New JWST observations are revealing the first galaxies to be prolific producers of ionizing photons which we argue gives rise to a tension between different probes of reionization. Over the last two decades a consensus has emerged where starforming galaxies are able to generate enough photons to drive reionization given reasonable values for their number densities ionizing efficiencies inlineformulatexmath idTM0001 notationLaTeXxi rm iontexmathinlineformula per unit ultraviolet luminosity and escape fractions inlineformulatexmath idTM0002 notationLaTeXfrm esctexmathinlineformula. However some new JWST observations infer high values of inlineformulatexmath idTM0003 notationLaTeXxi rm iontexmathinlineformula during reionization and an enhanced abundance of earlier inlineformulatexmath idTM0004 notationLaTeXzgtrsim 9texmathinlineformula galaxies dramatically increasing the number of ionizing photons produced at high z. Simultaneously recent lowz studies predict significant escape fractions for faint reionizationera galaxies. Put together we show that the galaxies we have directly observed inlineformulatexmath idTM0007 notationLaTeXMrm UV lt 15texmathinlineformula not only can drive reionization but would end it too early. That is our current galaxy observations taken at face value imply an excess of ionizing photons and thus a process of reionization in tension with the cosmic microwave background and Lymaninlineformulatexmath idTM0008 notationLaTeXalphatexmathinlineformula forest. Considering galaxies down to inlineformulatexmath idTM0009 notationLaTeXMrm UVapprox 11texmathinlineformula below current observational limits only worsens this tension. We discuss possible avenues to resolve this photon budget crisis including systematics in either theory or observations.
['Astrophysics - Cosmology and Nongalactic Astrophysics', 'Astrophysics - Astrophysics of Galaxies', 'High Energy Physics - Phenomenology']
Reionization after JWST a photon budget crisis
{'No Header': ', 1-9 (-)', 'Reionization after JWST: a photon budget crisis?': 'Julian B. Muñoz 1 ★ , Jordan Mirocha 2 , 3 , John Chisholm 1 , Steven R. Furlanetto 4 , and Charlotte Mason 5  \n- 1 Department of Astronomy, The University of Texas at Austin, 2515 Speedway, Stop C1400, Austin, TX 78712, USA\n- 2 Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA\n- 3 California Institute of Technology, 1200 E. California Boulevard, Pasadena, CA 91125, USA\n- 4 Department of Physics and Astronomy, University of California, Los Angeles, CA 90095, USA\n- 5 Niels Bohr Institute, University of Copenhagen, Jagtvej 128, 2200 København N, Denmark  \n6 September 2024', 'ABSTRACT': 'New James Webb Space Telescope (JWST) observations are revealing the first galaxies to be prolific producers of ionizing photons, which we argue gives rise to a tension between different probes of reionization. Over the last two decades a consensus has emerged where star-forming galaxies are able to generate enough photons to drive reionization, given reasonable values for their number densities, ionizing efficiencies 𝜉 ion (per unit UV luminosity), and escape fractions 𝑓 esc. However, some new JWST observations infer high values of 𝜉 ion during reionization and an enhanced abundance of earlier ( 𝑧 ≳ 9) galaxies, dramatically increasing the number of ionizing photons produced at high 𝑧 . Simultaneously, recent low𝑧 studies predict significant escape fractions for faint reionization-era galaxies. Put together, we show that the galaxies we have directly observed ( 𝑀 UV < -15) not only can drive reionization, but would end it too early. That is, our current galaxy observations, taken at face value, imply an excess of ionizing photons and thus a process of reionization in tension with the cosmic microwave background (CMB) and Lyman𝛼 forest. Considering galaxies down to 𝑀 UV ≈ -11, below current observational limits, only worsens this tension. We discuss possible avenues to resolve this photon budget crisis, including systematics in either theory or observations.  \nKey words: cosmology: theory - reionization - bubbles', '1 INTRODUCTION': "The epoch of reionization represents the last major phase transition of our universe. During reionization the intergalactic gas went from cold and neutral before the first cosmic structures formed (at redshift 𝑧 ∼ 30, or 100 Myrs after the Big Bang) to hot and ionized by 𝑧 ∼ 5 (roughly a billion years later). While we are certain that this process took place, we do not know how. The likely culprits for reionization are the first star-forming galaxies (Robertson et al. 2015, hereafter R15), but other suspects include supermassive black holes (Madau &Haardt 2015; Madau et al. 2024), and even dark matter (Liu et al. 2016). More broadly, the timing and topology of reionization hold a treasure trove of information on the astrophysics of the early universe, which we have yet to uncover.  \nThe accounting of reionization is rather simple: there have to be enough photons to ionize all the intergalactic hydrogen atoms, including their recombinations. During the WMAP era this was a stringent requirement, as cosmic microwave background (CMB) data implied an approximate midpoint of reionization at 𝑧 = 10 -11 (Komatsu et al. 2011), earlier than expected from standard galaxy-formation models and beyond the reach of contemporaneous direct observations. With the advent of the Planck satellite this tension was eased, as newer CMB data preferred later reionization (with an effective 𝑧 ∼ 7 -8, Ade et al. 2016), and by then Hubble Space Telescope  \n(HST) observations had characterized a population of star-forming galaxies at those redshifts (Madau & Dickinson 2014). Together, these observations alleviated the demand for ionizing photons and quickly led to the consensus that, under reasonable assumptions, star-forming galaxies were able to drive reionization (R15, Bouwens et al. 2015, Finkelstein et al. 2019, hereafter F19). In this Letter we examine whether this consensus holds in light of recent James Webb Space Telescope (JWST) observations of the high-redshift universe.  \nThree key factors determine the average reionization history: the production rate of ionizing photons (by early galaxies and black holes), the fraction 𝑓 esc of those photons that escape to the intergalactic medium (IGM) and can ionize neutral hydrogen, and the number of recombinations per hydrogen atom. While there remain open questions about the last factor (Davies et al. 2021), the first two are particularly uncertain.  \nThe production rate of ionizing photons is given by the earlygalaxy abundance, usually expressed through the UV luminosity function (UVLF, the comoving number density of galaxies per UV magnitude), times the ionizing efficiency 𝜉 ion of each galaxy. Though there is broad agreement on the bright end of the UVLF, the number density of ultra-faint (below 𝑀 UV ≈ -14) galaxies is virtually unconstrained. Theoretically, we expect the UVLF to 'turn over' at some magnitude 𝑀 turn UV due to feedback (Shapiro et al. 2004), and HST observations have constrained this turnover to be fainter than 𝑀 turn UV ≈ -15 (Atek et al. 2018). At the same time, some new JWST observations are finding early galaxies to have higher ionizing efficiencies 𝜉 ion than canonically assumed [with log 10 𝜉 ion / (Hz erg -1 )  \n≈ 25 . 5 -26 . 0 vs 25.2 Atek et al. 2024; Simmonds et al. 2024; Endsley et al. 2023; Prieto-Lyon et al. 2023; Curtis-Lake et al. 2023; Hsiao et al. 2023; Calabro et al. 2024, though see Matthee et al. 2023; Meyer et al. 2024; Pahl et al. 2024]. Moreover, JWST is also unveiling an enhanced population of both star-forming galaxies at 𝑧 ≳ 9 (Finkelstein et al. 2022, 2023; Eisenstein et al. 2023; Harikane et al. 2023; Castellano et al. 2022, with an unknown origin Mason et al. 2023; Ferrara et al. 2022; Muñoz et al. 2023; Mirocha & Furlanetto 2023) and supermassive black holes (Matthee et al. 2024, though they are likely obscured Greene et al. 2024), which would further boost the ionizing-photon budget. Such a wealth of photons will accelerate the process of reionization, if they escape their host galaxies.  \nTheescapefraction 𝑓 esc of early galaxies is a contentious topic. The basic problem is that the ionizing-photon production is dominated by very massive, short-lived stars, which may live and die before their birth clouds are dispersed, minimizing photon escape. The BPASS models (Eldridge & Stanway 2009) provided a new hope for high escape fractions, as binary interactions help to lengthen effective stellar lifetime and so boost the effective 𝑓 esc. Models in which the escape fraction is set by local, cloud-scale physics, suggest that 𝑓 esc could be independent of galaxy properties like mass or luminosity (Ma et al. 2016). However, different simulations predict 𝑓 esc growing for brighter galaxies (Sharma et al. 2016), declining (Wise et al. 2014; Kimm & Cen 2014), or peaking at intermediate masses (e.g., Yoo et al. 2020; Ma et al. 2020; Rosdahl et al. 2022; Yeh et al. 2023). From a theoretical perspective, there seems to be no clear consensus on the nature of 𝑓 esc in high𝑧 galaxies. Observationally, it is extremely challenging to measure 𝑓 esc while there is neutral hydrogen in the IGM. However, recent studies of low𝑧 analogues of reionizationera galaxies have found a strong correlation between their escape fractions and UV slopes 𝛽 UV : bluer galaxies exhibit larger values of 𝑓 esc (Flury et al. 2022; Chisholm et al. 2022; Begley et al. 2022; Saldana-Lopez et al. 2023). JWST and HST data show that early galaxies have bluer slopes than their average low𝑧 counterparts (e.g., Topping et al. 2022; Cullen et al. 2023; Weibel et al. 2024), such that the few studies of reionization-era galaxies indicate modest 𝑓 esc values near 5-15% (Mascia et al. 2023; Lin et al. 2024).  \nHere we argue that combining the abundance of directly observed reionization-era galaxies, the new JWST estimates of 𝜉 ion , and the low𝑧 insights on 𝑓 esc leads to too many ionizing photons at high redshifts, ending reionization too early. Such an early reionization is in contradiction with current CMB (Aghanim et al. 2020) and Lyman𝛼 forest observations (Bosman et al. 2022), and poses a tension in the photon budget during reionization . We will outline possible ways to ease this tension, including physical ingredients missing in our theoretical models, interpretation of observations, or both.  \nThrough this paper we assume a flat Λ CDM cosmology with ℎ = 0 . 7 and Ω 𝑀 = 0 . 3 to match that assumed in Bouwens et al. (2021) and Donnan et al. (2024), all magnitudes are AB (Oke & Gunn 1983), and quantities are spatially averaged unless otherwise indicated.", '2 MODELING REIONIZATION': "Wewillfollow a simple model of reionization to solve for the volumeaveraged hydrogen neutral fraction 𝑥 HI ≡ 𝑛 HI / 𝑛 H , and its complement the ionized fraction 𝑥 HII ≡ 1 -𝑥 HI . This quantity evolves as (Madau et al. 1999)  \n/ 𝑥 HII = / 𝑛 ion 𝑛 H -𝑥 HII 𝑡 rec , (1)  \nFigure1. ThenewJWSTandlow𝑧 observations imply an earlier reionization, in tension with the CMB. Bottom: Evolution of the neutral fraction 𝑥 HI as a function of redshift 𝑧 for a pre-JWST model (black solid, with a cutoff at 𝑀 UV = -13 and 𝑓 esc = 0 . 2, following R15), for the same model but with a JWST-calibrated 𝜉 ion (purple dashed, following Simmonds et al. 2024), and a model where in addition 𝑓 esc is determined from low𝑧 analogues (blue dotdashed, using the fit in Chisholm et al. 2022). Green points show a collection of observational constraints from (McGreer et al. 2015; Greig et al. 2017, 2018; Sobacchi & Mesinger 2015; Mason et al. 2019; Whitler et al. 2019; Wang et al. 2020; Nakane et al. 2023) (see also Bruton et al. 2023) Top: CMB optical depth 𝜏 CMB, where the red band is the measurement from Aghanim et al. (2020). The new galaxy observations give rise to far more ionizing photons, and at face value are in severe tension with CMB data.  \n<!