Predictions for measuring the cross power spectrum of the HI 21-cm
  signal and the Lyman-$\alpha$ forest using OWFA
  We have studied the possibility of measuring the cross-correlation of the
redshifted HI 21-cm signal and the Lyman-$\alpha$ forest using an upcoming
radio-interferometric array OWFA and an spectroscopic observation like SDSS-IV.
Our results shows that it is possible to have a $6 \sigma$ detection of the
cross-correlation signal with OWFA PII using an observing time of $200$ hrs
each in $N_p = 25$ independent fields-of-view. However, not much can be done
beyond this using the cross-correlation signal for $z_c = 3.35$ and $B = 30 \,
{\rm MHz}$. Apart from this, we have also envisaged a situation where
observations are carried out at $z_c = 3.05$ and $2.55$ which lie closer to the
peak of the quasar distribution at $z = 2.25$ and with a larger bandwidth of $B
= 60 \, {\rm MHz}$. We see that the SNR of the cross-correlation detection can
be significantly enhanced to $\sim 17$ for $z_c = 2.55$ and $B = 60 \, {\rm
MHz}$. It is then possible to measure $\beta_T$ and $\beta_F$ individually with
an ${\rm SNR} \ge 5$ by combining the cross-correlation with the HI 21-cm
auto-correlation measurements. We further find that a measurement of the binned
cross-correlation power spectrum with ${\rm SNR} \ge 5$ is also possible in
several bins at $k \le 0.3 \, {\rm Mpc}^{-1}$.
