The Low-redshift Lyman Continuum Survey. II. New Insights into LyC Diagnostics

As both Lyα and the LyC are sensitive to the line of sight, we anticipate the former to trace the LCE fraction rather well, even as the emission line experiences higher optical depths than the continuum for the same column density. We demonstrate that this relation is the case in Figure 2. The LCE fraction increases nearly monotonically with both ${f}_{\mathrm{esc}}^{\mathrm{Ly}\alpha }$ and the Lyα EW. Deviations from this trend occur at high ${f}_{\mathrm{esc}}^{\mathrm{Ly}\alpha }$ owing to two galaxies having abnormally high Lyα/Hβ ratios corresponding to values of ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$ close to 1.

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The overwhelming success of all three Lyα diagnostics in correlating with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ demonstrates that both Lyα and LyC escape depend on the distribution of neutral hydrogen in a galaxy. While all three are promising candidates for ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ indicators at high redshift, Lyα EW is perhaps the easiest to measure, as it requires neither rest-frame optical nor high-resolution spectroscopy. The wealth of Lyα EW measurements of LCEs at higher redshifts (z ∼ 3−4; e.g., Steidel et al. 2018; Marchi et al. 2018; Fletcher et al. 2019; Pahl et al. 2021) suggests that these diagnostics will likely remain applicable for galaxies at the epoch of reionization. We discuss this possibility in detail in Section 5.3.

3.1.1. Lyα Escape Fraction

3.1.2. Lyα Equivalent Width

In place of ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$, we consider Lyα EW as another possible indicator of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. While less directly tracing optical depth than ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$, Lyα EW is far easier to measure at high redshift because, unlike ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$, it does not require observing the Balmer lines. Furthermore, both Henry et al. (2015) and Yang et al. (2017a) demonstrate a strong correlation between ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$ and Lyα EW for Green Peas (GPs).

From Figure 3, ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ is bounded by an upper limit that increases with Lyα EW. We find that the relation between Lyα EW and ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ given by Pahl et al. (2021) provides a reasonable description of this envelope in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ values up to ∼150 Å. Interestingly, this trend extends beyond the 110 Å maximum predicted by Steidel et al. (2018), perhaps due to their assumed continuous star formation history.

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The correlation between ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ and Lyα EW is one of the stronger and more significant of the diagnostics we consider, with τ ≈ 0.3 across all three ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ indicators. Ten of the 16 galaxies with high Lyα EW are strong leakers, indicating a possible transition in Lyα EW at 100 Å. Galaxies with EWs above this value are far more likely to be strong LCEs than those below it (see also Figure 2). Further supporting this notion of a 100 Å transition, LCEs with EWs below this value are not as prodigious emitters as above it, which may suggest that LCEs with high EW contribute more significantly to the cosmic LyC budget.

Lyα is sensitive to both column density and ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$, which affects the distribution of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ over the EWs. As the optical depth decreases, more Lyα and LyC photons can escape. The drop in column density will then begin to limit the intrinsic emission of Lyα photons, causing Lyα EW to decrease with increasing ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ (Nakajima & Ouchi 2014; Steidel et al. 2018). This effect may explain why some strong LCEs persist at Lyα EWs at or even below 100 Å. However, Lyα EW also depends very strongly on the continuum flux and, by extension, the stellar population(s), making unclear how significantly ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ affects the Lyα EW. Nevertheless, Lyα EW is still one of the most promising diagnostics for ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$, performing comparably to ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$.

3.1.3. Lyα Peak Velocity Separation

Lyα profiles are typically double peaked, with the velocity separation of the two peaks directly depending on the H i column density (e.g., Verhamme et al. 2015). Previously, Izotov et al. (2018b, 2021) demonstrated that the velocity separation v_sep of Lyα peaks strongly correlates with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ as a result of the strong dependence of both values on the H i column. We compare ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ with v_sep for a subset of seven LzLCS galaxies with G160M measurements (Henry et al. 2015; Yang et al. 2017a) and a subset of 20 published LCEs (Verhamme et al. 2017; Izotov et al. 2018b, 2021) in Figure 4. We find a strong relationship between the values. Neither weak leakers nor nondetections persist below v_sep ∼ 250 km s⁻¹ regardless of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metric, which is consistent with predictions by Verhamme et al. (2015). This result favors the H i column density interpretation that motivated this diagnostic.

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In Figure 4, we also compare ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ and v_sep to the relation from Izotov et al. (2018b) and find that their fit roughly describes the envelope of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ values. Moreover, we find that v_sep has one of the most pronounced correlations of any indirect ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ indicator regardless of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metric with τ ∼ −0.4. However, additional measurements of v_sep from Lyα profiles are necessary to fully test this ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostic.

Few of the LCEs have detected [O i] λ6300, with 39 of the 50 LCEs in the combined sample having only upper limits in the emission-line flux, indicating that [O i] may be particularly weak in LCEs (see, however, Plat et al. 2019; Ramambason et al. 2020). The preponderance of [O i] upper limits in LCEs over nonemitters prevents determination of the shape of the distribution of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ with respect to the [O i] flux ratios, as shown in Figure 5. These upper limits may contribute to the lack of significant correlation (as shown in Table 1, p > 0.09 for all three ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metrics for both [O i] flux ratios).

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We compute the [O i] LCE fraction using upper limits when no flux is detected. The LCE fraction distribution (Figure 6) appears relatively monotonic over the [O i] flux ratios O₃₁ and [O i]/Hβ. As shown in Figure 6, there is little difference between the three LyC escape indicators. Above ${\mathrm{log}}_{10}{O}_{31}\sim 1.8$ and below [O i]/Hβ ∼ −1.3, the LCE fraction is a roughly constant 30%. The trends with both flux ratios suggest that LCE detection fraction increases with decreasing [O i] flux.

