Clustering of z~6.6 Quasars and [O III] Emitters Constrains Host Halo Masses and Duty Cycles in 25 ASPIRE Fields

Abstract

We use data from the JWST ASPIRE Wide Field Slitless Spectroscopy (WFSS) program to measure the auto-correlation function of [O,{\sc iii}] emitters at 5.3$<z<$7.0 and the quasar--[O,{\sc iii}] emitter cross-correlation around 25 ASPIRE quasars (6.51$<z<$6.82; $\langle z\rangle=6.6$). We use synthetic source injection to calibrate the selection function, which we combine with the large-volume FLAMINGO-10k simulation (2.8,cGpc box) to construct realistic mock observations. Our simulation-based approach captures nonlinear structure growth and scale-dependent bias on small scales and derives covariance matrices that include cosmic variance. The clustering yields correlation lengths of $r_0^{\rm GG}=4.7^{+0.4}{-0.5},h^{-1}$,cMpc for the [O,{\sc iii}] auto-correlation with fixed slope $\gamma{\rm GG}=1.8$, and $r_0^{\rm QG}=8.7^{+0.8}{-0.9},h^{-1}$,cMpc for the quasar--[O,{\sc iii}] cross-correlation with $\gamma{\rm QG}=2.0$. We infer $\log(M_{h,{\rm min}}^{[{\rm O,III}]}/M_\odot)=10.5^{+0.1}{-0.1}$ for [O,{\sc iii}] emitters and $\log(M{h,{\rm min}}^{\rm QSO}/M_\odot)=12.1^{+0.3}{-0.4}$ for quasars. These imply duty cycles of $2.5^{+1.0}{-0.8}$,per,cent for [O,{\sc iii}] emitters and $0.3^{+4.0}{-0.3}$,per,cent for quasars, corresponding to UV-bright lifetimes of $t{\rm Q}=2.6^{+30}_{-2.5}$,Myr (less than 10,per,cent of a Salpeter $e$-folding time). The results indicate that the observed UV-luminous phase contributes little to total SMBH growth, placing tight constraints on early black-hole formation.