Three- and two-point spatial correlations of intergalactic medium at z ∼ 2 using projected quasar triplets

 We present analysis of two- and three-point correlation functions of Lyα forest (at 2 ≤ z ≤ 2.5) using X-Shooter spectra of three background quasar triplets probing transverse separations of 0.5–1.6 pMpc. We present statistics based on transmitted flux and clouds identified using Voigt profile fitting. We show that the observed two-, three-point correlation functions and reduced three-point correlation (i.e. Q) are well reproduced by our simulations. We assign probabilities for realizing all the observed correlation properties simultaneously using our simulations. Our simulations suggest an increase in correlation amplitudes and Q with increasing NH i. We roughly see this trend in the observations too. We identify a concurrent gap of 17Å (i.e. 14.2 h−1 cMpc, one of the longest reported) wide along one of the triplets. Such gap is realized only in 14.2 per cent of our simulated sightlines and most of the time belongs to a void in the matter distribution. In the second triplet, we detect Damped Lyα systems (DLAs) along all three sightlines (with spatial separations 0.64 to 1.6 pMpc) within a narrow redshift interval (i.e. Δz = 0.088). Detection of a foreground quasar (∼1 pMpc from the triplet sightlines) and excess partial Lyman Limit systems (with NH i in the range $10^{16-17.2} \, \mathrm{cm}^{-2}$) around these DLAs suggest that we may be probing a large overdense region. We also report positive C iv–C iv correlations up to ∼500 km s−1 only in the longitudinal direction. Additionally, we conclude a positive C iv–Lyα correlations for higher NH i thresholds (${\gt}10^{15}\, \mathrm{cm}^{-2}$) up to a scale of ∼1000 km s−1 both in transverse and longitudinal directions.