Baryon acoustic oscillations from H{\Large I} intensity mapping: the importance of cross-correlations in the monopole and quadrupole

Cosmological parameter estimation in the post-reionisation era via the radio emission of neutral hydrogen (HI), is one of the key science goals of the forthcoming SKA Observatory (SKAO). In this paper, we explore detection capability for baryon acoustic oscillations (BAO) with a SKAO-like experimental set up, using a suite of 100 simulations inclusive of the main limitations from foreground contamination and poor angular resolution caused by the radio telescope beam. The latter represents a serious challenge for BAO detection with HI intensity mapping, hence we investigate adopting a multipole expansion approach as a means for mitigating the BAO detection limitations caused by the broad single-dish beam. We also showcase the gains made from cross-correlating the HI intensity mapping data with an overlapping spectroscopic galaxy survey, aiming to test the potential synergies between the SKA Project and other future cosmological experiments at optical/near-infrared wavelengths, like the Euclid satellite or the Dark Energy Spectroscopic Instrument. Whilst we were still able to achieve a ~4.5 sigma detection of BAO features in auto-correlation despite the dominant beam effect, a cross-correlation can increase this to a ~6 sigma detection. Furthermore, by adopting the widely studied multipole expansion formalism, we show that including the power spectrum quadrupole besides the monopole in a joint fit can approximately double the BAO detection significance. Despite not implementing a radial-only power spectrum analysis in favour of the three-dimensional power spectrum and its multipoles, we were still able to obtain robust constraints on the radial Alcock-Paczynski parameter, but found that perpendicular parameter remains unconstrained and prior dominated due to beam effects.