Low-mass bursty galaxies in JADES efficiently produce ionising photons and could represent the main drivers of reionisation

We study galaxies in JADES Deep to study the evolution of the ionising photon production efficiency, $\xi_{\rm{ion}}$, observed to increase with redshift. We estimate $\xi_{\rm{ion}}$ for a sample of 677 galaxies at $z \sim 4 - 9$ using NIRCam photometry. Specifically, combinations of the medium and wide bands F335M-F356W and F410M-F444W to constrain emission lines that trace $\xi_{\rm{ion}}$: H$\alpha$ and [OIII]. Additionally, we use the spectral energy distribution fitting code \texttt{Prospector} to fit all available photometry and infer galaxy properties. The flux measurements obtained via photometry are consistent with FRESCO and NIRSpec-derived fluxes. Moreover, the emission-line-inferred measurements are in tight agreement with the \texttt{Prospector} estimates. We also confirm the observed $\xi_{\rm{ion}}$ trend with redshift and M$_{\rm{UV}}$, and find: $\log \xi_{\rm{ion}} (z,\text{M}_{\rm{UV}}) = (0.05 \pm 0.02)z + (0.11 \pm 0.02) \text{M}_{\rm{UV}} + (27.33 \pm 0.37)$. We use \texttt{Prospector} to investigate correlations of $\xi_{\rm{ion}}$ with other galaxy properties. We see a clear correlation between $\xi_{\rm{ion}}$ and burstiness in the star formation history of galaxies, given by the ratio of recent to older star formation, where burstiness is more prevalent at lower stellar masses. We also convolve our $\xi_{\rm{ion}}$ relations with luminosity functions from the literature, and constant escape fractions of 10 and 20\%, to place constraints on the cosmic ionising photon budget. By combining our results, we find that if our sample is representative of the faint low-mass galaxy population, galaxies with bursty star formation are efficient enough in producing ionising photons and could be responsible for the reionisation of the Universe.


INTRODUCTION
The Epoch of Reionisation (EoR) describes one of the Universe's major phase changes, during which the intergalactic medium (IGM) became transparent to Lyman Continuum (LyC; E ≥ 13.6 eV) radiation.Observations place the end of this epoch at  ∼ 6 (Becker et al. ★ E-mail: cs2210@cam.ac.uk 2001;Fan et al. 2006;Yang et al. 2020), with some studies favouring a later reionisation closer to  ∼ 5 (Keating et al. 2020;Bosman et al. 2022).It is widely believed that young massive stars in galaxies are the main drivers of this transition, due to their copious production of LyC photons that escape the interstellar medium (ISM), and eventually ionise the IGM (Hassan et al. 2018;Rosdahl et al. 2018;Trebitsch et al. 2020).However, there is a debate whether faint, lowmass galaxies or bright, massive galaxies dominate the photon budget of reionisation (Finkelstein et al. 2019;Naidu et al. 2020;Robertson 2022).In particular, the mass of galaxies has been seen to correlate with both the production efficiency and escape of ionising photons (Paardekooper et al. 2015), both key factors to understand the EoR.Moreover, the contribution of Active Galactic Nuclei (AGN) to this budget might be more important than previously believed (AGN + host galaxy > 10%; Maiolino et al. 2023).For galaxies to be the main sources of reionisation, adopting canonical values of ionising photon production efficiencies, relatively high average escape fractions are necessary (  esc = 10-20%; Ouchi et al. 2009;Robertson et al. 2013Robertson et al. , 2015;;Finkelstein et al. 2019;Naidu et al. 2020).High  esc values have been observed in some galaxies (e.g.Borthakur et al. 2014;Bian et al. 2017;Vanzella et al. 2018;Izotov et al. 2021), but usually not in large samples (Leitet et al. 2013;Leitherer et al. 2016;Steidel et al. 2018;Flury et al. 2022).Another important quantity to measure is the ionising photon production efficiency ( ion ), which is a measure of the production rate of ionising photons over the non-ionising ultra-violet (UV) luminosity density.Promisingly, by gaining observational access to the early Universe (up to  ∼ 9), studies have found that as we go to higher redshifts,  ion increases (e.g.Bouwens et al. 2016;Faisst et al. 2019;Endsley et al. 2021;Stefanon et al. 2022;Tang et al. 2023;Simmonds et al. 2023;Atek et al. 2023).An increase of  ion implies that lower  esc values are required in galaxies, in order for them to be responsible for the reionisation of the Universe.Current constraints place the mean redshift of reionisation somewhere between  = 7.8 − 8.8 (Planck Collaboration et al. 2016).Since the launch and deployment of the James Webb Space Telescope (JWST; Gardner et al. 2023), we have an unprecedented view of the Universe deep into the EoR.Moreover, by using deep photometry taken with the Near-Infrared Camera (NIRCam; Rieke et al. 2023b), we can gain insight into the rest-frame optical properties of large and statistically significant samples of galaxies at this epoch.In particular, there are three important ingredients that contribute to our overall understanding of the ionising photon budget of the Universe: (1) a prescription for the  esc of the population, (2) an appropriate luminosity density function,  UV , describing how many objects per unit volume of a certain UV luminosity exist as a function of redshift (for example Bouwens et al. 2021), and (3)  ion .Until recently, it was common practice to set (1) and (3) as constants (e.g.Boyett et al. 2022).However, the launch of JWST has given us unprecedented access to the rest-frame optical regime at high redshift, providing enough additional constraints on the stellar population to better infer  ion across the population.Therefore, studies shedding light on how  esc and/or  ion evolve with galaxy properties, especially at high redshift, are of utmost relevance to the field.
In Simmonds et al. (2023), JWST Extragalactic Medium Band Survey (JEMS; Williams et al. 2023) photometry was used to estimate  ion for a sample of 30 Lyman- emitters (LAE) at  ∼ 6.In this work we use deep NIRCam imaging (Rieke et al. 2023a) to create a sample of 677 galaxies at  ∼ 4 − 9, with photometric redshifts provided by the template-fitting code EAZY (Brammer et al. 2008).We use two filter pair combinations: F335M-F356W, and F410M-F444W, to estimate H and/or [O iii] emission line fluxes, which can be used to infer  ion .To test the reliability of our derived fluxes, we compare (when available) our measurements to those obtained by First Reionisation Epoch Spectroscopic Complete Survey (FRESCO; Oesch et al. 2023, PI: Oesch) grism spectra.In addition, we compare our fluxes and ionising photon production efficiencies to NIRSpec measurements (Saxena et al. 2023).Simultaneously, we use the Spectral Energy Distribution (SED) fitting code Prospector (Johnson et al. 2019(Johnson et al. , 2021) ) to infer galaxy properties such as star formation rates (SFRs) and histories (SFHs), both closely related to the production of ionising photons through star formation.Finally, we investigate how our findings affect the cosmic ionising photon budget, and make conclusions about which kind of galaxies could be the main sources responsible for the reionisation of the Universe.
The structure of this paper is the following.In § 2 we present the data used in this work, along with the sample selection criteria.In § 3 we explain the two observational methods used to estimate  ion (through H𝛼 and [O iii] 5007 ), and how the respective fluxes were measured from photometry.In § 4 we present our Prospector fitting method.Our  ion constraints are given in § 5, followed by a discussion in § 6, and brief conclusions in § 7.

