The impact of relativistic effects on the 3D Quasar-Lyman-$\alpha$ cross-correlation

TL;DR

This paper investigates how relativistic effects, especially the Doppler contribution, influence the 3D cross-correlation between Lyman-alpha forest and quasars, highlighting the importance for upcoming large-scale structure surveys.

Contribution

It provides the first forecast that DESI can detect the Doppler effect in LSS and shows how neglecting it biases parameter estimation.

Findings

DESI will detect the Doppler contribution with S/N > 7 for r_min > 10 Mpc/h.

Relativistic effects significantly impact the cross-correlation function modeling.

Neglecting Doppler effects biases the physical parameter estimates in future surveys.

Abstract

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