SpringerLink
Forum Springer Astron. Astrophys.
Forum Whats New Search Orders


Astron. Astrophys. 322, 19-28 (1997)

Previous Section Next Section Title Page Table of Contents

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 [FORMULA] 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 [FORMULA] recombination line and an assumed thermal electron temperature [FORMULA]. The H [FORMULA] 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 [FORMULA] from the H [FORMULA] flux [FORMULA] in the following way (see e.g. Caplan & Deharveng 1986):

[EQUATION]

Using Eq. 2 it is possible to calculate the thermal radio flux density at every frequency for a galaxy with a given H [FORMULA] flux. Kennicutt & Kent (1983) carried out an H [FORMULA] survey of normal galaxies. For 29 galaxies from Table 1 H [FORMULA] fluxes were available from this survey. For these galaxies we calculated thermal radio fluxes [FORMULA] at those frequencies where radio flux densities are available, using Eq. 2. The assumed thermal electron temperature is [FORMULA]  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 [FORMULA]. The determination of [FORMULA] and [FORMULA] 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 [FORMULA] the residual spectrum will represent the pure synchrotron spectrum. The non-thermal spectral index from Table 1 and [FORMULA] 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 [FORMULA] should be larger than [FORMULA] from Table 1.

[FIGURE] Fig. 4. Test of the separation by estimating the thermal radio flux using H [FORMULA] data. The left diagrams show the integrated spectra for two representative examples. The line corresponds to the best-fit parameters of Table 1. The right graphs show the residual spectra after subtraction of the estimated thermal flux [FORMULA] from the H [FORMULA] data

Fig. 5 shows [FORMULA] plotted versus [FORMULA]. 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 [FORMULA] are not due to observational scatter. Hence, the values of [FORMULA] range indeed from [FORMULA] 0.5 to [FORMULA] 1.2. On the other hand, [FORMULA] generally tends to be smaller than [FORMULA]. This can be interpreted as an underestimate of the thermal emission using the H [FORMULA] fluxes, owing to absorption of the H [FORMULA] emission by dust. On average, the difference between [FORMULA] and [FORMULA] is [FORMULA]. The difference in the non-thermal spectral indices can be used to estimate the internal absorption. We assume a normal spiral galaxy with [FORMULA] and [FORMULA] evaluated from the radio spectrum. For the estimate of the H [FORMULA] absorption we assume a total radio flux density [FORMULA] at a frequency [FORMULA]. With [FORMULA] and [FORMULA] it is possible to calculate the total flux density [FORMULA] at a second frequency [FORMULA], as well as thermal and non-thermal flux densities at both frequencies ([FORMULA]). The smaller [FORMULA] is produced by an underestimate of the thermal flux density [FORMULA] using H [FORMULA] data. This can be expressed by [FORMULA] with [FORMULA]. It is important to note that k is frequency independent. The ratio [FORMULA] is given by [FORMULA]. [FORMULA] can be replaced by [FORMULA] at both frequencies because the sum of thermal and non-thermal flux densities has to be the total flux density. Now we use [FORMULA] and express [FORMULA] as [FORMULA]. The ratio k between [FORMULA] and [FORMULA] is then given by:

[EQUATION]

[FIGURE] Fig. 5. Plot of non-thermal spectral indices [FORMULA] obtained by an estimate of the thermal radio flux using the H [FORMULA] data, versus the non-thermal spectral indices [FORMULA] obtained by fitting Eq. 1 to the integrated radio spectra. The solid line represents perfect agreement between the two quantities

Using k one can compute the internal H [FORMULA] absorption [FORMULA]. As an example, for a normal spiral galaxy with [FORMULA] and [FORMULA] we assume a total radio flux density [FORMULA]. The parameters of the radio continuum spectrum give then [FORMULA] and the thermal flux densities at 1 and 10 GHz are 8 and 6.4 mJy, respectively. This gives [FORMULA] and [FORMULA] using the average [FORMULA]. The choice of [FORMULA] is arbitrary and the determination of k based solely on the parameters of the radio continuum spectrum and the difference between [FORMULA] and [FORMULA].

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.

Previous Section Next Section Title Page Table of Contents

© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
helpdesk.link@springer.de