Current experiments are providing measurements of the flux power spectrum from the Lyman- \alpha forests observed in quasar spectra with unprecedented accuracy .
Their interpretation in terms of cosmological constraints requires specific simulations of at least equivalent precision .
In this paper , we present a suite of cosmological N -body simulations with cold dark matter and baryons , specifically aiming at modeling the low-density regions of the inter-galactic medium as probed by the Lyman- \alpha forests at high redshift .
The simulations were run using the GADGET-3 code and were designed to match the requirements imposed by the quality of the current SDSS-III/BOSS or forthcoming SDSS-IV/eBOSS data .
They are made using either 2 \times 768 ^ { 3 } \simeq 1 billion or 2 \times 192 ^ { 3 } \simeq 14 million 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 2 \times 3072 ^ { 3 } \simeq 58 billion particles in a ( 100 { Mpc . h ^ { -1 } } ) ^ { 3 } box size , i.e .
a mean mass per gas particle of 1.2 \times 10 ^ { 5 } M _ { \odot } . 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 four cosmological parameters ( n _ { s } , \sigma _ { 8 } , \Omega _ { m } and H _ { 0 } ) and two astrophysical parameters ( T _ { 0 } and \gamma ) that are related to the heating rate of the intergalactic medium .
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 Lyman- \alpha forest power spectrum obtained with BOSS by shows an excellent agreement .