-- image -->  \nwhich showcases the competition between the 'sources' (first term) and 'sinks' (second) of ionizing photons. The former is given by the density of ionizing photons produced ( / 𝑛 ion ) divided by that of hydrogen 𝑛 H = 𝜌 b ( 1 -𝑌 He )/ 𝑚 H , where 𝑌 He is the Helium mass fraction, 𝑚 H the proton mass, and 𝜌 b the baryon energy density, which scales as ( 1 + 𝑧 ) 3 . The sink term captures the number of recombinations that hydrogen atoms suffer on average, characterized by a timescale (Shull et al. 2012)  \n𝑡 rec = [ 𝐶 𝛼 B ( 1 + 𝑥 He ) 𝑛 H ] -1 (2)  \nwhere 𝑥 He ≡ 𝑛 He / 𝑛 H ≈ 𝑌 He /[ 4 ( 1 -𝑌 He )] , 𝛼 B is the case-B recombination coefficient, and 𝐶 is the clumping factor. The clumping factor is difficult to estimate theoretically, as it depends on how ionized regions penetrate into high-density clumps. Simulations predict 𝐶 ≈ 2 -5 during reionization, growing towards lower 𝑧 (e.g., Pawlik et al. 2015). Recent work in Davies et al. (2021) instead suggests that more recombinations are needed to explain the short mean free path of ionizing photons at 𝑧 ∼ 6 (thanks to absorption by pervasive high-density clumps known as Lyman-limit systems, Becker et al. 2021; Zhu et al. 2023). For simplicity and comparison with past literature (R15), we will set 𝐶 = 3 and evaluate 𝛼 B at 𝑇 = 2 × 10 4 Kfor now (which yields nearly identical results to using the 𝐶 ( 𝑧 ) fit from Shull et al. 2012), and return to the effect of recombinations later.  \nFor reionization to progress the sources have to win over the sinks. Our sources will be star-forming galaxies, which produce a background of ionizing photons at a rate of  \n/ 𝑛 ion = ∫ 𝑑𝑀 UV Φ UV / 𝑁 ion 𝑓 esc , (3)  \nwhere all factors inside the integral are assumed to depend on 𝑀 UV , and we integrate down to a cutoff magnitude 𝑀 ion . cutoff UV that will be a free parameter. Here, Φ UV is the UVLF, taken at 𝑧 ≤ 9 from the pre-JWST fit in Bouwens et al. (2021) and at 𝑧 > 9 from the JWST  \ncalibrations of Donnan et al. (2024, see Appendix A for alternative analyses using only pre-JWST UVLFs, including that of Finkelstein & Bagley 2022), / 𝑁 ion ≡ 𝐿 UV 𝜉 ion is the production rate of ionizing photons per galaxy, given by their UV luminosity 𝐿 UV times the ionizing efficiency 𝜉 ion , of which a fraction 𝑓 esc escapes into the IGM.  \nIt is apparent that the product 𝜉 ion × 𝑓 esc will determine the timing of reionization, and that these two factors are, at face value, fully degenerate. Increasing 𝜉 ion per galaxy while decreasing 𝑓 esc will yield identical effects on the IGM. Fortunately, though, direct Balmer-line observations can be used to tease out the amount of ionizations in the galaxy, and thus the amount of non-escaping ionizing photons 𝜉 ion ( 1 -𝑓 esc ) . Using the Robertson et al. 2013 inference 1 of log 10 𝜉 ion = 25 . 2 Hz erg -1 (though see Bouwens et al. 2016; Lam et al. 2019; De Barros et al. 2019 for higher reported values), R15 showed that 𝑓 esc = 20% is sufficient if galaxies down to 0.001 𝐿 ★ ( 𝑀 ion . cutoff UV ≈ -13) contribute to reionization. We illustrate what reionization would look like for this pre-JWST calibrated model in Fig. 1. It is over by 𝑧 ∼ 6, and produces an optical depth 𝜏 CMB ≈ 0 . 055, bringing galaxy observations into agreement with Planck CMB measurements.  \nThe arrival of JWST is opening a new window to reionization. Observations from different teams are finding large values of 𝜉 ion , in some cases growing towards higher redshifts and fainter galaxies (though see Endsley et al. 2023 where 𝜉 ion is still high but grows towards the bright end instead, we study this case in Appendix A). In particular, Simmonds et al. (2024) find a consistent increase in 𝜉 ion up to 𝑧 = 9 and 𝑀 UV = -16 . 5 (where we will conservatively cap 𝜉 ion to avoid extrapolation), well fit by  \nlog 10 h 𝜉 ion /( Hzerg -1 ) i ≈ 25 . 8 + 0 . 11 ( 𝑀 UV + 17 ) + 0 . 05 ( 𝑧 -7 ) . (4)  \nSuch faint, early galaxies will produce ∼ 4 times more ionizing photons than expected pre-JWST (Atek et al. 2024, implying a very young stellar population). The purple line in Fig. 1 shows how reionization would progress assuming this JWST-calibrated 𝜉 ion , while keeping everything else the same. In this case the additional photons would kick-start reionization by 𝑧 ∼ 12 and finish it by 𝑧 ∼ 8, far overproducing the CMB optical depth ( 𝜏 CMB ≈ 0 . 08) when compared to observations. Here we have kept 𝑓 esc = 0 . 2 as in R15, so the astute reader may wonder if newer inferences of the escape fraction delay reionization.  \nWe do not have a direct handle on 𝑓 esc during reionization, as escaping ionizing photons will be absorbed by the neutral IGM before reaching us. However, detailed studies of low𝑧 analogues find a strong correlation, with significant scatter, between the FUV continuum slopes 𝛽 UV of galaxies and their LyC escape fractions. This is physically explained by the dust along the line-of-sight simultaneously attenuating the FUV stellar continuum and the ionizing photons. We will use the fit from Chisholm et al. (2022, calibrated on the 𝑧 ∼ 0 LzLCS survey Flury et al. 2022, see Trebitsch et al. 2022 for an implementation on reionization), where  \n𝑓 esc = 𝐴 𝑓 × 10 𝑏 𝑓 𝛽 UV (5)  \nwith 𝐴 𝑓 = 1 . 3 × 10 -4 and 𝑏 𝑓 = -1 . 22. In this relation galaxies that are bluer have less dust and low-ionization gas along the line-ofsight, and thus fewer sinks of ionizing photons. This correlation is similarly observed at 𝑧 ∼ 3 in different surveys (Steidel et al. 2018; Pahl et al. 2021; Begley et al. 2022; Saldana-Lopez et al. 2023). We  \ncan then employ the 𝑓 esc -𝛽 UV relation, with the 𝛽 UV -𝑀 UV measurements from Zhao & Furlanetto (2024, which incorporates both JWST and HST measurements from Bouwens et al. 2014; Topping et al. 2022; Cullen et al. 2023) to predict 2 𝑓 esc ( 𝑀 UV ) . Note that here, and throughout the text, we cap the UV slopes at 𝛽 UV = -2 . 7 when computing 𝑓 esc to avoid extrapolation in this relation (though we implicitly extrapolate in 𝑧 and 𝑀 UV , see Table A1), as that corresponds to the bluest galaxies where Eq. (5) is calibrated. We show the result of applying this calibration as the blue line in Fig. 1. The JWST-calibrated 𝜉 ion multiplied by 𝑓 esc (inferred using the high𝑧 𝛽 UV -𝑀 UV and low𝑧 𝑓 esc -𝛽 UV relations) produces an even earlier reionization, and consequently even more tension with 𝜏 CMB .  \nThe curves shown in Fig. 1 are meant to illustrate the impact of the new 𝜉 ion and 𝑓 esc results for a particular reionization model. Let us now move to perform a more detailed study, where we vary different underlying assumptions and compare against current observations.", '3 OBSERVATIONAL CONSTRAINTS': 'To understand reionization we need to know the ionizing-photon budget, i.e., how many photons are produced and what fraction escape their galaxies. We model the former by taking the ionizing efficiency 𝜉 ion from Eq. (4), as measured in JWST observations, and integrating the UVLF down to a cutoff magnitude 𝑀 ion . cutoff UV (below where we will assume galaxies do not emit ionizing photons efficiently, either because 𝑓 esc, 𝜉 ion , or the UVLF itself goes to zero, see Appendix B for an example). For the latter we define the ionization-averaged escape fraction as  \n⟨ 𝑓 esc ⟩ ion . ≡ / 𝑛 ion ( 𝑓 esc ) / 𝑛 ion ( 𝑓 esc = 1 ) , (6)  \nwith / 𝑛 ion defined in Eq. (3). These two free parameters, 𝑀 ion . cutoff UV and ⟨ 𝑓 esc ⟩ ion . , encapsulate our uncertainty about the impact of high𝑧 galaxies on reionization. They must obey three different observational constraints.  \nFirst, the cutoff 𝑀 ion . cutoff UV has to be fainter than -15 (Atek et al. 2018), given current HST and JWST observations, which we show as a green band in Fig. 2. Second, ⟨ 𝑓 esc ⟩ ion . should follow the constraints derived from low𝑧 analogues, shown as a blue band (using Eq. 5 with the best-fit amplitude and error from the LzLCS survey of 𝑧 ∼ 0 galaxies Chisholm et al. 2022, see Fig. A1 for the VANDELS 𝑧 ∼ 3 sample of Saldana-Lopez et al. 2023). Finally, the combination of 𝑀 ion . cutoff UV and ⟨ 𝑓 esc ⟩ ion . have to produce the correct reionization history, which we parametrize through the CMB optical depth 3  \n𝜏 CMB = ∫ 𝑑ℓ𝑛 𝑒 𝜎 𝑇 , (7)  \nwhere ℓ is proper distance, 𝜎 𝑇 is the Thomson cross section, and 𝑛 𝑒 is the physical (not comoving) electron density, computed assuming that HeI reionization tracks HI, and that HeII reionization takes place at 𝑧 = 4. The regions of parameter space that predict the correct 𝜏 CMB within 1 𝜎 are shown as red bands in Fig. 2. In the CMB bands a brighter cutoff 𝑀 ion . cutoff UV requires higher values of ⟨ 𝑓 esc ⟩ ion . to compensate the missing star formation - and subsequent photon production - at the faint end.  \nFigure 2. Tension in our models of reionization, expressed through the effective cutoff 𝑀 ion . cutoff UV on the UVLF (at which galaxies cease to emit ionizing photons), and the average escape fraction ⟨ 𝑓 esc ⟩ ion . above that cutoff. The three colored contours correspond to the regions allowed by the CMB optical depth 𝜏 CMB (red), the low𝑧 𝑓 esc studies (blue), and direct HST+JWST observations of no cutoff down to 𝑀 UV ≈ -15 (green). The left panel assumes a pre-JWST value of 𝜉 ion from Robertson et al. (2013), where the three colored regions nicely overlap for faint cutoffs and 𝑓 esc ≈ 0 . 2. The right panel instead takes the new JWST 𝜉 ion calibration from Simmonds et al. (2024), in which case the three regions do not overlap, showing a tension in reionization . In more detail, the blue region follows the results from the LzLCS survey of reionization-era analogues (Chisholm et al. 2022, evaluated at 𝑧 = 7, with solid lines corresponding to the 𝑀 UV directly observed, and dashed to extrapolation, in all cases capping UV slopes at 𝛽 UV = -2 . 7). We highlight three popular pre-JWST models from R15, F19, and M22 (the latter assumes a larger 𝜉 ion closer to the new JWST value) as colored stars. The red diamond and black circle on the right panel correspond to possible solutions to the tension (further explored in Fig. 3), which are in conflict with either the 𝑓 esc or 𝑀 ion . cutoff UV constraints.  \n<!-- image -->  \nFig. 2 showcases the tension between these three observations. The left panel shows the pre-JWST situation, where the lower 𝜉 ion allowed the three observational bounds (red, blue, and green regions) to overlap over a broad swath of parameter space fainter than 𝑀 ion . cutoff UV ≈ -15, with 𝑓 esc ≈ 15 -30%. The right panel, updated with the recent JWST observations, shows no overlap between the three. In this case the requirements from 𝜏 CMB (red) and the low𝑧 𝑓 esc studies (blue) only overlap for cutoffs brighter than 𝑀 ion . cutoff UV ≈ -15 (outside of the green region, and thus disfavored by direct HST+JWST observations). In other words, the new JWST observations imply an overproduction of photons during reionization, which would end this process earlier than allowed by the CMB. Note that the galaxies observed by JWST ( 𝑀 UV ≲ -15) already produce too many photons, including fainter objects would only worsen this tension.  \nFig. 2 also shows the parameter space of three popular reionization models: R15 ( ⟨ 𝑓 esc ⟩ ion . = 0 . 2 and 𝑀 ion . cutoff UV ≈ -13), F19 (their best fit is at ⟨ 𝑓 esc ⟩ ion . ≈ 0 . 05 and 𝑀 ion . cutoff UV ≈ -11), and the Lyman𝛼 emitter (LAE) model of Matthee et al. (2022, hereafter M22, which we approximate as having ⟨ 𝑓 esc ⟩ ion . = 0 . 17 for galaxies down to 𝑀 ion . cutoff UV = -17). Each of these models was calibrated to give rise to the correct 𝜏 CMB , though with different 𝜉 ion assumptions. R15 assumed log 10 𝜉 ion ≈ 25 . 2 Hz erg -1 , F19 fit for a somewhat higher 𝑧 -dependent value, whereas M22 used a larger log 10 𝜉 ion ≈ 25 . 8 Hz erg -1 , calibrated to low𝑧 LAEs (Naidu et al. 2022). Each of these models is at odds with one of the three observational constraints, and thus outside one of the color bands in Fig. 2, either 𝜏 CMB (R15, outside red band), 𝑓 esc (F19, blue), or 𝑀 ion . cutoff UV (M22, green). As such, they illustrate three possible avenues to reduce the photon budget during reionization and reconcile galaxy and CMB observations.', '4 POSSIBLE OUTS': "Let us now discuss possible physical mechanisms that may resolve this apparent photon budget crisis.  \n- · Perhaps some of the new 𝜉 ion calibrations are biased? It is possible that photometry alone cannot reliably recover 𝜉 ion , that dust produces a systematic shift in this quantity (Shivaei et al. 2018), or that the JWST samples used to infer 𝜉 ion are not representative of the high𝑧 galaxy population (if they are biased towards efficient ionizers or preferentially target galaxies in a burst). For example, the sample in Simmonds et al. (2024) is selected based on an emission line flux cut in photometry, which could bias the sample towards strong line emitters (and thus high 𝜉 ion ) at fixed UV magnitude. We have repeated our analysis with a lower fixed 𝜉 ion = 10 25 . 5 Hz erg -1 (in line with the lowest mean values reported in Endsley et al. 2023, which did not make an emission-line selection, as well as the 𝑧 > 4 mean in Pahl et al. 2024, though see e.g., Matthee et al. 2023 for lower values), finding that this still requires a cutoff at 𝑀 UV ≈ -14 or brighter (see Fig. A1 in Appendix A). An alternative solution involves keeping a high 𝜉 ion onaverage but cutting off photon production for faint galaxies (either smoothly or setting 𝜉 ion → 0 below a cutoff magnitude 𝑀 ion . cutoff UV ). Fig. 3 shows that a 𝜉 ion cutoff at 𝑀 ion . cutoff UV = -17 would be able to solve the tension. Such a cutoff would, however, be in conflict with the detections of ionizing photons down to 𝑀 UV ≈ -15 from Atek et al. (2024) and Prieto-Lyon et al. (2023, and down to 𝑀 UV ≈ -16 . 5 for the more statistically robust samples of Simmonds et al. 2024; Endsley et al. 2023). Further JWST observations of high𝑧 galaxies will be able to determine the 𝜉 ion distribution down to faint magnitudes and pinpoint the impact of burstiness on this quantity.\n- · Maybe 𝑓 esc is far lower than expected? From Fig. 2 it is apparent that little to no extrapolation of the LzLCS relation to bluer galaxies is required to overproduce reionization (see also Appendix B). One possibility is that the low𝑧 analogues in both LzLCS and VANDELS are biased (e.g., they may be more likely to be leakers), or that different mechanisms set 𝑓 esc at high and low redshifts (so that 𝑓 esc may not correlate well with 𝛽 UV at high 𝑧 ). Many of the LzLCS properties match those observed at high-redshift (Tang et al. 2023), but it is possible (perhaps likely) that high-redshift galaxies have larger neutral  \ngas fractions and lower dust-to-gas ratios than the low-redshift benchmarks (Heintz et al. 2023). This could lead to significantly lower 𝑓 esc at fixed 𝛽 UV , or a turnaround towards fainter/bluer galaxies. While plausible, this 𝑓 esc -𝛽 UV redshift evolution is not observed in 𝑧 ∼ 3 galaxies, which in fact appear to have larger 𝑓 esc at fixed 𝛽 UV (Pahl et al. 2021; Saldana-Lopez et al. 2023). Another possibility is that there is a covariance between 𝑓 esc and 𝜉 ion , such that galaxies that produce large amounts of ionizing photons have lower 𝑓 esc. This has been predicted by simulations (Rosdahl et al. 2022), though Tang et al. (2019); Naidu et al. (2022) observe the opposite trend in line emitters.  \nIf one wanted to integrate the UVLF down to the theoretically expected cutoff at 𝑀 UV ≈ -11 (Kuhlen & Faucher-Giguere 2012), the 𝑓 esc needed to fit 𝜏 CMB is ⟨ 𝑓 esc ⟩ ion . ≈ 3%, as shown in Fig. 3, slightly lower but comparable to F19. For such a low value, the LzLCSrelationship would require 𝛽 UV ≈ -1 . 93, significantly redder than JWST has observed at 𝑧 > 5 (Topping et al. 2022; Cullen et al. 2023). Moreover, even setting a modest ⟨ 𝑓 esc ⟩ = 5% still requires a cutoff at magnitudes brighter than 𝑀 UV ≈ -12 given the higher 𝜉 ion from JWST. These faint 𝑀 UV have not been statistically probed yet by JWST observations, but upcoming ultra-deep imaging of a gravitationally lensed cluster (the Glimpse program, PI: Atek, JWSTID: 3293) will measure 𝜉 ion and 𝛽 UV from lensed star-forming galaxies down to 𝑀 UV ≈ -12. Deeper measurements of analogues at moderate 𝑧 are also critical to examine how well the 𝑓 esc -𝛽 UV relation holds at fainter magnitudes (and bluer objects), as well as higher 𝑧 , pushing as close as possible to the epoch of reionization.  \n· What about the faint end of the UVLF? The slope and turnover magnitude remain as the key uncertainties of this observable. For a turnover to match reionization measurements it would have to be at a bright 𝑀 UV ≈ -17, as illustrated in Fig. 3, far above the current UVLF limits. An alternative is a shallow faint-end slope. We have repeated our analysis with the Finkelstein & Bagley (2022) UVLF, which assumes a double power-law functional form with a flattening towards the faint end, and found that the tension persists (see Appendix A). This is not surprising, as the tension in Fig. 2 requires little to no extrapolation of the UVLFs during reionization (down to 𝑀 UV ≈ -15, where the faint-end uncertainties affect galaxy abundances at the 30% level). If a turnover or flattening of the UVLF was the solution it would be of paramount importance to understand its physical origin, whether it is due to feedback during reionization (Shapiro et al. 2004) or a exotic cosmology (Sabti et al. 2022).  \n- · Maybe our theoretical models are wrong? The main uncertainty is how many recombinations take place, which we have modeled through a simple clumping factor 𝐶 . Past work has suggested additional recombinations can explain an extended reionization history inferred from the Lyman𝛼 forest at 𝑧 ∼ 5 -6 (Davies et al. 2021; Qin et al. 2021). Such a 'tax on the rich' (in terms of ionizing photons, Furlanetto & Oh 2005) could alleviate the budget crisis. As a test, we show in Fig. 3 how even a large 𝐶 = 20 - implying nearly an order of magnitude more recombinations throughout all of reionization - does not suffice to harmonize galaxy and CMB observations, still overproducing reionization (more than 3 𝜎 above 𝜏 CMB measurements). Of course, we expect the process of reionization to be complex and inhomogeneous, but we note that these many recombinations per hydrogen atom are not standard in Λ CDM cosmologies (even including mini-halos, Gnedin 2024), and could point to additional baryon fluctuations at very small scales, or missing ingredients in our theories.  \nFig. 3 summarizes how different possible solutions would affect the timing of reionization. While these scenarios can be re-calibrated to produce the correct 𝜏 CMB (e.g., increasing 𝑀 ion . cutoff or decreasing  \nx  \nFigure 3. Possible solutions to the photon budget crisis, and how they would affect the timing of reionization. The blue dot-dashed line corresponds to our current understanding of reionization, as in Fig. 1. The pink dotted line assumes a higher clumping factor 𝐶 = 20, which still does not produce enough recombinations. The red dashed line has 𝑀 ion . cutoff UV = -11 and a low 𝑓 esc = 3%, whereas the black line posits 𝑀 ion . cutoff UV = -17 with a larger 𝑓 esc = 15%. These two models produce the correct 𝜏 CMB, but disagree with one of the two galaxy observations, as indicated by the red diamond and black circle in the right panel of Fig. 2. Their reionization histories 𝑥 HI ( 𝑧 ) are potentially distinguishable from one another (measurements in green, which have not been used to calibrate the models).  \n<!-- image -->  \n𝑓 esc), measurements of 𝑥 HI ( 𝑧 ) can potentially distinguish between them, as posing a cutoff 𝑀 ion . cutoff UV makes reionization faster (like oligarchic models, Naidu et al. 2019), whereas decreasing 𝑓 esc slows it down (appearing democratic, F19). Of course, a 𝑧 -dependent 𝑓 esc can mimic this effect, so clustering measurements of reionization bubbles, for instance with the 21-cm line (Furlanetto et al. 2004; Muñoz et al. 2022) will be required to break degeneracies. We emphasize that each of the mechanisms invoked in this section requires giving up the constraints from at least one of our galaxy measurements, be it the UVLFs, 𝜉 ion , 𝑓 esc, or a combination of them. Further observations of galaxies, 𝑥 HI , and 𝜏 CMB will sharpen our understanding of the reionization process, as current error-bars are still sizeable and may hide underlying systematics. While the list presented here is not exhaustive, we hope it encourages theoretical and observational work to resolve the JWST photon budget crisis.", '5 CONCLUSIONS': "The launch of JWST is allowing us to directly access the properties of the first galaxies with unprecedented sensitivity. Early observations are showing that early, faint galaxies are prolific producers of ionizing photons. Here we have combined new JWST measurements with determinations of the escape fractions 𝑓 esc of reionization-era analogues to show that our current galaxy observations predict a process of reionization that ends too early. That is, the situation has been reversed from the WMAP era, where the concern was producing enough photons to match 𝜏 CMB , to the postPlanck and JWST era, where there may be too many photons .  \nTo match the CMB optical depth, the / 𝑛 ion of early galaxies must dramatically decrease. This is currently not observed in the high𝑧 galaxy population. For instance, the UVLFs do not show a significant turnover down to 𝑀 UV ≈ -15 (Atek et al. 2018), faint galaxies during the epoch of reionization are very blue down to 𝑀 UV ≈ -17 (Topping et al. 2022; Cullen et al. 2023, hinting at high 𝑓 esc), and on average galaxies produce significantly more ionizing photons than inferred from HST + Spitzer observations down to 𝑀 UV ≈ -15 (Simmonds et al. 2024; Atek et al. 2024; Endsley et al. 2023).  \nAs such, taken at face value the galaxies JWST has observed already produce enough ionizing photons to reionize the universe. This does not include faint galaxies still unprobed by JWST observations, or a contribution from early black holes (which appear prevalent in early JWST observations, Matthee et al. 2024). There must be a missing ingredient in either our modeling or observations to harmonize the galaxy and CMB inferences of reionization.  \nMoving forward, there are several avenues that can further audit the ionizing-photon budget. Future CMB surveys are expected to measure 𝜏 CMB to ≈ 0 . 002 (Allys et al. 2023), which would sharpen our understanding of reionization. Better constraints on the timing of reionization beyond 𝜏 CMB (e.g., via the kinematic SunyaevZel'dovich effect and the transmission of Lyman𝛼 photons from high-redshift sources Raghunathan et al. 2024; Chen et al. 2024; Nakane et al. 2023; Ouchi et al. 2020; Lu et al. 2024) and tomographic measurements of the distribution of neutral and ionized hydrogen through the 21-cm line (Morales & Wyithe 2010; Abdurashidova et al. 2022), will provide invaluable information on how different sources contribute to the photon budget. Further studies of both 𝑓 esc (at low 𝑧 ) and 𝜉 ion (at high 𝑧 ) are critical to account for selection biases in our samples, or for missed assumptions in their interpretation. The biggest theoretical uncertainty is quantifying the recombination rate, which has a substantial effect on the reionization history (see Fig. 3) and may alleviate the requirements on the sources. In particular, it is crucial to understand how an increase in the recombination rate at 𝑧 ∼ 6 due to dense IGM clumps would carry over to higher redshifts, during the bulk of reionization.  \nIn summary, recent observations have found that early galaxies were numerous, efficient producers of ionizing photons, and likely to have non-negligible escape fractions. Together, these galaxy observations imply an excess in the ionizing-photon budget during reionization, which would end this cosmic epoch earlier than allowed by CMB data. The JWST era has just begun, and here we have examined how future observations and theoretical efforts can shed light on this tension. As of the time of writing, the different solutions are in conflict with at least one observational constraint. Resolving this tension on reionization is a key step to finally understanding the last major phase transition of our universe.", 'ACKNOWLEDGEMENTS': 'Weare grateful to V. Bromm, R. Endsley, S. Finkelstein, K. Hawkins, A. Pahl, C. Scarlata, M. Shull, E. Thelie, and the anonymous referee for insights on a previous version of this manuscript. JBM was supported by the National Science Foundation under Grants AST2307354 and AST-2408637, and thanks the Yukawa Institute for Theoretical Physics and the Kavli Institute for Theoretical Physics for their hospitality during part of this work. JM was supported by an appointment to the NASA Postdoctoral Program at the Jet Propulsion Laboratory / California Institute of Technology, administered by Oak Ridge Associated Universities under contract with NASA. SRF was supported by NASA through award 80NSSC22K0818 and by the National Science Foundation through award AST-2205900. CAMacknowledges support by the VILLUM FONDEN under grant 37459 and the Carlsberg Foundation under grant CF22-1322. The Cosmic Dawn Center (DAWN) is funded by the Danish National Research Foundation under grant DNRF140.', 'DATA AVAILABILITY': 'The data underlying this article will be shared on reasonable request to the author. Software: numpy (van der Walt et al. 2011), scipy (Jones et al. 2001), matplotlib (Hunter 2007), Zeus21 (Muñoz 2023), CLASS (Blas et al. 2011).', 'REFERENCES': "Lam D., et al., 2019, A&A, 627, A164  \nLin Y.