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We present a suite of cosmological N-body simulations with cold dark matter and baryons aiming at modeling the low-density regions of the IGM as probed by the Lyman-$\alpha$ forests at high redshift. The simulations are designed to match the requirements imposed by the quality of BOSS and eBOSS data. They are made using either 2x768$^3$ or 2x192$^3$ particles, spanning volumes ranging from (25 Mpc.h$^{-1})^3$ for high-resolution simulations to (100 Mpc.h$^{-1})^3$ for large-volume ones. Using a splicing technique, the resolution is further enhanced to reach the equivalent of simulations with 2x3072$^3$= 58 billion particles in a (100 Mpc.h$^{-1}$)^3 box size, i.e. a mean mass per gas particle of 1.2x10$^5$M_sun.h$^{-1}$. We show that the resulting power spectrum is accurate at the 2% level over the full range from a few Mpc to several tens of Mpc. We explore the effect on the one-dimensional transmitted-flux power spectrum of 4 cosmological parameters ($n_s, \sigma_8, \Omega_m, H_0$) and 2 astrophysical parameters ($T_0, \gamma$) related to the heating rate of the IGM. By varying the input parameters around a central model chosen to be in agreement with the latest Planck results, we built a grid of simulations that allows the study of the impact on the flux power spectrum of these six relevant parameters. We improve upon previous studies by not only measuring the effect of each parameter individually, but also probing the impact of the simultaneous variation of each pair of parameters. We thus provide a full second-order expansion, including cross-terms, around our central model. We check the validity of the second-order expansion with independent simulations obtained either with different cosmological parameters or different seeds. Finally, a comparison to the one-dimensional Ly-$\alpha$ forest power spectrum obtained with BOSS shows an excellent agreement., Comment: 30 pages, 11 figures, accepted for publication in JCAP. Has a companion paper Rossi et al. (2014)

We present a suite of cosmological N-body simulations with cold dark matter and baryons aiming at modeling the low-density regions of the IGM as probed by the Lyman-$\alpha$ forests at high redshift. The simulations are designed to match the requirements imposed by the quality of BOSS and eBOSS data. They are made using either 2x768$^3$ or 2x192$^3$ particles, spanning volumes ranging from (25 Mpc.h$^{-1})^3$ for high-resolution simulations to (100 Mpc.h$^{-1})^3$ for large-volume ones. Using a splicing technique, the resolution is further enhanced to reach the equivalent of simulations with 2x3072$^3$= 58 billion particles in a (100 Mpc.h$^{-1}$)^3 box size, i.e. a mean mass per gas particle of 1.2x10$^5$M_sun.h$^{-1}$. We show that the resulting power spectrum is accurate at the 2% level over the full range from a few Mpc to several tens of Mpc. We explore the effect on the one-dimensional transmitted-flux power spectrum of 4 cosmological parameters ($n_s, \sigma_8, \Omega_m, H_0$) and 2 astrophysical parameters ($T_0, \gamma$) related to the heating rate of the IGM. By varying the input parameters around a central model chosen to be in agreement with the latest Planck results, we built a grid of simulations that allows the study of the impact on the flux power spectrum of these six relevant parameters. We improve upon previous studies by not only measuring the effect of each parameter individually, but also probing the impact of the simultaneous variation of each pair of parameters. We thus provide a full second-order expansion, including cross-terms, around our central model. We check the validity of the second-order expansion with independent simulations obtained either with different cosmological parameters or different seeds. Finally, a comparison to the one-dimensional Ly-$\alpha$ forest power spectrum obtained with BOSS shows an excellent agreement., Comment: 30 pages, 11 figures, accepted for publication in JCAP. Has a companion paper Rossi et al. (2014)