The galaxy UV luminosity function at z ≃ 11 from a suite of public JWST ERS, ERO and Cycle-1 programs

We present a new determination of the evolving galaxy UV luminosity function (LF) over the redshift range 9 . 5 < 𝑧 < 12 . 5 based on a wide-area ( > 250 arcmin 2 ) data set of JWST NIRCam near-infrared imaging assembled from thirteen public JWST surveys. Our relatively large-area search allows us to uncover a sample of 61 robust 𝑧 > 9 . 5 candidates detected at ≥ 8 𝜎 , and hence place new constraints on the intermediate-to-bright end of the UV LF. When combined with our previous JWST +UltraVISTA results, this allows us to measure the form of the LF over a luminosity range corresponding to four magnitudes ( 𝑀 1500 ). At these early times we find that the galaxy UV LF is best described by a double power-law function, consistent with results obtained from recent ground-based and early JWST studies at similar redshifts. Our measurements provide further evidence for a relative lack of evolution at the bright-end of the UV LF at 𝑧 = 9 − 11, but do favour a steep faint-end slope ( 𝛼 ≤ − 2). The luminosity-weighted integral of our evolving UV LF provides further evidence for a gradual, smooth (exponential) decline in co-moving star-formation rate density ( 𝜌 SFR ) at least out to 𝑧 ≃ 12, with our determination of 𝜌 SFR ( 𝑧 = 11 ) lying significantly above the predictions of many theoretical models of galaxy evolution.


INTRODUCTION
Although JWST has not yet completed its first year of science operations, it is already transforming our view of the young Universe.Despite its many achievements, the Hubble Space Telescope (HST) was unable to advance the search for early galaxies significantly beyond redshifts  10, due to its limited near-infrared wavelength coverage ( < 1.6 m) (e.g., Ellis et al. 2013;Coe et al. 2013;Oesch et al. 2016).By contrast, the exquisite near/mid-infrared imaging now being provided by the NIRCam instrument on-board the larger and colder JWST has already pushed the redshift frontier out to  13 (Naidu et al. 2022;Finkelstein et al. 2022b;Robertson et al. 2023), with candidate high-redshift galaxies already being uncovered at redshifts as extreme as  = 16 − 17 (Harikane et al. 2023b).
The photometric selection of high-redshift galaxy candidates from deep imaging not only supplies targets for spectroscopic follow-up to determine their astrophysical properties, but also enables the statistical study of the evolution of the galaxy population provided sufficiently large and robust samples can be assembled.
★ Email: mcleod@roe.ac.uk In particular, a key goal is to chart the evolution of the galaxy luminosity function (LF) back to early times for comparison with theoretical predictions.At very high redshifts, near/mid-infrared imaging enables the evolving rest-frame ultraviolet (UV) galaxy LF to be determined, the luminosity-weighted integral of which gives the evolution of (co-moving) UV luminosity density, which can then be converted into the evolution of cosmic star-formation rate density,  SFR .In large part due to the impact of HST, there is now a general consensus over the evolution of  SFR out to  8.However, before the advent of JWST, the lack of significant galaxy samples at higher redshifts resulted in considerable disagreement over the evolution of star-formation rate density at earlier times.Specifically, some studies concluded in favour of a rapidly steepening decline in  SFR with increasing look-back time beyond  8 (e.g., Oesch et al. 2013Oesch et al. , 2018)), while others presented evidence for a continued smooth, more gradual evolution implying the existence of substantial star-formation activity at still earlier times (McLeod et al. 2015(McLeod et al. , 2016)).This debate/disagreement over the very high-redshift evolution of the UV LF, and hence  SFR , was largely a consequence of the limitations of pre-JWST facilities mentioned above.Specifi-cally, at redshifts  ≥ 9 the WFC3/IR camera on HST rapidly runs out of filters capable of sampling continuum emission beyond the Lyman break at  rest = 1216 Å.For most of the deep extragalactic imaging surveys performed with HST only F125W and F160W imaging are available for this purpose, at least for the majority of the CANDELS (Grogin et al. 2011) area.The addition of the F140W filter for such surveys as the HUDF (Beckwith et al. 2006;Ellis et al. 2013), CLASH (Postman et al. 2012) and the Frontier Fields (Lotz et al. 2017) was key for selecting  = 9 galaxies in McLeod et al. (2015McLeod et al. ( , 2016) ) as it provided a third filter with high-resolution imaging that probes beyond the Lyman break.The Spitzer space telescope (e.g., S-CANDELS; Ashby et al. 2015) and the deepest ground-based   −band imaging (e.g.Very Large Telescope (VLT)'s HUGS; Fontana et al. 2014) helped to extend the wavelength baseline beyond  = 1.6 m and provided constraints on the rest-frame optical continuum of some brighter high-redshift galaxies, but this redder non-HST imaging lacked the resolution and the depth to benefit searches for more typical galaxies at  > 8.
JWST has effectively unlocked the longer wavelength near/mid-infrared coverage previously only provided by groundbased facilities and Spitzer, but now with enormous improvements in both angular resolution and depth.Several early, public JWST NIR-Cam surveys have reached 5 limiting depths of 28.5 − 29.0 mag in filters spanning the wavelength range  1 − 5 m, already probing several magnitudes deeper than typical Spitzer surveys, and with diffraction-limited imaging down to  1 m delivering nearinfrared imaging of much improved resolution compared to HST's WFC3/IR.This combination of depth and resolution has already been transformative in the selection of ultra-high redshift galaxies.Encouragingly, many of the  > 10 candidates photometrically selected from the early NIRCam imaging are already being confirmed spectroscopically with JWST NIRSpec (Arrabal Haro et al. 2023a,b;Harikane et al. 2023a).
While several theoretical models of galaxy evolution appear to predict a rapid decline in  SFR at  > 8 (e.g., Mason et al. 2015;Yung et al. 2019), early JWST studies have provided evidence to the contrary.Donnan et al. (2023a) conducted a wide-area, groundbased search for bright  = 8 − 10 galaxy candidates using COS-MOS/UltraVISTA DR5 (McCracken et al. 2012), in combination with a search for fainter galaxies at these redshifts with the JWST CEERS (Finkelstein et al. 2023), GLASS-parallel (Treu et al. 2022) and SMACS0723-73 (Pontoppidan et al. 2022) public surveys.The resulting UV LF determination was found to be consistent with the earlier HST-based works of McLeod et al. (2015McLeod et al. ( , 2016)), with  SFR displaying an extended smooth decline at  > 8 and indeed continuing to display a log-linear relation with redshift until at least  ∼ 12.At the bright-end, the number densities of  = 8 − 10 galaxy candidates found using the latest COSMOS/UltraVISTA groundbased data suggested that the UV LF follows a double power-law functional form, as previously found by Bowler et al. (2020).Although the exceptionally bright  = 16 candidate CEERS-93316 first reported in Donnan et al. (2023a) has now been spectroscopically confirmed to be a lower redshift interloper at  = 4.9 (Arrabal Haro et al. 2023a), this is a particularly pathological case in which a peculiar combination of very strong emission lines conspired to masquerade as the blue continuum above the Lyman-break.Another potential  = 16 candidate behind Stephan's Quintet may yet suggest that significant star-formation activity is still taking place at  ≥ 14 (Harikane et al. 2023b).
As well as the discovery of extremely high-redshift galaxies at  > 12 (Naidu et al. 2022;Atek et al. 2023;Donnan et al. 2023a;Harikane et al. 2023b), JWST has been yielding surprisingly large numbers of bright  10 galaxies, with a particularly high number density reported by Castellano et al. (2022a) in the area around the Abell 2744 cluster.Such densities are potentially up to a factor ten times greater than expectations based on previous observations and theoretical models of galaxy evolution.This would challenge our existing understanding, with many existing theoretical models of galaxy evolution having to invoke more efficient star formation or less dust attenuation at the highest redshifts to match these observational results.Alternatively, these early observations may be biased to a particular population of young and rapidly star-forming galaxies (Mason et al. 2023).There is thus an open question as to how accurately the early JWST-selected galaxy samples represent the true number densities of bright  = 10 galaxies, with existing high-redshift galaxy searches typically restricted to small areas.
The address this issue, the study presented here aims to exploit all relevant available JWST NIRCam Early Release Observations (ERO), Early Release Science (ERS) and public Cycle-1 programs to conduct a systematic wide-area search for extreme-redshift galaxy candidates with high signal-to-noise (≥ 8).The resulting combined survey, covering a raw area of 260 arcmin 2 , provides a new opportunity to uncover statistically significant samples of galaxies in the redshift range 9.5 <  < 12.5, and hence yield improved constraints on the number densities of bright to intermediate  1500 galaxies over this redshift range.By combining the new results with our previously-derived constraints on the number densities of fainter galaxies (Donnan et al. 2023a), we are hence able to determine the evolving UV LF and  SFR at  = 10 − 12, deep into the redshift range where the results derived using HST had diverged.Moreover, our wide-area search may also uncover other examples of extremely high-redshift ( > 12) galaxy candidates, such as those found in the ERO surveys (e.g.Atek et al. 2023;Harikane et al. 2023b).
The structure of this paper is as follows.In Section 2 we describe each of the data sets included in our high-redshift galaxy search.Section 3 describes the construction of our multi-wavelength catalogues and candidate selection.We discuss our candidates and draw comparisons with other recent JWST searches in the literature in Section 4. In Section 5, we use our high-redshift galaxy sample to determine the form of the UV LF over the redshift range 9.5 <  < 12.5 and how it evolves from  8 to  12.In Section 6 we integrate the UV LF in order to determine the star-formation rate density and how it evolves with cosmic time.Finally, in Section 7 we summarise our conclusions.Throughout the paper, we adopt a cosmology with Ω 0 = 0.3, Ω Λ = 0.7 and  0 = 70 kms −1 Mpc −1 , and use the AB magnitude system (Oke 1974;Oke & Gunn 1983).