DATA AND SELECTION CRITERIA
In this section we describe the data and selection criteria applied to build a sample for which we can infer  ion through emission line fluxes, specifically H and [O iii] 5007 .We caution the reader that by making this choice we are introducing a bias towards galaxies with strong emission lines, which will be discussed later.

Data
We make use of the NIRCam Deep imaging (Rieke et al. 2023a) released by the JWST Advanced Deep Extragalactic Survey (JADES; Eisenstein et al. 2023).This data covers an area of ∼ 25 arcmin 2 overlapping with the Hubble Ultra Deep Field (HUDF; Beckwith et al. 2006), and portions of the Great Origins Deeps Survey South (GOODS-S; Giavalisco et al. 2004).The images were taken by a combination of 9 medium and wide-band infrared filters: F090W, F115W, F150W, F200W, F277W, F335M, F356W, F410M, and F444W.When in an overlapping region, some galaxies also have JEMS photometry, adding 5 more medium filters: F182M, F210M, F430M, F460M and F480M.This exquisite data set is ideal to estimate photometric redshifts (photo-z) with great accuracy.In this work we use photo-z inferred by the template-fitting code EAZY, as described in Hainline et al. (2023) and Rieke et al. (2023a). 1  Regarding the photometric catalogue, the source detection and photometry leverage both the JEMS NIRCam medium band and JADES NIRCam broad and medium band imaging.Detection is performed using the photutils (Bradley et al. 2022) Software package, identifying sources with contiguous regions of the SNR mosaic with signal > 3 and five or more contiguous pixels.We also use photutils to perform circular aperture photometry with filterdependent aperture corrections based on empirical point-spreadfunctions measured from stars in the mosaic.The details of the catalogue generation and photometry will be presented in Robertson et al., (in prep).In this work we adopt a circular aperture of diameter 0.3 ′′ throughout, and impose a floor error of 5% in each band.
Finally, when available, we compare our photometry-derived emission-line fluxes to those obtained through an independent reduction of the spectra taken with the FRESCO program (Oesch et al. 2023), which will be presented in Sun et al. (in prep), and to NIRSpec measurements provided in Saxena et al. (2023).

Sample selection criteria
The focus of this work is to constrain  ion for a large sample of emission line galaxies, thought to have had a significant role in reionisation (e.g.Rinaldi et al. 2023a,b).As is discussed in Section 3, this requires H and/or [O iii] 5007 in emission.The combination of broad and medium photometric bands is powerful to estimate emission lines when spectra are not available (e.g.Bunker et al. 1995;Stark et al. 2013;Faisst et al. 2016).Therefore, we select galaxies where the desired emission lines fall on one (or more) of the following filters: F335M, F356W, F410M or F444W.Figure 1 shows the throughput and wavelengths of these filters, as well as the redshift evolution of the observed wavelength of H and [O iii] 5007 .
As shown in the right vertical axis, this constrains the sample to  = 3.9 − 9.0.We note that the medium bands from the JEMS survey cover a smaller region in the sky, therefore, we use them (when available) to feed our SED-fitting routine, but not for estimating emission line fluxes.
We apply this redshift cut to galaxies based on their photo-z.Furthermore, in order to be able to detect emission lines, we impose a conservative minimum flux difference between medium and wide bands to ensure a 5 line detection, as follows: Where the excess in flux in a given band (depending on redshift) is assumed to be dominated by either H or [O iii] (i.e.neglecting [N ii], H and [S ii] contamination).A visual inspection was then performed on all the SEDs that satisfied this condition.
Once the sample has been constructed, we compare our flux excesses to a grid of simple Cloudy (Ferland et al. 2017) photoionisation models, using stellar populations from the Binary Population and Spectral Synthesis version 2.2.1 (BPASS; Eldridge et al. 2017) as intrinsic SEDs.The models were run to convergence assuming a constant SFH.The stellar and nebular parameters were varied to cover a broad range of metallicities (Z = 0.001, 0.006, 0.014 and 0.030; in this convention Z ⊙ = 0.014), ages (3 × 10 6 ,5 × 10 6 ,10 7 and 5 × 10 7 years), ionisation parameters (log⟨⟩ = −3.5 to -0.5 in steps of 0.5), and densities (log /[cm −3 ] = 0, 1, 2 and 3).The net transmitted SEDs (that include nebular emission) were then redshifted between  = 3.9 and 9.0, in steps of 0.1, and photometry was simulated in the filters of interest (F335M, F356W, F410M and F444W) using the code Bagpipes (Carnall et al. 2018).Figure 2 shows the results of this Cloudy exercise, for visualisation purposes the models are shown as shaded areas colour-coded by log⟨⟩, and represent the shape expected in each filter pair, as a function of redshift.The regions where the respective emission lines dominate either filter pair are highlighted as vertical bands.As expected, there is a strong dependency of [O iii] 5007 emission with log⟨⟩.The final sample, composed of 677 galaxies in the redshift range  = 3.9 − 8.9 is shown as purple circles.

USING PHOTOMETRY TO CONSTRAIN THE IONISING PHOTON PRODUCTION EFFICIENCY OF GALAXIES
To estimate  ion photometrically we use two methods, both of which rely on emission lines measurements, particularly H and [O iii] 5007 .We now briefly present them, along with a description of how they were applied in this work.We remind the reader that all errors in photometric points were floored to 5% in these calculations.

H𝛼 as proxy for ionising radiation production
If we assume no ionising photons escape from a galaxy (  esc = 0) and Case B recombination, the dust-corrected H luminosity is directly related to the amount of ionising photons (  ion ) that are being emitted.Adopting a temperature of 10 4 K and an electron density of 100 cm −3 , these quantities are related by:  ion = 7.28 × 10 11 L(H) as given in Osterbrock & Ferland (2006), where  ion is in units of photon s −1 , and L(H) in erg s −1 .This equation has a slight dependence on temperature and metallicity (Charlot & Longhetti 2001), but for the purpose of this work this has been ignored.We note that the Case B recombination assumption yields a conservative estimation of the amount of ionising photons being produced, and non-zero escape fractions would lead to a boost in the derived  ion values.Additionally, instead of ionising the surrounding gas or escaping, a significant amount of ionising photons could be absorbed by dust (∼ 30%; Tacchella et al. 2022a), resulting in a lack of nebular emission lines.
To estimate the ionising photon production efficiency per UV luminosity assuming Case B recombination,  ion,0 (the zero subscript indicates  esc = 0), we insert  ion into the following equation: where L UV is the observed monochromatic luminosity in units of erg s −1 Hz −1 , measured at the rest-frame wavelength of  = 1500 Å.

