O32 Parameter in Nebular Diagnostics

• O32 parameter is a nebular oxygen line ratio that compares [O III] and [O II] emissions, serving as a proxy for ionization conditions in diverse astrophysical environments.
• It is sensitive to calibration choices, reddening corrections, and instrumental resolution, which significantly influence its measured value and interpretation.
• O32 is widely employed to infer ionization parameter, metallicity, and potential LyC or Lyα escape, though its interpretation often requires complementary diagnostics.

The $O_{32}$ parameter is a nebular oxygen line ratio used to characterize the ionization state of photoionized gas in star-forming galaxies and active galactic nuclei, and to relate that state to Ly$\alpha$ transfer, Lyman-continuum escape, metallicity inference, and narrow-line region excitation. Across the cited literature, $O_{32}$ is not a single invariant convention but a family of closely related ratios built from [O III] and [O II] lines; the common physical content is the comparison of $\mathrm{O}^{2+}$-dominated emission to $\mathrm{O}^{+}$-dominated emission. This suggests that the parameter is best understood simultaneously as an observable ratio, a proxy for ionization conditions, and a quantity whose interpretation depends on calibration choice, reddening treatment, and astrophysical context (Izotov et al., 2018, Strom et al., 2017, Cleri et al., 28 May 2026).

1. Definitions and line-ratio conventions

In low-redshift LyC-leaker work, $O_{32}$ is often defined in linear form as the extinction-corrected flux ratio

$$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$

with $[\mathrm{O\,II}]\,\lambda3727$ denoting the usual blended $\lambda3726+\lambda3729$ feature at the relevant spectral resolution (Izotov et al., 2018, Izotov et al., 2017, Izotov et al., 2023). In that literature, the numerator is explicitly the single $[\mathrm{O\,III}]\,\lambda5007$ line rather than the summed $\alpha$0 doublet (Izotov et al., 2018, Izotov et al., 2023).

Other work adopts the summed doublets. A common high-redshift convention is

$\alpha$1

or the equivalent air-wavelength notation with $\alpha$2 over $\alpha$3 (Strom et al., 2017, Calabro et al., 2024, Liu et al., 18 Jan 2026). Some AGN and intermediate-redshift studies instead define

$\alpha$4

again emphasizing that the logarithm, not the raw ratio, is the reported quantity (Bornancini et al., 11 Jul 2025). The ratio is dimensionless (Izotov et al., 2019).

The parameter is frequently used together with $\alpha$5, which is defined with the summed oxygen nebular lines divided by $\alpha$6. For example,

$\alpha$7

in several low-redshift star-forming-galaxy studies, while logarithmic versions are common in high-redshift work (Izotov et al., 2018, Izotov et al., 2017, Izotov et al., 2023, Strom et al., 2017). The coexistence of these conventions is fundamental: numerical thresholds such as $\alpha$8, $\alpha$9, or $O_{32}$0 are only meaningful once the precise definition—linear or logarithmic, single-line or summed-doublet numerator—has been specified.

2. Measurement, reddening treatment, and observational systematics

Because [O II] and [O III] are widely separated in wavelength, reddening treatment is central to any operational use of $O_{32}$1. In the low-redshift compact-galaxy studies, the quoted values are best understood as rest-frame, extinction-corrected optical emission-line ratios derived from SDSS spectra, with observed fluxes corrected first for Milky Way reddening and then for internal extinction using Balmer decrements (Izotov et al., 2018). The same issue appears in resolved and high-redshift work: O32 maps in SAMI were built from dereddened flux maps and then smoothed specifically because the large wavelength separation makes the ratio sensitive to differential atmospheric refraction aliasing (Poetrodjojo et al., 2018). In lensed $O_{32}$2 galaxies, spatially resolved reddening corrections were found to be necessary because integrated reddening values could alter even the rank ordering of regional O32 values (Florian et al., 2020).

The measurement details also depend on instrumental resolution. At SDSS-like resolution, $O_{32}$3 is generally the blended doublet (Izotov et al., 2018). In HST grism work on lensed galaxies, the unresolved $O_{32}$4 doublet required the spatially integrated $O_{32}$5 ratio from ground-based spectroscopy to be imposed on all subregions (Florian et al., 2020). In JWST/NIRSpec and MIRI analyses, O32 can require combining line measurements from different instruments or gratings, as in GHZ2/GLASS-z12 where [O II] came from NIRSpec and [O III] from MIRI/LRS (Calabro et al., 2024).

