Redshift space three-point correlation function of IGM at $z<0.48$
  The Ly$\alpha$ forest decomposed into Voigt profile components allow us to
study clustering properties of the intergalactic medium and its dependence on
various physical quantities. Here, we report the first detections of
probability excess of low-z (i.e z<0.48) Ly$\alpha$ absorber triplets over a
scale of $r_\parallel\leq8$pMpc with a maximum amplitude of
$8.76^{+1.96}_{-1.65}$ at a longitudinal separation of 1-2pMpc. We measure
non-zero three-point correlation ($\zeta=4.76^{+1.98}_{-1.67}$) only at this
scale with reduced three-point correlation value of Q=$0.95^{+0.39}_{-0.38}$.
The measured $\zeta$ shows an increasing trend with increasing HI column
density ($N_{HI}$) while Q does not show any $N_{HI}$ dependence. About 88% of
the triplets contributing to $\zeta$ (at z$\le0.2$) have nearby galaxies (whose
distribution is known to be complete for 0.1L$_*$ at z<0.1 and for L$_*$ at
z~0.25 and within 20' to the quasar sightlines) within a velocity separation of
500$kms^{-1}$ and a median impact parameter of 405pkpc. The measured impact
parameters are consistent with appreciable number of triplets at z$\le0.2$ not
originating from individual galaxies but tracing the underlying galaxy
distribution. Frequency of occurrence of high-b absorbers in triplets (~85%) is
a factor~3 higher than that found among the full sample (~32%). Using four
different cosmological simulations, we quantify the effect of peculiar
velocities, feedback effects and show that most of the observed trends are
broadly reproduced. However, $\zeta$ at small scales ($r_\parallel<1$pMpc) and
b-dependence of $\zeta$ in simulations are found inconsistent with the
observations. This could either be related to the fact that none of these
simulations reproduce the observed b-distribution and $N_{HI}$ distribution for
$N_{HI}>10^{14}$cm$^{-2}$ self-consistently or to the widespread of
signal-to-noise ratio in the observed data.