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As shown in Figure 7, we see increasing average and maximum ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ with increasing O₃₂. The total combined sample exhibits a significant (∣τ∣ > 0.2 at >3σ confidence) correlation with O₃₂ in all three ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metrics (see Table 1). The ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ relation proposed in Izotov et al. (2018a; dashed line in Figure 7) serves as a description of the envelope in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ values, particularly in the case of the UV-derived escape fraction (right panel of Figure 7). For the other two ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metrics, several strong LCEs have ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ in excess of the predicted relation, notably the two LCEs from Wang et al. (2019). These outlying galaxies have higher stellar masses >10⁹ M_⊙, which makes values like F_λLyC/F_λ1100 and ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$(Hβ) more sensitive to the star formation history. Because the majority of the outlying objects exhibit agreement with this envelope when using the UV ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metric (which assumes a nonparametric star formation history), we interpret these outliers as having ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ systematically biased by this effect rather than evidence that the Izotov et al. (2018b) prescription is not appropriate at low O₃₂.

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Scatter of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ below the envelope could be caused by a number of effects related to line-of-sight optical depth and other galaxy properties. Galaxy-to-galaxy variations in opening angle, covering fraction, burst age, ionization parameter, SFR, metallicity, extinction law and dust, and/or optical depth may indicate that additional physical properties are relevant to determining ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. Unfortunately, the degenerate dependence of O₃₂ on metallicity and ionization parameter substantially complicates any physical interpretation of this result (Sawant et al. 2021). While the mass–metallicity relation appears to evolve with redshift (Sanders et al. 2021), the coupling of $12+\mathrm{log}({\rm{O}}/{\rm{H}})$ to ionization parameter observed at low redshift persists at z ∼ 2−4 (Sanders et al. 2020). Therefore, the underlying properties that affect O₃₂ remain related in the same way regardless of epoch, supporting the extension of the O₃₂ diagnostic to higher redshifts. Regardless of the physical connection between O₃₂ and ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$, the scatter in this diagnostic indicates that an isotropic density-bounded escape scenario alone is likely incompatible with the observations. We discuss interpretations and caveats of O₃₂ as an ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostic in greater detail in Sections 4 and 5.

With these nuances to O₃₂ in mind, we do find that ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ correlates strongly with O₃₂, particularly for ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ derived from the UV spectrum. Further evidence for this relationship is the LCE fraction shown in Figure 8. The highest-O₃₂ galaxies in the combined sample (O₃₂ ≳ 10) have LCE fractions ≳0.5. However, LCE fractions >0.1 persist across the full range of O₃₂ values regardless of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ indicator. As we demonstrate in Figure 7, while most galaxies with O₃₂ > 5 in the combined sample are strong LCEs along the line of sight, some galaxies with lower O₃₂ can still be strong LCEs. Two scenarios might contribute to this trend with O₃₂: separate populations of LCEs with LyC escaping under different conditions, or an evolutionary sequence in which LyC escape recurs at later times when fewer early-type stars persist.

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As evident in Figure 9, the average and maximum values of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ increase with Hβ EW. ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$(UV) has a significant and strong correlation with Hβ EW, indicating at least a moderate relationship between the two. The distribution of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ appears to occupy two distinct ranges in EW (see also Figure 10), one with high (≳150 Å) EW containing the most prodigious strong LCEs (${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ ≳ 0.1), and one with low (≲150 Å) EW containing additional strong LCEs and the majority of weaker LCEs. Two-thirds of the galaxies in our combined sample with Hβ EW >150 Å have detected LyC. Similarly, 28 of the 39 nondetections appear concentrated at EWs below 150 Å.

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Quantifying these results, the fraction of galaxies that are strong LCEs appears to increase with EW, which we demonstrate in Figure 10. This may indicate a preference for young, strong bursts of star formation. As noted above, though, strong LCEs have a wide range in EWs. Thus, the increase in strong LCE fraction with EW demonstrates a dearth of weak LCEs and nonemitters rather than an increase in the prevalence in LCEs at high EW. In other words, high Hβ EW indicates a strong LCE, but high-EW galaxies do not account for the full population of LCEs. Some scatter persists in LCE fraction, particularly at lower EW, depending on the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ indicator. Uncertainties in the LCE fraction are large enough to suggest that any change in LCE fraction between the various indicators may not be significant. However, our results suggest a significant occurrence of LCEs for EWs below 150 Å, consistent with the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ trends in Figure 9.

The prevalence of LCEs at high EW demonstrates that Hβ EW is more sensitive to star formation history or sSFR than it is to optical depth. Studies at higher redshifts find similar results in combined Hβ+[O iii] EWs (e.g., Castellano et al. 2017; Endsley et al. 2021; Saxena et al. 2022), suggesting that this trend persists in earlier cosmological epochs. As stellar mass and starburst age dominate the Hβ EW, LCEs with high EWs are likely young starbursts and/or low-mass galaxies. The lack of weak LCEs and nonemitters at high EWs may indicate that young ages and/or low masses better facilitate high LyC escape fractions. However, a subset of between 6 and 10 strong LCEs have EWs below 150 Å, indicating that strong LCEs occupy a wide range of ages, star formation histories, and/or sSFRs. These low-EW LCEs are likely more evolved galaxies with higher stellar mass and metallicity. We discuss age and mass further in Section 4.

The immense scatter in Figure 11 anticipates the weak, insignificant correlation coefficients for observed M₁₅₀₀ in all three ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metrics. Strong leakers persist below M₁₅₀₀ = −20.25, implying a population of strong LCEs at higher stellar mass or higher UV luminosity. Figure 12 illustrates this persistence of LCEs across a range of M₁₅₀₀. The LCE fraction is relatively constant with observed FUV magnitude, with a slight increase at the faint end of the distribution (M₁₅₀₀ > −19.25), especially in the UV ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$, where LCEs have ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ ≳ 0.02 and 9/15 LCEs are strong LCEs. This mild increase may indicate that strong LCEs are more likely fainter and/or less massive galaxies, particularly given the slight trend in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ upper bounds with M₁₅₀₀.

