The correlation function and detection of baryon acoustic oscillation peak from the spectroscopic SDSS-GalWCat galaxy cluster catalogue

We measure the two-point correlation function (CF) of 1357 galaxy clusters with a mass of log<SUB>10</SUB>M<SUB>200</SUB> ≥ 13.6 h<SUP>-1</SUP> M<SUB>⊙</SUB> and at a redshift of z ≤ 0.125. This work differs from previous analyses in that it utilizes a spectroscopic cluster catalogue, $\tt {SDSS-GalWCat}$, to measure the CF and detect the baryon acoustic oscillation (BAO) signal. Unlike previous studies which use statistical techniques, we compute covariance errors directly by generating a set of 1086 galaxy cluster light-cones from the GLAM N-body simulation. Fitting the CF with a power-law model of the form ξ(s) = (s/s<SUB>0</SUB>)<SUP>-γ</SUP>, we determine the best-fitting correlation length and power-law index at three mass thresholds. We find that the correlation length increases with increasing the mass threshold while the power-law index is almost constant. For log<SUB>10</SUB>M<SUB>200</SUB> ≥ 13.6 h<SUP>-1</SUP> M<SUB>⊙</SUB>, we find s<SUB>0</SUB> = 14.54 ± 0.87 h<SUP>-1 </SUP>Mpc and γ = 1.97 ± 0.11. We detect the BAO signal at s = 100 h<SUP>-1</SUP> Mpc with a significance of 1.60σ. Fitting the CF with a Lambda cold dark matter model, we find $D_\mathrm{V}(z = 0.089)\mathit{r}^{\mathrm{ fid}}_\mathrm{ d}/\mathit{r}_\mathrm{ d} = 267.62 \pm 26$ h<SUP>-1 </SUP>Mpc, consistent with Planck 2015 cosmology. We present a set of 108 high-fidelity simulated galaxy cluster light-cones from the high-resolution Uchuu N-body simulation, employed for methodological validation. We find D<SUB>V</SUB>(z = 0.089)/r<SUB>d</SUB> = 2.666 ± 0.129, indicating that our method does not introduce any bias in the parameter estimation for this small sample of galaxy clusters.