Blowing star formation away in AGN hosts (BAH) -- V: The Feeding-Feedback Cycle in local AGNs as revealed by their stellar populations
We present a spatially resolved analysis of the stellar populations in the inner kiloparsec of NGC 3884, 3C 293, and CGCG 012-070. Using near-infrared spectroscopy, we reconstruct their star formation histories (SFHs) by comparing the M13, XSL, and FSPS stellar population synthesis models. The stellar light is dominated by intermediate-age to old populations (t >= 1 Gyr) with super-solar metallicities (Z >= 1 Z_sun). All models clearly indicate recent star formation (rejuvenation) in these AGN hosts, with young to intermediate-age populations contributing significantly in the nuclear regions. The SFHs from M13 and XSL broadly agree in showing coexisting old and young components, whereas FSPS favours a larger fraction of very young (t < 50 Myr) stars. Moreover, XSL- and FSPS-based SFHs are generally more irregular and "bumpy," while M13 yields smoother, more continuous SFHs. In NGC 3884 and 3C 293, stars with 0.2 < t <= 0.7 Gyr form a ring-like structure around the nucleus. The nuclear spectra further require non-stellar components: a featureless power-law continuum (FC) and hot dust emission (HD). In 3C 293, the FC component appears in two spatially separated regions, possibly indicating a dual active galactic nucleus, though a heavily reddened starburst origin for the secondary component cannot be excluded. Nearly all fits show a central drop in stellar metallicity, consistent with inflow of metal-poor gas that fuels recent accretion and AGN activity. Radial profiles show that HD and FC contributions decrease with radius, while younger stellar populations become more prominent outward. Together, these results support a feeding-feedback scenario in which gas inflows trigger circumnuclear star formation and, via stellar mass loss, help sustain ongoing AGN activity. .