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The persistence of LCEs at higher UV luminosities could imply that LCEs consist of multiple epochs of recent star formation and/or higher stellar masses. Indeed, EW Hβ declines with increasing UV luminosity such that, for the UV ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$, five of the six strong LCEs and 9 of the 12 weak LCEs with M₁₅₀₀ < −20.25 have Hβ EWs < 100 Å. A major caveat to this interpretation is the effect of dust on the observed UV magnitude. With the LzLCS, we find that ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ depends on both dust (Saldana-Lopez et al. 2022) and age (Section 3.4), but less so on mass (Section 3.7). Such effects complicate direct interpretation of M_FUV as an ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostic without ancillary information. We discuss M₁₅₀₀ in a high-redshift context further in Section 5.3.

Flury et al. (2022) measured the UV slope β₁₂₀₀ from the COS spectra over a range of 1050−1350 Å. While we present results for this measurement below, we note that β₁₂₀₀ can be quite different from the commonly used β₁₅₀₀. Therefore, β₁₂₀₀ provides only a relative sense of the relationship between β₁₅₀₀ and ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$.

Figure 13 demonstrates that the highest ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ values occur for the steepest values of β₁₂₀₀. Indeed, the highest values of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ all occur where β ≤ −2, while a distinct envelope in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ describes ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ values for β ≳ −2. Though strong LCEs can persist across a wide range of β ∈ [−3, −1], the UV slope has a significant correlation coefficient for two of the three ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ indicators (τ ∼ −0.25; see Table 1). As implied by the correlation coefficients and Figure 13, bluer galaxies tend to have higher ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. The distribution of LCE fraction over UV β₁₂₀₀ in Figure 14 is equally informative. LCE fraction increases as the slope steepens from ∼0 at β₁₂₀₀ > −1 to nearly 0.6 at β₁₂₀₀ ∼ −2.5, suggesting that the strongest LCEs contain young stellar populations without substantial dust attenuation.

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These trends in β₁₂₀₀ make sense because early-type stars produce the majority of the LyC and low dust extinction better facilitates LyC escape. However, some galaxies with −2 < β < −1 are strong LCEs, with the Wang et al. (2019) strong LCEs being even redder than −1. One or a combination of scenarios could describe LCEs with β₁₂₀₀ > −2: (i) a patchy dust screen that reddens the UV spectrum but still allows FUV and LyC photons to escape (the so-called "picket fence" model; e.g., Heckman et al. 2001; Saldana-Lopez et al. 2022), and/or (ii) multiple generations of stars that, through feedback processes, facilitate LyC escape by clearing out gas while bolstering the redder part of the UV spectrum with emission from older stellar populations (see discussion in Micheva et al. 2017 of this effect in Mrk 71). We discuss the relationship between β₁₂₀₀, dust, and stellar population age further in Section 4.1.

Simulations disagree as to whether dwarf or more massive star-forming galaxies are the major source of LyC photons for reionization. Figure 15 suggests that dwarf galaxies (M_⋆ < 10⁹ M_⊙) are more likely to be strong LCEs. More than half (31/52) of the dwarf galaxies in the combined sample are LCEs, 13 of which are strong LCEs.

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With increasing mass, the number of strong LCEs and corresponding ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$(UV) values appear to decrease. Even so, galaxies with M_⋆ > 10⁹ M_☉ can still be prodigious LCEs, some even having ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ > 0.1. The τ coefficient and corresponding p value suggest that the correlation is neither strong nor significant for any ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metric. Furthermore, the other two ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metrics do not indicate much of an envelope in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ with M_⋆. As evident in Figure 16, the LCE fraction distribution is also relatively flat over the range of stellar masses. Like M₁₅₀₀, the distribution of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ with respect to M_⋆ suffers from substantial scatter. Unlike M₁₅₀₀, the stellar masses have relatively large uncertainties. These large uncertainties may contribute to the apparent scatter and even to the flat LCE fraction distribution.

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Σ_SFR exhibits a threshold of Σ_SFR ∼ 10 M_⊙ yr⁻¹ kpc⁻² above which nearly all strong LCEs appear, as evidenced by Figure 17. We see scatter in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ similar to other diagnostics examined here, again implying the effects of orientation or variations in host galaxy properties. For comparison, we also show ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ as it varies with half-light radius in Figure 17. The prominent transition in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ at r₅₀ ≈ 0.7 kpc suggests that the concentration of star formation dominates Σ_SFR in strong LCEs.

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This affinity of strong LCEs for high Σ_SFR and low r₅₀ suggests that higher concentrations of star formation provide the feedback necessary to clear LyC escape paths in the ISM. Consistent with this interpretation, we find that the maximum observed value of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ increases with sSFR. Although less pronounced, this envelope in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ is similar to the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ ∝ Σ_SFR ^0.4 relation described by Naidu et al. (2020). These trends suggest that concentrated star formation may be a good indicator of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ and could be pivotal to understanding the origin of reionization.

We show the LCE fraction with respect to both Σ_SFR and sSFR in Figure 18. In both cases, LCE fraction clearly increases with the concentration of star formation. The LCE fraction changes relatively little with Σ_SFR until reaching ≈10 M_⊙ yr⁻¹ kpc⁻², at which point LCE fraction increases from ∼10% to 60% over half a decade in Σ_SFR. LCE fraction increases more gradually with sSFR, suggesting that the concentration of star formation is more important than the effects of stellar mass.

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Comparing Σ_SFR, sSFR, and Σ_sSFR = Σ_SFR/M_⋆ highlights this point, as Σ_SFR and Σ_sSFR yield much higher τ values than sSFR. The τ values of Σ_SFR and Σ_sSFR are also quite comparable, which demonstrates that factoring in stellar mass does not produce a better diagnostic. This result comes with the caveat that the LzLCS stellar masses have high uncertainties, which could mitigate any effects stellar mass may have on the observed trends.

