Seyfert/LINER Index (SLI) Overview

Updated 29 October 2025

SLI is a quantitative metric using optical emission-line ratios to differentiate Seyfert-like and LINER-like excitation in active galactic nuclei.
It leverages diagnostic diagrams, such as BPT diagrams with data-driven boundaries, to accurately classify excitation mechanisms.
Spatially resolved SLI mapping reveals sub-kpc structures and rapid transitions, offering insights into AGN feedback and host–nucleus interactions.

The Seyfert/LINER Index (SLI) is a quantitative parameter introduced to describe and spatially map the excitation state of ionized gas, specifically within active galactic nuclei (AGN) and their host galaxies, based on emission-line diagnostics. Its purpose is to systematically classify the relative degree and nature of excitation—Seyfert- or LINER-like—using measured line ratios and robust boundary definitions derived from diagnostic diagrams such as the Baldwin-Phillips-Terlevich (BPT) diagrams. The SLI provides a physically motivated, continuous metric for distinguishing excitation mechanisms, enabling both large-scale statistical studies and high-resolution spatial analysis of AGN feedback, ionization structure, and host–nucleus interactions.

1. Foundations and Quantitative Definition

The core principle of the Seyfert/LINER Index is the use of optical emission-line ratios to locate the position of an individual measurement (pixel, spaxel, aperture-integrated spectrum, or galaxy) with respect to a dividing line separating Seyfert-like and LINER-like excitation. The division is established in BPT diagrams, typically plotting log([O III]/Hβ) vs. log([N II]/Hα), log([S II]/Hα), or log([O I]/Hα). SLI is defined as follows (Fabbiano et al., 25 Oct 2025):

For a point at $(x_0, y_0)$ in BPT parameter space and a division line $y = m x + c$ : $\mathrm{SLI} = \frac{m x_0 - y_0 + c}{\sqrt{1 + m^2}}$

$x = \log_{10}([\mathrm{S\,II}]/\mathrm{H}\alpha)$ (or $[\mathrm{N\,II}]/\mathrm{H}\alpha$ , depending on diagram)
$y = \log_{10}([\mathrm{O\,III}]/\mathrm{H}\beta)$

Points with $\mathrm{SLI} > 0$ are Seyfert-like; $\mathrm{SLI} < 0$ are LINER-like. SLI quantifies not only the class but also the degree of excitation.

Alternatively, SLI can be formulated as the normalized fractional distance between locus points representative of LINER and Seyfert archetypes (Falcão et al., 17 Jun 2025): $\text{SLI} = \frac{d_\text{LINER}}{d_\text{LINER} + d_\text{Seyfert}}$ where $d_\text{LINER}$ and $d_\text{Seyfert}$ are Euclidean or Mahalanobis distances in line-ratio space.

2. Boundary Determination in BPT Diagrams

Accurate division between Seyfert and LINER populations is critical for meaningful SLI calculation. Recent work established improved, data-driven boundaries in the BPT diagrams, resolving inconsistencies among previous linear empirical demarcations (Cheng et al., 23 May 2025):

For the [N II] diagram:

$\log([\mathrm{O\,III}]/\mathrm{H}\beta) = 0.44 + 0.85\,x + 0.55\,x^2 - 0.82\,x^3$

where $x = \log([\mathrm{N\,II}]/\mathrm{H}\alpha)$ (“SO” line). This cubic division matches the actual contours of robustly classified Seyfert and LINER populations as sourced from [S II] and [O I] diagrams (“intersection boundary method”).

Comparison to previous demarcations (Sc07, Fe10) reveals that the SO line greatly improves classification efficiency and harmonizes Seyfert/LINER assignments across different diagnostic planes. The SLI is thus rendered consistent and physically interpretable by the choice of this boundary.

3. Spatially Resolved SLI Mapping and Morphological Structures

SLI has been implemented not only as a galaxy-integrated value, but most powerfully pixel-by-pixel in spatially resolved emission-line imaging and integral-field spectroscopic data (Fabbiano et al., 25 Oct 2025, Maksym et al., 2016, Ma et al., 2020, Falcão et al., 17 Jun 2025). This reveals sub-kpc structures, sharp transitions, and layered morphologies in the AGN environment.

