Predictions for measuring the cross power spectrum of the HI 21-cm signal and the Lyman-α forest using OWFA

We have studied the possibility of measuring the cross-correlation of the redshifted HI 21-cm signal and the Lyman-α 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 σ 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 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 MHz. We see that the SNR of the cross-correlation detection can be significantly enhanced to ∼ 17 for z_c = 2.55 and B = 60 MHz. It is then possible to measure β_T and β_F individually with an SNR ≥ 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 SNR ≥ 5 is also possible in several bins at k ≤ 0.3 Mpc⁻¹.