We report the detection of morphology dependent stellar age in massive quenched galaxies (QGs) at z~1.2. The sense of the dependence is that compact QGs are 0.5-2 Gyr older than normal-sized ones. The evidence comes from three different age indicators, Dn4000, Hdelta and fits to spectral synthesis models, applied to their stacked optical spectra. All age indicators consistently show that the stellar populations of compact QGs are older than their normally-sized counterparts. We detect weak [OII] emission in a fraction of QGs, and the strength of the line, when present, is similar between the two samples; however, compact galaxies exhibit significantly lower frequency of [OII] emission than normal ones. A fraction of both samples are individually detected in 7 Ms Chandra X-ray images (luminosities$sim10^{40}$-$10^{41}$ erg/sec). 7 Ms stacks of non-detected galaxies show similarly low luminosities in the soft band only, consistent with a hot gas origin for the X-ray emission. While both [OII] emitters and non-emitters are also X-ray sources among normal galaxies, no compact galaxy with [OII] emission is an X-ray source, arguing against an AGN powering the line in compact galaxies. We interpret the [OII] properties as further evidence that compact galaxies are older and further along into the process of quenching star-formation and suppressing gas accretion. Finally, we argue that the older age of compact QGs is evidence of progenitor bias: compact QGs simply reflect the smaller sizes of galaxies at their earlier quenching epoch, with stellar density most likely having nothing directly to do with cessation of star-formation.
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