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Quasar absorption systems encode a wealth of information about the abundances, ionization structure, and physical conditions in intergalactic and circumgalactic media. Simple (often single-phase) photoionization models are frequently used to decode such data. Using five discrete absorbers from the COS Absorption Survey of Baryon Harbors (CASBaH) that exhibit a wide range of detected ions (e.g. Mg  ii , S  ii – S  vi , O  ii – O  vi , Ne  viii), we show several examples where single-phase ionization models cannot reproduce the full set of measured column densities. To explore models that can self-consistently explain the measurements and kinematic alignment of disparate ions, we develop a Bayesian multiphase ionization modelling framework that characterizes discrete phases by their unique physical conditions and also investigates variations in the shape of the UV flux field, metallicity, and relative abundances. Our models require at least two (but favour three) distinct ionization phases ranging from T ≈ 104 K photoionized gas to warm-hot phases at T ≲ 105.8 K. For some ions, an apparently single absorption 'component' includes contributions from more than one phase, and up to 30 per cent of the H  i is not from the lowest ionization phase. If we assume that all of the phases are photoionized, we cannot find solutions in thermal pressure equilibrium. By introducing hotter, collisionally ionized phases, however, we can achieve balanced pressures. The best models indicate moderate metallicities, often with subsolar N/ α , and, in two cases, ionizing flux fields that are softer and brighter than the fiducial Haardt & Madau UV background model. [ABSTRACT FROM AUTHOR]

We present new measurements of the flux power-spectrum P (k) of the z < 0.5 H   i Lyman-α Forest spanning scales |$k \sim 0.001\!-\!0.1\, \mathrm{s \, km}^{-1}$|⁠. These results were derived from 65 far-ultraviolet quasar spectra (resolution |$R \sim 18\, 000$|⁠) observed with the Cosmic Origin Spectrograph (COS) on board the Hubble Space Telescope. The analysis required careful masking of all contaminating, coincident absorption from H   i and metal–line transitions of the Galactic interstellar medium and intervening absorbers as well as proper treatment of the complex COS line-spread function. From the P (k) measurements, we estimate the H   i photoionization rate (⁠|$\Gamma _{\rm H\,{\small I}}$|⁠) in the z < 0.5 intergalactic medium. Our results confirm most of the previous |$\Gamma _{\rm H\,{\small I}}$| estimates. We conclude that previous concerns of a photon underproduction crisis are now resolved by demonstrating that the measured |$\Gamma _{\rm H\,{\small I}}$| can be accounted for by ultraviolet emission from quasars alone. In a companion paper, we will present constraints on the thermal state of the z < 0.5 intergalactic medium from the P (k) measurements presented here. [ABSTRACT FROM AUTHOR]