Introducing the Seyfert-LINER Index (SLI): High Resolution (<100pc) Ionization Structures in the ISM of AGN ESO~137-G34

Abstract: We present a detailed, spatially resolved Baldwin-Phillips-Terlevich (BPT) analysis of ESO 137-G034, a Compton-thick Active Galactic Nucleus (AGN), based on narrowband {\it HST} imaging in [O III], [S II], H$\alpha$, and H$\beta$ emission lines. We dissect the Interstellar Medium (ISM) into Seyfert-, LINER-, and H II-dominated regions with a resolution of $\sim0.1^{\prime\prime}$ ($\sim20$ pc at $z=0.009$). To characterize the fine spatial structure of the { different excitation mechanism}, we introduce a new parameter: the Seyfert/LINER Index (SLI), defined as the perpendicular distance of each point in the BPT diagram from the Seyfert/LINER division line. The narrowband optical emission exhibits a bi-conical morphology and traces the diffuse X-ray emission observed with \textit{Chandra}. Most of the emission within the bi-cones is Seyfert-like, with SLI values consistent with AGN photoionization. The North-West Seyfert cone is surrounded by a $\sim100$--$200$ pc thick LINER cocoon with a smooth, monotonic SLI profile, shaped by either AGN wind-ISM interactions, and/or obscured AGN radiation; three radial SLI peaks suggest episodic nuclear outbursts, with estimated timescales of a few $10^3$ yrs and $<100$ yrs duration. The South-East cone shows inhomogeneous excitation, with a higher SLI region in its inner part, coinciding with a wider region of enhanced soft emission and the radio lobe inner edge. This region is characterized by line ratios consistent with fast shocks ($>1000$ km s$^{-1}$) induced excitation. The LINER cocoon in the SE cone appears more irregular, with inter-cone LINER points likely shaped by both local ISM structure and shocks. Our findings highlight the complex interplay of different AGN feedback mechanisms in the ISM.