Measurements from photometry
We define four redshift bins to estimate H fluxes, based the expected wavelength of H, as follows: Where we assume the excess flux in the filter containing H is dominated by H emission, reasonable at high redshifts (e.g.Cameron et al. 2023).To obtain L UV we fit a straight line in logarithmic space using the curve_fit function in SciPy (Virtanen et al. 2020), between rest-frame 1250 and 2500 Å, in the form   ∝   , where  is the rest-frame UV continuum slope (; Calzetti et al. 1994).We use all the available photometry in this region for each redshift bin.
Figure 3 shows a representative example SED of each H redshift bin.The identifier and redshift of each galaxy are given in the caption.The expected wavelengths of H and [O iii] 5007 are shown as vertical lines, it can be seen that H falls primarily in a different filter as redshift increases.The photometry of the four NIRCam filters of interest are highlighted with red edges.The  slope is given in the legend, and corresponds to the purple dashed line.Finally, the blue cross shows the observed wavelength and flux corresponding to rest-frame 1500 Å.
Once H fluxes have been calculated, they must be corrected for dust attenuation.This is not trivial for our sample since this parameter is not well understood at high redshifts (Gallerani et al. 2010;Ma et al. 2019), and we do not have measurements for Balmer line ratios.Moreover, the geometry and effect of dust attenuation in early galaxies is highly uncertain (Bowler et al. 2018(Bowler et al. , 2022)).Nevertheless, it has been shown that a steep attenuation curve, such as seen in the Small Magellanic Cloud (SMC; Prevot et al. 1984;Gordon & Clayton 1998), is appropriate for young high-redshift galaxies (Shivaei et al. 2020).Thus, we apply an average SMC attenuation curve (Gordon et al. 2003) to our H and UV measurements, using  to infer the nebular continuum colour excess E(B-V) , given by E(B-V) = ( + 2.616) × 1 11.259 (Reddy et al. 2018, ;adopting SMC attenuation).
We note that in redshift bins (ii) and (iv), H falls in the wide band filter, and thus, more noise is introduced.In addition, they could be affected by [N ii] and/or [S ii] contamination.As discussed in Simmonds et al. (2023), this contamination is not expected to be significant at high redshift (see also ;Maiolino & Mannucci 2019;Onodera et al. 2020;Sugahara et al. 2022;Cameron et al. 2023).

[O iii] equivalent widths as proxy for ionising radiation production
The previous method has some limitations, such as the assumption of Case B recombination, and the high dependence on the attenuation curve adopted.Moreover, at  ≳ 6, H is redshifted to wavelengths challenging to observe.To circumvent these limitations, an alternative method that depends on [O iii] 5007 instead was proposed in Chevallard et al. (2018), granting access to higher redshifts (up to  ∼ 9.If the line falls in the medium band, then the wide band also includes it, so the local continuum is measured from the corresponding wide band minus the line contribution.On the other hand, if the line falls in the wide band, then the corresponding medium band is assumed to represent the continuum.The differential dust attenuation between continuum and nebular emission is uncertain at high redshifts.Here we assume a ratio of 1.3 between the reddening affecting emission lines and continuum, appropriate at  ∼ 1 (Pannella et al. 2015), but caution that this value can be closer to 2 for galaxies with low metallicities (Shivaei et al. 2020).Adopting the latter would systematically increase our [O iii] EWs and consequently, our inferred  ion measurements.We note that [O iii] might suffer from H contamination, below we investigate the importance of this contamination by comparing our fluxes to those measured in FRESCO grism spectra.

Flux comparisons to FRESCO grism spectra
To investigate the importance of contamination from other emission lines in our H and [O iii] fluxes, as well as to test the simplistic approach to measuring the fluxes, we compare our measurements (when available) with those obtained through an independent reduction of FRESCO grism spectra.The detailed FRESCO grism line flux measurements and validation for a larger sample of  = 5 − 9 galaxies will be presented in a forthcoming paper (Sun et al. in prep).We find 122 (36) overlapping galaxies with H ([O iii]) flux measurements.Figure 4 shows the results for both H (circles) and [O iii] (squares).The filled and open symbols in each case denote if the emission line falls in a medium or wide band, respectively.We find that most measurements are within 3 of a 1:1 relation, confirming that our approach, while simplistic, is overall acceptable.Moreover, it indicates that if other lines are contaminating our flux estimations ([N ii] or [S ii] in the case of H, H in the case of [O iii]), then the contribution is not significant on average.We draw attention to the limitations of estimating emission-line fluxes using these two methods: grism spectra can potentially be affected by background ( = 5.74 ± 0.06).The coloured curves show the transmission of the filters used in this work.Specifically, the HST/ACS bands: F435W, F606W, F775W, F814W, and F850LP.Followed by the JADES NIRCam bands: F090W, F115W, F150W, F200W, F277W, F335M, F356W, F410M, and F444W.Finally (when available), JEMS medium band photometry in the bands: F182M, F210M, F430M, F460M, and F480M.HST fluxes are shown as triangles, while the circles show JWST NIRCam photometry.The photometry of the filter-pairs of interest are highlighted in red (circles for F335M-F356W, squares for F410M-F444W).The purple vertical band marks the rest-frame 1250 -2500 Å region.The  slope is given in the legend of each panel, and corresponds to the purple dashed line.Finally, the blue cross shows the observed wavelength and flux corresponding to rest-frame 1500 Å.For every redshift bin the H line falls dominantly on either F335M, F356W, F410M or F444W.The detection and flux measurement of [O iii] 5007 is performed in an analogous manner.subtraction, while aperture photometry can neglect some flux in extended sources.Both cases would lead to an underestimation in the measurement of emission line fluxes.