High Σ_SFR, like those seen for GP galaxies, need not imply unusually strong SN feedback (e.g., Chisholm et al. 2017; Jaskot et al. 2017). Because Σ_SFR is derived from Hβ, the apparent envelope in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ could instead arise from an increased compactness of H ii regions. Indeed, τ is higher and more significant for r₅₀ than for Σ_SFR, sSFR, or Σ_sSFR. Such concentrated star-forming regions could deplete the surrounding gas so that LyC photons can leave the local H ii region and escape into the more diffuse host galaxy and potentially escape into the IGM.

In Figure 19, we compare ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ to the gas-phase metallicity $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$. The LCEs with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ ≳ 10% all reside below $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$ ∼ 8.1. Much like the case of M_⋆, the strong LCEs with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ ≲ 10% and the weak LCEs are more evenly distributed from $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$ = 7.7 to 8.5. While substantial scatter appears in all three diagnostics, roughly two-thirds (28/39) of the non-LCEs fall above $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$∼8.1. With a correlation coefficient of τ ∼ −0.2 at about 2σ significance, ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ does not have a significantly strong correlation with $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$; however, the preferences of the most prodigious LCEs for lower metallicities and non-LCEs for higher metallicities are promising as a diagnostic.

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The LCE fraction shown in Figure 20 also suggests that $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$ is a promising, albeit complicated, diagnostic. As with the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ trends shown in Figure 19, we see strong LCEs both above and below $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$ ∼ 8.1. Given the uncertainty in the LCE fraction, it is unclear whether the lack of LCEs at intermediate values of $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$ ∼ 8.1 implies the existence of distinct LCE populations separated by metallicity.

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Ten of the 17 indirect ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostics considered above are significantly strong (∣τ∣ > 0.2 with p < 0.00135, 3σ significance): ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$, EW Lyα, v_sep, O₃₂, EW Hβ, β₁₂₀₀, M_1500,int, NUV r₅₀, Σ_SFR, and Σ_sSFR. The ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$, EW Lyα, β₁₂₀₀, NUV r₅₀, and Σ_SFR diagnostics are significantly strong across both ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ metrics. These five diagnostics are thus the most compelling for identifying LCEs and inferring ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. Hβ EW and M_1500,int are significantly strong correlations only with the COS UV ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. In general, ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ derived from fitting the UV spectrum gives the strongest, most significant correlations for nearly all the indirect diagnostics. The success of this particular LyC escape indicator is particularly compelling because, as discussed in Section 2, it is the most reliable and direct measure of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$.

The indirect ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostics motivated by optical depth contain the majority of the strong correlations. Likely owing to their unique sensitivity to H i, the diagnostics based on Lyα—${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$, Lyα EW, and profile peak separation—have the strongest correlations as measured by Kendall's τ for censored data. However, the v_sep correlations lack the significance of the other Lyα correlations, in part because of insufficient data. While not as strongly correlated with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ as the Lyα properties, the O₃₂ flux ratio still exhibits a strong, significant correlation. The [O i] flux relative to other emission lines' is less successful as an ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostic, likely owing to the faintness of [O i].

Of the remaining diagnostics, which are motivated by the physical mechanism behind LyC escape, the half-light radius and Σ_SFR have the strongest, most significant correlations with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. Indeed, strong LCEs exhibit clear associations with highly concentrated star formation, distinguishing which sorts of galaxies or regions within galaxies are emitting LyC. Both Hβ EW and UV β₁₂₀₀ also correlate strongly and significantly with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. While stellar mass and attenuated UV magnitude lack strong, significant correlations, these two diagnostics still exhibit envelopes in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ and suggest that the strongest LCEs have M_⋆ < 10⁹ M_⊙. Such envelopes in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ indicate that multiple properties contribute to an ideal escape scenario, including starburst age, ionization parameter, SFR, and orientation of optically thin channels.

Although most galaxies with Hβ EWs < 150 Å do not appear to be associated with LyC escape (Section 3.4), Zackrisson et al. (2013) propose that the UV β₁₂₀₀–Hβ EW plane could constrain ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. We compare their model predictions for ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ = 0.0, 0.5, and 0.9 to the LzLCS results in Figure 21 for ∼30% solar-metallicity picket fence nebulae over a range of 10⁶–7 × 10⁸ yr burst ages. Our combined results do not agree with their predictions. We do see a mild gradient in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ over UV β₁₂₀₀ that appears to shift to steeper continua with increasing EW, as their predictions suggest. However, the observed locus appears shifted to higher spectral slopes: only one previously published LCE falls into the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ > 0 space predicted by Zackrisson et al. (2013).

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A major caveat to this apparent disagreement is the effect of dust, which may substantially affect the predicted sequences in the UV β₁₂₀₀–Hβ EW plane (Zackrisson et al. 2017). Moreover, the star formation history also determines where a galaxy resides in Figure 21, as underlying older stellar populations can strongly affect the optical continuum and thus the Hβ EW. LzLCS galaxies appear to be older and/or dustier than the Zackrisson et al. (2013) models, which places our sample at lower Hβ EW and higher UV β₁₂₀₀ than their predictions. Interpreting the discrepancy comes with an additional complication that the UV β predicted in Zackrisson et al. (2013) is measured at redder wavelengths than those accessible in the COS spectrum. Because an attenuated young stellar SED peaks at ∼1100–1200 Å, β₁₂₀₀ is necessarily different from the Zackrisson et al. (2013) UV β predictions. That being said, we find no distinguishable trends in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ in the β₁₂₀₀–EW(Hβ) plane.

Whereas the Zackrisson et al. (2013) models suggest that strong LCEs should have low Hβ EWs and low UV β₁₂₀₀, the strongest LCEs have high (>100 Å) Hβ EWs, while those LCEs with lower EWs have higher UV β₁₂₀₀. The latter group of LCEs may contain porous H ii regions with optically thin channels cleared by SN feedback or turbulence (see Section 5). In particular, a two-stage starburst or dusty young starburst could be responsible for the high UV β₁₂₀₀, low Hβ EW exhibited by some of the strong LCEs.

