Assembly Bias in eRASS1 X-ray Galaxy Clusters: Accounting for Non-uniform Survey Exposure
Halo assembly bias describes the dependence of halo clustering on properties beyond halo mass and provides a means of connecting halo assembly history to the large-scale matter distribution. We develop and test a relative clustering methodology for measuring differences in the large-scale bias of two halo populations using the ratio of their cluster--galaxy pair counts. In the linear regime, this ratio can be related to the difference in cluster bias, while the galaxy autocorrelation independently constrains the galaxy bias. We apply the method to a volume-limited X-ray selected galaxy clusters from the eROSITA eRASS1 catalogue, dividing them into high- and low-temperature subsamples with matched distributions in X-ray luminosity, redshift, and exposure. We first verify the validity of the linear approximation, finding $ξ(r)\ll1.0$ over $4$--$10\,h^{-1}\mathrm{Mpc}$. The joint clustering analysis yields $b_{\rm g}=1.610^{+0.018}_{-0.019}$ and a bias difference $Δb=0.8\pm1.1$. DES Y3 weak gravitational lensing measurements provide an independent test of the halo masses, yielding $\log(M_{200\mathrm{m}}/h^{-1}M_\odot)=14.33^{+0.07}_{-0.07}$ and $14.33^{+0.10}_{-0.09}$ for the high- and low-temperature samples, respectively, with a mass difference of $Δ\log M_{200\mathrm{m}}=-0.01\pm0.12$. We therefore find no statistically significant evidence for assembly bias at the $1σ$ level, but our measurement is consistent with the bias difference measured for analogous halo populations in the FLAMINGO simulation. The result therefore does not rule out assembly bias at the level expected from the simulation, while demonstrating that the relative clustering methodology provides a framework for future assembly-bias measurements with larger X-ray cluster and galaxy surveys.