We present an analysis of AGN activity within recently quenched massive
galaxies at cosmic noon ($z\sim 2$), using deep Chandra X-ray observations of
the Ultra-Deep Survey (UDS) field. Our sample includes over 4000 massive
galaxies ($M_\ast > 10^{10.5}$ M$_{\odot}$) in the redshift range $1 < z < 3$, including more than 200 transitionary post-starburst (PSB) systems. We find that X-ray emitting AGN are detected in $6.2 \pm 1.5$ per cent of massive PSBs at these redshifts, a detection rate that lies between those of star-forming and passive galaxies ($8.2 \pm 0.5$ per cent and $5.7 \pm 0.8$ per cent, respectively). A stacking analysis shows that the average X-ray luminosity for PSBs is comparable to older passive galaxies, but a factor of $2.6 \pm 0.3$ below star-forming galaxies of similar redshift and stellar mass. The average X-ray luminosity in all populations appears to trace the star-formation rate, with PSBs showing low levels of AGN activity consistent with their reduced levels of star formation. We conclude that, on average, we see no evidence for excess AGN activity in the post-starburst phase. However, the low levels of AGN activity can be reconciled with the high-velocity outflows observed in many PSBs, assuming the rare X-ray detections represent short-lived bursts of black hole activity, visible $\sim$5 per cent of the time. Thus, X-ray AGN may help to maintain quiescence in massive galaxies at cosmic noon, but the evidence for a direct link to the primary quenching event remains elusive.

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