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We measure the two point correlation function (CF) of 1357 galaxy clusterswith a mass of $\log_{10}{M_{200}}\geq 13.6$~\hm~and at a redshift of $z \leq0.125$. This work differs from previous analyses in that it utilizes aspectroscopic cluster catalogue, $\mathtt{SDSS-GalWCat}$, to measure the CF anddetect the baryon acoustic oscillation (BAO) signal. Unlike previous studieswhich use statistical techniques, we compute covariance errors directly bygenerating a set of 1086 galaxy cluster lightcones from the GLAM $N$-bodysimulation. Fitting the CF with a power-law model of the form $\xi(s) =(s/s_0)^{-\gamma}$, we determine the best-fit correlation length and power-lawindex at three mass thresholds. We find that the correlation length increaseswith increasing the mass threshold while the power-law index is almostconstant. For $\log_{10}{M_{200}}\geq 13.6$~\hm, we find $s_0 =14.54\pm0.87$~\h~and $\gamma=1.97\pm0.11$. We detect the BAO signal at $s =100$~\h~with a significance of $1.60 \sigma$. Fitting the CF with a$\Lambda$CDM model, we find $D_\mathrm{V}(z =0.089)\mathrm{r}^{fid}_d/\mathrm{r}_d = 267.62 \pm 26$ \h, consistent withPlanck 2015 cosmology. We present a set of 108 high-fidelity simulated galaxycluster lightcones from the high-resolution \U~N-body simulation, employed formethodological validation. We find $D_\mathrm{V}(z = 0.089)/r_d = 2.666 \pm0.129$, indicating that our method does not introduce any bias in the parameterestimation for this small sample of galaxy clusters.

The Correlation Function and Detection of Baryon Acoustic Oscillation Peak from the Spectroscopic SDSS GalWCat Galaxy Cluster Catalogue