SED FITTING WITH PROSPECTOR
We use the galaxy SED fitting code Prospector (Johnson et al. 2019(Johnson et al. , 2021) ) to study our sample, and compare to our  ion estimations.This code uses photometry and/or spectroscopy as an input in order to infer stellar population parameters, from UV to IR wavelengths.In this work we use photometry from the HST ACS bands: F435W ( eff = 0.432 m), F606W ( eff = 0.578 m), F775W ( eff = 0.762 m), F814W ( eff = 0.803 m), F850LP ( eff = 0.912 m).
For the redshift, we adopt a normal distribution using the EAZY photo-z as a mean, with the sigma given by the photo-z errors.We vary the dust attenuation and stellar population properties following Tacchella et al. (2022b).In particular, we use a two component dust model described in Conroy et al. (2009).This model accounts for the differential effect of dust on young stars (< 10 Myr) and nebular emission lines, through a variable dust index.We adopt a Chabrier initial mass function (Chabrier 2003) Ferland et al. 2013).This earlier version of Cloudy introduces an upper limit on the permitted ionisation parameters (log⟨⟩ max = −1.0).Due to the stochastic nature of the IGM absorption, we set a flexible IGM model based on a scaling of the Madau model (Madau 1995), with the scaling left as a free parameter with a clipped normal prior ( = 1.0,  = 0.03, in a range [0.0, 2.0]).Last but not least, we use a non-parametric SFH (continuity SFH; Leja et al. 2019).This model describes the SFH as six different SFR bins, the ratios and amplitudes between them are in turn, controlled by the bursty-continuity prior (Tacchella et al. 2022c).
In this work we use Prospector to calculate  ion for our entire sample, as well as to infer galaxy properties.The latter can be found in Appendix A. Prospector has the ability to reconstruct the full SED of galaxies, therefore,  ion is calculated from direct integration of the spectra, allowing to marginalise over most of the assumptions made for the most direct observational estimates from the emission line excess presented in Section 3.

CONSTRAINTS ON 𝜉 ion
After confirming the overall consistency of our flux measurements, we estimate  ion following the methods described in Section 3, and compare them to those inferred by Prospector.We provide an excerpt of the results in Table 1, and present them visually in Figure 5.We find a good agreement between the  ion obtained through H, [O iii], and Prospector, this agreement is highlighted in Figure 6.In addition, we include seven LAEs studied in (Saxena et al. 2023) using NIRSpec spectra, for which  ion was measured directly from Balmer recombination lines (H and H).These seven LAEs overlap with our sample and our results are consistent with theirs (see Table 2).Moreover, our  ion values agree with those found in literature.For example, Stefanon et al. (2022) compiled  ion measurements up to  ∼ 8 (using data points from Stark et al. 2015Stark et al. , 2017;;Mármol-Queraltó et al. 2016;Nakajima et al. 2016;Bouwens et al. 2016;Matthee et al. 2017;Harikane et al. 2018;Shivaei et al. 2018;De Barros et al. 2019;Lam et al. 2019;Faisst et al. 2019;Tang et al. 2019;Nanayakkara et al. 2020;Emami et al. 2020;Endsley et al. 2021;Naidu et al. 2022;Atek et al. 2022).With this extensive compilation, they provided a best fit to the slope of  ion as a function of redshift (given by dlog  ion,0 / dz = 0.09 ± 0.01), which is consistent within errors with this work (dlog  ion / dz = 0.07 ± 0.02).More recently, JWST has been used to estimate  ion for individual galaxies up to  ∼ 8 (see Ning et al. 2023;Prieto-Lyon et al. 2023;Simmonds et al. 2023;Rinaldi et al. 2023a), and this work is also consistent with those.In the bottom panel of Figure 5,  ion is shown as a function of redshift but colour-coded by M UV .The horizontal dashed lines show the intercepts of the best-fit relations between  ion and M UV per redshift bin, discussed in the next paragraph, for a constant M UV of -18.Their increase demonstrates that for a fixed M UV ,  ion evolves with redshift.
ion has been shown to vary due to the metallicity, age and dust content of galaxies (Shivaei et al. 2018), as well as due to their UV luminosities (Duncan & Conselice 2015), where fainter galaxies are more efficient at producing ionising radiation.This is clearly illustrated in Figure 3 from Maseda et al. (2020), which consists of a compilation of measurements from literature (specifically; Bouwens et al. 2016;Matthee et al. 2017;Harikane et al. 2018;Lam et al. 2019).We check for this relation in our data and find a similar trend, shown in Figure 7.For clarity, the sample is separated into redshift bins.As expected, there are less galaxies in the higher redshift bins, however, we consistently find the fainter galaxies in our sample have increased  ion .In addition, the higher redshift bins in our sample ( > 7) are populated by fainter galaxies than the other bins.This is potentially a result of our selection function, and will be discussed later.We note that an opposite trend is seen with  ion , namely, that  ion decreases for fainter galaxies (see Appendix B).Given the observed trends of  ion with redshift and with M UV , and the reliability of the Prospectorinferred  ion (and M UV ) measurements for our sample, we perform a 2-dimensional line fit combining these parameters and find: log  ion (, M UV ) = (0.05±0.02)+(0.11±0.02)MUV +(27.33±0.37) where  ion is in units of Hz erg −1 .This equation simultaneously describes the positive evolution of  ion with  and M UV , which is shown in Figure 5.
Regarding the use of  ∼ 3 − 6.7 in Boyett et al. (in prep.).We include our [O iii] EWs obtained from photometry and the  ion from Prospector.We remind the reader that the use of a fixed circular aperture in the photometry might result in an underestimation of fluxes when sources are extended.Additionally, differences in dust treatments affect the EW measurements, for example, adopting a higher ratio between nebular and continuum dust attenuation would increase the measurements of this

DISCUSSION
We begin by first addressing the biases that could potentially affect the results from this work.By construction, only galaxies with emission lines that can be measured from photometry were selected.Therefore, we are mostly focusing on star-forming galaxies.This was a necessary step in order to estimate  ion from either H or [O iii].
As an experiment, we used Prospector to fit a small subsample of galaxies with no obvious emission lines in the filter pairs of interest (F335M-F356W and F410M-F444W).As previously stated, Prospector does not rely on emission lines for the measurement of  ion .We find that in these cases  ion is consistently below 10 25 Hz erg −1 , with values as low as 10 23 Hz erg −1 , suggesting that there is a population of galaxies for which  ion falls below the relation shown in Figure 5, possibly explaining the origin of the trend of  ion with M UV .This work is not representative of those galaxies, rather, it sheds light on the galaxies and mechanisms most likely responsible for reionising the Universe.It must be noted that recent work by Looser et al. (2023a) and Looser et al. (2023b), among others, show that galaxies with no emission lines might be only temporarily quiescent, as a result of extremely bursty SFHs (Dome et al. 2023).Therefore, these kinds of galaxies are interesting to study (Katz et al. 2023), and are potentially important in the context of the EoR.The contribution of each galaxy population to the cosmic reionisation budget is beyond the scope of this work, and will be presented in a future work, where the full capacity of JADES photometry will be combined with the power of Prospector to quantify the relative importance of different populations.
Using our sample, we now investigate the nature of the positive slope of  ion with redshift, aiming to answer two questions: (1) Is it physical or is it a result of our selection?and (2) If it is real, what is driving it?