Imaging data
We begin with a description of the various data sets employed in this study.Each of the data sets were downloaded as "rate" products, either from the CADC or STScI MAST database, and processed through the Primer Enhanced NIRCam Image Processing Library (PENCIL; Magee in prep) software, which is a customised version of the JWST pipeline version 1.6.2.This version of the pipeline includes additional routines for the removal of snowballs and wisps, as well as background subtraction and correcting for 1/f noise striping.Given the different timeframes in which the various data sets were taken, released, reduced and analysed, there are very slight differences in the CRDS context depending on when the data set was released, although the pmap is always at least pmap 0989, Although we do not perform a new search over JEMS for this study, we utilise the sample as found in Donnan et al. (2023b), and so we include the F182M depth here.The solid teal line shows the predicted number of galaxies at  ≥ 9.5 in the area of one NIRCam pointing assuming the luminosity functions from Donnan et al. (2023a).The top −axis shows the absolute UV magnitude for a  = 11 galaxy with an apparent magnitude given by bottom −axis at  = 11.which included the most recent zero-point corrections at the time of writing.Where applicable, HST data sets were downloaded as their high-level science products from the STScI MAST, aligned to the JWST imaging and registered using SWARP (Bertin 2010).The exception is for CEERS, where HST EGS imaging in F606W and F814W was provided in a data release by the CEERS team (see Koekemoer et al. 2011).
The global 5 limiting magnitudes for each of the different surveys and in each filter can be found in Table 1.These global depths were measured in 0.35 −diameter apertures and corrected to total assuming a point-source correction.Note that the global depth in a given survey is subject to potentially significant spatial variations in local depth, owing to differences in exposure time, source-crowding (particularly for the Quintet, Cartwheel and cluster fields) or sensitivities of the NIRCam modules.We also include the effective survey area for each of the fields, accounting for de-lensing where applicable.
We illustrate the distribution in depths across the various surveys in Fig. 1.Assuming a flat UV spectral slope (f  ), we derive a rest-frame  1500 limiting magnitude for each survey, corresponding to a  = 11 galaxy at the 8 apparent magnitude limit in the F200W filter.Using the UV luminosity function determined in Donnan et al. (2023a), we also show the predicted average number of  ∼ 11 galaxies found per NIRCam pointing ( 9.6 sq.arcmin).
The first ERO field we will discuss is the SMACS 0723 cluster field (PID 2736, PI Pontoppidan; Pontoppidan et al. 2022).This field has already seen extensive study by various groups in search of high-redshift candidates since the July 2022 data release (e.g.Atek et al. 2023;Adams et al. 2023;Donnan et al. 2023a;Harikane et al. 2023b;Bouwens et al. 2023).This survey is covered by two NIRCam modules, with one module centred on the cluster field and the other on a "blank" parallel field.Due to lensing by the foreground galaxy cluster, which serves to magnify objects in the background, there is also a reduction in the effective area of the search.
To avoid uncertain lensing volume corrections and areas with significantly shallower depths than the global depth, we remove the portion of the image worst affected by intracluster light and enhanced crowding.We then determine the magnification of sources and the remaining effective survey area by utilising the recent lighttraces-mass (LTM) model from Golubchik et al. (2022).Although the raw survey area of the SMACS 0723 field is 11.5 sq.arcmin, after excluding the cluster and accounting for lensing this is reduced to an effective area of 7.0 sq.arcmin.This area is calculated with the assumption that any part of the field-of-view that is not covered by a gravitational lensing map has a magnification =1.2, which is what we adopt for all cluster+parallel pair surveys to take into account that the "blank" field is still subject to magnification (see Section 5).
Over the cluster portion of the field there is ancillary HST data from the RELICS survey (PI Coe; Coe et al. 2019), with ACS imaging in F435W, F606W and F814W as well as WFC3/IR imaging in F105W, F125W, F140W and F160W.We include the HST ACS data in order to provide wavelength coverage in the optical portion of the spectrum.Although the 5 limiting magnitudes of the HST ACS data are significantly shallower than the JWST data, the data still serves to verify any non-detections short-ward of the Lyman break.The 5 depths (0.35 −diameter apertures corrected to total) of the ACS F435W and F814W imaging are approximately 26.8 mag, with the F606W deeper at 27.7 mag.

Stephan's Quintet
The Stephan's Quintet field was also imaged as part of the Early Release Observations (PID 2732, PI Pontoppidan;Pontoppidan et al. 2022).To date, this field has had one published search for highredshift galaxies by Harikane et al. (2023b), which yielded one galaxy candidate at  12 and another candidate at  16.This field has the same NIRCam filter set as SMACS 0723, but lacks sufficiently deep ancillary HST data.The Quintet field has significant variations in depth across the imaging owing to crowding and enhanced background light.The overall area of the field is approximately 46.7 sq.arcmin, which reduces to an effective area of 40.9 sq.arcmin after removing the Quintet.

Cartwheel galaxy
The Cartwheel galaxy, or PGC 2248, was imaged as part of the Early Release Observations (ERO PID 2727, PI Pontoppidan).Once again, the complement of NIRCam filters for this field is the same as for SMACS 0723 and Stephan's Quintet, and there is no useful ancillary HST ACS imaging.Similarly to the Quintet field, the depth across the imaging varies significantly, even when masking out the Cartwheel galaxy itself.The field spans ∼ 5.7 sq.arcmin, which reduces to 4.2 sq.arcmin after masking out the Cartwheel galaxy and the two large foreground galaxies to the north east.Note that for some fields e.g. the clusters and Quintet, these global values are subject to significant variations (as high as > 0.5 mag) across the field of view owing to crowding and enhanced background, as illustrated in Fig. 5.We also provide the effective areas in each field, accounting for cluster subtraction and de-lensing where applicable.

WHL 0137
The WHL0137 cluster, known for the lensed "sunrise arc" galaxy and the  = 6.2 star candidate "Earendel", was imaged as part of Cycle 1 GO PID 2282 (PI Coe; see Welch et al. 2022;Bradley et al. 2022).Imaging was taken over a single NIRCam pointing, with one module on the cluster and the other on a parallel blank field.The filter set includes the SW channel F090W, F115W, F150W and F200W bands, as well as the LW channel F277W, F356W, F410M and F444W bands.The raw survey area of this field is approximately 10.5 sq.arcmin, which reduces to an effective area of 5.9 sq.arcmin when accounting for the gravitational lensing.This data set has been the subject of a previous search for high-redshift galaxies by Bradley et al. (2022), which yielded a sample of twelve  = 9 − 13 candidates.Our current study covers the first epoch of observations from July 2022.As with SMACS 0723, this field has ancillary HST RELICS (Coe et al. 2019) data over the cluster region, which we use both in SED fitting and to check against any potential low-redshift interlopers in our final sample.The 5 depths (0.35 −diameter apertures, corrected to total) of the ACS F435W and F814W imaging are approximately 26.7 mag, with the F606W imaging significantly deeper at 27.4 mag.

MACS 0647
The MACS 0647 galaxy cluster was previously one of the HST CLASH clusters (Postman et al. 2012).The field in which MACS 0647 resides is known to contain a triply-lensed  = 11 galaxy candidate, MACS0647-JD1 (Coe et al. 2013), which was one of the highest-redshift galaxy candidates in the pre-JWST era.MACS 0647 was imaged as part of JWST GO proposal 1433 (PI Coe) in order to follow-up this object, with a cluster+parallel pair of NIRCam modules imaged in F115W, F150W, F200W, F277W, F356W and F444W.With this imaging, taken in September 2022, the object was re-analysed and found to be a potential merger system at  ∼ 10 (Hsiao et al. 2022).Most recently, the object was spectroscopically confirmed to lie at  = 10.17 (Harikane et al. 2023a).
To complement the JWST photometry, we also employ the HST ACS optical imaging from the CLASH survey, which covers the cluster module and has a 5 depth of 27.0 mag.The raw area of the MACS 0647 field was found to be 10.5 sq.arcmin, which reduces to 5.1 sq.arcmin after de-lensing, and the removal of un-useable regions due to the presence of particularly bright stars.
We use the lensing maps that were produced as part of CLASH, i.e the Zitrin-NFW and Zitrin-LTM-Gauss models (Zitrin et al. 2015).