-H., et al., 2024, MNRAS, 527, 4173  \n- Liu H., Slatyer T. R., Zavala J., 2016, Phys. Rev. D, 94, 063507\n- Lu T.-Y., Mason C. A., Hutter A., Mesinger A., Qin Y., Stark D. P., Endsley R., 2024, MNRAS, 528, 4872\n- Ma X., Hopkins P. F., Kasen D., Quataert E., Faucher-Giguère C.-A., Kereš D., Murray N., Strom A., 2016, MNRAS, 459, 3614\n- Ma X., Quataert E., Wetzel A., Hopkins P. 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In this last case there is a region of parameter space where the constraints overlap, showing that a downward revision of 𝜉 ion plus a cutoff brighter than 𝑀 UV ≈ -14 could resolve the tension. We also show the median 𝑓 esc from the VANDELS sample of 𝑧 ∼ 3 galaxies (Saldana-Lopez et al. 2023), extrapolated to bluer galaxies as a dashed line.  \n<!-- image -->  \nTopping M. W., Stark D. P., Endsley R., Plat A., Whitler L., Chen Z., Charlot S., 2022, ApJ, 941, 153 Trebitsch M., et al., 2022 Wang F., et al., 2020, Astrophys. J., 896, 23 Weibel A., et al., 2024, arXiv e-prints, p. arXiv:2403.08872 Whitler L. R., Mason C. A., Ren K., Dĳkstra M., Mesinger A., Pentericci L., Trenti M., Treu T., 2019, ] 10.1093/mnras/staa1178 Wise J. H., Demchenko V. G., Halicek M. T., Norman M. L., Turk M. J., Abel T., Smith B. D., 2014, MNRAS, 442, 2560 Yeh J. Y. C., et al., 2023, MNRAS, 520, 2757 Yoo T., Kimm T., Rosdahl J., 2020, MNRAS, 499, 5175 Zhao J., Furlanetto S. R., 2024, arXiv e-prints, p. arXiv:2401.07893 Zhu Y., et al., 2023, ApJ, 955, 115 van der Walt S., Colbert S. C., Varoquaux G., 2011, Computing in Science and Engineering, 13, 22", 'APPENDIX A: ALTERNATIVE ASSUMPTIONS': 'Through the text we have taken the pre-JWST UVLF from Bouwens et al. (2021) for 𝑧 ≤ 9, and the JWST-era UVLFs from Donnan et al. (2024) for higher 𝑧 . These data reach 𝑀 UV ≈ -17 at 𝑧 ∼ 7, so in order to find the abundance of galaxies at fainter magnitudes some extrapolation is required. Additionally, we have used the 𝛽 UV -𝑀 UV relation from Zhao & Furlanetto (2024), which includes JWST data, and the 𝜉 ion fit from Simmonds et al. (2024). The purpose of this Appendix is to cross check these assumptions. For that we will first repeat our analysis removing the new JWST calibrations of the 𝑧 ≳ 9 UVLF and 𝛽 UV and revert to pre-JWST estimates. Then we will use the Finkelstein & Bagley (2022) UVLF, which uses a compilation of data and has a different functional form that includes flattening towards the faint end. Finally, we will find whether there is still tension for a value of 𝜉 ion comparable to that of Endsley et al. (2023) or Pahl et al. (2024), rather than Simmonds et al. (2024).  \nTable A1. Table summarizing the different mean/median assumed relations in this work, their origin, calibration region, and estimated uncertainty (not intrinsic scatter). Last column shows the optical depth derived by taking each relationship and its uncertainty, while keeping the rest of the analysis fixed. 𝑎 First relation shown for each variable corresponds to our fiducial through the paper. 𝑏 In both cases added to Donnan et al. (2024) for 𝑧 ≳ 9. 𝑐 Uncertainty in 𝛽 UV and Φ UV depends on magnitude and redshift, so we report typical values at 𝑧 ∼ 7 and 𝑀 UV ∼ -17. 𝑑 Assuming a cutoff at 𝑀 UV = -13. These ought to be compared to the Planck measurement of 𝜏 CMB = 0 . 054 ± 0 . 007 (Aghanim et al. 2020).', 'A1 How much do the new JWST UVLFs impact the tension?': 'Not significantly. We re-run our analysis returning to the pre-JWST UVLFfromBouwensetal.(2021), and using the 𝛽 UV -𝑀 UV relation from Bouwens et al. (2014, fixing its 𝑧 = 8 value for earlier times). Fig. A1 shows how the region that gives rise to the correct 𝜏 CMB is still in tension with galaxy observables, as it only overlaps the low𝑧 constraints on 𝑓 esc for cutoffs brighter than 𝑀 UV ≈ -15, which are disfavored (barring a tiny edge region around 𝑀 ion . cutoff UV = -15 and ⟨ 𝑓 esc ⟩ ion . = 15%). The tension is then largely driven by the high 𝜉 ion values inferred by JWST observations, rather than the enhancement of the UVLF at high 𝑧 . Nevertheless, the extra 𝑧 ≳ 9 galaxies can kickstart reionization earlier. Adding the recently discovered population of supermassive black holes in JWST would potentially increase the ionizing-photon production (unlike the pre-JWST expectations, e.g., Matsuoka et al. 2018), exacerbating the crisis if the accretion disks are unobscured.', 'A2 Re-analysis with Finkelstein & Bagley (2022)': 'Fig. A1 shows how the tension in the ionization-photon budget remains when changing the UVLF to the pre-JWST fit from Finkelstein &Bagley (2022, and 𝛽 UV from Bouwens et al. 2014). The three observations ( 𝜏 CMB , the 𝑓 esc measurement from low 𝑧 , and the no-cutoff down to the HST+JWST limit) still do not overlap. This is not surprising, since the different UVLFs broadly agree at the bright end, only diverging towards faint magnitudes and high 𝑧 (for instance, at 𝑧 = 7 the uncertainty in the faint-end slope 𝛼 ★ of both Finkelstein & Bagley 2022 and Bouwens et al. 2021 translates into 30% more or fewer 𝑀 UV = -15 galaxies). This is visible towards the faint side ( 𝑀 ion . cutoff UV ∼ -13 ) of Fig. A1, where the CMB-preferred region flattens at 𝑓 esc ≈ 6%, whereas in the Bouwens et al. (2021) case it does so at 𝑓 esc ≈ 3%. Part of the reason is the turnover built into the UVLF fit of Finkelstein & Bagley (2022, not included in the Bouwens et al. 2021 fit), regardless of our additional 𝑀 ion . cutoff UV . This test serves to benchmark the differences in the faint end of the UVLF.', 'A3 A lower 𝜉 ion value?': 'Through the main text we have used the fit for 𝜉 ion as a function of 𝑀 UV and 𝑧 from Simmonds et al. (2024). Other reionizationera results from Atek et al. (2024) and Endsley et al. (2023) also find enhanced ionizing-photon production, though in the latter case it decreases towards the faint end, rather than increase. We have found that the photometric results in Endsley et al. (2023) can be  \napproximately fit by  \nlog 10 𝜉 ion = 25 . 