6 Dust heating mechanism

 There are several mechanisms that in principle could account for the dust heating, among them the evolved hot star populations. However Binette et al. (1994) developed a starburst evolution model and showed that Post-AGB stars are by far the main source of UV photons at an age of 10¹⁰ years, while other sources, such as nuclei of planetary nebulae can contribute significant amounts of UV photons for ages up to $2\,10^9$ years. There are also other alternatives, such as hot electrons in hot emitting gas or exposed hot cores (10⁵ K) of post red giant stars. The problem with the latter two mechanisms is that they will also produce X-ray emission, which is only observed for a small number of galaxies in this sample.

In Paper I we found a strong correlation between the $\mathrm{H}\alpha+[\mathrm{NII}]$luminosity and the luminosity in the B band, inside the region occupied by the line emitting gas. We also demonstrated that Post-AGB stars provide enough ionized radiation to account for the observed $\mathrm{H}\alpha$ luminosity. In most cases there were considerably more UV photons available than those needed to produce the observed $L_{\mathrm{H}\alpha}$ (typically by a factor of 1.5 - 2). This excess of UV photons are available to heat the dust which then reprocesses these photons reemiting them at IR wavelengths. The correlation between the dust mass and the blue luminosity inside the emitting region, shown in Fig. 3, is exactly as expected if the post-AGB stars are the main source of the UV photons and also heat the dust.

A simple estimate for dust luminosity can be obtained by assuming a model where the dust is distributed roughly uniformly around the sources or concentrated in spherically symmetric dust clouds. The total energy absorbed by the dust and reemited in the infrared ($L_{\mathrm{IR}}$) is related to the total incident UV luminosity ($L_{\mathrm{UV}}$) as (Bonatto & Pastoriza 1997)  

$$\frac{L_{\mathrm{IR}}}{L_{\mathrm{UV}}} = \frac{\Omega}{4 \pi} \, (1 - {\rm e}^{-\tau_{\rm eff}})$$ (6)

where $\Omega$ is the solid angle subtended by the dust distribution and $\tau_{\mathrm{eff}}$ is the effective optical depth to the incident UV/optical continuum along the line of sight. The optical depth is defined as $\tau_{\mathrm{eff}} = A_{\mathrm{UV}}/1.086$ and assuming a Galactic extinction law $A_{\mathrm{UV}} \simeq 5 \, A_{{V}}$. The visual extinction was computed from the extinction maps (see Table 2). The UV photons emited by post-AGB stars were calculated from $L_{\mathrm{H}\alpha}^{\mathrm{calc}}$ (see Table 5 of Paper I) using recombination theory (Osterbrock 1974).

$$L_{\mathrm{UV}} = \frac{L_{\mathrm{H}\alpha}}{h\nu_{\mathrm{... ...mathrm{T})}{ \alpha_{\mathrm{H}\beta}(\mathrm{H}^0\mathrm{T}) }$$ (7)

where $\alpha_{\mathrm{B}}(\mathrm{H}^0\mathrm{T})$ and $\alpha_{\mathrm{H}\beta}(\mathrm{H}^0\mathrm{T})$ are the recombination coefficients. From the $L_{\mathrm{UV}}^{\mathrm{calc}}$ emited by the post-AGB stars we have computed the $L_{\mathrm{IR}}^{\mathrm{calc}}$, using Eq. (6). From the observed IRAS fluxes we can compute the two components of the IR luminosities, namely the warm component $L_{\mathrm{IR}}^{\mathrm{W}}$, which assumes that most of the dust emission is produced at 25 and $60\, \mu$m, and the cold component $L_{\mathrm{IR}}^{\mathrm{C}}$, derived from the 60 and $100 \,\mu$m luminosities, as in Bonatto & Pastoriza (1997). Figure 4 shows a good agreement between the calculated and both of the observed IR luminosities for most of the galaxies, except NGC 3311 and NGC 4473 at the lower right, which seem to have a very luminous IR emission.

This simple calculation suggests that post-AGB stars are an ideal source of ionizing photons for the gas and heating photons for the dust. The post-AGB stars are known to exist and are distributed throughout the galaxy as the old stellar population thus providing in-situ sources of ionizing photons. This does, of course, not prove that they are the only mechanism capable of producing the observed dust emission and indeed more than one mechanism is likely to contribute in different amounts in each individual galaxy.

  

Figure 4: Relation between the observed and calculated infrared luminosities