RXJ 2129
Another HST CLASH cluster, the RXJ 2129 field was imaged in October 2022 as part of Director's Discretionary Time (DDT, PID 2767; PI Kelly).One NIRCam module was imaged in F115W, F150W, F200W, F277W, F356W and F444W, although the exposure times vary significantly between filters, with the F356W imaging being particularly deep.The complement of HST imaging matches that of MACS 0647.The lensing maps also include Zitrin-LTM-Gauss and Zitrin-NFW but with an additional model from Caminha et al. (2019).This field was initially selected as a DDT proposal to follow up a supernova at  = 1.5, but has also yielded a very faint, yet highly magnified ( ∼ 20) galaxy confirmed with spectroscopy to be at  = 9.51 (Williams et al. 2022).The raw area of this field is 5.3 sq.arcmin, with a de-lensed effective area of 3.1 sq.arcmin.

GLASS
As part of JWST PID 1324 (PI Treu;Treu et al. 2022; see also Paris et al. 2023), a pair of NIRCam pointings were taken in parallel to NIRISS observations of the Abell 2744 cluster field.The first epoch of observations was taken in July 2022, and has been the subject of numerous searches for high-redshift galaxies, including the discovery of an exceptionally bright  = 12 galaxy candidate GLASS-z12 (Castellano et al. 2022b;Naidu et al. 2022).The second epoch of observations was taken in November 2022, and has yielded yet fur-ther exciting results, including the discovery of an over-density of bright  = 10 galaxy candidates (Castellano et al. 2022a).
We include both epochs of observations in our present study.The NIRCam filter set comprises F090W, F115W, F150W, F200W, F277W, F356W and F444W.One NIRCam module benefits from increased exposure time from repeated observation, and there is an additional two NIRCam modules with significant overlap, producing a total raw search area of 13.3 sq.arcmin.Some of the GLASS parallel field is covered by the Furtak et al. ( 2022) lensing model of the Abell 2744 cluster, which was released as part of UNCOVER Data Release 1.Where there is coverage we adopt this lensing map, and set a floor of =1.2 for the rest of the area that is not covered.This gives us an effective de-lensed area of 10.1 sq.arcmin.

North Ecliptic Pole Time Domain Field (NEP TDF)
The NEP TDF field was imaged in September 2022 as part of the PEARLS survey (PID 2738, PI Windhorst; see Windhorst et al. 2023).NIRCam imaging was taken in F090W, F115W, F150W, F200W, F277W, F356W, F410M and F444W.The majority of this data set is proprietary, however one of the pointings in the NEP TDF was made publicly available immediately for use by the community.Although the footprint of the F150W and F356W imaging is larger, we focus on the 10.5 sq.arcmin overlap between all of the available NIRCam filters.

CEERS
The Cosmic Evolution Early Release Science Survey (CEERS, ERS 1345, PI Finkelstein; see Bagley et al. 2023b for imaging release) is an early release science program covering approximately 100 sq.arcmin of the CANDELS Extended Groth Strip (EGS) field.This field has been studied extensively since the first epoch of observations was taken in July 2022 (e.g.Finkelstein et al. 2022bFinkelstein et al. , 2023;;Donnan et al. 2023a;Bouwens et al. 2023.This study has also already seen the spectroscopic confirmation of several high-redshift galaxies at  = 8 − 11, including "Maisie's galaxy" (Finkelstein et al. 2022b;Arrabal Haro et al. 2023a,b).
In this study, we include an analysis of both the first and second epochs of observations, taken in July and December 2022, respectively.JWST imaging is available in seven NIRCam bands: F115W, F150W, F200W, F277W, F356W, F410M and F444W.We also employ HST ACS imaging to provide additional wavelength coverage in the optical.As noted earlier, a reduction of the HST imaging in ACS F606W and F814W has been made publicly available by the CEERS team (HDR1; see Koekemoer et al. 2011).Additional F435W imaging was available from the UVCANDELS survey (GO 15647, PI Teplitz; DOI: 10.17909/8s31-f778).

UNCOVER
The UNCOVER survey (Cycle 1 2561, PI Labbe; Bezanson et al. 2022) is an ultra-deep survey of the Abell 2744 cluster field covering a raw area of 29 sq.arcmin ( 12 sq.arcmin after delensing and masking) to a depth in excess of 29 mag (0.35 −diameter apertures).The NIRCam filter set is F115W, F150W, F200W, F277W, F356W, F410M and F444W.The lensing map used for this data set was the Furtak et al. (2022) model that was publicly released as part of UNCOVER's Data Release 1.We also employ this lensing map for the regions of GLASS and DDT 2756 where there is coverage.
Abell 2744 was imaged with HST as one of the Hubble Frontier Fields (Lotz et al. 2017).This survey includes among the deepest HST observations in the ACS and WFC3/IR filters, with depths of 28.2 − 28.6 mag.Although the ACS observations cover less than half of the UNCOVER survey area, we include the ACS F435W, F606W and F814W data in order to extend our wavelength coverage into the optical.

DDT 2756: Abell2744
The Abell 2744 cluster was imaged with NIRCam as part of DDT program 2756 (PI Chen), a program designed to follow-up a  = 3.47 supernova.Two epochs of observations in six NIRCam bands (F115W, F150W, F200W, F277W, F356W and F444W) were taken in October 2022 and December 2022.Although the Abell 2744 module imaging was included in the UNCOVER reduction, each epoch includes an additional parallel NIRCam module.These two partially overlap, but together provide another 6.6 sq.arcmin of effective search area.This field was also found by Castellano et al. (2022a) to contain a very bright  10 galaxy candidate, with reported    −21.60.Ultimately, the object has been spectroscopically confirmed to lie at  = 9.31, and is likely an interacting system (Boyett et al. 2023).That being said, an independent search over both epochs of data for this survey is clearly desirable to discover if there are other exceptionally bright candidates at similarly extreme redshifts.

PID 1063 Nircam Flats: J1235
As part of NIRCam commissioning (PID 1063, PI Sunnquist), exceptionally deep imaging was taken of a field centred at RA=12:35:48, Dec= +04:55:45.The filter set included is also more extensive than the other JWST surveys: F070W, F090W, F115W, F150W, F200W, F277W, F300M, F356W and F444W.The coverage across this rich filter set is not homogeneous, and so we restrict our analysis to an area of 9.9 sq.arcmin covered by all of the available filters.This field was recently studied as part of a search for quiescent galaxies by Valentino et al. (2023).

JEMS
Deep medium band observations of the HUDF were taken as part of the JEMS survey (ID 1963; PI Williams; see Williams et al. 2023).This included SW F182M and F210M imaging along with LW imaging in F430M, F460M and F480M.The total 5 global depths are 29 mag for the SW channel filters and 28.5 mag for the LW channel filters.
Using this data set, Donnan et al. (2023b) uncovered a sample of six high-redshift candidates, including three spectroscopically confirmed  > 10 galaxies (Curtis-Lake et al. 2023;Robertson et al. 2023).Among these is UDFj-39546284, a  12 galaxy first discovered a decade previously with HST imaging (Bouwens et al. 2011;Ellis et al. 2013).Although we do not search the JEMS data set in this study, we include the six candidates found in Donnan et al. (2023b) in our LF analysis in Section 5.

Catalogue Construction
For each of the fields, we construct multi-wavelength catalogues using S -E (Bertin & Arnouts 1996) in dual-image mode.As our study is focused on selecting 9.5 <  < 12.5 galaxies, the position of the Lyman break will move through the F150W filter as we probe to higher redshift, with the IGM absorption having attenuated half of the flux in the F150W band by  = 11.Hence, in order to facilitate the detection of galaxies beyond a Lyman break of 1.5 m, we use the F200W imaging as our primary detection band.We create additional catalogues using each of the broadband LW filters (F277W, F356W, F444W) as detection images, in order to supplement this first catalogue with any sources that may have been missed.For the three fields lacking F115W coverage (SMACS 0723, Cartwheel, Quintet), we cannot search as effectively for  < 11 galaxies and a F150W detection image would not add significant value.Hence for consistency across all of the fields, we do not include F150W detection images in this study.We also adjust our selection criteria in these three fields to account for the reduced filter coverage (see Section 3.3).
Prior to any aperture photometry, we homogenized the PSF of all of the NIRCam images to match that of the F444W image, in order to minimize any colour systematics in subsequent analyses.Aperture photometry was performed on these PSF-homogenized images with fluxes measured in 0.35 −diameter apertures.Photometric uncertainties were calculated object-by-object by taking the median absolute deviation of the nearest 150-200 blank-sky 0.35 −diameter apertures, and scaling to  by multiplying by 1.4826, following the method by McLeod et al. (2021).
For each of our initial catalogues, we required a 5 detection in the detection image, as well as an additional 3 detection in at least one other band to reduce the number of spurious detections.

