The miniJPAS & J-NEP surveys: Identification and characterization of the Ly α Emitter population and the Ly α Luminosity Function at redshift 2 . 05 < z < 3 . 75

We present the Lyman-α (Ly α ) Luminosity Function (LF) at 2 . 05 < z < 3 . 75, estimated from a sample of 67 Ly α -emitter (LAE) candidates in the Javalambre Physics of the Accelerating Universe Astronomical Survey (J-PAS) Pathfinder surveys: miniJPAS and J-NEP. These two surveys cover a total e ff ective area of ∼ 1 . 14 deg 2 with 54 Narrow Band (NB) filters (FWHM ∼ 145 Å) across the optical range, with typical limiting magnitudes of ∼ 23. This set of NBs allows to probe Ly α emission in a wide and continuous range of redshifts. We develop a method for detecting Ly α emission for the estimation of the Ly α LF using the whole J-PAS filter set. We test this method by applying it to the miniJPAS and J-NEP data. In order to compute the corrections needed to estimate the Ly α LF and to test the performance of the candidates selection method, we build mock catalogs. These include representative populations of Ly α Emitters at 1 . 9 < z < 4 . 5 as well as their expected contaminants, namely low-z galaxies and z < 2 quasars (QSOs). We show that our method is able to provide the Ly α LF at the intermediate-bright range of luminosity (43 . 5 ≲ log 10 ( L Ly α / ergs − 1 ) ≲ 44 . 5) combining both miniJPAS and J-NEP. The photometric information provided by these surveys suggests that our samples are dominated by bright, Ly α -emitting Active Galactic Nuclei (i.e., AGN / QSOs). At log 10 ( L Ly α / ergs − 1 ) < 44 . 5, we fit our Ly α LF to a power-law with slope A = 0 . 70 ± 0 . 25. We also fit a Schechter function to our data, obtaining: log 10 ( Φ ∗ / Mpc − 3 ) = − 6 . 30 + 0 . 48 − 0 . 70 , log 10 ( L ∗ / ergs − 1 ) = 44 . 85 + 0 . 50 − 0 . 32 , α = − 1 . 65 + 0 . 29 − 0 . 27 . Overall, our results confirm the presence of an AGN component at the bright-end of the Ly α LF. In particular, we find no significant contribution of star-forming LAEs to the Ly α LF at log 10 ( L Ly α / ergs − 1 ) > 43 . 5. This work serves as a proof-of-concept for the results that can be obtained with the upcoming data releases of the J-PAS survey.

One of the main drivers of Lyα surveys is to measure the Lyα luminosity function (LF) over a specific redshift interval.The LF is a statistical measurement of the abundance of Lyα emitters (LAEs), defined as the number density of LAEs per unit comoving volume as a function of the Lyα luminosity (L Lyα ).Many works have managed to estimate the Lyα LF for different redshift ranges (e.g., Konno et al. 2016;Sobral et al. 2018;Spinoso et al. 2020;Zhang et al. 2021;Liu et al. 2022b).Generally, the observed LAE population is divided in two main kinds of sources: quasi-stellar objects (QSO) with an active galactic nucleus (AGN) and star forming galaxies (SFG).It was found that the population that dominates the low luminosity regime of the Lyα LF (log 10 (L Lyα /erg s −1 ) ≲ 43.5) is that of SFGs (e.g., Guaita et al. 2011;Drake et al. 2017).These objects are typically low-mass galaxies with a high star formation rate, low dust content, small rest-frame half-light radius and in general, faint emission lines except Lyα (see e.g., Arrabal Haro et al. 2020;Santos et al. 2020).In SFGs, Lyα emission is produced through recombination processes in the inter-stellar medium (ISM), heated by recent star formation events (e.g., Charlot & Fall 1993;Pritchet 1994;Arrabal Haro et al. 2020).Meanwhile the brightest part of the LF (log 10 (L Lyα /erg s −1 ) ≳ 43.5) is populated mainly by QSOs, where the recombination processes are triggered by the action of the AGN (e.g., Calhau et al. 2020).
