The signature left in quasar spectra by neutral hydrogen in the Universe allows constraining the sum of the neutrino masses with a better sensitivity than laboratory experiments and may shed new light on the neutrino mass hierarchy and the absolute mass-scale of neutrinos. Constraints on cosmological parameters and on the dark energy equation of state can also be derived from a joint parameter estimation procedure. However, this requires a detailed modeling of the line-of-sight power spectrum of the transmitted flux in the Lyman-alpha (Ly alpha) forest on scales ranging from a few to hundreds of megaparsecs, which in turn demands the inclusion and careful treatment of cosmological neutrinos. To this end, we present here a suite of state-of-the-art hydrodynamical simulations with cold dark matter (CDM), baryons and massive neutrinos, specifically targeted for modeling the low-density regions of the intergalactic medium (IGM) as probed by the Ly alpha forest at high-redshift. The simulations span volumes ranging from (25 h(-1) Mpc)(3) to (100 h(-1) Mpc)(3), and were made using either 3 x 192(3) similar or equal to 21 million or 3 x 768(3) similar or equal to 1.4 billion particles. The resolution of the various runs was further enhanced, so that we reached the equivalent of 3 x 3072(3) similar or equal to 87 billion particles in a (100 h(-1) Mpc)(3) box size. The chosen cosmological parameters are compatible with the latest Planck 2013 results, although we also explored the effect of slight variations in the main cosmological and astrophysical parameters. We adopted a particle-type implementation of massive neutrinos, and consider three degenerate species with masses Sigma m(v) = 0.1, 0.2, 0.3, 0.4, and 0.8 eV, respectively. We improved on previous studies in several ways, in particular with updated routines for IGM radiative cooling and heating processes, and initial conditions based on second-order Lagrangian perturbation theory (2LPT) rather than the Zel'dovich approximation. This allowed us to safely start our runs at relatively low redshift (z = 30), which reduced the shot-noise contamination in the neutrino component and the CPU consumption. In addition to providing technical details on the simulations, we present the first analysis of the nonlinear three-and one-dimensional matter and flux power spectra from these models, and characterize the statistics of the transmitted flux in the Ly alpha forest including the effect of massive neutrinos. In synergy with recent data from the Baryon Acoustic Spectroscopic Survey (BOSS) and the Planck satellite, and with a grid of corresponding neutrino-less simulations, our realizations will allow us to constrain cosmological parameters and neutrino masses directly from the Ly alpha forest with improved sensitivity. In addition, our simulations can be useful for a broader variety of cosmological and astrophysical applications, ranging from the three-dimensional modeling of the Ly alpha forest to cross-correlations between different probes, studying the expansion history of the Universe including massive neutrinos, and particle-physics related topics. Moreover, while our simulations have been specifically designed to meet the requirements of the BOSS survey, they can also be used for upcoming or future experiments - such as eBOSS and DESI.