SED-fitting and photometric redshifts
We performed SED fitting on all of the sources within our initial catalogues using the SED fitting code L P (Arnouts & Ilbert 2011).The SED library that we used was Bruzual & Charlot (2003) (BC03), using a Chabrier (2003) initial mass function, a Calzetti et al. (2000) dust attenuation law and the IGM absorption prescription from Madau (1995).These SED templates included declining star-formation histories with various  values from 0.1 to 15 Gyr, and metallicities of 0.2 Z and Z .We included emission lines, and the   was allowed to range from 0 to as high as 6 to clean the sample of any extremely reddened low-redshift interlopers masquerading as high-redshift galaxies.We measured rest-frame  1500 magnitudes using a 100 Å-wide tophat filter on the best-fitting SED.

Selection of high-redshift candidates
We initially selected candidates with a photometric redshift solution  phot ≥ 8.5 and a goodness of fit  2  ≤ 10.Only candidates considered "robust", with Δ 2 ≥ 4 between the primary and secondary photo-z solutions, were retained for the final sample.We also further refined our sample selection to require a ≥ 8 detection in at least one of the F150W, F200W and F277W images, to ensure that we were only analysing high signal-to-noise objects.Due to the IGM absorption of any flux short-ward of the Lyman break at  ≤ 9.5, we further required a non-detection (≤ 2) in the F090W band, as well as in F115W and the HST ACS imaging if available.The condition of F115W<2 precludes any complete statistical investigation of the 8.5 <  < 9.5 population, given than a  9.0 galaxy can still be detectable in F115W.Consequently, we confine our later LF analysis to  > 9.5, but include any 8.5 <  < 9.5 candidates in our tabulated sample.
We double-checked any high-redshift candidates by also performing SED fitting using the code EAZY (Brammer et al. 2008), including the P (Fioc & Rocca-Volmerange 1999) templates.The primary solution is determined allowing the templates to vary over the redshift range 0 <  < 25 with a secondary lower-redshift solution by restricting to the range 0 <  < 6.
As well as performing the flux cuts to remove any significant detections shortward of the break, we inspected the F090W, F115W and ACS imaging, in order to verify that our candidates do not have any marginal detections.
The Cartwheel, SMACS 0723 and Quintet fields lack the F115W filter, and this creates additional challenges in determining the redshift of any candidates in those fields.As the F090W transmission ends at 1.0 m, any F090W-dropout followed by a significant F150W detection can essentially lie anywhere between  ∼ 7.2 and  ∼ 12.0, assuming it is not a low-redshift interloper.This issue is mitigated where there is a F115W non-detection, which helps narrow down the redshift solution to  9. We therefore included an extra criterion for these fields, whereby we required either a non-detection (≤ 2) in F150W, or a red F150W-F200W≥ 0.75 colour.Although this shifts our selection window for these three fields to above z 11.5, these criteria prevent the final sample from being contaminated by z 7 − 8 interlopers.

HIGH-REDSHIFT CANDIDATES
In Tables 2-3 we list basic properties for the candidates uncovered across the various fields.We also provide a colour-coded illustration of the distribution of intrinsic  1500 with redshift, and the distribution of F200W 0.35 −diameter aperture magnitude with redshift for our final sample in Fig. 2. In Fig. 3 and Fig. 4 we present some example SEDs and postage stamps for a sub-set of the final candidates.
Given the remarkably high resolution of JWST's NIRCam imaging, even the highest-redshift galaxies are often not well approximated by point-sources.Hence, we apply an additional correction to total fluxes, which we also apply to the  1500 .We measure the total fluxes by scaling to the FLUX_AUTO value measured by S -E and add a further 10% correction.In the Appendix, we provide a field-by-field analysis of the high-redshift candidates that we have selected, where we draw comparisons with other works in the literature.Although we do not search the HUDF for candidates in this particular study, we performed a search for  > 9.5 galaxies in Donnan et al. (2023b) very recently using the JEMS (Williams et al. 2023) data.We include the six robust F182M-selected candidates found over one NIRCam pointing in our UV LF determination in Section 5.

UV LUMINOSITY FUNCTION
In this section, we present our determination of the UV luminosity function at 9.5 ≤  ≤ 12.5.We first describe our methods for assigning survey areas, effective volumes, completeness corrections and uncertainties in galaxy number densities.We then calculate and fit the UV LF, before comparing our new results with relevant determinations from the literature.

Survey Area Definition
As this study is conducted over many inhomogeneous fields, care must be taken in order to define an accurate overall survey area.
In particular, the fields with clusters are subject to the effects of gravitational lensing.At the faintest luminosities, the differences between lensing models has been shown to have a potentially large impact on the faint end of the UV luminosity function, with the high magnification regime ( >10) more subject to systematic uncertainties (see e.g.Bouwens et al. 2017).Moreover, the cluster regions are typically significantly shallower than the survey global depth due to enhanced background from intracluster light and source crowding.
For each of our cluster fields, we therefore mask out these shallow cluster regions.Any candidates positioned on these masks are excluded from the UV LF calculation.
For the cluster surveys, we subtract the clusters in a fairly simple way.We first measure the global depth   across the whole field of view, as well as local depths across the survey pixel by pixel, and produce a depth map as shown in Fig. 5.We then mask out all pixels that have a local depth that is shallower than 2 ×   , removing the cluster and any regions particularly impacted by large foreground galaxies or stars.We then re-calculate   as our final global depth for the survey.We adopt the same strategy for the fields that are hampered by large foreground objects, e.g. the Cartwheel and Quintet fields.
We de-lens each of the cluster surveys using the lensing models described in Section 2.1.To measure effective survey areas, we calculate the magnification map taking the mid-point of our redshift bin,  = 11.However, for each candidate, we calculate  by generating a magnification map using its  phot .Where there are multiple lensing models considered (i.e. for WHL 0137, MACS 0647 and RXJ 2129), we perform this calculation for each lensing model, and then take the median  and de-lensed area.For SMACS 0723 and Abell2744 (UNCOVER, GLASS and DDT 2756) we simply use the magnification and areas calculated using the single lensing model.
For RXJ 2129, we only have one module on the cluster; how-ever for the three surveys with cluster+parallel survey configurations, the lensing maps typically do not to extend to the parallel module, and so we lose the ability to measure the magnification .For cluster+parallel pairs, and for the GLASS and DDT-2756 parallels to Abell 2744, we adopt a constant value of =1.2where we do not have any lensing map coverage.This value is motivated by the typical  values found around the edge of the lensing maps of the various surveys.We note that adopting an alternative choice of =1.1 reduces the overall number densities at the 1-2% level, as the parallel regions comprise <15% of the overall survey area.

Completeness
An accurate determination of the UV LF requires that the incompleteness of the galaxy sample is accounted for.This becomes of particular importance close to the detection limit of the data.Due to our adoption of a more stringent 8 detection limit throughout, this becomes less of an issue in this survey.The completeness as a function of apparent magnitude in the F200W imaging (F182M for the JEMS data) is determined using the method described in Donnan et al. (2023a).Point sources were injected into the F200W imaging in 3 regions for each field from  F200W = 24 − 31 in steps of 0.1 mag.At each step 800 sources are injected and the rate of recovery is measured, producing the completeness as a function of the apparent magnitude in F200W.This process is repeated 10 times for each region and therefore a total of 1,680,000 sources are injected into each field.We correct the effective volumes of our candidates by their completeness as determined in this procedure.
In a study of the first Hubble Frontier Fields, Oesch et al. (2015) showed the impact of including shear on completeness simulations, finding that large  can affect the relative completeness of sources close to the completeness limit.Having removed much of the area around the cluster regions, the effective area of the lensed fields with significant magnification probed in our study presents a modest fraction of the total search area (< 10%).This, and the fact that we are conservative in only selecting SNR>8 sources, allows us to be confident that the impact of shear on our overall completeness and effective survey volumes is negligible.spectroscopy to be at  = 9.31 (Boyett et al. 2023).

