INTRODUCTION

The intergalactic medium (IGM) occupies the space between galaxies and galaxy clusters, and houses the majority of baryonic matter in the universe. The major phase changes in the history of the IGM are fairly well understood, with recombination ( ∼ 1100) leading to the formation of a highly neutral IGM, and H ( ∼ 5.5 -8) (Fan et al. 2006;Robertson et al. 2010;Komatsu et al. 2011;Planck Collaboration et al. 2018;Boera et al. 2019) and He ( ∼ 3) (Madau et al. 1999;Miralda-Escudé et al. 2000;Wyithe & Loeb 2003;Furlanetto & Oh 2008;Shull et al. 2010;Worseck et al. 2016) reionization events leading to the current, highly ionized IGM (for a review on the IGM, see McQuinn 2016). The sources of the ionizing photons are thought to be stars in galaxies (Bouwens et al. 2016), and quasars (Madau et al. 1999;McQuinn et al. 2009;Haardt & Madau 2012) for H and He reionization, respectively.

During reionization, ionizing photons heat the IGM by tens of thousands of degrees. This heating, combined with cooling from adiabatic expansion and atomic processes, are the primary processes that influence the thermal state of the low density (1 -100 times the cosmic mean density) IGM (Miralda-Escudé & Rees 1994;Hui & Gnedin 1997;Schaye et al. 2000;Hui & Haiman 2003;Upton Sanderbeck et al. 2016;D'Aloisio et al. 2019). The thermal energy of the IGM smooths and extends the distribution of the gas, which ★ mfern027@ucr.edu † simeon.bird@ucr.edu ‡ phoebeu@ucr.edu in turn affects structure formation. After each reionization event, the low density IGM cools asymptotically towards an equilibrium temperature (Hui & Gnedin 1997;McQuinn & Upton Sanderbeck 2016). During this time the ionization state is well understood, as the neutral fraction is set by the equilibrium between photoionizations and recombinations. All of this makes the IGM, and especially the low density IGM, a valuable probe of the post-reionization universe ( < 6) and the scales probed make it useful for both astrophysics and cosmology. Conveniently, there are numerous observations probing intergalactic gas at 2 < < 6. Generally, these are observations of the Lyman-forest, the series of absorption features blueward of the rest-wavelength Lyman-emission observed in quasar spectra (Gunn & Peterson 1965). A single forest spectrum is a onedimensional map of the gaseous structure along that line of sight, making it a useful probe of structure formation. Knowledge of the large scale structure, either through the flux power spectrum or the inferred matter power spectrum, constrains warm dark matter (WDM) models (Viel et al. 2005;Walther et al. 2019). In addition to probing structure formation, the Lyman-forest can be used to measure the thermal state of the IGM, leading to a set of measurements describing the thermal history of the IGM. Using the thermal and ionization history of the IGM, one can test models of the makeup and evolution of the ionizing background, and thus infer properties of the ionizing sources and sinks over time (Boera et al. 2019).

There are several ways in which Lyman-forest spectra are processed to constrain cosmological models and the thermal state of intergalactic gas. Cosmological contexts generally make use of the flux power spectrum from a sample of Lyman-forest spectra (Zaldarriaga et al. 2001;Palanque-Delabrouille et al. 2013;Nasir et al. 2016;Boera et al. 2019). The flux power is the Fourier transform of the flux over-density, = / -1. The flux power spectrum is sensitive to cosmological parameters on large scales ( < 0.02 s/km for velocity wavenumber ), and constrains small scale smoothing at higher (Kulkarni et al. 2015). For example, smoothing is enhanced in WDM models, leading to a reduction in power above some critical value of , (dependent on the mass of the WDM particle). This makes the flux power spectrum a robust tool for constraining WDM models (Walther et al. 2019).

The spectral statistics used in determining the thermal state of the IGM are more varied. Common methods include statistics which encapsulate an entire forest spectrum (Theuns & Zaroubi 2000;Theuns et al. 2002;Zaldarriaga 2002;Lidz et al. 2010;Becker et al. 2011;Boera et al. 2014), as well as analyses which make use of absorption features from spectra decomposed via Voigt profile fitting (Schaye et al. 1999;Ricotti et al. 2000;Schaye et al. 2000;McDonald et al. 2001;Bolton et al. 2014;Hiss et al. 2018). The small scale flux power spectrum and the distribution of flux are also used to constrain the IGM thermal state (Zaldarriaga et al. 2001;Gaikwad et al. 2020).

The Lyman-forest probes scales on which non-linear structure growth is important, and so cosmological hydrodynamic simulations of the IGM are necessary to build a map between model parameters and observations. These simulations require two components: collisionless cold dark matter modelled using N-body techniques, and collisional baryons which include pressure forces. One common simplification is that, although baryons are evolved hydrodynamically, the initial conditions for both species are identical, using the transfer function for the total matter fluid (Emberson et al. 2019).