Starburst age and ionization parameter are related since the earliest O stars die off within the first 2–4 million years. Because these stars dominate the LyC flux, properties sensitive to ionization parameter like O₃₂ will consequently depend, at least in part, on the age of the starburst (e.g., Jaskot & Oey 2013; Izotov et al. 2017), in addition to other properties. Figure 22 demonstrates a tight relationship between O₃₂ and Hβ EW.

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The trend in Figure 22 could result from a variety of processes. Decreasing Hβ flux due to fewer ionizing photons would decrease the EW in tandem with O₃₂ as the O⁺² zone declines relative to O⁺. Due to the mass–metallicity correlation for galaxies (e.g., Tremonti et al. 2004), increased continuum flux due to higher galaxy mass would decrease the EW while increasing the metallicity, the latter serving to decrease O₃₂. We find that O₃₂ and EW decrease with increasing mass, but because mass correlates with $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$, it is not clear whether mass dominates this trend.

We find that LCEs occupy a wide range in O₃₂ and Hβ EW. Roughly half of the LCEs occur at ${\mathrm{log}}_{10}$ O₃₂ > 1 or Hβ EW > 100 Å. Nonemitters do not appear in this part of the diagram, while all the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ > 0.2 leakers reside here. The remaining LCEs have lower Hβ EWs (≈50–150 Å), where many of the nonemitters also reside. These separate sets of LCEs may imply different starburst ages or stellar mass populations at which LyC escape occurs.

Escaping LyC photons should affect both Hβ EW and O₃₂. The former should decrease owing to a drop in Hβ flux, while the latter should increase owing to a drop in [O ii] flux. A lack of preference of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ for any part of the distribution demonstrates that age and ionization parameter mitigate any effects of escaping LyC photons on the measured properties.

Gas-phase and stellar metallicities also affect O₃₂. As collisionally excited lines, [O iii] and [O ii] depend on electron temperature, which is higher in low-metallicity gas owing to decreased cooling by metal emission lines. Higher stellar metallicity changes the opacity of stellar interiors and thus affects their photosphere temperatures. Secondarily, high stellar metallicity increases line blanketing in the LyC of O and B stars. These metallicity effects on stellar atmospheres serve to decrease the ionizing photon budget. These dependencies on gas-phase and stellar metallicity indicate that O₃₂ correlates with an abundance indicator like $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$, which we show in Figure 23.

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While there is some scatter, a trend persists between O₃₂ and $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$ over nearly an entire decade. Although high ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ LCEs tend to have higher O₃₂ and lower $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$, LCEs populate the majority of the distribution in Figure 23. Harder ionizing spectra at lower metallicity could facilitate a density-bounded escape scenario. Weaker feedback from low-metallicity stars may also generate a dense, clumpy gas geometry that enables LyC escape (Jaskot et al. 2019), perhaps owing to low covering fractions (e.g., Gazagnes et al. 2020; Saldana-Lopez et al. 2022). Mechanical feedback from stars is stronger at higher metallicity, which might explain the subpopulation of high LCEs at higher metallicity. However, higher metallicity is also linked to higher UV attenuation (e.g., Wang et al. 2019), thereby limiting LyC escape. The reduced ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ of LCEs at higher metallicity may also be due to the fact that, at higher galaxy masses, increased gravity may reduce the effectiveness of feedback and thus limit LyC escape.

Following the known mass–metallicity relation, O₃₂ ought to anticorrelate with M_⋆ just as it does with $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$. Indeed, in Figure 23 we see such a trend until M_⋆ ≲ 10⁹ M_⊙ (corresponding to O₃₂ ≈ 2–3), at which point the two properties appear to decouple. With weaker gravitational potentials, low-M_⋆ galaxies also undergo more bursty star formation (e.g., Weisz et al. 2012; Guo et al. 2016). Such episodic star formation results in a range of stellar feedback and ionization parameters, which would lead to a wide range in O₃₂.

For a given metallicity or stellar mass, strong LCEs tend to have the highest O₃₂ values. The leakers with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ > 0.2 concentrate at low $12+{\mathrm{log}}_{10}({\rm{O}}/{\rm{H}})$, low M_⋆, and high O₃₂. Thus, the strength of a starburst relative to the mass of a galaxy may determine its likelihood of leaking LyC.

Photoionization models predict that O₃₁ should increase by 0.5 dex or more as the LyC optical depth decreases from ionization to density boundary conditions at a fixed O₃₂ (e.g., Stasińska et al. 2015; Plat et al. 2019; Ramambason et al. 2020). We compare our results to the predicted sequences for radiation- and density-bounded nebula models from Stasińska et al. (2015) in Figure 24. The combined samples reside on or above the radiation-bounded sequence. We find no relationship between ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ and any offset from the locus. Because the strongest LCEs have only upper limits in [O i], these galaxies may in fact be consistent with density-bounded or picket fence scenarios. LCEs with detected [O i] reside along the radiation-bounded model predictions, which may suggest that an isotropic density-bounded escape scenario is not realized. Indeed, Ramambason et al. (2020) predict that density-bounded channels within an otherwise optically thick medium can describe the distribution of O₃₂ and O₃₁ flux ratios we observe for LCEs with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ ≲ 0.1. The [O i] flux from LCEs with high O₃₂ and disproportionately low O₃₁ may also be contaminated by shocks, causing O₃₁ to shift to lower values than other LCEs (Stasińska et al. 2015; Plat et al. 2019).

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Σ_SFR describes the concentration of O and B stars. As a result, Σ_SFR influences the ionization parameter, which depends strongly on the number density of early-type stars. At least in the case of density-bounded LyC escape, we anticipate higher O₃₂ for LCEs than for nonemitters of the same Σ_SFR owing to a deficit in [O ii] flux.