Identifying the LAEs population and characterizing its luminosity census is a crucial step in order to understand a multitude of processes in the high-z Universe.SFG LAEs are thought to be analogous to the progenitors of many galaxies that we observe in the nearby Universe, for this reason they provide useful insight about early phases of galaxy evolution (e.g., Gawiser et al. 2007;Ouchi et al. 2010).Furthermore, at high-z, these objects constitute a probe of high-z galaxy clustering and the large structure formation history (e.g., Guaita et al. 2010;Khostovan et al. 2019).On the other hand, the characterization of the galactic features of LAEs are key to understanding processes such as the AGN fueling and feedback and their effects on star formation (e.g., Bridge et al. 2013).In addition, through the study of the fraction of ionizing photons in the ISM of LAEs, it is possible to measure the ionization state of the high-z Universe, shortly after the cosmic epoch of reionization (EoR,; see e.g., Bouwens et al. 2012;Nakajima & Ouchi 2014;Jaskot & Oey 2014).
The evolution of the Lyα LF with redshift is another interesting topic.Past studies claim that the SFG Lyα LF grows substantially from z ∼ 0.3 up to z ∼ 2-3 and remains broadly constant up to z ∼ 6-7.At higher redshift, the SFG Lyα LF shows a strong evolution, resulting in a decrease of the LAE observed number density.This is generally interpreted as an indirect probe of the Universe's reionization progress, since the higher fraction of neutral hydrogen would efficiently absorb Lyα radiation, hindering the detectability of z ∼ 6-7 SFG LAEs (e.g., Malhotra & Rhoads 2004;Kashikawa et al. 2006;Clément et al. 2012;Dijkstra 2016;Ning et al. 2022).On the other hand, the Lyα LF of AGN/QSOs shows an evolution compatible with the progress of AGN activity through cosmic history (see e.g., Hasinger et al. 2005;Miyaji et al. 2015;Sobral et al. 2018).
Many works in the last decade have sought to estimate the Lyα LF at different luminosity regimes.The works of Konno et al. (2016); Sobral et al. (2017) and Sobral et al. (2018) estimate the Lyα LF at various redshifts, in the faint and intermediate regime using deep NB imaging.In all of these works, it was found that the LF deviates from a Schechter function (Schechter 1976) to a power-law like shape for 43.5 ≲ log 10 (L Lyα /erg s −1 ) ≲ 44.5.The analysis of the X-ray counterparts in Ouchi et al. (2008); Konno et al. (2016) and Sobral et al. (2018) revealed that essentially every LAE with log 10 (L Lyα /erg s −1 ) > 43.5 is associated with X-ray emission, typically interpreted as a signature of AGN activity.
More recently, a few works have explored the brightest end of the Lyα LF.In Spinoso et al. (2020), the Lyα LF is built from ∼ 10 3 deg 2 of data from the J-PLUS survey (Cenarro et al. 2019), at four redshifts defined by 4 NB-filters (z = 2. 24, 2.38, 2.54, 3.23) and focusing on the bright regime of log 10 (L Lyα /erg s −1 ) ≳ 44.5.On the other hand, Zhang et al. (2021) combined the spectroscopic data from HETDEX (Gebhardt et al. 2021) with the r-band images of Subaru/HSC to obtain the Lyα LF, covering ∼ 11.4 deg 2 of sky at 2 < z < 3. Later, Liu et al. (2022b) obtained analogous results for the Lyα AGN LF from the spectroscopic QSO sample of HETDEX, over 30.61 deg 2 .The latter work showed great agreement with the J-PLUS LF Schechter fit, while covering a wider range of luminosity (42.3 ≲ log 10 (L Lyα /erg s −1 ) ≲ 45.9).While the LAEs sample of Zhang et al. (2021) relies on the r-band detection of HSC, in Liu et al. (2022b) the selection is made using purely HETDEX blind spectroscopy, allowing to obtain a more complete sample over a broader area.Overall, the Lyα LF at the full range of luminosity (41 ≲ log 10 (L Lyα /erg s −1 ) ≲ 46) can be well fit by a double Schechter curve, making evident the contributions of both, SFG and AGN/QSO populations (e.g., Zhang et al. 2021;Spinoso et al. 2020).