Does 𝜉 ion evolve with redshift?
In order to answer this question we conduct a simple null-hypothesis test, shown in Figure 9 (for simplicity, errors have been ignored in this test).We first select a subsample of galaxies at  ∼ 5.5 − 6 from the galaxies used in this work, for which  ion has been inferred through the [O iii] EW (framed with a blue rectangle in the top panel).We assume that there is no evolution of  ion with redshift, and that any observational study that says the contrary suffers from a luminosity bias (i.e. that at higher redshift we can only see the fainter galaxies with stronger emission lines).Under that assumption, we use our selected galaxies as seeds to produce 1000 simulated galaxies located randomly between  ∼ 5.5 − 9, and that have been dimmed according to their luminosity distance (white circles with grey edges in middle panel).For these galaxies the rest-frame [O iii] EWs estimated originally are used to obtain  ion (see equation 3), so  ion does not change with redshift for a specific seed.Finally, we apply the same selection criteria we did when constructing our sample, i.e. a difference of 10 nJy between filter pairs (F335M-F356W or F410M-F444W).The galaxies deemed observable and that would be selected in our sample are shown as blue plus signs.The  ion slope derived through emission line fluxes is shown in all panels as a dashed blue line, whereas the slope obtained after this test is shown in red.It is clear that these slopes do not match and that the red slope is flat.From this exercise we can conclude that the increase of  ion with redshift is not mainly due to our selection criteria.Furthermore, we investigate the possibility of a stellar mass bias driving the observed  ion evolution with redshift.In the bottom panel we conduct a similar experiment as the one just described, but now using as seeds the galaxies in our sample with low stellar masses (log M/M ⊙ < 8.0; shown as purple crosses in the top panel), it is important to note that in our sample, this is equivalent to studying galaxies fainter than M UV ≃ −19.We find that lower mass (fainter) galaxies have higher  ion , but that this property alone is insufficient in explaining the increase of  ion with redshift.Therefore, we go forward under the assumption that, even if there is a degree of observational    2019), and the light blue circles those from Chevallard & Charlot (2016).We also include the EELGs from Boyett et al. (in prep.) as grey crosses.The ion for our sample is provided by Prospector.Except for a few outliers, our sample follows the same trend as the previous works, confirming that [O iii] strength is also a reliable tracer of  ion in the early Universe.
bias, there is a physical cause driving the observed  ion evolution with redshift.

What drives the 𝜉 ion evolution?
We now aim to investigate the main driver of the observed increase of  ion with redshift.Throughout this paper we have demonstrated that our simple prescription to measure line fluxes from photometry is adequate, agreeing with both NIRSpec and FRESCO grism flux measurements (when available).We have also shown that our  ion values agree with those found in the literature, and finally, with those inferred with Prospector.We now focus particularly on this last point, and exploit the synergy between observations and SED fitting to find which galactic property (or properties) is (are) driving the  ion evolution.For this purpose we calculate a Spearman's rank correlation coefficient for  ion against the following properties: redshift, stellar mass, UV magnitude (both observed and intrinsic), recent SFR (SFR 10 ; in the past 10 Myr), SFR in the past 100 Myr (SFR 100 ), stellar metallicity, ionisation parameter, dust index (dust2 in the prescription of Conroy et al. 2009), half-mass assembly time (t50), and ionising photons emitted per second (  ion ).All of the results are shown in Appendix A, with their correlation and p-value shown in the title of each panel.An excerpt of the table containing all the values can be found in Table A1.We find that in our sample  ion correlates with M UV , half-mass stellar age and metallicity, however, the strongest correlations are those of  ion with stellar mass, where lower masses lead to higher  ion values, and with SFR.Motivated by these findings, we explore the correlation of  ion with the SFH burstiness, which translates into the ratio between both recent and older SFR (SFR 10 /SFR 100 ). Figure 10 shows how burstiness becomes increasingly important at lower stellar masses, and that low-mass galaxies The blue rectangle shows the galaxies selected as seeds in order to simulate 1000 galaxies covering the whole redshift range shown ( ∼ 5.5 − 9) in the middle panel.While the purple crosses mark the galaxies that have low stellar masses (log M < 8.0 M ⊙ ), and are used as seeds to simulate 1000 galaxies in the bottom panel.Middle panel: simulated galaxies (white circles with grey edges) and ones that would be observable according to our sample selection criteria (blue plus signs; flux difference between filter pairs of at least 10 nJy).Bottom panel: simulated galaxies (white circles with grey edges) and ones that would be observable according to our sample selection criteria (purple crosses; flux difference between filter pairs of at least 10 nJy).The red solid line in the middle and bottom panels is the best fit to the blue plus signs and purple crosses, respectively.The slope of the red line does not match the slope of the blue dashed one, indicating that the null hypothesis is wrong in both cases, and that the increase of  ion with redshift is not due to a luminosity or mass bias in our selection criteria.
with bursty star formation have the highest  ion values in the sample.Also shown is the correlation between stellar mass and M UV , and recent star formation versus stellar mass (colour-coded by  ion and  ion , respectively).The Spearman's correlation coefficient value for SFR 10 /SFR 100 is 0.914, with a p-value consistent with zero, indicating a strong positive correlation between  ion and burstiness of the SFH.Therefore, from Prospector we conclude that low mass and burstiness in a galaxy are the most important properties driving  ion .
Burstiness in star formation is usually associated with low stellar masses (Weisz et al. 2012;Guo et al. 2016), mainly due to stellar feedback.In brief, supernovae occurring after intense star formation heat up and expel gas.This leads to star formation being temporarily quenched (Stinson et al. 2007;Dome et al. 2023), followed by new gas accretion, which results in new star forming episodes.Burstiness in high redshift galaxies can also be explained by their dynamical timescale, which becomes too short for supernovae feedback to respond to gravitational collapse (Faucher-Giguère 2018; Tacchella et al. 2020).At high redshift, galaxies with low stellar masses are expected to be more numerous (Bouwens et al. 2015;Austin et al. 2023;Bouwens et al. 2023;Harikane et al. 2023).Additionally, these types of galaxies are thought to be the main sources responsible for reionising the Universe (Hassan et al. 2018;Rosdahl et al. 2018;Trebitsch et al. 2020).In a recent work, Atek et al. (2023) present spectroscopic observations of extremely low mass lensed galaxies (log M/M ⊙ ∼ 6 − 7) with high  ion (log  ion /Hz erg −1 ∼ 25.8, measured through the H recombination line).These kinds of galaxies are likely key in the reionisation of the Universe.Our results support the scenario of low-mass galaxies being efficient producers of ionising radiation, in agreement with previous findings.

