Exploring gas thermodynamics around galaxies from the Sunyaev-Zel'dovich effects: impact of galaxy-halo connection, 2D projection and velocity field

A complete picture of the gas thermodynamics around galaxies is imprinted on the cosmic microwave background (CMB). Indeed, the thermal, kinematic, and relativistic Sunyaev-Zel'dovich effects (tSZ, kSZ, rSZ) measure the gas density, temperature, pressure of baryonic feedback and bulk velocity around galaxies, along with the gravitational potential it sits in. This full thermodynamic picture promises to constrain galaxy formation models and gas related uncertainties in the impact on galaxy lensing. Recent kSZ measurements around galaxies suggest that the gas may be more extended than anticipated, pointing to powerful feedback processes and large baryonic corrections to lensing. How robust are these conclusions about the galaxy-halo connection, including satellite fraction and high-mass outliers, or to 2D projection effects and large-scale velocity modes? In this paper, we give estimates for these effects using a simulated sample of DESI-like luminous red galaxies within the IllustrisTNG hydrodynamical simulation and the Abacus N-body simulation. We show that analyzing projected 2D profiles can lead to biases when computing quantities like the gas fraction. We also find that in the absence of spatial filtering, the 2-halo term is non-negligible for kSZ even at the smaller radii where the 1-halo term dominates. We show that a 1% uncertainty in the satellite fraction of galaxies can propagate into uncertainties of $\pm$1%, $\pm$3% and $\pm$5% in the 1-halo terms of the kSZ, tSZ, and rSZ signals, respectively. We show that masking the 2% most massive objects in the sample reduces the profile amplitudes by up to 10%, 40%, and 75% for the kSZ, tSZ, and rSZ signals, respectively. Finally, we show that naive simulations of the kSZ effect can be biased by an artificial Doppler term, which is automatically removed when high-pass or compensated aperture filtering is applied.