The z = 11 UV luminosity function
To determine the UV luminosity function for our 9.5 ≤  ≤ 12.5 sample we use the 1/ max estimator (Schmidt 1968).We only include objects for which our F200W detection is greater significance than 8  , where   is the global depth for a given survey.We split our sample into four number density bins between  1500 = −21.8and  1500 = −19.3.At the bright-end, we scale the  1500 = −22.57ground-based LF bin from Donnan et al. (2023a) to match our redshift range, add in the area we searched, and include it as a fifth bin.
In Table 4 we present our number densities  in each  1500 bin, along with their errors.To calculate the uncertainty in our number densities, we sum in quadrature the uncertainty found through a bootstrap analysis (  ) and cosmic variance (  ) as estimated using the Trenti & Stiavelli (2008) cosmic variance calculator.One of the key advantages of using many non-contiguous fields for this study is that the relative uncertainties across all the bins are significantly reduced.
In the left-hand panel of Fig. 6 we present our determination of the UV LF at  = 11, along with determinations across a host of other studies in the literature.There have been numerous LF measurements based on early CEERS epoch 1 and GLASS data, including Harikane et al. (2023b), Bouwens et al. (2023) and Finkelstein et al. (2023).In the range  1500 = −21.5 to −19.5, we find good agreement with the general consensus in the literature, although we note that they are all over slightly different selection windows: the Bouwens et al. (2023)   SED plots for high-redshift candidates selected in this study.We include both the primary high-redshift solution (blue line), as well as the competing lower-redshift secondary solution (red line).Each plot includes an inset of the  2 distribution with redshift for the SED fitting.Downward arrows in the plot denote the 1 upper limit for non-detections.
we recover all of the candidates in GLASS from Castellano et al. (2022a), our number densities at  1500 ≤ −20.5 are significantly lower.This suggests that the GLASS footprint does cover an overdensity, which is smoothed out by having a much larger overall search area in this study.The faintest  1500 bin is in concordance with our earlier work in Donnan et al. (2023a) and indeed with earlier HST  = 10 results from McLeod et al. (2016).However, the excess in the  1500 <= −20.5 bins presents a clear departure from HST-based determinations of the UV LF (e.g.McLeod et al. 2016;Oesch et al. 2018).
In order to increase the overall dynamic range, we incorporate the faintest two bins of the UV LF as determined in Donnan et al. (2023a), encouraged by the excellent agreement between our faintest bin and their bin at a similar  1500 .As well as sharing a similar set of reductions, SED fitting codes and selection criteria, the median redshift of our 9.5 ≤  ≤ 12.5 sample is  = 10.7, which is close to the mid-point of their bin at  = 10.5.The amalgamation of these two studies allows us to determine a UV LF spanning approximately four magnitudes in seven bins, from which we can determine the functional form.
We proceed to fit a double power law, found by Bowler et al. (2014Bowler et al. ( , 2020) ) and Donnan et al. (2023a) to be the preferred functional form at the highest redshifts, rather than a Schechter (Schechter 1976) Donnan et al. (2023a) where the absolute magnitude bin has been marked with an asterisk.Note that the  1500 = −22.57bin from Donnan et al. (2023a) is based on a search over the 1.8 deg 2 area of COSMOS/UltraVISTA DR5.2015, 2016;Bouwens et al. 2021).We fit the seven number density bins both with a free fit and with a fixed faint-end slope.The tabulated double power law fits are presented in Table 5, and the combined LF and functional forms are shown in the right panel of Fig. 6.
We find the free fit double power law is steep at  = −2.59± 0.35, however the errors attached to each of the parameters are large, particularly for  ★ .For the fixed fit, we use  = −2.35,which is the  = 10 slope predicted by the prescription for the evolving double power law as determined by Bowler et al. (2020).It is also the mid-point between the fixed  = −2.10slope utilised by early JWST studies at similar redshifts such as Donnan et al. (2023a,b) and Harikane et al. (2023b), and the free-fit value determined in this study.The fit with fixed  mitigates the uncertainties of the free fit significantly, and so we adopt this as our fiducial fit for the functional form of the UV LF at  = 11 for the rest of this paper.Encouragingly, our fiducial double power law fit appears to be in good agreement with the faintest bin from Pérez-González et al.Table 5.The parameters determined for our double power law fits to the  = 11 UV luminosity function.We include both our free fit and the fit fixing  = −2.35.We also provide the integrated luminosity density  UV for each of the cases, integrated to a limit of  1500 = −17 (see Section 6).
with this first tranche of JWST surveys.With deeper data sets such as NGdeep (ID 2079, PI Finkelstein;Bagley et al. 2023a), studies will be able to constrain  at  > 10 to the accuracy made possible at  = 8 with HST.
As well as drawing comparisons to recent JWST-based determinations of the UV LF, it is instructive to compare to studies probing the bright-end ( 1500 <  ★ ) of the UV LF at high-redshift.In the left panel of Fig. 7 we plot our fiducial LF but also include a compendium of studies probing the bright-end of the LF, including a suite of ground-based studies (Stefanon et al. 2019;Bowler et al. 2020;Kauffmann et al. 2022;Donnan et al. 2023a) and combined HST Legacy fields from Bouwens et al. (2023).We also include a comparison of our double power law fit to those determined by Donnan et al. (2023a) in the right-hand panel.
It is clear from Fig. 7 that our results suggest there is very little evolution in the bright end of the UV LF between  = 9−11, a feature previously reported by Bowler et al. (2020) between  = 8 − 10.In the left-hand panel, it can be seen that the  = 9−10 literature points at  1500 < −21.50 scatter symmetrically around our  = 11 double power law fit.Moreover, in the right-hand panel, it can be seen that  (2023, grey), Bouwens et al. (2023, red), Pérez-González et al. (2023, navy).For the right panel, we have adopted the two fainter  1500 bins from Donnan et al. (2023a) in order to increase our dynamic range in  1500 .We have hence fitted a double power law function (DPL) to our LF, adopting as our fiducial DPL fit the fixed  = −2.35case shown in Table 5.We also plot the HST-based Schechter function fits from Oesch et al. (2018, red) and McLeod et al. (2016, blue).
A relatively un-evolving bright-end has also been reported by Finkelstein et al. (2022a) over the CANDELS fields (see also Finkelstein & Bagley 2022).Although there have been some surprisingly high number densities of bright  > 10 galaxies reported in early JWST studies (Castellano et al. 2022b,a), reports of high number densities of bright  > 8 galaxies had become commonplace even pre-JWST, with studies reporting high number densities with widearea pure parallel HST studies (Rojas-Ruiz et al. 2020;Bagley et al. 2022), albeit with a greater potential risk of contamination due to limited filter sets.
The interpretation for greater numbers of bright  > 8 galaxies has been discussed previously in Bowler et al. (2020), who suggest that the double power law shape reflects a reduction in dust attenuation and/or inefficient mass quenching.Another explanation could lie in the star-formation efficiency, which may be higher at the bright-end to produce the double power law shape at high-redshift (e.g.Harikane et al. 2022).After the early JWST studies reporting large number densities of bright  > 8 galaxies, Mason et al. (2023) presented predictions of  > 8 LFs under the assumption of 100% star-formation efficiency (SFE).They demonstrated that a 100% SFE scenario yields LFs several orders of magnitude higher than current results, i.e. observations thus far are fully consistent with current cosmological frameworks.They conclude that our view may be biased in that we are predominantly witnessing young galaxies that are undergoing bursts of star-formation, rather than a representative population.
There is also the potential for significant field-to-field variation resulting in skewed number densities at the bright-end, where number statistics are generally low.For example, (Finkelstein et al. 2022a) found the CANDELS EGS field to be over-dense, with 7/11 of their bright 8.5 <  < 10.5 candidates across the five CANDELS fields coming from that field alone.More recently, the over-density found in GLASS by (Castellano et al. 2022a) causes their number densities to lie ∼ 3× higher than other JWST studies.
This study mitigates some of the field-to-field variation with numerous non-contiguous pointings over a relatively large area, while also bridging some of the disconnect between the groundbased and early JWST results at  > 9.5.Yet more progress at the bright-end of the UV LF can be gained through using wide-area surveys such as PRIMER (ID 1837; PI Dunlop) and COSMOS-Web (ID 1727, PI Casey;Casey et al. 2022).