The sensitivity of $O_{32}$6 to extinction can be large enough that anomalous Balmer-line physics changes the inferred ratio materially. In J1046+4047, the authors concluded that $O_{32}$7 was enhanced by non-recombination processes; when $O_{32}$8 was included in the Balmer decrement, the extinction coefficient became abnormally high and the corrected $O_{32}$9 flux was boosted more strongly than $\mathrm{O}^{2+}$0, lowering the inferred $\mathrm{O}^{2+}$1 from $\mathrm{O}^{2+}$2 to $\mathrm{O}^{2+}$3 (Izotov et al., 2023). This example established that extinction methodology is not a peripheral detail but part of the definition of the measured quantity.

Not all studies apply the same correction scheme. The zCOSMOS AGN analysis used platefit-vimos line measurements and discussed stellar-continuum subtraction, but did not report a dust-extinction correction for O32 and did not discuss reddening correction for the [O III]/[O II] ratio (Bornancini et al., 11 Jul 2025). This suggests that comparisons of absolute O32 values across samples require attention not only to numerator convention but also to whether the ratio is corrected for dust at all.

3. Physical interpretation: ionization state, radiation hardness, metallicity, and geometry

The basic physical meaning of $\mathrm{O}^{2+}$4 is the balance between $\mathrm{O}^{2+}$5 and $\mathrm{O}^{2+}$6 emission. High values indicate that the nebula is weighted toward the doubly ionized state, which is why the parameter is widely used as a proxy for ionization parameter or excitation (Izotov et al., 2017, Poetrodjojo et al., 2018, Strom et al., 2017). In this sense, O32 is an oxygen-only analog of a state variable: it compares emission from higher- and lower-ionization zones of the same element and therefore responds strongly to the intensity and hardness of the radiation field relative to gas density.

The cited literature is equally clear that O32 is not controlled by one parameter alone. In compact star-forming galaxies, high O32 can reflect a high ionization parameter, hard ionizing radiation, low metallicity, young starburst age, or density-bounded structure, and shocks can also perturb the ratio (Izotov et al., 2017). In the LyC-leaker studies, the authors explicitly state that O32 depends on ionization parameter, hardness of ionizing radiation, and metallicity, while viewing angle and inhomogeneous leakage can decouple the global excitation state from the line-of-sight escape of ionizing photons (Izotov et al., 2018). High-redshift JWST work likewise treats O32 as a useful but degenerate proxy: CEERS found a large spread in $\mathrm{O}^{2+}$7 of $\mathrm{O}^{2+}$8 dex at fixed nebular metallicity, implying that metallicity alone cannot explain the observed O32 variation (Reddy et al., 2023).

Extreme systems illustrate the breadth of the parameter’s astrophysical content. In J1046+4047, $\mathrm{O}^{2+}$9 was associated with weak low-ionization lines, strong [O III], detection of $\mathrm{O}^{+}$0 and $\mathrm{O}^{+}$1, very high specific star-formation rate, and a very young burst age inferred to be $\mathrm{O}^{+}$2 Myr (Izotov et al., 2023). In GHZ2/GLASS-z12 at $\mathrm{O}^{+}$3, the logarithmic value $\mathrm{O}^{+}$4 corresponded to an underlying linear [O III]/[O II] ratio of order $\mathrm{O}^{+}$5, together with extreme ionization conditions, low metallicity, and $\mathrm{O}^{+}$6 (Calabro et al., 2024). These cases do not imply a unique causal pathway, but they show that extreme O32 is empirically associated with hard ionizing continua and highly excited nebular gas.

The same logic extends to AGN, with an important change of scale. In X-ray selected AGN hosts, O32 is described as ionization-level sensitive and connected to the ionization state of the narrow-line region rather than to the torus-scale obscurer (Bornancini et al., 11 Jul 2025). This suggests that the parameter retains its meaning as an excitation diagnostic across source classes, even though the underlying ionizing engine differs.

4. O32 as an indicator of Ly$\mathrm{O}^{+}$7 and Lyman-continuum escape

A central use of $\mathrm{O}^{+}$8 has been the pre-selection of candidate LyC leakers. Compact low-mass star-forming galaxies with $\mathrm{O}^{+}$9 were motivated as likely candidates because high ratios may indicate density-bounded H II regions (Izotov et al., 2018). In one HST/COS program, five galaxies with $O_{32}$0–27 were all detected in the Lyman continuum, with $O_{32}$1 spanning $O_{32}$2–$O_{32}$3 (Izotov et al., 2018). This established that extreme O32 is an efficient screening criterion.

The same study also showed the limitations of that criterion. Within $O_{32}$4–27, $O_{32}$5 ranged from roughly $O_{32}$6 to $O_{32}$7, including J1011+1947 with the largest $O_{32}$8 but only moderate escape, and J1243+4646 with lower $O_{32}$9 but $$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$0 (Izotov et al., 2018). The authors’ conclusion was explicit: a high $$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$1 ratio is a necessary but not sufficient condition for a large amount of Lyman continuum radiation escaping from star-forming galaxies (Izotov et al., 2018). This has become the canonical caution attached to the parameter.