In this work, we develop a method for detecting Lyα emission in the photometric data of multi-NB surveys such as the Javalambre-Physics of the Accelerating Universe Astronomical Survey (J-PAS 1 ; Benitez et al. 2014) and its pathfinder surveys, namely miniJPAS (Bonoli et al. 2021) and J-NEP (Hernán-Caballero et al. 2023).More specifically, we develop our method on the already-observed fields of miniJPAS and J-NEP, in order to pave the ground for the upcoming J-PAS survey.Multi-NB photometric surveys such as J-PAS allow to perform blind search of LAEs at various redshifts over a wide field of observation, with a more efficient selection function than typical spectroscopic surveys (e. g.Zhang et al. 2021;Liu et al. 2022b).Furthermore, the availability of a photospectrum (λ ∼ 3750-9000 Å) for each source in the survey catalog can be used for contaminant identification.
We characterize the performance of our selection method by building mock-survey data and we ultimately build the Lyα LF at 2.05 < z < 3.75 in the medium-bright luminosity range (43.5 ≲ log 10 (L Lyα /erg s −1 ) ≲ 45).This range is yet poorly con-strained by photometric surveys, due to the small areas probed and the limited number of NBs used (e.g., Konno et al. 2016;Sobral et al. 2017;Matthee et al. 2017;Sobral et al. 2018;Spinoso et al. 2020).At the same time, Lyα is an excellent tracer for z > 2 AGNs due to its intrinsic brightness.The estimation of the Lyα LF is motivated by the need to constrain the evolution of the AGN population across cosmic times.For instance, the role played by AGNs at the EoR is still debated.While some works point out that AGNs could be a significant source to the ionizing photon budget (e.g., Giallongo et al. 2015;Dayal et al. 2020), others conclude that AGNs could only make a marginal contribution, in favor of star formation activity (e.g., Qin et al. 2017;Hassan et al. 2018).At lower redshifts, being able to trace the fraction of active galaxies as well as the AGN luminosity distribution is useful to shed light on processes such as AGN-driven feedback and its effect on the host galaxy (e.g., Brownson et al. 2019;Mezcua et al. 2019;Jin et al. 2023) or the build-up of scaling relations between active super-massive BHs and their host galaxies (see e.g., Reines & Volonteri 2015, for a review).Therefore, developing reliable methods to estimate the Lyα LF allows systematic studies of AGN populations since the EoR down to cosmic noon (z ∼ 2).Furthermore, optical multi-NB surveys offer the possibility to perform these analyses in a tomographic fashion across redshift.
This paper is structured as follows.In Sect. 2 we describe the observations used to obtain the scientific results of this work.In Sect. 3 we define the procedure to build mock catalogs that mimic the observations, which we use to assess the performance of our method.In Sect. 4 we explain our LAE candidate selection method, the procedure used to estimate the Lyα LF and present the LAE catalog for miniJPAS&J-NEP.In Sect. 5 we present the Lyα LF in different intervals of redshift and estimate the QSO/SFG fraction of our candidates.Finally, Sect.6 summarizes the content of this work.

Observations
2.1.J-PAS: Javalambre-Physics of the Accelerating Universe Astronomical Survey J-PAS is a ground-based survey that will be performed by the JST/T250 telescope at the Javalambre Astrophysical Observatory at Teruel (Spain).It is planned to observe ∼ 8500 deg 2 of the northern sky via narrow-band imaging with the JPCam instrument.The JPCam is a 1.2 Gpixel multi-CCD camera composed of an array of 14 CCDs, with a field of view of ∼ 4.2 deg 2 (see Taylor et al. 2014;Marín-Franch et al. 2017).