The impact of 𝜉 ion on the cosmic ionisation budget
We first study how the number of ionising photons produced per volume unit,  ion , varies with M UV and redshift.We adopt the UV luminosity functions from Bouwens et al. (2021), and two different prescriptions for  esc : constant (of 10 and 20%; Ouchi et al. 2009;Robertson et al. 2013Robertson et al. , 2015)), and varying with M UV .For the variable prescription we follow the work of Anderson et al. (2017), who estimate  esc over a large range of galaxy masses, using the high-resolution, uniform volume simulation Vulcan.This simulation provides detailed distributions of gas and stars in resolved galaxies, allowing precise measurements of  esc .Anderson et al. (2017) find a dependence of  esc with M UV given by: log f esc = (0.51 ± 0.4)M UV + 7.3 ± 0.08.For  ion , we assume the best fit lines to our observations given in Figure 7.It is important to mention that by following this prescription we are assuming that the  ion evolution is representative for all low-mass faint galaxies, when in fact, it does not represent galaxies in quiescent phases (without detectable emission lines).Therefore, the cosmic ionising photon budgets here derived should be taken as upper limits.In a future work we will quantify the contribution of different galaxy populations to reionisation, and these calculations will be further constrained.
The  ion results as a function of M UV are presented in Figure 11, where each panel shows a different escape fraction.At every redshift bin, the fainter galaxies dominate the budget of cosmic reionisation.In particular, that galaxies fainter than M UV ∼ −19 account for at least 90% of the total  ion .This is especially true for the case with the variable  esc from (Anderson et al. 2017), where  ion has a steeper dependence with M UV , and galaxies fainter than M UV = -18 account for more than 90% of the total ionising budget at all redshift bins.It is important to mention that the curves start to flatten at M UV ∼ −20 for the constant  esc cases, which means that faint (but not necessarily extremely faint) galaxies are significant contributors to reionisation.If we use the same luminosity functions but instead adopt a constant  ion value of log  ion = 25.2Hz erg −1 (motivated by stellar populations, as in Robertson et al. 2013), and a constant  esc of 10% (seen as black shaded area in top panel), we find that at the highest redshift bin investigated ( = 8 − 9) our results are significantly higher, and can translate to a reduction in the average  esc from 10 to ∼ 2%.This is a natural result of a  ion dependant on both galaxy mass and redshift (Finkelstein et al. 2019).Using the curves derived in the previous step, we now investigate the effect of our  ion estimation in the evolution of the cosmic ionisation budget,  ion with redshift, given by: where  ion is in units of photon s −1 Mpc −3 ,  ion is in units of Hz erg −1 , and  UV in units of erg s −1 Mpc −3 .The escape fraction is dimensionless and can be assumed constant.In addition to the (Bouwens et al. 2021) luminosity functions, we now include the red solid curve provided in Figure 7 of Sun & Furlanetto (2016), which fits a power law to the low-mass end.To estimate  ion we use the equation that describes the best fit to our data (see Figure 5), and assume  esc values of 10 and 20%, in accordance to the canonical average  esc values needed for galaxies to be capable of ionising the Universe (Ouchi et al. 2009;Robertson et al. 2013Robertson et al. , 2015)).In addition, we integrate the curves from Figure 11 down to M UV = −16, and show the results as open triangles in Figure 12.The values adopting the variable  ion from this work (triangles) are consistent with those from literature up to  ∼ 8 (e.g.Bouwens et al. 2015;Mason et al. 2015Mason et al. , 2019;;Naidu et al. 2020;Rinaldi et al. 2023a).However, there is an upturn in the last redshift bin, where faint low-mass galaxies dominate and the  ion dependence with M UV and redshift becomes more important.As comparison, we add the estimated  ion that is required to maintain the ionisation of Hydrogen according to the models of (Madau et al. 1999), adopting clumping factors of 1, 3 and 10.A clumping factor of unity represents a uniform IGM, whereas larger clumping factors imply that an increased number of recombinations are taking place in the IGM.This leads to the need for a higher number of ionising photons to be produced, in order to reach a balance between ionisation and recombination rates.If the  ion derived in this work is representative of the faint low-mass galaxy population, then these kind of galaxies would produce an ionising photon budget sufficient to ionise the Universe by the end of the EoR.

Implications for reionisation
The connection between the cosmic  ion estimations and our previous conclusions comes through the stellar mass of galaxies.Stellar mass has been seen to decrease as galaxies become fainter, for example, Bhatawdekar et al. (2019) analyse this relation at  = 6 − 9 using data from the Hubble Frontier Fields.They notice that despite seeing a few high-mass galaxies with faint UV luminosities, there is a clear trend (with a large scatter) of stellar mass decreasing as galaxies become fainter in M UV (see also; Song et al. 2016).In particular, galaxies fainter than M UV ∼ −18 have stellar masses below ∼ 10 8 M ⊙ .In our sample, galaxies with comparable mass have the highest  ion , which is illustrated in Figure 10, where we also show the correlation between stellar mass and M UV .Therefore, the conclusions made from estimating the cosmic ionising photon budget agree with the ones drawn from combining our emission line estimations with Prospector.In particular, that low-mass galaxies in the fainter end of luminosity functions are more efficient in producing ionising radiation, and might be the main drivers of reionisation.our sample is of the general galaxy population, and how common low-mass bursty galaxies in a quiescent phase are, both topics to be presented in a future study.Promisingly, Rinaldi et al. (2023a) find that H emitters (HAEs) contribute significantly more to  ion than their non-H emitting counterparts, for a sample of galaxies at  ∼ 7 − 8.
In brief, based on our sample of galaxies with detectable H and/or [O iii] emission lines, we conclude that the increase of  ion with redshift in this population is likely physical in origin.The main driver of the observed evolution is the stellar mass of galaxies, which leads to bursty SFHs and result in higher  ion (and possibly higher  esc ).Additionally, we convolve our  ion estimations with UV luminosity functions from literature, and find that if our findings are representative of the faint low-mass galaxy population, then these galaxies can produce enough ionising photons to ionise the Universe by the end of the EoR.In particular, we find that the  ion relations found in this work can reduce the requirement of average escape fractions, if assumed constant, to < 10%.The effect is more significant at higher redshifts where faint low-mass galaxies dominate luminosity functions.We show the results obtained when adopting the UV luminosity density from Sun & Furlanetto (2016) (circles labelled "S16"), as well as results obtained by integrating the UV luminosity density curves from Bouwens et al. (2021) down to M UV = -16 (triangles labelled "B21", curves shown in Figure 11).
As comparison, we include the curve from Mason et al. (2015) assuming constant  ion and  esc , integrated down to a M UV of -15 (as in Mason et al. 2019), as well as the  ion reported in Rinaldi et al. (2023a) for H emitters at  ∼ 7 − 8 (blue square).Finally, we include the estimated  ion needed to maintain Hydrogen ionisation in the IGM (Madau et al. 1999), adopting clumping factors of 1, 3 and 10.We find a cosmic  ion consistent with literature up to  ∼ 8, but that starts to rise at the highest redshift bin due to the dependence of  ion with M UV .

