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Turbulent motions in the circumgalactic medium (CGM) play a critical role inregulating the evolution of galaxies, yet their detailed characterizationremains elusive. Using two-dimensional velocity maps constructed fromspatially-extended [OII] and [OIII] emission, Chen et al. (2023b) measured thevelocity structure functions (VSFs) of four quasar nebulae at$z\approx\!0.5$--1.1. One of these exhibits a spectacular Kolmogorov relation.Here we carry out an ensemble study using an expanded sample incorporating fournew nebulae from three additional QSO fields. The VSFs measured for all eightnebulae are best explained by subsonic turbulence revealed by the line-emittinggas, which in turn strongly suggests that the cool gas ($T\!\sim\!10^4$ K) isdynamically coupled to the hot ambient medium. Previous work demonstrates thatthe largest nebulae in our sample reside in group environments with clear signsof tidal interactions, suggesting that environmental effects are vital inseeding and enhancing turbulence within the gaseous halos, ultimately promotingthe formation of the extended nebulae. No discernible differences are observedin the VSF properties between radio-loud and radio-quiet QSO fields. Weestimate the turbulent heating rate per unit volume, $Q_{\rm turb}$, in the QSOnebulae to be $\sim 10^{-26}$--$10^{-22}$ erg cm$^{-3}$ s$^{-1}$ for the coolphase and $\sim 10^{-28}$--$10^{-25}$ erg cm$^{-3}$ s$^{-1}$ for the hot phase.This range aligns with measurements in the intracluster medium and star-formingmolecular clouds but is $\sim10^3$ times higher than the $Q_{\rm turb}$observed inside cool gas clumps on scales $\lesssim1$ kpc using absorption-linetechniques. We discuss the prospect of bridging the gap between emission andabsorption studies by pushing the emission-based VSF measurements to below$\approx\!10$ kpc.

An ensemble study of turbulence in extended QSO nebulae at $z\approx0.5$--1