The impact of relativistic effects on the 3D Quasar-Lyman-α cross-correlation

Abstract

We study the impact of relativistic effects in the 3-dimensional\ncross-correlation between Lyman-$\\alpha$ forest and quasars. Apart from the\nrelativistic effects, which are dominated by the Doppler contribution, several\nsystematic effects are also included in our analysis (intervening metals,\nunidentified high column density systems, transverse proximity effect and\neffect of the UV fluctuations). We compute the signal-to-noise ratio for the\nBaryonic Oscillation Spectroscopic Survey (BOSS), the extended Baryonic\nOscillation Spectroscopic Survey (eBOSS) and the Dark Energy Spectroscopic\nInstrument (DESI) surveys, showing that DESI will be able to detect the Doppler\ncontribution in a Large Scale Structure (LSS) survey for the first time, with a\nS/N $>7$ for $r_{\\rm min} > 10$ Mpc$/h$, where r$_{\\rm min}$ denotes the\nminimum comoving separation between sources. We demonstrate that several\nphysical parameters, introduced to provide a full modelling of the\ncross-correlation function, are affected by the Doppler contribution. By using\na Fisher matrix approach, we establish that if the Doppler contribution is\nneglected in the data analysis, the derived parameters will be shifted by a\nnon-negligible amount for the upcoming surveys.\n