STAR-FORMATION RATE DENSITY
We proceed to calculate the luminosity-weighted integral for our functional fits to the UV luminosity function in order to determine the UV luminosity density  UV .The integral limit that we choose is  1500 = −17, as has been convention with previous HST-based studies.Our  UV values are tabulated along with the UV LF functions in Table 5.To convert this to a star-formation rate density,  SFR , we use the conversion factor K UV = 1.15 × 10 −28 M yr −1 /erg s −1 Hz −1 (Madau & Dickinson 2014).The free-fit and fixed  = −2.35double power law cases yield very similar values of  UV .We adopt  UV = 25.15 +0.12 −0.17 as our fiducial value.We also include a tentative measurement of  UV at  = 13.5, based on our 12.5 <  < 14.5 sample.We fit a double power law fixing both  and  to the fiducial  = 11 LF values and allowing  ★ and  ★ to float.Based on the lack of evolution in the bright-end of the UV LF between  = 9 − 11, we anchor our double power law fit at the bright-end to the  1500 = −22.57bin from our  = 11 LF.Although the resulting double power law is highly uncertain, integrating this yields  UV = 24.56+0.16  −0.26 at  = 13.5.In the left-hand panel of Fig. 8 we present our determination of  UV along with those from other observations in the literature.Overplotted is the previous HST-based results from Oesch et al. (2018) and their rapidly declining  SFR (z) relation, following the evolution of the dark matter halo mass function.We also include the constant star-formation efficiency model from Harikane et al. (2023bHarikane et al. ( , 2022)), which follows  SFR ∝ (1 + ) −0.5 , and the log-linear relation we previously determined in Donnan et al. (2023a) log 10 ( UV ) = −0.231z + 27.5.
(1) As can be seen from the left-hand panel, our new determination of  UV , and hence  SFR , at  = 11 is found to be slightly higher than, although still consistent with, our previous estimates from Donnan et al. (2023a,b).With our significantly larger area spread over numerous additional fields, we once again find evidence in support of a smoothly declining  SFR at least to  = 12.Although tentative, our  = 13.5 data point also appears to be consistent with Given that the  UV can be sensitive to the assumed faintend slope, we want to ensure that our result is robust against the assumed  slope, particularly as the current JWST data are still unable to robustly constrain this parameter to the same level seen at  = 8 with HST.Hence, we also explore the impact of adopting  = −2.04,which was the slope found at  = 8 by Donnan et al. (2023a) and still presents an acceptable fit to our UV LF at  = 11.We find that  UV (z = 11) = 25.08 +0.12 −0.17 , which is in excellent agreement with the log-linear relation from Donnan et al. (2023a).Our conclusion of a smoothly declining  SFR (z) between  = 8−11 is therefore robust against the assumed value of .
Pre-JWST, the rate that  SFR declined at  > 8 was a matter of debate, with Oesch et al. (2018) advocating a rapid decline based on a lack of  = 10 galaxies found among HST Legacy fields.This was a conclusion shared by Ishigaki et al. (2018) when integrating to a limit of  1500 = −17, the limit of HST's capabilities, although they noted that this depends on the choice of  1500 limit, and that a limit of  1500 = −15 resulted in a smoothly declining  SFR .Many theoretical models of galaxy evolution also follow such a trend of rapidly declining  SFR (z) beyond  > 8.In the right-hand panel of Fig. 8, we include a comparison between our results and those of theoretical models of galaxy evolution, where  UV has been determined by integrating to the same  1500 limit.Our new results lie above a number of theoretical models that follow more closely the rapidly declining relation, such as Yung et al. (2019), FiBy (Paardekooper et al. 2013), Millenium TNG (Kannan et al. 2022) and Mason et al. (2015).However, the Behroozi & Silk (2015) and FLARES (Wilkins et al. 2023) models appear to be entirely consistent with our  = 11 results.
As well as lying above the Oesch et al. ( 2018) rapidly declining  SFR relation we also lie above the constant star-formation efficiency model from Harikane et al. (2022).Although the constant star-formation efficiency model is in close agreement with Harikane et al. (2023b) and Donnan et al. (2023a) up to  = 9, the observations begin to diverge from the model at higher redshifts.This is discussed in detail by Harikane et al. (2023b), who show that increasing the star-formation efficiency at  > 10, or adjusting the initial mass function (IMF) to be more top-heavy, can account for such discrepancies.Alternatively, as was mentioned earlier, Mason et al. (2023) suggest that observations thus far with JWST may be biased towards young galaxies with copious star-formation, drawn from the upper envelope of the  1500 − M halo relation, and that a more representative sample may be found when probing fainter apparent magnitudes, e.g. 200 > 30.
On the other hand, a study by Bouwens et al. (2023) suggests that perhaps the star-formation rate density may yet lie higher than the results of Harikane et al. (2023b), Donnan et al. (2023a) and this study.They compute  SFR when considering a more inclusive (but still referred to as "solid") sample of high-redshift candidates, rather than solely the most "robust" candidates, and find a significantly higher  SFR .Their study highlights the requirement for spectroscopy to confirm or refute the high-redshift nature of candidates.That said, it is worth noting that early JWST NIRSpec results from e.g.Curtis-Lake et al. ( 2023), Roberts-Borsani et al. (2022), Bunker et al. (2023) and Arrabal Haro et al. (2023a) suggest that  = 9 − 11 candidate selection with photometric redshifts has been largely successful.

CONCLUSIONS
We have presented a search for high signal-to-noise  ≥ 9.5 galaxy candidates across a suite of twelve JWST surveys spanning a raw survey area of ∼260 sq.arcmin.We uncover 61  ≥ 9.5 candidates detected at 8 , of which eighteen are at  ≥ 11.5.The exceptional brightness of many of these candidates makes them ideal for followup spectroscopy with NIRSpec.
With the inclusion of six additional candidates found in our ear- We also include a tentative  = 13.5 measurement based on our handful of 12.5 <  < 14.5 candidates.In the left-hand panel, we include a compilation of early JWST studies integrating to the same limit of  1500 = −17.Note that we have corrected the quoted value from Pérez-González et al. ( 2023), who adopted a  1500 = −16.5 limit in their study.We also include the HST-based determination at  = 10 from Oesch et al. (2018), based on the HST Legacy Fields, and the rapidly declining  SFR () relation based on the evolution of the dark matter halo mass function (pink shading).Finally, we also show the constant star-formation efficiency model (purple line) from Harikane et al. (2023b).We find that our new results are slightly higher than, but fully consistent with, the log-linear  UV (z) relation (blue line) from Donnan et al. (2023a).In the right-hand panel, we compare our measurements with a suite of theoretical models of galaxy evolution.Typically, the models under-predict the  SFR measurements found both in this study and Donnan et al. (2023a,b), with the exception of the Behroozi & Silk (2015) and FLARES Wilkins et al. (2023) models.
lier study, Donnan et al. (2023b), we proceed to construct the UV LF over 9.5 <  < 12.5.When combined with faint-end constraints from Donnan et al. (2023a), and UVISTA-based constraints at the bright-end, our  = 11 LF spans four magnitudes of dynamic range in  1500 .Our LF is consistent with previous JWST-based number densities in the literature at similar redshifts, but with tighter constraints owing to our wider search area.At the bright-end, our LF is consistent with a lack of evolution between  = 9 − 11, similar to results from Bowler et al. (2020), who found such trends between  = 8 − 10.This lack of evolution suggests that we are entering a regime where mass quenching efficiency is lower or that there is reduced dust attenuation (Bowler et al. 2020).
At the faint-end, our  measurements suggest a steep , which we fix to  = −2.35for our fiducial LF.With the present data, we are not yet able to robustly determine how  evolves between  = 8 − 11, given that a fit with  = −2.04(as measured at  = 8 by Donnan et al. 2023a) still provides an acceptable fit.
By integrating our LF, we arrive at the luminosity density and hence star-formation rate density.Our  UV at  = 11 lies slightly above, but is still consistent with, our previous log-linear  UV (z) relationship from Donnan et al. (2023a).Our  SFR at  = 11 suggests a continued smoothly declining  SFR to at least  = 12, with tentative  = 13.5 measurements based on a handful of  > 12.5 candidates further re-inforcing this.This result lies above both the rapidly declining  SFR suggested in pre-JWST studies (e.g.Oesch et al. 2018;Ishigaki et al. 2018) and the constant star-formation efficiency model from Harikane et al. (2022), as well as numerous theoretical models of galaxy evolution.
There are numerous potential interpretations for the high number densities of bright  10 galaxies and the higher  SFR than predicted by models.At the highest redshifts, we may be seeing a rise in the star-formation efficiency (Harikane et al. 2023a), or that we are potentially viewing the upper envelope of the  1500 − M halo relation (Mason et al. 2023).Although there have been suggestions that the early JWST studies may be subject to significant contamination by low-redshift interlopers, particularly as the overlap in sources between studies has hitherto been relatively low (see discussion by Bouwens et al. 2023), we can be encouraged by the number of spectroscopic confirmations of many photometrically selected  > 8 candidates (e.g.Curtis-Lake et al. 2023;Arrabal Haro et al. 2023a,b).
The prospects for building upon this LF determination with further JWST Cycle 1 surveys are excellent.In the bright-tointermediate regime, PRIMER will be instrumental in providing homogeneous coverage of COSMOS and UDS at even greater areas than those probed in this study, and to comparable depths.At the very brightest luminosities, COSMOS-Web (Casey et al. 2022) will provide > 0.5 sq.deg. of imaging, which will be crucial for uncovering the brightest (and rarest) high-redshift galaxies.At the faint-end, exceptionally deep surveys such as NGDeep (Bagley et al. 2023a) and JADES (Robertson et al. 2023) will help to better constrain the evolution of the faint-end slope .

