tokens: ) UVB model – scaled to the effective optical depth fitting function of Kim et al. ( 2007 ). The solid curves represent our fiducial model (purple), our model with α QSO = 1.3 (pink), with α QSO = 2.0 (black), and our model with an ionization fraction based on the quasar emissivity function of Kulkarni et al. ( 2019 , green). These curves have all been scaled by the same factor as our uniform UVB model. The effective optical depth varies up to tens of percent, with our α QSO = 1.3 model showing the largest discrepancy due to the largest variance in IGM temperature. Figure 6. The evolution of the effective optical depth of the H i Lyman α forest for three of our He ii reionization models compared with a model with a uniform UVB (dashed, teal curve). The solid purple curve shows our model with α QSO = 1.7, C He iii = 3, E max = 150 eV, and z reion,He ii = 2.8−4. The pink and black curves shows the same model, but with α QSO = 1.3 and 2.0, respectively. The light green curve shows our model based on the quasar emissivity function of Kulkarni et al. ( 2019 ). The error bars show measurements from Schaye et al. ( 2003 ), Kim et al. ( 2007 ), and Calura et al. ( 2012 ). The bottom panel shows the relative differences between our four He ii reionization models and the uniform UVB model. From our simulated H i Lyman α forest spectra, we calculate the flux PDF for our two simulations shown in Fig. 5 . Because the patchiness of reionization will result in multiple temperatures at the same gas density, the flux PDF will reflect more bimodality after He ii reionization is underway. The left-hand panel of Fig. 7 shows the flux PDF for a redshift at the onset of He ii reionization ( z = 4) and towards the end of reionization in the right-hand panel ( z = 3). The solid curve shows our model with inhomogeneous reionization and the dashed curve shows the effect of a homogeneous UVB. Indeed, in the midst of He ii reionization, we find a more bimodal distribution in comparison to our simulation without inhomogeneous He ii reionization. We compare these cases with observational measurements of the flux PDF from Kim et al. ( 2007 ) and Calura et al. ( 2012 ) at z ≈ 3. While these measurements show broad agreement with both simulations, and may slightly favour our inhomogeneous He ii reionization, the uncertainty in the measurements is nearly equal to, or greater than the difference between our model and the uniform UVB case. Figure 7. Flux PDF from a simulation with inhomogeneous He ii reionization model (solid) and from a simulation with a uniform UVB (dashed). The left-hand panel shows a redshift at the onset of He ii reionization ( z = 4) and the right-hand panel shows a redshift just before its completion ( z = 3). The error bars show measurements from Kim et al. ( 2007 ) and Calura et al. ( 2012 ). From these same simulations, we show the 1D flux power spectrum in Fig. 8 . The left-hand panel presents the flux power spectrum for a redshift at the onset of He
ner_tags: O B-Model I-Model O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O B-Model I-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O