Measuring the Clustering of tSZ-Selected Galaxy Clusters with SPT-3G

We present a measurement of the spatial clustering of galaxy clusters selected via the thermal Sunyaev-Zel'dovich (tSZ) signal. Using a cluster catalog derived from five years of SPT-3G Main field survey data, we define a sample spanning 0.25 < z < 1.1, as well as two subsamples spanning 0.25 < z < 0.67 and 0.67 < z < 1.1. We detect cluster clustering at 12.8σ, the highest significance detection in a tSZ-selected sample to date. We detail our analytic modeling and theoretical covariance models, including validations performed on synthetic data created from numerical simulations. The measurements and inference pass a variety of null tests, and show minimal sensitivity to common spatially varying systematics that impact optical clustering measurements, such as depth, stellar density, and extinction. We use our pipeline to place constraints on the halo bias of our sample, b = 5.30 plus or minus 0.24, and the normalization of our mass-observable relation, sz = 0.43+0.17-0.21. We also demonstrate the useful synergies between cluster clustering and abundance measurements, which manifest in the breaking of high-dimensional parameter degeneracies. Samples of clusters selected using the tSZ effect serve as a unique probe of clustering that is insensitive to common systematics, relative to conventional galaxy datasets, and the detection significance of this measurement will increase substantially with existing data from the SPT-3G Ext-10k survey and upcoming data from SPT-3G+ and the Simons Observatory.