5 -0 . 03 × ( 𝑀 UV + 18 ) , (A1)  \nfor the two faint bins in their calibration (and this relation underestimates 𝜉 ion for the brightest bin). We show in Table A1 how taking this relation still overpredicts 𝜏 CMB . A recent spectroscopic analysis in Pahl et al. (2024) finds a mean GLYPH<10> log 10 𝜉 ion /( Hzerg -1 ) GLYPH<11> = 25 . 38 for their 𝑧 > 4 sample, which translates into a mean ⟨ 𝜉 ion ⟩ = 10 25 . 57 Hzerg -1 (Pahl, Private Communication) as expected of a lognormal variable with a 0.4 dex scatter. We can, then, conservatively bracket the uncertainty in 𝜉 ion by performing a run with log 10 𝜉 ion /( Hzerg -1 ) = 25 . 5, comparable to the lowest mean values measured in Endsley et al. (2023, see third panel of Fig. B1) and the running mean of Pahl et al. (2024). We show the result of this analysis in Fig. A1, where the three observational constraints overlap over a small range of parameter space. This represents a possible compromise solution, requiring both a cutoff brighter than 𝑀 UV ∼ -14 (potentially detectable) plus a downward revision on 𝜉 ion (possibly indicating an observational bias or mismodeling).', 'A4 Summary of Assumptions': 'We summarize the relations taken in this work, their origin in either JWST or HST data, and the reported uncertainties in Table A1. We compute in each case the expected 𝜏 CMB and associated errorbars from each relationship, keeping the rest fixed and setting a fiducial cutoff at 𝑀 UV = -13 as in Robertson et al. (2015). We find that changing the UVLF calibration makes a difference of 20% on 𝜏 CMB (due to the cutoff included in Finkelstein & Bagley 2022), whereas changing the 𝛽 UV relation is at the sub-10% level. The biggest uncertainties are 𝑓 esc and 𝜉 ion , as expected, and in particular we find that going from the Simmonds et al. (2024) to the Endsley et al. (2023) 𝜉 ion calibration reduces 𝜏 CMB by 20%, though in all cases shown in Table A1 𝜏 CMB is higher than allowed by the CMB.', 'APPENDIX B: THE ORIGIN OF A FAINT CUTOFF': "Through the main text we have used the variable 𝑀 ion . cutoff UV to express a generic cutoff below where galaxies do not contribute to reionization. This cutoff can have an origin in three different mechanisms, which we illustrate in Fig. B1.  \nFirst, the UVLF may have a 'turn over', so the abundance of star-forming galaxies drops below some magnitude. Current UVLF observations suggest that this cutoff has to be fainter than 𝑀 UV ≈ -15 during reionization (Atek et al. 2018). This is shown in the second panel of Fig. B1.  \nFigure B1. The ionization-photon production ( first panel , at 𝑧 ∼ 7) can be cut off at the faint end from three different sources: the UVLF ( Φ UV, second panel ), the ionizing efficiency ( 𝜉 ion , third panel ), or the escape fraction ( 𝑓 esc, last panel ). We shade the regions that are not observed on each respective panel. Dotted curves show the result with no cutoffs, and thick with each cutoff. The vertical black line is at 𝑀 ion . cutoff UV = -17, as required to fit reionization in Fig. 3, which is in tension with observations. In the third panel we show not only the 𝜉 ion fit from Simmonds et al. (2024, S+24, used through the main text) but also measurements from Endsley et al. (2023, E+23), Atek et al. (2024, A+24), and Prieto-Lyon et al. (2023, PL+23, evaluated at 𝑧 ∼ 7). All the JWST-inferred 𝜉 ion values are well above the pre-JWST canonical value (black dotted).  \n<!-- image -->  \nSecond, the ionizing efficiency may vanish for faint galaxies. Some JWST observations suggest the opposite, in fact, with 𝜉 ion seemingly growing towards the faint end at least until 𝑀 UV ≈ -15 (Atek et al. 2024, or 𝑀 UV = -16 . 5 for the broader but photometric sample of Simmonds et al. 2024). This trend is also reported in Prieto-Lyon et al. (2023) at ⟨ 𝑧 ⟩ ≈ 4, which we show in Fig. B1 (extrapolating their results to 𝑧 = 7 by using the scaling in Eq. 4). The results in Endsley et al. (2023) instead point to 𝜉 ion growing towards the bright end, as shown in Fig. B1, though with a large variance in the distribution at each bin. This variance also makes the average 𝜉 ion slightly larger than expected from the median of log 10 𝜉 ion , as in  \nfootnote 2, which we account for when plotting the Endsley et al. (2023) data (as it is the only one with measured variance). All the JWST measurements in the third panel of Fig. B1 are significantly above the pre-JWST canonical value, following pre-JWST hints in e.g., Maseda et al. (2020).  \nLast, the escape fraction 𝑓 esc may stop growing towards the faint end. This is, however, the opposite behavior seen at low 𝑧 in both LzLCS( 𝑧 ∼ 0) and VANDELS( 𝑧 ∼ 3). For reference, the median 𝑓 esc in the VANDELS sample reported by Saldana-Lopez et al. (2023) can be fit using Eq. (5) with 𝐴 𝑓 = 1 . 12 × 10 -4 and 𝑏 𝑓 = -1 (from their Fig. 15), which we show in both Figs. A1 and B1. The bluest galaxies sampled in the LzLCS ( 𝛽 UV = -2 . 7) correspond to 𝑀 UV ≈ -15 . 7 at 𝑧 ∼ 7 (using the 𝛽 UV -𝑀 UV relation from Zhao & Furlanetto 2024), indicating we do not expect a cutoff on 𝑓 esc until at least that magnitude, as shown in the last panel of Fig. B1.  \nTogether, different galaxy observations have probed the 𝑀 ion . cutoff UV ≈ -17 region, disallowing a cutoff at such magnitudes, unless there is an observational bias or systematic uncertainty.  \nThis paper has been typeset from a T E X/L A T E X file prepared by the author."}