In the context of this work, the most relevant feature of J-PAS is its filter-set.This set is composed of 54 narrow bands with FWHM of ∼145 Å, covering the optical range of the electromagnetic spectrum.In addition, this filter-set features two medium bands, respectively at the blue and red ends of the optical range, and four broad bands (BBs) equivalent to those used by the SDSS survey: u, g, r and i (York et al. 2000).These technical features make J-PAS particularly suitable to detect line emitters (e.g., Martínez-Solaeche et al. 2021, 2022;Iglesias-Páramo et al. 2022).Indeed, the NB set provides a wide and continuous coverage of the optical range (∼ 3 500-10 000 Å), allowing the development of algorithms for photometric source identification (e.g., Baqui et al. 2021;González Delgado et al. 2021), and precise determination of photometric redshifts (Hernán-Caballero et al. 2021;Laur et al. 2022).The same filter set was used by the pathfinder surveys miniJPAS and J-NEP.

The pathfinder surveys of J-PAS: miniJPAS & J-NEP
The miniJPAS survey (Bonoli et al. 2021) is a scientific project designed to pave the ground for J-PAS data analysis.The observations of miniJPAS were carried out between May and September 2018 using the JPAS-Pathfinder camera mounted in the JST/T250.The JPAS-Pathfinder camera is an instrument composed of one single CCD with an effective field of view of 0.27 deg 2 .The miniJPAS data cover a total of ∼ 1 deg 2 (effective area after masking 0.895 deg 2 ) of the AEGIS field (Davis et al. 2007), in the northern galactic hemisphere.This field is covered by miniJPAS in 4 pointings (AEGIS001-AEGIS004).AEGIS is a widely studied region of the sky, located within the Extended Groth Strip, for which a plethora of multi-band and spectroscopic observations are available in the literature.For instance, the entirety of the miniJPAS area is covered by the Sloan Digital Sky Survey (SDSS; Blanton et al. 2017), granting spectroscopic counterparts to many sources in the miniJPAS catalogs.The outcome of miniJPAS serves as a demonstration of the potential of J-PAS and allows us to make a forecast about the results that will be possible to achieve once the survey delivers the first set of data.
J-NEP (for Javalambre North Ecliptic Pole) is the second data release obtained using the JST/T250 and the Pathfinder camera, covering the James Webb Space Telescope North Ecliptic Pole Time-Domain Field (JWST-TDF; Jansen & Windhorst 2018).This survey was carried out in a single pointing, with an effective area of ∼ 0.24 deg 2 (Hernán-Caballero et al. 2023).The JWST-TDF will be covered by JWST via a dedicated program in the near future.J-NEP has slightly longer exposure times than miniJPAS, reaching deeper magnitudes.
In Table 1, we list the limiting 5σ magnitudes of both surveys for all relevant filters for this work.We use 20 NBs to probe for Lyα emission covering a redshift range of z = 2.05-3.75, the choice of this range is discussed in Sect.4.3.The number in the J-PAS NB names makes reference to the approximate pivot wavelength (λ pivot ) in nanometers.
Throughout this work we use the dual mode catalogs of mini-JPAS and J-NEP described in Bonoli et al. (2021) and Hernán-Caballero et al. (2023), respectively.These catalogs are generated using the "dual-mode" of the SExtractor code (Bertin & Arnouts 1996).In this operating mode, SExtractor performs a first source-detection on a specific band (r for J-PAS, since this is the deepest among the BBs).Then, the positions of these rband detected sources is used to perform forced-photometry in the images obtained with all the remaining filters.We use the 3 ′′ forced aperture photometry fluxes and magnitudes.The PSF FWHM of the miniJPAS&J-NEP images varies in the range 0.6-2 ′′ .The total effective area, after masking, combining miniJPAS and J-NEP is 1.14 deg 2 .