Key findings include:

Seyfert-like regions (high SLI) are confined to ionization cones or nuclear zones, with emission consistent with AGN photoionization and/or fast shocks.
LINER cocoons (SLI negative and near-zero), manifest as thin (20–250 pc) shells enveloping the Seyfert cones, interpreted as the product of AGN wind/ISM interaction, filtered radiation, or perimeter shocks.
Sharp boundaries: The transition between high- and low-SLI regions is abrupt, occurring over $\sim$ 10–100 pc, signaling rapid changes in excitation conditions and aligning with morphological features of the host and outflows.

This mapping exposes complex feedback mechanisms, the impact of local ISM geometry, and distinguishes between true nuclear, circumnuclear, and host-driven excitation.

4. Physical Interpretation and Diagnostic Power

The value of SLI at each location encodes both excitation class and strength:

SLI $>0.4$ designates strongly Seyfert-like, likely associated with peak AGN activity or high-velocity shocks.
SLI $<0$ signals LINER-like, typically linked to lower ionization, shocks without precursors, post-AGB stars, or diluted/obscured AGN radiation.

SLI thus differentiates mechanisms:

AGN photoionization (hard spectrum, high SLI)
Shock excitation (variable SLI, spatially correlated with jets, radio or [Fe II] features, SLI transitions)
Filtered or aged emission (cocoon, monotonic SLI gradients)
Stellar contributory ionization (extended LINER, low SLI, post-AGB stars)

Continuous SLI mapping allows detection of gradients, episodic variability markers (SLI arcs), and feedback signatures with time/space coherence.

5. Population Statistics, SLI Ratios, and AGN Demographics

Integrated SLI evaluates the fraction or log-ratio of Seyfert- to LINER-like regions, relating to AGN demographics or evolutionary state. Using improved boundaries, recent surveys report (Cheng et al., 23 May 2025):

Type-1 AGN: Seyfert/LINER ratio $\sim$ 12
Type-2 AGN: Seyfert/LINER ratio $\sim$ 1.2

The disparity implies that most Type-2 LINERs are not bona fide AGN, often powered by evolved stars rather than active accretion. SLI-calibrated boundaries purify Seyfert samples and clarify the nature of LINERs—critical for unification paradigm tests, feedback modeling, and population analyses.

6. SLI in Multiwavelength Context and Additional Physical Diagnostics

Synoptic studies extend SLI by correlating optical excitation mapping with radio, X-ray, and kinematic diagnostics (Zajaček et al., 2019, Balmaverde et al., 2015, Younes et al., 2010). The SLI boundary is mirrored physically in radio spectral index sequences:

Seyferts: steep spectrum, high radio loudness, AGN jets/lobes, high SLI.
LINERs: flat/inverted spectrum, lower radio loudness, core-dominated, lower SLI.

High-resolution optical studies reveal that underlying NLR structure (density, temperature, presence of ILR/torus) further stratifies SLI, with physical distinctions observable in forbidden-line widths and component ratios (Balmaverde et al., 2015, Zhang et al., 2013).

7. Limitations, Methodological Considerations, and Future Directions

SLI construction relies fundamentally on robust emission-line measurements, precise continuum subtraction, and accurate extinction corrections. Limitations arise from signal-to-noise, line blending, aperture effects, and diagnostic completeness. For comprehensive SLI-based analysis, inclusion of multiple BPT planes, advanced statistical boundary calibration, and multiwavelength morphological context is recommended. Ongoing efforts integrate SLI with integral-field units (e.g., MUSE), spatially resolved spectroscopy, and kinematic feedback tracers, advancing insights into excitation geometry and feedback topology.

Summary Table: SLI Division Lines in [N II] BPT Diagram

S-L Line Designation	Formula	Shape
SO (optimal)	$0.44 + 0.85x + 0.55x^2 - 0.82x^3$	Non-linear
Sc07	Linear diagonal	Linear
Fe10	Alternative linear	Linear

The Seyfert/LINER Index provides a robust, physically interpretable, and spatially resolved quantitative tool, advancing AGN excitation diagnostics, feedback characterization, and the analysis of AGN-host evolutionary states within large surveys and targeted high-resolution studies. Its implementation enables new research into the structure and role of excitation modes in galactic nuclei.