DATA AVAILABILITY
At the time of writing, the data sets used in this manuscript were all publicly available from the JWST archive on MAST and on the CADC.

APPENDIX A: DISCUSSION OF HIGH-REDSHIFT CANDIDATES
In the following sections, we discuss the results of our search for high-redshift galaxies field-by-field, along with a (non-exhaustive) comparison to some previous searches in the literature.The variation between JWST high-redshift candidate samples has been a theme in the literature (see Bouwens et al. 2023 for a comprehensive discussion).We stress that differences in the candidate lists can result from a number of factors such as differing reductions, photometry measurement and selection criteria such as non-detection and Δ 2 thresholds.
The nomenclature adopted for our final candidate IDs is Fieldredshift-catalogueID (e.g.GLASS-z11-1481).When referring to candidates from other studies we use their naming convention.
There have been numerous studies of this cluster field to date, yielding contrasting samples.We only compare candidates that have passed the additional criteria of 150 − 200 > 0.75 or 150 < 2.Adams et al. (2023) reported a sample of four 9 <  < 12 galaxies, but only one of which can be compared to our final sample.Their candidate with ID 10234 was initially selected in our sample, where we found  phot = 11.8 +0.2 −0.1 .However, there appeared to be a marginal F090W detection upon visual inspection of the imaging, and so we discarded the candidate.Atek et al. (2023) reported a sample of high-redshift candidates, including two potential  > 15 candidates and two potential  = 12 candidates.We do not include their ID z16a due to a > 3 detection in F150W, which rules out a potential  > 13 solution.While we do find a  phot = 15.6 +0.5 −0.9 solution for their ID z16b, we exclude it from our final sample as it has Δ 2 2. Both their objects z12a and z12b have Δ 2 1 between the high-redshift and low-redshift solutions, so are also excluded.
Most of the SMACS 0723 sample from Donnan et al. (2023a) was not included in our final sample due to our more stringent selection and brightness criteria.Their candidate with ID 8347 is in our final sample as SMACS0723-z12-7442.While we find  phot = 12.2 +0.5 −0.4 for their object with ID 1566, it just misses out on being in our final sample through having Δ 2 = 3.4.Finally, their candidate with ID 10566 had been excluded from our final sample due to a > 2 detection in the HST ACS imaging in our present analysis, potentially due to a noise spike that contaminated the aperture.

A2 GLASS
Using the maximum-depth combination of the epoch1+2 GLASS survey, we report a sample of twelve  ≥ 9.3 galaxy candidates, including five in the range 10.5 <  < 11.5 and three at  > 12.The high density of bright  ∼ 10 galaxies seen in Castellano et al. (2022a) is confirmed by this study, as we re-select all five of their candidates at similar redshifts.
A comprehensive study by Bouwens et al. (2023) also covered the GLASS data set.Their final sample includes the two aforementioned candidates in common with our study, Naidu et al. (2022) and Castellano et al. (2022b).We re-select their  = 13.7 candidate, GLASSP2H-3576218534 in our final sample as GLASS-z14-33570.Although we also recover a high-redshift solution for their candidate ID 4002721259, the Δ 2 was insufficient to include in our final sample.Their alternative sample includes an additional  = 13.3 candidate, GLASSP1H-4015021230, but we cannot confirm its redshift owing to a flat p(z) distribution.Finally, GLASSP1YJ-4016420474 and GLASSP1YJ-4043920397 are  = 9.6 and  = 9.7 candidates that we do not include as they appear to have a marginal detection in F115W.This is likely a result of the increased depth when adding epoch 2, as the epoch 1-only version of the data appeared consistent with non-detections for both objects.

A3 CEERS
The first epoch of observations was split into two fields, north-east (NE) and south-west (SW).In CEERS-NE we selected six candidates, among which are CEERS-93316 (Donnan et al. 2023a) and Maisie's galaxy (Finkelstein et al. 2022b).While the former has recently been revealed by spectroscopy to be lower redshift, Maisie's galaxy has been spectroscopically confirmed to be at high-redshift (DDT 2750, PI Arrabal Haro;Arrabal Haro et al. 2023a).We also note that CEERS-NE-z11-2543 has also been recently spectroscopically confirmed at high-redshift with the same program.Given its new spectroscopic redshift  spec = 4.9, we exclude CEERS-93316 from the subsequent analysis.Four of the five remaining candidates were included in Finkelstein et al. (2023).
There are five galaxies from Finkelstein et al. (2023) that we also find to be  > 9.0, but do not include in our final sample due to insufficient Δ 2 and/or < 8 detection.A further six candidates are not included due to > 2 detection in F115W, but five of those are consistent with their  phot = 8 − 9 solutions.The only higher redshift candidate excluded by our study for a F115W detection is their candidate ID CEERS-7227, for which we find the F115W to be marginally detected at 2.6.We note that Finkelstein et al. (2023) find a 2.2 flux for this object in F115W.Only CEERS-NE-z10-3069854 is unique to this study.
Four objects in the Finkelstein et al. (2023) sample (their IDs 7603, 1748, 2324 and 4012) were also found to have preferred highredshift solutions in our catalogues, but were detected at < 8 so were excluded.Finally, four  = 8 − 9 candidates were F115W> 2 and so were excluded.
Epoch two of the CEERS observations were split into six NIR-Cam pointing pairs, and we adopt this naming convention into our candidate IDs.We report twelve high-redshift candidates across the ∼ 60 sq.arcmin.Two of these objects (CEERS-2-5-z10-9617 and CEERS-2-6-z10-3530) have very recently been independently confirmed with spectroscopy to lie at  10 (Arrabal Haro et al. 2023b).

A4 Stephan's Quintet
Our search over the Quintet field yielded one high-redshift candidate over 11.5 <  < 12.5.Harikane et al. (2023b) also reported two candidates at  > 12 from the Quintet field.Their  ∼ 12 candidate was in our initial catalogue, and with our photometry appears to be a robust candidate at  phot = 11.7 +0.4  −0.5 and Δ 2 = 4.8.It also passes our additional F150W-F200W colour criteria, but we do not include it in our final sample as it is only detected at ∼ 6 in F200W and F277W.For the  = 16 candidate, we obtain a low-z preferred solution of  = 0.6, with other solutions at  = 16.4 and  = 4.9 being of similar probability (within 1).We cannot rule out that it is indeed a  = 16.4 galaxy, but based on the current fits we do not include it in our final sample.Interestingly, the high and lowredshift solutions that we derive are very similar to CEERS-93316.The low-redshift solution with emission lines was ultimately the spectroscopic redshift, suggesting that candidates around  = 16.4 are vulnerable to this class of contaminant, especially in the absence of photometric constraints from key medium bands such as F250M and F300M.

A5 UNCOVER
From our analysis of the UNCOVER field, we amass a sample of sixteen candidates.We find UHZ1 from Castellano et al. (2022a) as UNCOVER-z10-32757 with a similar  phot = 10.4 +0.1 −0.2 and Δ 2 > 100.One additional candidate was a duplicate of GLASS-z10-3283 and so was excluded.
We also find two components from the triply lensed  10 galaxy from Zitrin et al. (2014), which has now been spectroscopically confirmed to lie at  = 9.8 (Roberts-Borsani et al. 2022).We find JD1B as UNCOVER-z11-15452 which was observed to be exceptionally bright  1500 = −20.9,but is magnified 11×.JD1A was in our initial catalogue as UNCOVER-z10-15137 with a robust  phot = 10.3 +0.3  −0.9 , Δ 2 = 17 solution.This component had a magnification of 13.4 and  1500 = −17.3.As it was only 7 local in each of our detection catalogues, it was not propagated to the final sample.The remaining component, JD1C, was of insufficient signal-to-noise to make it into our catalogues at > 5, due to enhanced background and crowding.

A6 DDT 2756
In the DDT 2756 parallel field to Abell2744, we found more examples of bright and robust  ∼ 10 candidates, providing more evidence that the region around Abell2744 is over-dense with such galaxies.We report five 9.5 <  < 11.7 candidates, including a particularly robust (Δ 2 43) candidate with  phot = 10.6 +0.1 −0.3 , DDT2756-z11-1001979.
The DDT 2756 survey was also explored in Castellano et al. (2022a), who found one remarkably bright  ∼ 10 candidate, DHZ1.Due to the high-resolution of the F200W imaging, our F200Wdetected catalogue had de-blended DHZ1 into two components.The north-east component was selected for our final sample as DDT2756-z10-1010612, and yielded a robust high-redshift solution of  phot = 9.5 +0.6 −0.3 .Although the south-west component was excluded from our final sample due to a 2.2 detection in F115W, we performed SED fitting and found an ultra robust  phot = 9.5±0.1 (Δ 2 > 150) solution, consistent with the north-east component.The system has since been spectroscopically confirmed to be  = 9.31 (Boyett et al. 2023).