Mock catalogs
Given our wavelength coverage (3 700Å-5 700Å) our sample is prone to be contaminated by sources with prominent emission lines other than Lyα, such as C iv (λ 1549 Å), C iii] (λ 1908 Å), Mg ii (λ 2799 Å) and Si iv (λ 1397 Å) AGN lines; and galactic emission lines associated to star formation at low-z such as H β We have designed mock catalogs of LAEs and its main contaminants in order to estimate completeness and purity of our selection methodology as well as the uncertainty on our measured Lyα LF.

Characterization of the photometry flux uncertainties
The first step in building the mock catalogs is to characterize the photometric uncertainty distribution of the survey we want to emulate.We assume that the distribution of measured magnitude errors (σ[m]) in each observed pointing can be modeled as a simple exponential: We perform a fit for the parameters A, B and C for every NB in every pointing of miniJPAS&J-NEP.Following this fit, we add Gaussian uncertainties in magnitude to our mock objects in order to mimic the JPAS-Pathfinder observations.Next, all magnitudes are converted to fluxes ( f λ ).The bands with a flux below the 5σ limiting flux of that band f λ 5σ , are assigned an error equal to f λ 5σ /5.The reason for this is that assuming Gaussian magnitude uncertainties is only valid for m ≲ m 5σ , as some parts of many of the synthetic spectra have fluxes compatible with zero, and the Gaussian approximation of the magnitude errors is no longer For brevity, we show the magnitudes of 4 NBs and 2 BBs (colored dots) of J-NEP and their corresponding fits (dashed black lines).We get highly similar results for every filter in J-NEP and all pointings of miniJPAS.
valid due to the logarithmic nature of the magnitude system.A few examples of these fits can be found in Fig. 1.We generate five versions of our mocks, each one with the uncertainty distribution corresponding to each field of miniJPAS&J-NEP.

Star Forming Galaxies mock
In order to reproduce the population of SFGs, we generate a set of synthetic spectra of galaxies.We use the stellar population models from Bruzual & Charlot (2003), where the stellar continuum of a galaxy is described by three parameters: metallicity, age and extinction (MET, AGE and EXT, respectively).In order to generate a realistic LAEs population, we start from a sample of 397 spectra of LAEs at 2 < z < 5 from the VIMOS VLT Deep Survey (VVDS) and VIMOS Ultra-Deep Survey (VUDS) (Cassata et al. 2011(Cassata et al. , 2015)).We convert all the spectra to the rest-frame, using the spectroscopic redshifts, then stack them to obtain a composite spectrum.We fit the stacked spectrum to a grid of templates in MET, AGE and EXT using a Markov Chain Monte Carlo algorithm (MCMC). 2 The positions of the walkers in the final steps of the chain in the parameter space describe a disperse distribution of the most likely combinations of MET, AGE and EXT to reproduce the continuum of a SFG LAE.First we use the triplets of parameters sampled from this distribution to interpolate the Bruzual & Charlot (2003) templates and generate the normalized spectral continua of our mock catalog of SFG LAEs.
In a second step, we add the Lyα emission lines to the spectra, following the expected distributions for L Lyα and equivalent width.We sample values of L Lyα from the best Schechter fit in Sobral et al. (2018): log 10 (Φ * /Mpc −3 ) = −3.45,log 10 (L * /erg s −1 ) = 42.93,α = −1.93.The Lyα LF has been proven to show little variation with redshift at z = 2.5-7 (Sobral et al. 2017;Drake et al. 2017;Sobral et al. 2018;Ouchi et al. 2020).In Appendix C we discuss the effect of assuming this prior LF at z = 2-2.5.We sample values of Lyα EW 0 from an exponential distribution, where N 0 is a normalizing factor and α = 129 Å (see Zheng et al. 2014;Santos et al. 2020;Kerutt et al. 2022).The fluxes of each object are re-scaled applying a multiplicative factor so that the integrated line flux F Lyα and the observed equivalent width (EW) follow the definition: where f λ Lyα and f λ cont.are the flux densities of the Lyα line and the continuum, respectively.The approximation at the rightmost part of Eq. 3 assumes a flat continuum over the width of the emission line.The relation between the observed EW and the rest-frame equivalent width is EW = EW 0 • (1 + z).The redshift values are sampled from a distribution within z ∈ [1.9, 4.5] such as the number density per unit volume is constant.Finally, the Lyα line is added as a gaussian profile with σ = 5 Å (see e.g., Gurung-López et al. 2022;McCarron et al. 2022;Davis et al. 2023) and the adequate integrated flux to match the required L Lyα .