We find that LCEs prefer high Σ_SFR and high O₃₂, although only one of the two is necessary to demonstrate the likelihood of LyC escape. Figure 25 demonstrates that, with few exceptions, LCEs have high O₃₂, high Σ_SFR, or a combination thereof. The LCE population with ${\mathrm{log}}_{10}{{\rm{\Sigma }}}_{\mathrm{SFR}}\lt 1$ M_⊙ yr⁻¹ kpc⁻² is sparse. Thus, high O₃₂ and high Σ_SFR are each indicative of LCEs, in particular strong LCEs, with the most extreme LCEs having both high O₃₂ and high Σ_SFR.

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Combined with the results of UV β₁₂₀₀ and Hβ EW, the combination of Σ_SFR and O₃₂ could suggest two different types of strongly star-forming LCEs. One population is younger with high O₃₂, high Hβ EW, and low metallicity. The other population has lower O₃₂, lower Hβ EW, and higher metallicity and resides in the upper left corner of Figure 25. The latter suggests mechanical feedback, while the former population may point to the additional role of ionization.

The substantial scatter evident in all considered diagnostics could be attributed to one or both of two physical explanations. First, orientation could cause the observed scatter since ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ likely depends on line of sight in an anisotropic, radiation-bounded escape scenario (e.g., Zastrow et al. 2013; Cen & Kimm 2015). Alternatively, the observed scatter might be due to a time delay between the onset of star formation and the escape of the LyC since feedback requires sufficient time to clear out escape channels, thus decoupling properties from ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ to some extent (e.g., Trebitsch et al. 2017; Barrow et al. 2020; Naidu et al. 2022). Whatever might cause this scatter, it is likely physical because an upper envelope in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ persists across several diagnostics. These envelopes suggest that genuine trends do exist between ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ and different parameters, but orientation, time delays, and/or starburst properties like age and ionization parameter might influence the values of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$, causing the observed scatter.

As implied by the envelopes and correlations in the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostics, the strongest correlations are Lyα EW, ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$, and v_sep for the diagnostics motivated primarily by optical depth. Other diagnostics with strong correlations include O₃₂, Hβ EW, Σ_SFR, and r₅₀, which may give insights into the physical mechanisms responsible for LyC escape. Some properties, notably O₃₂ and Hβ EW, exhibit a broad range in galaxies with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ > 0.05. Different LyC escape scenarios (e.g., Kakiichi & Gronke 2021; Gazagnes et al. 2020) could populate different parts of these diagnostics because the corresponding conditions (e.g., optical depth, porosity of the ISM, or feedback mechanism driving LyC escape) correspond to different ranges of the observable parameter space of O₃₂ and Hβ EW.

Investigation of two-dimensional diagnostics sheds light on these possible explanations. At higher mass and higher metallicity, the lower O₃₂, lower Hβ EW LCEs likely clear out their birth cloud by mechanical feedback from early-type stars. This serves to more uniformly distribute the dense gas and dust leftover from star formation into an optically thick bubble around the O and B stars. SN feedback and turbulent feedback subsequently clear optically thin channels in this bubble.

The younger, lower-mass, lower-metallicity nature of the high O₃₂, high Hβ EW LCEs indicates that this second class of LyC leakers are like the GP galaxies. Such galaxies, while strongly star-forming, likely lack the high-velocity outflows necessary to expel the remnant birth cloud material and form a uniform obscuring medium (Jaskot et al. 2019). However, they may have sufficient radiative feedback to evacuate cavities in the ISM (Kakiichi & Gronke 2021). As a result, these GP LCEs might contain an ISM that is optically thin except where dense clouds cause optically thick patches of relatively small covering fractions. We speculate that the range of parameter spaces occupied by LCEs indicates a shift in conditions and escape mechanism from young GP starbursts with large optically thin cavities to older, optically thick star-forming galaxies with a porous ISM.

While these putative differences in LCEs spurred our comparison of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ proxies, the two-dimensional diagnostics also demonstrate how different parameters depend on one another. These comparisons show that metallicity, mass, Σ_SFR, age, and ionization parameter are inextricably linked. Furthermore, we find that age and ionization parameter dominate any optical depth effects on properties like O₃₂ and Hβ EW. In other words, young ages and strong radiation boost O₃₂ and Hβ EW in the strongest LCEs and may be critical for high levels of LyC escape. It is also plausible that a feedback-induced time delay introduces LCE "stragglers" into the distributions of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ (e.g., Trebitsch et al. 2017; Secunda et al. 2020).

Cosmological simulations provide a critical link between the low-redshift LCEs and high-redshift surveys. Predictions from simulations connect parameters such as stellar mass and Σ_SFR to ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ at the epoch of reionization. Because LzLCs galaxies and other GP-like galaxies are reasonable analogs of high-redshift galaxies, comparing our results to these predictions from simulations can be useful both for translating indirect diagnostics to high redshift and for interpreting the distributions we observe.

One of the most contentious issues regarding reionization is the mass regime of galaxies that provide the ionizing photons. Some simulations predict that ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ decreases with stellar mass (e.g., Kimm & Cen 2014) and UV luminosity (e.g., Trebitsch et al. 2017; Secunda et al. 2020), while others predict that ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ increases with stellar mass and UV luminosity (e.g., Ma et al. 2020). The strongest LCEs in the combined sample of local LCEs are smaller, fainter galaxies with M_⋆ ≲ 10⁹ M_⊙ and M_FUV ≳ − 19. Reionization is likely driven by galaxies with similar properties.

