreted as an underestimate of the thermal emission using the H fluxes, owing to absorption of the H emission by dust. On average, the difference between and is . The difference in the non-thermal spectral indices can be used to estimate the internal absorption. We assume a normal spiral galaxy with and evaluated from the radio spectrum. For the estimate of the H absorption we assume a total radio flux density at a frequency . With and it is possible to calculate the total flux density at a second frequency , as well as thermal and non-thermal flux densities at both frequencies (). The smaller is produced by an underestimate of the thermal flux density using H data. This can be expressed by with . It is important to note that k is frequency independent. The ratio is given by . can be replaced by at both frequencies because the sum of thermal and non-thermal flux densities has to be the total flux density. Now we use and express as . The ratio k between and is then given by:
Using k one can compute the internal H absorption . As an example, for a normal spiral galaxy with and we assume a total radio flux density . The parameters of the radio continuum spectrum give then and the thermal flux densities at 1 and 10 GHz are 8 and 6.4 mJy, respectively. This gives and using the average . The choice of is arbitrary and the determination of k based solely on the parameters of the radio continuum spectrum and the difference between and .
Of course, this value is an approximation because the remaining curvature of the spectrum in case of an underestimated thermal flux was neglected. Nevertheless internal absorption of this magnitude is what one would expect for normal spiral galaxies.
© European Southern Observatory (ESO) 1997
Online publication: June 30, 1998