CONCLUSIONS
In summary, we use NIRCam Deep imaging to build a sample of 677 galaxies at  = 3.9 − 8.9, for which H and/or [O iii] 5007 fluxes can be estimated from photometry.By construction, this sample does not include galaxies in quiescent phases.Depending on the redshift, we estimate  ion through H and/or EW([O iii] 5007 ), measured from photometry in the filter pairs: F335M-F356W and F410M-F444W.We adopt an SMC dust attenuation curve, proven to be adequate at high redshifts.Simultaneously, we fit all the photometry with Prospector and derive  ion , in addition to relevant galaxy properties.The  ion measurements inferred through emission line fluxes agree with the values derived by Prospector.We find that  ion evolves with both redshift and M UV , and this evolution is not only due to observational biases.To place our results on a cosmic scale, we combine our relations of  ion with redshift and M UV , along with two different  esc treatments: constant (10 and 20%), and variable as a function of M UV , to constrain the cosmic budget of reionisation,  ion , and make conclusions about which kind of galaxies dominate this budget.The main conclusions of this work are the following: • By comparing the resulting  ion using [O iii] EWs with those inferred by Prospector, we confirm the effectiveness of EW([O iii]) to estimate  ion in the high redshift Universe • For our sample,  ion evolves positively with redshift as: log  ion = (0.07 ± 0.02) + (25.05 ± 0.11) • We perform a 2-dimensional fit to account for the evolution of  ion with both redshift and M UV , and find: log  ion (, M UV ) = (0.05 ± 0.02) + (0.11 ± 0.02)M UV + (27.33 ± 0.37) • The observed evolution of  ion is likely has a physical origin, and is driven by specific star formation rate of galaxies.Specifically, lower mass leads to burstier SFHs, which we find is the property that has the strongest correlation with  ion • By comparing  ion obtained by adopting a constant  esc of 10% and a constant ionising photon production efficiency of log  ion /[Hz erg −1 ] = 25.2, with our evolving  ion prescriptions, we conclude that the average  esc requirement can be reduced to < 10%, an effect that increases with redshift (as low as ∼ 2% for our highest redshift bin) • If our sample is representative of faint-low mass galaxies, then these kind of galaxies can account for the budget of ionising photons required to ionise the Universe by the end of the EoR In this study, we conclude that low-mass faint galaxies with bursty SFHs are efficient enough in producing ionising photons to be the main sources responsible for ionising the Universe.We note that the sample used in this work was constructed to have detectable emission lines, particularly, H and/or [O iii] 5007 , and is therefore not representative of every galaxy population.However, the population here studied is likely representative of the galaxies responsible for ionising the Universe.In a future study, we will use the full potential of JADES photometry to shed light on the contribution different galaxy populations have to the total cosmic ionising budget.The number of galaxies in each redshift bin is indicated in the top left corner of each panel.The filled (dashed) line is the best fit to the data obtained via photometry (Prospector).Contrary to  ion ,  ion decreases as galaxies become fainter.

Figure 1 .
Figure 1.Medium and wide band NIRCam filters used to estimate H and/or [O iii] emission line fluxes in this work.From left to right: F335M, F356W, F410M, F444W.The left y-axis indicates their throughput.The black lines show the observed wavelength of H (filled) and [O iii] 5007 (dashed) with redshift (right axis).Depending on the redshift, the emission lines can be estimated by combining the medium and wide band filter pairs: F335M-F356W and/or F410M-F444W.

Figure 2 .
Figure 2. Expected shape for each filter pair flux differences, along with the corresponding emission lines, shown as vertical grey (H) and light blue ([O iii] [ 5007]) bands.The purple circles represent the sample analysed in this work, they overall follow the idealised Cloudy models, shown as shaded areas colour-coded by ionisation parameter (log⟨⟩).This agreement corroborates the reliability of the photo-z inferred using EAZY.Fluxes are in units of nJy.Top panel: F335M -F356W.Bottom panel: F410M -F444W.
5).Strong [O iii] emission is indicative of intense ionisation conditions, such as those found at the early Universe.In brief, they use 10 local analogues ( ∼ 0) to high-redshift galaxies and derive an empirical relation between  ion and [O iii] 5007 equivalent widths (EWs).Tang et al. (2019) conducted a similar project but with a larger sample and at higher redshift ( ∼ 2).Since their sample is closer in parameter space to ours, we follow Equation 4 of their work, log  ion = (0.73 ± 0.08) × log(EW [OIII] 5007 ) + (23.45 ± 0.23) (3) assuming an SMC attenuation law.Measurements from photometry As in the H case, we define four redshift bins to estimate [O iii] 5007 fluxes, as follows: (i) 5.37 ≤  ≤ 6.15: f([O iii] 5007 ) falls in F335M (ii) 6.15 <  < 6.77: f([O iii] 5007 ) falls in F356W but outside F335M (iii) 6.77 ≤  ≤ 7.55: f([O iii] 5007 ) falls in F410M (iv) 7.55 <  ≤ 9.00: f([O iii] 5007 ) falls in F444W but outside F410M Our data allows us to estimate [O iii] 4959+5007 fluxes, therefore, to obtain [O iii] 5007 we adopt the standard ratio between the components of the [O iii] doublet: [O iii] 5007 = 0.75× [O iii] 4959,5007 .Unless stated differently, all [O iii] fluxes in this work hereafter represent [O iii] 5007 .The EWs are then the division between the [O iii] line fluxes and the local continuum.The latter was estimated following two prescriptions depending if the line falls on the medium or the wide band of each filter pair (F335M-F356W or F410M-F444W).

Figure 5 .
Figure5. ion values inferred through H and [O iii] 5007 emission lines, as well as through through SED fitting.For comparison, we include NIRSpec measurements for 7 galaxies fromSaxena et al. (2023) that overlap with our sample (white stars), most of which were derived from H fluxes.We note that for the H and [O iii] 5007 results, an SMC dust attenuation curve was assumed, and remind the reader that the H method in addition assumes an escape fraction of zero.Top panel:  ion versus redshift for the entire sample (677 galaxies).The symbols and colours of the values estimated by photometry are the same as in Figure4.The Prospector estimations are shown in grey.The line represents the best fit to the photometrically-inferred results.As expected, there is more scatter when the emission lines fall on wide bands (either F356W or F444W), due to more noise and continuum being introduced.Middle panel: residuals between the values inferred through photometrically-estimated emission lines and via Prospector.The symbols are the same as in the upper panel, light grey corresponds to comparisons with the H method, while dark grey corresponds to comparisons with the [O iii] 5007 method.We find a good agreement between all methods, and confirm an increased  ion with redshift given by log  ion = (0.07 ± 0.02)  + 25.05 ± 0.11, consistent with literature.Bottom panel: same as top panel but only showing the photometrically-estimated  ion values, and colour-coded by M UV .The dashed horizontal lines represent the intercepts of the best-fit relations shown in Figure7for a fixed M UV of -18.It can be seen that at fixed M UV ,  ion evolves with redshift.