The result is a sample of synthetic spectra of SFG LAEs at 2 < z < 4 that mimics the Lyα LF measured by Sobral et al. (2018) over 400 deg 2 .All these spectra are convolved with the transmission curves of the J-PAS filters in order to obtain a mock catalog of fluxes.Then, the uncertainties are added as detailed in Sect.3.1.

QSO mock
For the construction of our QSO mock we follow a very similar procedure to that used in Queiroz et al. 2023.In their work, they provide mock catalogs of QSOs (0 < z < 4.2), morphologically point-like galaxies and stars for miniJPAS, based on the SDSS DR12Q Superset (Pâris et al. 2017).We build a new QSO mock catalog following Queiroz et al. (2023) instead of using the already available mock for various reasons.In the first place, our mock needs to accurately represent the L Lyα distribution of the QSO population at z > 2. Secondly, we add the flux uncertainties according to Eq. 1 in order to be consistent with the rest of the populations in our mocks.Finally, we need to substantially increase the size of the mock sample in order to obtain significant statistics, as explained below.
Our aim is to generate a set of QSOs with redshifts z = 0-4.5.For this, we use spectra from the SDSS DR16Q Superset (Lyke et al. 2020).We select all sources with good median signal-tonoise over all pixels (SN_MEDIAN_ALL>0), so we can neglect the errors of the spectroscopy when performing the synthetic photometry; no redshift warning flags (ZWARNING=0); and classified as QSO by the SDSS pipeline (IS_QSO_FINAL=1).We sample values of z and r magnitude from the 2D PLE+LEDE model in Palanque-Delabrouille et al. (2016).This model predicts the number counts of detected QSOs in a photometric survey as a function of magnitude and redshift per unit area.We compute the total number of objects to include in the mock by integrating the Palanque-Delabrouille et al. ( 2016) model over an area of 400 deg 2 .For QSOs with log 10 (L Lyα /erg s −1 ) > 44, due to the exponential drop of sources at this luminosity, we use a 10 times bigger area for better statistics.For each pair of values (z, r), a source is selected randomly from the SDSS DR16Q within a redshift interval smaller than 0.06, then the spectral flux is corrected by a multiplicative factor in order to match the sampled value of r.
As shown in the top panel of Fig. 2, the resulting QSO mock yields a 2 < z < 4 distribution in line with a Schechter function for Lyα line luminosity.The depth of SDSS is lower than that of miniJPAS and J-NEP, and their catalog is only complete up to r ∼ 20.5.Hence, to obtain sources up to r = 24, we need to largely correct some objects under the assumption of a weak dependecy of the QSO properties with luminosity (for a similar procedure and discussion see Abramo et al. 2012;Queiroz et al. 2023).The bottom panel of Fig. 2 shows that the distribution of L Lyα of the QSO mock extrapolates reasonably at r ≳ 22, far out of the range of SDSS.

Low-z Galaxy mock
As stated at the beginning of Sect.3, a significant part of the contaminants are expected to be low-z galaxies (z ∼ 0-1) with prominent emission lines, especially at the faintest regime of the Lyα LF.To reproduce this population, we generate a synthetic miniJPAS observation, analogous to that designed by Izquierdo-Villalba et al. ( 2019) for the J-PLUS survey.In our case, the mock-observation is built over a total area of 3 deg 2 , by employing the L-Galaxies semi-analytic model (Guo et al. 2011;Henriques et al. 2015) to predict the continuum features of galaxies over the halos of the Millennium N-body dark matter simulation (Springel et al. 2005), selecting the line of sight oriented at RA = 58.9deg, DEC = 56.3deg.This simulated observation directly produces synthetic photometry of all the 60 miniJPAS filters for a catalog of 144 183 galaxies with magnitude r < 24 and z < 4 (∼ 90% of which are at z < 1).For simplicity, hereafter we refer to this mock-observation as "lightcone".
