Resolving the Nuclear Environments of Tidal Disruption Event Host Galaxies within 45 pc

Using HST/STIS observations, we present the highest-spatial-resolution spectroscopic study to date of four tidal disruption event (TDE) host galaxies, with the best observed being the post-starburst (PSB) host of ASASSN-14li. The stellar population of ASASSN-14li's host, within 44 pc of the nucleus, reveals a younger recent starburst ($\sim$340 Myr) compared to the population at an offset radius of 88 pc that excludes the nucleus ($\sim$550 Myr), a radial age gradient suggesting gas inflows from a minor merger. We estimate a stellar density of $\sim5900 \pm 800 \, M_\odot / \mathrm{pc}^3$ within 30 pc of the nucleus of ASASSN-14li's host, exceeding densities expected for nuclear star clusters. High-ionization ``coronal" emission lines, [Fe VI] $\lambda 5677$, [Fe VII] $\lambda 6087$, and [Fe X] $\lambda 6375$, are also detected within the nuclear spectra of the hosts of ASASSN-14li and PTF09ge, importantly alongside the non-detection of [O III] at the same scale. We similarly do not detect [O III] in the nuclear region of ASASSN-14ae's host despite its presence in the SDSS spectrum. The different ionization radiation levels detected at various radii from TDE host nuclei may indicate echoes of earlier accretion episodes, including, potentially, a prior TDE. We posit that a minor merger driving gas inflow to the nucleus could drive the enhanced TDE rates in post-starburst galaxies, inducing variation in nuclear gas properties and star formation history on $<$150 pc scales in TDE hosts.