A7 WHL 0137
We report four high-redshift candidates in the WHL 0137 clus-ter+parallel data set, three of which are  9 candidates and the other with  = 11.1.There has been one reported search for  > 9 galaxies over the WHL 0137 data set to date, with Bradley et al. (2022) uncovering a sample of twelve galaxies over 8.3 <  < 13.0.We include in our final catalogue two of the twelve candidates, WHL0137-z9-10187 (their WHL0137-2796) and WHL0137-z11-22312 (their WHL0137-5330).Three candidates, while showing high-redshift solutions in agreement with Bradley et al. (2022), had too low a Δ 2 to be included in the final sample.Notably, our initial catalogue has a  = 13 galaxy in common, their WHL0137-5021 was found by our study to have a robust  phot = 12.8 +0.8 −0.5 solution.The candidate was excluded due to being detected at ≤ 8.Six of the candidates are not in our initial catalogue due to > 2 detections in F115W, although a detection in F115W is still consistent with the 8.3 ≤  ≤ 9.3 solutions reported by Bradley et al. (2022).

A8 MACS 0647
We report three high-redshift candidates in the MACS 0647 clus-ter+parallel data set.There has been a detailed analysis of MACS 0647 JD (Coe et al. 2013) by Hsiao et al. (2022).We recover two of the three multiply imaged components of JD: MACS0647-z11-20148 is JD1 and MACS0647-z11-26400 is JD3.Both have extremely robust solutions Δ 2 > 100, and in excellent agreement with the reported value of  phot = 10.6 ± 0.3 in Hsiao et al. (2022).This object has since been spectroscopically confirmed to lie at  = 10.17 by Harikane et al. (2023a).
We do not include JD2 in our final sample as it has a 2.8 detection in F435W, which aligns with Hsiao et al. (2022)'s F435W photometry also being > 2.For completeness, we note that we recover a  = 10.8 ± 0.2 solution for JD2 using our photometry, with a Δ 2 = 63 showing it is an extremely robust object despite the F435W SNR>2 measurement.For our subsequent LF analysis in Section 5, we only propagate JD1 so as not to double-count multiple images.In addition to MACS0647 JD, we find a notably robust  = 9.5 galaxy in the cluster module, MACS0647-z9-20158.

A9 RXJ 2129
We report two  9 galaxy candidates in this field, however we do not uncover any  ≥ 9.5 candidates.To date, there has been one reported  ≥ 9.5 galaxy in the RXJ 2129 field with the new JWST data (Williams et al. 2022).This galaxy is reported to be intrinsically very faint with  1500 = −17.4,but high magnification factor ( 20).We do not recover this spectroscopically confirmed galaxy due to its position near the RXJ 2129 cluster.The enhanced background in the region around the object had caused the object to fail our signal-to-noise cuts in all of the catalogues.

A10 NEP TDF
Our study of the NEP TDF data set uncovered one  ∼ 10 candidate and one  ∼ 11 candidate.To date, there have been no published candidates in the literature.

A11 Cartwheel
Our final sample does not include any galaxy candidates at  > 9 from the Cartwheel galaxy field.

A12 J1235
From our study of the J1235 field we report three high-redshift galaxy candidates over 9.7 ≤  ≤ 11.8.To date, there have been no other published high-redshift candidates in the literature.This paper has been typeset from a T E X/L A T E X file prepared by the author.

Figure 1 .
Figure 1.An illustration of the distribution of F200W 8 global depths across the various surveys utilised in our search for  ≥ 9.5 galaxies.Although we do not perform a new search over JEMS for this study, we utilise the sample as found inDonnan et al. (2023b), and so we include the F182M depth here.The solid teal line shows the predicted number of galaxies at  ≥ 9.5 in the area of one NIRCam pointing assuming the luminosity functions fromDonnan et al. (2023a).The top −axis shows the absolute UV magnitude for a  = 11 galaxy with an apparent magnitude given by bottom −axis at  = 11.

Figure 3 .
Figure 3. Examples of L PSED plots for high-redshift candidates selected in this study.We include both the primary high-redshift solution (blue line), as well as the competing lower-redshift secondary solution (red line).Each plot includes an inset of the  2 distribution with redshift for the SED fitting.Downward arrows in the plot denote the 1 upper limit for non-detections.
function as found in earlier HST studies (e.g.McLeod et al.

Figure 4 .
Figure 4. Postage stamps for each of the candidates shown in Fig.3.The shortest wavelength column is NIRCam F090W or HST F814W, depending on availability, followed by each of the broadband NIRCam filters from F115W to F444W.Note that in some surveys lacking ACS ancillary data, e.g.DDT-2756, our shortest wavelength band is F115W.The greyscale has been set to the median background flux ±2, after excluding flux contributions from sources defined by a segmentation map.
(2023), who probe exceptionally deep imaging of HUDF-par2 as part of their MIRI deep survey of the UDF (PID 1283, PI Oestlin).It should be noted that alternative fits utilising a range of different fixed faint-end slope are almost indistinguishable over the luminosity range spanned by this study.At  = 8, Donnan et al. (2023a) fitted a faint-end slope  = −2.04 ± 0.29, leveraged by the excellent HST-based constraints of the faint-end which reach  1500 = −17 (McLure et al. 2013).Although our free fit double power law suggests some steepening between the  = 8 faint-end slope and that of our  = 11 LF, fitting our data with fixed  = −2.04 also presents an acceptable fit over the magnitude range spanned by this study.This does leave the evolution of the faint-end slope at  > 8 an open question, despite all of the recent advances brought

Figure 5 .
Figure 5. Depth for the cluster fields and Stephan's Quintet, demonstrating the inhomogeneities in depth across the imaging.The top row is MACS 0647 (left) and WHL 0137 (right), the middle row is SMACS 0723 and RXJ 2129, and the bottom row is UNCOVER and Stephan's Quintet.

Figure 6 .
Figure 6.The UV luminosity function over 9.5 <  < 12.5 as found by this study.On the left panel, we include our five number density bins along with data-points from a host of other studies: Donnan et al. (2023a, green), Harikane et al. (2023b, purple  = 9), Castellano et al. (2022a, orange), Finkelstein et al.(2023, grey),Bouwens et al. (2023, red),Pérez-González et al. (2023, navy).For the right panel, we have adopted the two fainter  1500 bins fromDonnan et al. (2023a) in order to increase our dynamic range in  1500 .We have hence fitted a double power law function (DPL) to our LF, adopting as our fiducial DPL fit the fixed  = −2.35case shown in Table5.We also plot the HST-based Schechter function fits fromOesch et al. (2018, red)  andMcLeod et al. (2016, blue).

Figure 7 .
Figure7.A comparison between our fiducial  = UV LF and results from other studies.In the left-hand panel we plot a compendium of data points from literature studies at  = 9 − 10, whereas the right-hand panel compares our LF with functional fits fromDonnan et al. (2023a).Overall, our  = 11 results appear to be consistent with a lack of evolution in the very bright-end of the LF from  = 9 − 11.

Figure 8 .
Figure8.Our of the luminosity density and star-formation rate density at  = 11, integrated to a limit of  1500 = −17.We also include a tentative  = 13.5 measurement based on our handful of 12.5 <  < 14.5 candidates.In the left-hand panel, we include a compilation of early JWST studies integrating to the same limit of  1500 = −17.Note that we have corrected the quoted value from Pérez-González et al. (2023), who adopted a  1500 = −16.5 limit in their study.We also include the HST-based determination at  = 10 fromOesch et al. (2018), based on the HST Legacy Fields, and the rapidly declining  SFR () relation based on the evolution of the dark matter halo mass function (pink shading).Finally, we also show the constant star-formation efficiency model (purple line) fromHarikane et al. (2023b).We find that our new results are slightly higher than, but fully consistent with, the log-linear  UV (z) relation (blue line) fromDonnan et al. (2023a).In the right-hand panel, we compare our measurements with a suite of theoretical models of galaxy evolution.Typically, the models under-predict the  SFR measurements found both in this study andDonnan et al. (2023a,b), with the exception of theBehroozi & Silk (2015) and FLARESWilkins et al. (2023) models.

Table 1 .
The 5 global limiting magnitudes for each of the fields analysed in this study.These have been measured in 0.35 −diameter apertures on the PSF-homogenized imaging, and corrected to total assuming a point-source correction.
Castellano et al. (2022a)o a floor of 1.2 due to a lack of lensing map coverage.†DDT2756-z10-1010612is the north-east component of what is believed to be a merging system, first found byCastellano et al. (2022a)and confirmed with

Table 4 .
Our number density measurements for the  11 UV LF, including those from