The nebular emission lines of the galaxies in the lightcone are computed using the method of Orsi et al. (2014), which employs the Levesque et al. (2010) model for H ii regions in order to compute the output line fluxes of simulated galaxy spectra.Several emission lines are considered, including the potential interlopers of a LAEs sample (e.g., H β, [O iii] and [O ii], as stated in Sect.3).These line fluxes are corrected with an empirical dust attenuation model in order to reproduce the H α, H β, [O ii] and [O iii] luminosity functions from several observations.This dust model performs well for almost every galactic line for a wide range of redshift.However, as discussed in Izquierdo-Villalba et al. (2019), this dust model tends to overcorrect the line flux in the case of [O ii] for z ≤ 0.5, the interval in which this line has particular relevance for our work.In order to avoid underestimating the fraction of contaminants, we remove the dust attenuation coefficient from the [O ii] lines in our mock for z < 0.5.By doing so, the [O ii] LF is better reproduced in the lightcone, for this specific redshift interval.

Methods
In this section, we describe our methods to obtain a LAE sample in miniJPAS&J-NEP and estimate the Lyα LF.The parameters used in this pipeline were chosen to optimize the selection of LAEs, after extensive testing using the mocks described in Sect.3. In this section we also characterize the candidate sample obtained from the observations and provide the catalog of LAEs.

Candidate selection method
In this subsection, we describe the procedure we use to select sources from the miniJPAS&J-NEP catalogs, and classify them as LAEs.In the first place, in Sect.4.1.1we define a parent sample from which to perform the selection.Second, in Sect.4.1.2we explain how the continuum flux is computed.Finally, in Sect.4.1.3we enumerate the criteria for selecting candidates based on NB flux excess with respect to the continuum.

Parent sample
Our LAE candidate selection is based on the dual mode catalogs of miniJPAS and the J-NEP field (see Sect. 2.2).We remove every source flagged by the catalog masks.The masks cover the window frames, artifacts, bright stars and objects near them.We also remove objects marked with SExtractor photometry flags.After this first cut, we are left with a total of 63 923 objects: 46 477 in miniJPAS and 17 446 in J-NEP.
We continue the preliminary cuts by requiring 17 ≤ r ≤ 24.Sources fainter than this threshold may have very low signal-tonoise to be classified reliably; r ∼ 24 is the 5σ detection limit for miniJPAS&J-NEP (see Table 1).On the other hand, we expect the number of LAEs at z ≥ 2 with magnitudes brighter than r = 17 to be very low (see Fig. 2).At these bright magnitudes, the number counts will be dominated by stars (see, e.g., Fig. 18 of Bonoli et al. 2021).For this reason, we remove these bright sources which are very likely to be stars.In any case, the exact value for this bright cut is somehow arbitrary.
Objects showing significant proper motion or parallax are likely to be stars.We remove these objects making use of the cross-match tables of the miniJPAS&J-NEP dual mode catalogs with the the Gaia survey Early Data Release 3 (EDR3) (Gaia Collaboration et al. 2021).Among all the non-flagged sources in the miniJPAS&J-NEP dual catalogs, only 2 739 (4.3%) have a counterpart in Gaia EDR3.In the spectroscopic follow up program of Spinoso et al. (2020), it was found that stars constituted a non-negligible part of the NB emitters sample from J-PLUS.Therefore, we remove secure stars following Spinoso et al. 2020, imposing where σ pmdec , σ pmra and σ µ are the relative errors of the proper motion in declination and right ascension and parallax, respectively.
After these cuts the dual-mode catalogs we are left with 36 026 sources in total (28 447 in miniJPAS and 7 549 in J-NEP).This constitutes our starting sample for the selection of LAE candidates.

