QSO MUSEUM II: Search for extended Ly$\alpha$ emission around eight $z \sim 3$ quasar pairs

Extended Ly$\alpha$ emission is routinely found around single quasars (QSO) across cosmic time. However, few studies have investigated how such emission changes in fields with physically associated QSO pairs, which should reside in dense environments and are predicted to be linked through intergalactic filaments. We present VLT/MUSE snapshot observations (45 min./source) to unveil extended Ly$\alpha$ emission on scales of the circumgalactic medium (CGM) around the largest sample of physically associated QSO pairs to date, encompassing 8 pairs (14 observed QSOs) at $z$~3 with $i$-band magnitude between 18 and 22.75. The pairs are either at close (~50-100 kpc, 5 pairs) or wide (~450-500 kpc, 3 pairs) separation with velocity differences of $\Delta$v < 2000 km s$^{-1}$. We detect extended emission around 12 of the 14 targeted QSOs and investigate the luminosity, size, kinematics and morphology of these Ly$\alpha$ nebulae. On average, they span 90 kpc and are 2.8 $\times 10^{43}$ erg s$^{-1}$ bright. Irrespective of the QSOs' projected distance, the nebulae often (~45 %) extend toward the other QSO in the pair, leading to asymmetric emission whose flux-weighted centroid is at an offset position from any QSO location. We show that large nebulae are preferentially aligned with the large-scale structure as traced by the two QSOs, and conclude that the cool gas (10$^4$ K) in the CGM traces well the direction of cosmic web filaments. Additionally, the radial profile of the Ly$\alpha$ surface brightness around QSO pairs can be described by a power law with a shallower slope (~$-1.6$) with respect to single QSOs (~$-2$), indicative of increased CGM densities out to large radii and/or enhanced contribution from the intergalactic medium (IGM). The sample presented in this study contains excellent targets for ultra-deep observations to directly study filamentary IGM structures in emission.