Subsequent work strengthened that caution. In eight compact galaxies at $$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$2–0.06540 deliberately selected for extreme $$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$3–39, the Ly$$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$4 properties were diverse: five galaxies showed strong Ly$$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$5 emission, while three showed weak Ly$$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$6 superposed on broad damped absorption and $$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$7. The authors concluded that there is no correlation between $$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$8 and $$O_{32}=\frac{[\mathrm{O\,III}]\,\lambda5007}{[\mathrm{O\,II}]\,\lambda3727},$$9, and likely no reliable standalone relation to LyC escape either (Izotov et al., 2019). In that paper, $[\mathrm{O\,II}]\,\lambda3727$0, the separation of the Ly$[\mathrm{O\,II}]\,\lambda3727$1 peaks, was presented as a better indirect tracer of both Ly$[\mathrm{O\,II}]\,\lambda3727$2 and LyC leakage than O32 (Izotov et al., 2019).

Keck/MOSFIRE work at $[\mathrm{O\,II}]\,\lambda3727$3 made the same point from a different direction. Candidate LyC emitters had high average O32 and some tentative nonzero escape fractions, but the authors argued for possible tension with published O32–$[\mathrm{O\,II}]\,\lambda3727$4 relations and emphasized clumpy geometry, mergers, shocks, and anisotropy as mechanisms that can produce high O32 with low observed escape, or the reverse (Bassett et al., 2018). Radiation-hydrodynamic simulations of reionization-era galaxies similarly found that simulated leakers often exhibit high O32 and overlap observed $[\mathrm{O\,II}]\,\lambda3727$5 LyC leakers in the $[\mathrm{O\,II}]\,\lambda3727$6–O32 plane, but also that viewing angle, metallicity, and ionization parameter all affect where a galaxy lies on the O32–$[\mathrm{O\,II}]\,\lambda3727$7 plane (Katz et al., 2020).

An important extension connects O32 to the neutral-gas reservoir. In a $[\mathrm{O\,II}]\,\lambda3727$8 Green Pea sample, a literature-motivated threshold of $[\mathrm{O\,II}]\,\lambda3727$9 was used as an indicator of likely LyC leakage. The galaxies above that threshold had a much lower H I 21 cm detection fraction, lower H I masses, lower H I-to-stellar-mass ratios, and shorter depletion times than the $\lambda3726+\lambda3729$0 subsample (Khasnovis et al., 4 Sep 2025). This does not make O32 a unique escape-fraction calibrator, but it supports the idea that very high O32 is associated with H I-poor or density-bounded conditions favorable for leakage.

5. O32 in ionization-parameter and metallicity inference

O32 is one of the most widely used proxies for the ionization parameter. In the KBSS-MOSFIRE analysis of typical $\lambda3726+\lambda3729$1 galaxies, the logarithmic definition

$\lambda3726+\lambda3729$2

yielded a tight empirical calibration,

$\lambda3726+\lambda3729$3

with $\lambda3726+\lambda3729$4 dex (Strom et al., 2017). In that framework, O32 was one of the cleanest strong-line correlates of model-inferred $\lambda3726+\lambda3729$5. Resolved SAMI spectroscopy used O32 iteratively with $\lambda3726+\lambda3729$6 to infer spaxel-by-spaxel $\lambda3726+\lambda3729$7, explicitly because the ratio is sensitive to ionization parameter but also strongly dependent on metallicity (Poetrodjojo et al., 2018).

Later work has retained O32 as a proxy while stressing its degeneracies. CEERS/JWST analysis used O32 first as a binning variable and proxy for $\lambda3726+\lambda3729$8, then replaced that simplification with full photoionization modeling of all available strong lines; the resulting sample showed a $\lambda3726+\lambda3729$9 dex spread in $[\mathrm{O\,III}]\,\lambda5007$0 at fixed $[\mathrm{O\,III}]\,\lambda5007$1 (Reddy et al., 2023). RUBIES extended this logic to $[\mathrm{O\,III}]\,\lambda5007$2, inferring $[\mathrm{O\,III}]\,\lambda5007$3 from O32 with large Cloudy model libraries rather than a single linear fit. The resulting analysis found that O32 alone leaves a systematic uncertainty in $[\mathrm{O\,III}]\,\lambda5007$4 of $[\mathrm{O\,III}]\,\lambda5007$5 dex even at zero measurement uncertainty because many different photoionization models predict the same O32 ratio without informative priors (Cleri et al., 28 May 2026).

