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Constraining the ISM properties of the Cloverleaf quasar host galaxy with Herschel spectroscopy

We present Herschel observations of far-infrared (FIR) fine-structure (FS) lines [CII]158$μ$m, [OI]63$μ$m, [OIII]52$μ$m, and [SiII]35$μ$m in the z=2.56 Cloverleaf quasar, and combine them with published data in an analysis of the dense interstellar medium (ISM) in this system. Observed [CII]158$μ$m, [OI]63$μ$m, and FIR continuum flux ratios are reproduced with photodissociation region (PDR) models characterized by moderate far-ultraviolet (FUV) radiation fields $G_0=$ 0.3-1$\times10^3$ and atomic gas densities $n_{\rm H}=$ 3-5$\times10^3$ cm$^{-3}$, depending on contributions to [CII]158$μ$m from ionized gas. We assess the contribution to [CII]158$μ$m flux from an active galactic nucleus (AGN) narrow line region (NLR) using ground-based measurements of the [NII]122$μ$m transition, finding that the NLR can contribute at most 20-30% of the observed [CII]158$μ$m flux. The PDR density and far-UV radiation fields inferred from the atomic lines are not consistent with the CO emission, indicating that the molecular gas excitation is not solely provided via UV-heating from local star-formation, but requires an additional heating source. X-ray heating from the AGN is explored, and we find that X-ray dominated region (XDR) models, in combination with PDR models, can match the CO cooling without overproducing observed FS line emission. While this XDR/PDR solution is favored given the evidence for both X-rays and star-formation in the Cloverleaf, we also investigate alternatives for the warm molecular gas, finding that either mechanical heating via low-velocity shocks or an enhanced cosmic-ray ionization rate may also contribute. Finally, we include upper limits on two other measurements attempted in the Herschel program: [CII]158$μ$m in FSC~10214 and [OI]63$μ$m in APM~08279+5255.