The LzLCS samples the upper end of the simulated M_⋆−Σ_SFR distribution of LCEs in Naidu et al. (2020). We find that the combined sample of LCEs is largely consistent with their predictions, including the range in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. However, our average ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ toward higher stellar mass bins is about 0.1 dex lower than theirs even if considering only the strongest LCEs. Moreover, although we find qualitative agreement between the envelope in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ with respect to Σ_SFR and the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ $\propto {{\rm{\Sigma }}}_{\mathrm{SFR}}^{0.42}$ relation prescribed by Naidu et al. (2020), the M₁₅₀₀ < −20 LCEs in the LzLCS are not strong leakers at the same rate as their M₁₅₀₀ > −19 counterparts. While seemingly contrary to predictions by Naidu et al. (2020), the fact that brighter, higher-mass galaxies are less likely to be prodigious LCEs in our sample may be consistent with their simulations, as intermediate-mass galaxies at z > 4 tend to have emission-line properties similar to those of the z ∼ 0.3 low-mass galaxies of this study. The ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$−Σ_SFR envelope also agrees with the sharp increase in ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ predicted by Sharma et al. (2017), although we do not see the 20% ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ values they suggest for M_⋆ > 10⁹ M_⊙. This might suggest that properties in addition to Σ_SFR (e.g., metallicity, dust) affect LyC escape.

O₃₂ is a more empirical measurement than M_⋆ or Σ_SFR and directly traces the ionization parameter. Together, these attributes have favored O₃₂ as an ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostic in the past. Unfortunately, properties like Σ_SFR and metallicity can also contribute to O₃₂, thus making interpretation of O₃₂ unclear (see Nakajima & Ouchi 2014). As with the LzLCS, recent studies have found substantial scatter in the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$−O₃₂ diagnostic (e.g., Izotov et al. 2018b; Bassett et al. 2019), which Bassett et al. (2019) attribute to a combination of orientation and opening angle effects. With these physical and empirical caveats in mind, recent cosmological hydrodynamic simulations have predicted where high-redshift LCEs should appear in the O₃₂−R₃₂ diagnostic (e.g., Katz et al. 2020). We show the distribution of LzLCS (Izotov et al. 2016a, 2016b, 2018a, 2018b, 2021; Wang et al. 2019) and published LCEs (de Barros et al. 2016; Nakajima et al. 2020) and LAEs (Reddy et al. 2022) at z ∼ 2−3 in Figure 26, along with z ∈ [0.2, 0.4] star-forming galaxies taken from the Thomas et al. (2013) SDSS catalog for comparison. Simulations by Barrow et al. (2020) suggest that the entire distribution of LCEs shifts 0.5 dex lower in R₂₃ at high redshift owing to decreases in metallicity while maintaining high O₃₂ through high ionization parameter. On the other hand, simulations by Katz et al. (2020) suggest that LCEs at high redshift shift to a locus ∼1 dex higher in O₃₂ than that of the SDSS galaxies, intersecting the low-metallicity "tail" where the combined low-redshift LCEs reside.

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In contrast to these theoretical predictions, LCEs at moderate redshift (z ∼ 3; Nakajima et al. 2020) still reside in this tail, despite having f_esc values in excess of 10%. Thus, even in earlier epochs, properties like age, ionization parameter, and metallicity may continue to outweigh the effects of LyC escape in setting O₃₂. Star-forming galaxies from the MOSDEF survey at z ∼ 2−3 have O₃₂ values more consistent with non-LCEs and typical SDSS star-forming galaxies. These galaxies are likely analogous to LBGs, suggesting that LBGs are only weakly leaking, if at all. Reddy et al. (2022) find that these galaxies have older burst ages (continuous star formation ages of ∼100 Myr), moderate ionization parameters ($\mathrm{log}U\sim -3$), and relatively higher metallicities (∼30%−40% solar), which could readily account for the observed O₃₂ values. These same properties may be associated with low levels of LyC escape. The LzLCS results suggest that O₃₂ and ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ may be indirectly related, as both O₃₂ and ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ may depend on the same physical properties, such as ionization parameter and metallicity. As such, these underlying properties will predominantly determine the observed O₃₂ flux ratio at z ∼ 3 and at z ∼ 6.

One of the principal objectives of the LzLCS is to ascertain which diagnostics are best suited to identifying LCEs and inferring their ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. While ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$, EW Lyα, v_sep, O₃₂, β₁₂₀₀, NUV r₅₀, and Σ_SFR all exhibit strong significant correlations with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ at z ∼ 0.3, comparisons with observations of these properties at higher redshifts are necessary to extend our results to the epoch of reionization.

Lyα offers one of the most promising indicators of LyC escape: both ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$ and Lyα EW correlate well with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$, at least in part because Lyα is also sensitive to the line-of-sight neutral hydrogen column density. However, this sensitivity complicates the detection of Lyα because the neutral hydrogen fraction in the IGM increases dramatically with redshift (Tang et al. 2019; Thomas et al. 2021), accounting for the steep drop in LAEs observed at z ≳ 6 (e.g., Pentericci et al. 2011; Treu et al. 2013; Schenker et al. 2014). Although Lyα falls in the optical observing window at redshifts of z ∼ 6, few Lyα emitters may be observable (an effect exacerbated by the shift of Lyα into the near-infrared at z > 7). But it does suggest that LCEs are frequently LAEs. The few LAEs detected at z > 6 may be leaking LyC. Indeed, the size of ionized bubbles necessary to produce observed double-peaked Lyα at z ∼ 6 implies LyC escape (Meyer et al. 2021).

Star-forming galaxies observed at higher redshifts allow a more direct comparison with the LCEs from our sample. The z ∼ 2−3 LBG-like star-forming galaxies from Reddy et al. (2022) have lower ${f}_{\mathrm{esc}}^{{\rm{Ly}}\alpha }$ and EW Lyα than the z ∼ 0.3 LCEs, suggesting that LBGs are either extremely weak LCEs or nonemitters. The z ∼ 3 individual LCEs from Nakajima et al. (2020) and z ∼ 2−3 stacked spectra LCEs with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ ≥ 0.2 from Steidel et al. (2018), Pahl et al. (2021), and Naidu et al. (2022) exhibit Lyα EWs of 30–110 Å and LyC escape fractions slightly larger than those of z ∼ 0.3 LCEs at similar EWs. As shown in Figure 3, the Pahl et al. (2021) relation between ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ and EW Lyα (based on the z ∼ 3 stacks from Steidel et al. 2018) is qualitatively consistent with the ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$–Lyα envelope in the LzLCS galaxies.

