tokens: by a factor of 10. b The two photon indexes shown in bold, i.e., and , are for cases with and 10 −3 , respectively, where they are estimated from the relationship reported in Yang et al. ( 2015 ; see their Equation (5)), with (Ho 2008 ). Besides this statistical investigation of for LLAGNs, we have also calculated the Compton temperature of several individual LLAGNs. Such an investigation is a little too ambiguous, since most of these sources lack the hard X-ray and soft γ -ray observations to constrain the value of E c . So we use the theoretical SED results for such information, which is obtained by the accretion flow modeling to the sources (see Yuan Narayan 2014 for details of the accretion model of LLAGNs). We select several representative sources from Yuan et al. ( 2009 ). The results are shown in Table 3 . Again, we have tried three different electron temperatures. The Compton temperature is systematically higher than the “normal case” shown in Table 2 , but more consistent with the results of the “reduced-IR” case. The reason is that the IR flux calculated from the theoretical model is significantly weaker than that shown in Figure 1 , since we only consider the radiation from accretion flow and the jet. In other words, the Compton temperature derived here is applicable to the regions close to the black hole, as we argue above. Table 3 Compton Temperature of Individual LLAGNs Note. Observational data and theoretical modeling are taken from Yuan et al. ( 2009 ). We caution that the hard X-rays and soft γ -rays in these sources are actually from SED modeling because there are no direct observations at these energy bands. 4. The Total Radiative Heating and Cooling in LLAGNs In addition to Compton scattering, there are several additional radiative processes that can heat or cool the gas. In this section, we compare their relative magnitude. One process is the bremsstrahlung radiation ( and ), which always plays a cooling role. The other processes relate to the atomic energy-level transition, i.e., the photoionzation/recombination and line emission ( and ). The total radiative heating/cooling rate per unit volume can be expressed as (e.g., Proga et al. 2000 ; Sazonov et al. 2005 ) Here and n e are the number density of hydrogen atomics and electrons, respectively. For hot gas (i.e., temperature K) with solar abundance, . Consequently, the radiative heating/cooling rate can be expressed as The value of depends on both the metallicity (fixed to solar abundance in this work) and the ionization parameter ξ . The definition of ξ isHere R is the distance to the central black hole, is the ionization luminosity, and is the ionization luminosity factor. As shown in Figure 2 , we derive the ionization luminosity factors, i.e., , respectively, for the composite SEDs shown in Figure 1 with and . Detailed formulae of is provided in the Appendix (see Equation ( 17 )). It is a heating (cooling) term when ξ is large (small). Figure 2. Ionization
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