tokens: turn depends on much of the physics of the cloud. Section 2 reviews briefly the details of the particle heating model grid and discusses the physical and chemical properties of the grid. Section 3.1 explores the effect of a large quantity of cold clouds on the composite model spectrum for BCGs. Section 3.2 discusses the effects of optical depth on the predictions for the BCG line ratios and Sections 3.3 and 3.4 explore the effect of turbulence and magnetic fields. Some words of caution about the models are given in Section 3.5 . A discussion and predictions for future observations are presented in Section 4 . 2 MODEL The particle heating model used in this paper is essentially that described in F2009 for optically thin emission from warm ionized gas adapted to include physics pertinent to very cold clouds. The model is motivated by spectra from extended emission-line regions in BCGs which show spatially coincident emission from molecular, atomic and ionized gas, suggesting that the total emission in the filaments is from clouds with a range of densities and temperatures. F2009 parametrize the contribution of the different phases to the total volume as a weighted sum of ‘cloudlets’ of different densities but constant pressure. The weighting function, α, is taken to be a power law in the cloud density, and hence the cloud density function will be this power law. The line emissivity ( in erg cm −3 s −1 ) summed over the distribution of clouds is where n i are the specific densities and we simulate the grid in density bins of 0.1 dex from log 10 ( n ) 0 to 6. The pressure in the ionized filaments has been measured by Heckman et al. ( 1989 ) and is similar to the X-ray derived pressure of the ICM. Throughout the paper we will refer to ‘hot gas’ as X-ray emitting ( T ≳ 10 6 K) gas, ‘warm gas’ as ionized, optical emitting clouds ( T ∼10 000 K) which emit strongly in Hα, ‘cool gas’ as T ∼ 1000 K gas which emits strongly in H 2 12 μm and ‘cold gas’ as gas with temperatures T ≲ 100 K, which emit in the strong fine structure lines of [C ii ] λ157 μm , and many molecular emission lines. F2009 use the Hα and H 2 12 μm emission-line ratios to determine α for the Perseus cluster (a constant pressure of ∼10 6.5 is used for the Perseus cluster). They find α = −0.35 can reproduce all emission lines from the warm ionized ( T ∼ 10 000 K) gas to within a factor of 2 (but see Johnstone et al. 2012 for a discussion of the Hα flux in the Perseus cluster). This value of α implies the majority of the volume is filled by hot ionized gas with only a minor contribution from the more massive, cold clouds. Hα emission is predominantly from ∼10 4 K gas while the H 2 12 μm emission line is from gas ∼10 3 K. The authors point out that the data available at the time are not able to constrain a large reservoir of very low temperature clouds. However, extrapolation of α to low-temperature clouds gives good agreement with mass estimates from CO emission lines though these may be
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