The parameter is also embedded in metallicity diagnostics, where its role is more ambivalent. In extremely metal-poor dwarf galaxies, O32 can act as an explicit correction for ionization-parameter effects in strong-line abundance work. J1046+4047, with $[\mathrm{O\,III}]\,\lambda5007$6, enabled an updated calibration for $[\mathrm{O\,III}]\,\lambda5007$7 and $[\mathrm{O\,III}]\,\lambda5007$8: $[\mathrm{O\,III}]\,\lambda5007$9 with

$\alpha$00

(Izotov et al., 2023). At high redshift, updated indicators similarly incorporate O32 as one of the corrective variables: $\alpha$01 with analogous definitions for $\alpha$02 and $\alpha$03, precisely because classical one-dimensional calibrations fail when ionization parameter and nitrogen enrichment vary strongly at fixed oxygen abundance (Liu et al., 18 Jan 2026).

At the same time, multiple studies show that O32 is poor as a standalone metallicity estimator. Testing local strong-line calibrations at $\alpha$04, Patrício et al. found that O32 yielded large dispersions of $\alpha$05–$\alpha$06 dex relative to direct-method abundances, worse than the best cases of $\alpha$07 and O3 (Patrício et al., 2018). Reionization-era synthetic spectra from Technicolor Dawn led to an even stronger warning: applying an observational O32 metallicity calibration to the synthetic spectra overestimated oxygen abundance by about $\alpha$08 dex relative to the intrinsic simulation metallicity, implying that O32 can be badly biased in composite EoR spectra (Kusmic et al., 22 Oct 2025). The consistent lesson is that O32 is often indispensable in multivariate abundance inference, but unreliable when treated as a one-parameter metallicity axis.

6. Population trends, regime dependence, and broader applications

Population studies show that O32 systematically depends on galaxy class and cosmic epoch, but not always in a simple univariate way. In a MUSE sample of 406 star-forming galaxies at $\alpha$09, 104 galaxies had $\alpha$10 and 15 had $\alpha$11, corresponding to 26% and 3.7% of the sample, respectively (Paalvast et al., 2018). That study found no significant correlation between O32 and stellar mass, star-formation rate, or distance from the star-forming main sequence on an object-by-object basis, while arguing that the decline in the fraction of high-O32 emitters with increasing stellar mass is most likely driven by metallicity rather than mass itself (Paalvast et al., 2018). The same paper found no evidence for a dependence of the fraction of high-O32 emitters on redshift over $\alpha$12 (Paalvast et al., 2018).

In intermediate-redshift dwarf galaxies, O32 was used jointly with Ne3O2 to show that typical $\alpha$13 dwarf stacks have higher O32 at fixed Ne3O2 than typical local galaxies, especially at low mass, while individually selected [Ne III] emitters are more extreme and resemble $\alpha$14 systems (Pharo et al., 2023). At much higher redshift, GHZ2/GLASS-z12 showed $\alpha$15 in the logarithmic convention, well above typical lower-redshift ISM values and compatible with either an AGN or a compact, dense star-forming environment with high $\alpha$16, low metallicity, and probable $\alpha$17 LyC leakage (Calabro et al., 2024). RUBIES then generalized the evolutionary picture by showing that inferred $\alpha$18 increases with redshift and sSFR and decreases with stellar mass from $\alpha$19, with a factor of $\alpha$20 increase from $\alpha$21 to $\alpha$22 even at fixed stellar mass and sSFR (Cleri et al., 28 May 2026).

O32 also has a distinct role in AGN studies. In X-ray selected AGNs at $\alpha$23, the parameter was defined logarithmically and described as ionization-level sensitive, with the main empirical results being a stronger O32–$\alpha$24 correlation in unobscured AGNs than in obscured ones, systematically depressed O32 in low-excitation obscured AGNs, and a weak positive correlation between O32 and specific black-hole accretion rate (Bornancini et al., 11 Jul 2025). The same study argued that O32 is not a simple obscuration indicator because it probes the larger-scale narrow-line region rather than the torus-scale absorber (Bornancini et al., 11 Jul 2025).

A recurring misconception is that a large O32 uniquely identifies a LyC leaker or a low-metallicity galaxy. The literature does not support either claim in that form. High O32 efficiently selects unusual, highly excited systems and is often associated with low metallicity, high ionization parameter, hard spectra, or density-bounded geometry. Yet local LyC studies, resolved spectroscopy, AGN work, and reionization-era simulations all show that the ratio is degenerate with geometry, density, radiation hardness, metallicity, and line-of-sight effects (Izotov et al., 2018, Florian et al., 2020, Bornancini et al., 11 Jul 2025, Kusmic et al., 22 Oct 2025). The most durable interpretation is therefore not that O32 fails, but that it is intrinsically multivalent: a powerful first-order excitation diagnostic whose full physical meaning emerges only when paired with additional observables such as $\alpha$25, Ne3O2, He I line ratios, Ly$\alpha$26 peak separation, density diagnostics, or full photoionization modeling (Izotov et al., 2017, Izotov et al., 2019, Cleri et al., 28 May 2026).