Figure 6 .
Figure 6.Comparison of  ion inferred through H fluxes (orange circles) and [O iii] 5007 EWs (red squares), with the values inferred by Prospector.We have also included the measurements from Saxena et al. (2023) as stars.The values scatter around the 1:1 relation, shown as a dashed grey line with 1,2 and 3 shaded areas.

Figure 8 .
Figure 8.  ion versus [O iii] 5007 equivalent widths (figure adapted from Tang et al. (2019)).The red squares represent our sample, described by log  ion = (0.57± 0.09) × log(EW[[O iii] 5007 ]) + (23.97 ± 0.25) , while the purple diamonds show the results from Tang et al. (2019), and the light blue circles those fromChevallard & Charlot (2016).We also include the EELGs fromBoyett et al. (in prep.)  as grey crosses.The ion for our sample is provided by Prospector.Except for a few outliers, our sample follows the same trend as the previous works, confirming that [O iii] strength is also a reliable tracer of  ion in the early Universe.

Figure 9 .
Figure9.Null hypothesis test. ion versus redshift, the blue dashed line (in all panels) is the best fit to the  ion inferred via emission lines, as seen in Figure5.For simplicity, errors have been omitted.Top panel:  ion values from this work, obtained via [O iii] EWs.The blue rectangle shows the galaxies selected as seeds in order to simulate 1000 galaxies covering the whole redshift range shown ( ∼ 5.5 − 9) in the middle panel.While the purple crosses mark the galaxies that have low stellar masses (log M < 8.0 M ⊙ ), and are used as seeds to simulate 1000 galaxies in the bottom panel.Middle panel: simulated galaxies (white circles with grey edges) and ones that would be observable according to our sample selection criteria (blue plus signs; flux difference between filter pairs of at least 10 nJy).Bottom panel: simulated galaxies (white circles with grey edges) and ones that would be observable according to our sample selection criteria (purple crosses; flux difference between filter pairs of at least 10 nJy).The red solid line in the middle and bottom panels is the best fit to the blue plus signs and purple crosses, respectively.The slope of the red line does not match the slope of the blue dashed one, indicating that the null hypothesis is wrong in both cases, and that the increase of  ion with redshift is not due to a luminosity or mass bias in our selection criteria.

Figure 10 .
Figure10.Relations between relevant galactic properties, as inferred by Prospector.Top left panel: ratio between recent (within 10 Myr) and sustained over 100 Myr star formation, SFR 10 /SFR 100 (i.e.burstiness of star formation), over stellar mass, and colour-coded by  ion .The Spearman's rank correlation coefficient value is 0.914, while the p-value is consistent with zero.Lower mass galaxies with bursty SFHs have an increased  ion with respect to non-bursty higher-mass galaxies.Bottom left panel: correlation between UV luminosity and stellar mass, colour-coded by  ion .There is a strong trend of decreasing stellar mass with increasing M UV .Top and bottom right panels: relation between recent star formation, stellar mass and  ion (top) or  ion (bottom).

Figure 12 .
Figure12.Cosmic rate of ionising photons being emitted per second and per unit of volume,  ion , as a function of redshift, assuming a  esc as indicated, and a  ion described by our data (i.e.log  ion = (0.07±0.02)  +25.05±0.11).We show the results obtained when adopting the UV luminosity density from Sun & Furlanetto (2016) (circles labelled "S16"), as well as results obtained by integrating the UV luminosity density curves fromBouwens et al. (2021) down to M UV = -16 (triangles labelled "B21", curves shown in Figure11).As comparison, we include the curve fromMason et al. (2015) assuming constant  ion and  esc , integrated down to a M UV of -15 (as inMason et al. 2019), as well as the  ion reported inRinaldi et al. (2023a) for H emitters at  ∼ 7 − 8 (blue square).Finally, we include the estimated  ion needed to maintain Hydrogen ionisation in the IGM(Madau et al. 1999), adopting clumping factors of 1, 3 and 10.We find a cosmic  ion consistent with literature up to  ∼ 8, but that starts to rise at the highest redshift bin due to the dependence of  ion with M UV .

Figure A1 .Figure B1 .
Figure A1.Exploring tentative correlations between  ion and different properties.The vertical axis is  ion in all panels, while the name of each property is given in the x-label.The title of the panels show the Spearman's rank coefficients for each parameter, indicating how strong the correlation is with  ion .The strongest correlations are found for SFR 100 (right panel of second row) and stellar mass (left panel of second row).From top to bottom and left to right, the parameters are: redshift, observed UV magnitude (M 1500 ), intrinsic UV magnitude (M 1500, ), stellar mass (M * ), SFR in the past 10 Myr (SFR 10 ), SFR in the past 100 Myr (SFR 100 ), metallicity (), ionisation parameter (log⟨⟩), dust2, half-mass assembly time (t50), and rate of ionising photons being emitted (  ion ).

Table 1 .
Tableexcerptshowing a selection of galaxies in our sample.Depending on the redshift and the detection of emission lines, galaxies can have  ion , with mass cutoffs (Byler et al. 2017)n of fluxes obtained via photometry with those obtained through FRESCO grism spectra (when available).There are 122 overlapping cases with H fluxes (orange circles), and 36 with [O iii] 5007 fluxes (red squares).The filled and open symbols indicate if the emission line falls predominantly in a medium (F335M or F410M) or wide (F356W or F444W)band.The shaded areas show 1, 2 and 3, respectively.We find the values obtained by photometry in this work are in significant agreement with those measured with grism spectra, suggesting there is minimal contamination from other emission lines ([N ii], [S ii], H).The fluxes that fall in wide bands contain more continuum and noise, resulting in a larger scatter.We note the background subtraction in grism spectra can lead to an underestimation of emission line fluxes.In a similar manner, our photometrically-derived fluxes have a fixed aperture of diameter 0.3 ′′ , and might not capture the total flux of a source. of 0.1 and 100 M ⊙ , respectively, allowing the stellar metallicity to explore a range between 0.01 -1 Z ⊙ , and include nebular emission.The continuum and emission properties of the SEDs are provided by the Flexible Stellar Population Synthesis (FSPS) code(Byler et al. 2017), based on Cloudy models (v.13.03; Bouwens et al. (2021))ction of M UV , by redshift bins, assuming a  esc indicated in each panel and a  ion described by our data.The prescription of  esc that varies with M UV was taken fromAnderson et al. (2017), while the UV luminosity functions were adopted fromBouwens et al. (2021), for the redshifts relevant to this work.For comparison, in the top panel, results adopting a constant log  ion = 25.2Hz erg −1 are shown in black.At every redshift and for every  esc , galaxies fainter than M UV ∼ −19 dominate the ionisation budget, indicating that faint (but not necessarily extremely faint) galaxies contribute significantly to reionisation.
As mentioned previously, this conclusion depends on how representative