At higher redshifts, the Marchi et al. (2018) analysis of stacked spectra of z = 3.5–4.3 LAEs indicates that galaxies with Lyα EWs ≥ 50 Å have relative ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ significantly higher than 0.05, while those with Lyα EWs < 50 Å do not. The individual LyC detection in Ion3 at z = 4 exhibits quadruply peaked Lyα with an EW of ∼40 Å and a relative escape fraction of 0.6 (Vanzella et al. 2018). These z ∼ 2−4 results are consistent with the fact that 22/26 of the LzLCS strong LCEs have EW Lyα > 40 Å. Thus, EW Lyα as an LCE identifier and ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostic should be readily extensible to the epoch of reionization.

Studies by Steidel et al. (2018) and Pahl et al. (2021) at z ∼ 3 suggest that fainter galaxies have higher ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$. As shown in Section 3.5, we only find weak correlations with M₁₅₀₀, although we do see a possible dependence of maximal ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ on M₁₅₀₀. That being said, our sample probes fainter magnitudes than studies at higher redshifts. Saldana-Lopez et al. (2022) found that individual LCE detections at higher redshifts are consistent with LzLCS results for F_λLyC/F_λ1500 (see their Figure 16). LyC measurements using stacked spectra from Steidel et al. (2018) suggest that a possible envelope in F_λLyC/F_λ1500 persists out to M₁₅₀₀ ∼ −22. Despite scatter, the increase in max F_λLyC/F_λ1500 with magnitude suggests that M₁₅₀₀ may still be a useful tool to estimate galaxy contributions to reionization. However, additional observations of UV-faint LCEs at z ∼ 3 are necessary to confirm that the dependence of maximal F_λLyC/F_λ1100 on M₁₅₀₀ at z ∼ 3 is similar to that observed in the combined LzLCS at z ∼ 0.3.

Several indirect diagnostics driven by physical mechanism also show promise at high redshift. Star-forming galaxies at z ∼ 6−8 have UV slopes and SFRs comparable to those of LCEs in this study (e.g., Bhatawdekar & Conselice 2021), which may suggest that the β₁₂₀₀ and Σ_SFR diagnostics at z ∼ 0.3 can be used to identify LCEs and even infer ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ at the epoch of reionization. Shibuya et al. (2015, 2019) find that star-forming galaxies become increasingly compact, approaching UV half-light radii of 0.5–0.7 kpc at z ∼ 6. Such compactness is typical for the z ∼ 0.3 LCEs in this study and LAEs in other studies (e.g., Kim et al. 2021). Moreover, this UV concentration corresponds to an average increase in Σ_SFR up to values ≳10 M_⊙ yr⁻¹ kpc⁻² at z ∼ 6 (Shibuya et al. 2015), which is comparable to the Σ_SFR of z ∼ 0.3 LCEs. Such concentrated star formation at the epoch of reionization may be indicative of LyC escape. Star-forming galaxies at z ∼ 5−6 could have higher-velocity outflows than galaxies of the same SFRs and stellar masses at z ∼ 0 (Sugahara et al. 2019). Such extreme outflows might indicate augmented stellar feedback, in turn improving LyC escape indicators like Σ_SFR, M_⋆, and UV β at z ∼ 6 relative to z ∼ 0.3.

The effect of gravity on ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ diagnostics is not straightforward. In Section 3.7, we found no correlation of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ with M_⋆. We did find a significant trend between ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ and sSFR in Section 3.8, which may indicate that strong feedback better facilitates LyC escape in weaker gravitational potentials. At z ∼ 2.3 (Sanders et al. 2016), z ∼ 3 (Reddy et al. 2022), and z = 7 (Endsley et al. 2021), galaxies tend to have sSFR in the 1–10 Gyr⁻¹ range, which corresponds to weaker LCEs and nonemitters at z ∼ 0.3. Taking the Section 3.8 results at face value, these higher-redshift galaxies might not be prodigious LCEs. However, the analysis by Saxena et al. (2022) of individual LCEs at z ∼ 3 suggests that galaxies with lower sSFR values of 1–10 Gyr⁻¹ have ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ in excess of 10% at higher redshift. No z ∼ 0.3 LCEs with ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ > 10% have sSFR <10 Gyr⁻¹. This striking difference at z ∼ 3 may point to an increase in burst-enabled LyC escape with redshift.

Other properties may readily persist at higher redshifts (e.g., Hβ EW, [O iii] λ5007 EW, O₃₂, R₂₃; see Nakajima et al. 2020; Boyett et al. 2021; Endsley et al. 2021; Reddy et al. 2022; Saxena et al. 2022) but are difficult to observe at z ≳ 6 without space-based facilities like JWST. However, as we enter the JWST era, indirect indicators of ${f}_{\mathrm{esc}}^{\mathrm{LyC}}$ will prove immensely useful via the trends presented in Section 3. Indeed, unlike observing the LyC, the reionization of the IGM is relatively insensitive to the anisotropic escape of LyC photons. The broad range of LCE properties may still complicate interpreting some diagnostics, as might the interdependent nature of parameters, since it is not clear how either will differ at z ∼ 6.

LCEs at the epoch of reionization could be intrinsically unlike those in the LzLCS. Dust and the corresponding attenuation laws might alter the optical depth of the ISM at the epoch of reionization. Low metallicities in the early universe could suppress fragmentation during star formation, resulting in a top-heavy IMF with higher concentrations of O and B stars than at low redshift for the same Σ_SFR. Thus, a more physically complete understanding of the ISM and star formation at high redshift is paramount to successfully interpreting the signatures of LyC escape. Nevertheless, we find that young ages, concentrated star formation, and high ionization parameter are important for LyC escape.