Cross-correlating the EMU Pilot Survey 1 with CMB lensing: Constraints on cosmology and galaxy bias with harmonic-space power spectra

We measured the harmonic-space power spectrum of galaxy clustering auto-correlation from the Evolutionary Map of the Universe Pilot Survey 1 data (EMU PS1) and its cross-correlation with the lensing convergence map of cosmic microwave background (CMB) from Planck Public Release 4 at the linear scale range from $\ell=2$ to 500. We applied two flux density cuts at $0.18$ and $0.4$mJy on the radio galaxies observed at 944MHz and considered two source detection algorithms. We found the auto-correlation measurements from the two algorithms at the 0.18mJy cut to deviate for $\ell\gtrsim250$ due to the different criteria assumed on the source detection and decided to ignore data above this scale. We report a cross-correlation detection of EMU PS1 with CMB lensing at $\sim$5.5$\sigma$, irrespective of flux density cut. In our theoretical modelling we considered two redshift distribution simulation models that yield consistent results, a linear and a non-linear matter power spectrum, and two linear galaxy bias models. That is a constant redshift-independent galaxy bias $b(z)=b_g$ and a constant amplitude galaxy bias $b(z)=b_g/D(z)$. By fixing a cosmology model and considering a non-linear matter power spectrum, we measured a constant galaxy bias at $0.18$mJy ($0.4$mJy) with $b_g=2.32^{+0.41}_{-0.33}$ ($2.18^{+0.17}_{-0.25}$) and a constant amplitude bias with $b_g=1.72^{+0.31}_{-0.21}$ ($1.78^{+0.22}_{-0.15}$). When $\sigma_8$ is a free parameter for the same models at $0.18$mJy ($0.4$mJy) with the constant model we found $\sigma_8=0.68^{+0.16}_{-0.14}$ ($0.82\pm0.10$), while with the constant amplitude model we measured $\sigma_8=0.61^{+0.18}_{-0.20}$ ($0.78^{+0.11}_{-0.09}$), respectively. Our results agree at $1\sigma$ with the measurements from Planck CMB and the weak lensing surveys and also show the potential of cosmology studies with future radio continuum survey data.