Before recombination, baryons couple to radiation, suppressing their clustering on sub-horizon scales and reducing clustering relative to the dark matter. After recombination, baryons fall into the potential well of the cold dark matter and so the linear transfer functions differ by < 1% at = 0. The effect is larger at higher redshifts, = 2 -5, where the Lyman-forest is a sensitive probe of the gas (Naoz & Barkana 2005). Bird et al. (2020) showed that separate transfer functions can affect the one-dimensional Lymanforest flux power spectrum by 5 -10% on scales 0.001 -0.01 s/km in the redshift range = 2 -4.

The aim of this work is to determine whether species specific initial transfer functions have an appreciable effect on probes of the Lyman-forest. We use the simulation technique developed in Bird et al. (2020), which reproduces the theoretical offset between the dark matter and baryon power (Angulo et al. 2013), to model separate initial transfer functions. Recently, Rampf et al. (2020) (see also Hahn et al. 2020;Michaux et al. 2020) resolved this discrepancy by perturbing the particle masses, in agreement with the results from Bird et al. (2020). We will examine the effect of these initial conditions on measures of the thermal state of the IGM; the curvature (Becker et al. 2011), Doppler width cutoff (Schaye et al. 1999), and Doppler width distribution (Gaikwad et al. 2020). We also examine the effect on the matter and flux power spectrum, which could have consequences for warm dark matter models (Narayanan et al. 2000). The simulations we use are higher resolution than in Bird et al. (2020), allowing us to better probe smaller scales.

In Section 2 we outline the simulations and artificial spectra used throughout. In Section 3 we discuss the methods used to calculate each measure of the IGM, as well as the results of those calculations. Measures of the thermal history of the IGM, includ-ing the curvature, and the Doppler width cutoff and distribution, are covered in sections 3.1 & 3.2, respectively. The WDM relevant measures are examined in Sections 3.3 (flux power spectrum) and Section 3.4 (matter power spectrum). In Section 4 we summarize and conclude. We include Appendix A, which discusses numerical convergence with box size, resolution, and number of artificial spectra used.

We assume throughout a flat ΛCDM cosmology with Ω 0 = Ω + Ω = 0.288, Ω = 0.0472, ℎ = 0.7, = 0.971, and 8 = 0.84 (consistent with 9-year WMAP results Hinshaw et al. 2013).

SIMULATIONS

Our set of hydrodynamical simulations were performed using the N-body and smoothed particle hydrodynamics (SPH) code MP-Gadgetfoot_1 , described in Bird et al. (2018Bird et al. ( , 2019)). MP-Gadget is a fork of Gadget-3, itself the descendent of Gadget-2 (Springel 2005). Initial conditions are generated with MP-GenIC, the initial conditions generator packaged with MP-Gadget. The initial power spectrum, and transfer functions are generated with the Boltzmann code CLASS (Lesgourgues 2011).

Simulations using offset grids for both particle species (which is common in the literature) often introduce a spurious growing mode to the CDM-baryon difference. This can be avoided by using a glass to initialize the baryons (Yoshida et al. 2003;Bird et al. 2020), or by an appropriate perturbation of the particle masses (Hahn et al. 2020). Two sets of simulations are used throughout this work, with initial conditions set using the baryon-glass method. Both sets of simulations use a glass to initialize the baryons and a grid to initialize the CDM. A glass procedure, with 14 time-steps, is then applied to the combined distribution to minimize CDM-baryon overlap, avoiding chance overdensities set by the initialization. The two sets of simulations then differ, with the first set using a single transfer function for both species, and the second set using separate, species specific transfer functions. Scale-dependent perturbations are included via first-order Lagrangian perturbation theory (during final preparation of this manuscript, Hahn et al. (2020); Rampf et al. (2020) proposed an alternative method based on second-order perturbation theory, which gives similar results). The phases of the Fourier modes are identical, leading to the same realization of cosmic structure on scales larger than the particle grid.

Gas is assumed to be in ionization equilibrium with a uniform ultraviolet background using the model of Faucher-Giguère et al. ( 2009)foot_2 . Faucher-Giguère (2020) recently updated their UV background model and showed that simulations using uniform UV backgrounds do not accurately model the timing and photoheating associated with reionization. In our simulations reionization has completed by = 6 (the average neutral hydrogen fraction in low density regions of our simulations is less than 1%). Our results are generated in the redshift range 2 < < 6, after hydrogen reionization. We do not implement He reionization because the scale of our simulation box size is smaller than a typical He bubble (Upton Sanderbeck & Bird 2020), leading to an effectively instantaneous reionization.

Star formation is implemented using the standard approach for Lyman-forest analyses. Gas particles in the simulations are turned