Continuum estimation
In order to find emission lines within the sources of the miniJPAS&J-NEP catalogs, we look for NBs with a reliable flux excess with respect to the continuum flux at the central wavelength of those NBs.The continuum flux density can be estimated using the information from the filters near the narrow band of interest.In particular, for a given NB filter n, we compute the continuum estimate f λ cont by considering an equal number k of NBs both at bluer and redder wavelengths than n.We obtain f λ cont as the weighted average of this set of 2k NBs, after excluding the two NBs directly adjacent to n, on each side.The reason for excluding these two NBs is that emission lines can be broad enough to be detected in more than one NB at a time, as in many cases of QSO's Ly α lines (see e.g., Greig et al. 2016).Narrow emission lines can also contribute to more than one NB due to the overlap of the transmission curves of the J-PAS filters.
We chose to set k = 6, so that our f λ cont estimate is based on 12 NBs.With this number of NBs, we cover the widest wavelength range possible without contamination of other luminous lines near Lyα (O vi+Ly β and C iv).We underline that the 7 NBs at the bluest-end of the miniJPAS filter set do not have enough NBs on their bluer side.In these cases we still use the same computation described before, but only with the available filters; this leads to a bias in the line luminosity estimation that will be corrected later on, as detailed in Sect.4.2.
We note that by estimating f λ cont as the average flux around the wavelength of the emission line we are implicitly assuming that the continuum has an anti-symmetric shape with respect to that wavelength.However, at bluer wavelengths than the observed λ Lyα the effect of the Lyman-alpha forest comes into play.The Lyα forest is a series of absorption lines caused by the scattering of the Lyα photons by neutral hydrogen in the intergalactic medium (IGM) (see e.g., Weinberg et al. 2003;Gurung-López et al. 2020).The Lyα forest cannot be resolved through NB photometry, but its overall effect is a significant attenuation of the measured flux in a given band.The effective transmission of the IGM due to the Lyα forest can be approximated with an Fig. 3: Color distributions of the selected candidates in our mock before applying the color cut.The objects in the shaded area are removed from the sample after applying the cut.Through these BB color cuts we remove objects showing significant red colors, which are likely to be nearby galaxies.
exponential law, with a = −0.001845and b = 3.924, as found by Faucher-Giguère et al. (2008).Having this in mind, we can compensate the attenuation due to the Ly α forest on our continuum estimate.We do this for each of the NBs i which are at bluer wavelengths than n.In particular, we divide the flux f i by the IGM transmission computed at the central wavelength of the i-th NB (λ i ).That is: Then, the continuum flux density is estimated as where Correcting for the average IGM transmission allows us to both: i) improve our continuum estimate and reduce the bias on our Lyα luminosity estimate and ii) discard low-z contaminants from our selection.Indeed, the latter do not suffer from the Lyα forest effect, therefore our correction produces an artificial over-estimation of their continua.This translates into an underestimate of their measured EW, pushing these sources out of our selection cut.

LAE candidate selection criteria
After the estimation of the continuum for every source at the central wavelength of every NB, we check every filter for a reliable excess that is compatible with a Lyα emission line.The criteria of this selection are the following: -3σ flux excess: The NB flux density, f λ NB , must show an excess with respect to the continuum f λ cont larger than a 3σ confidence interval (see e.g., Bunker et al. 1995;Fujita et al. 2003;Sobral et al. 2009;Bayliss et al. 2011).That is: where σ NB and σ cont are the uncertainties of the NB and continuum fluxes.When multiple NBs satisfy this condition in one source (either in adjacent or non-contiguous NBs), we consider as a candidate Lyα emission only the NB with the highest measured flux.We adopt this criterion under the assumption that Lyα is the most luminous line in the optical range for z > 2 QSOs, and the only relevant line in the case of SFGs.Then, we assign a redshift z NB assuming λ pivot of the detection NB as the observed Lyα wavelength.-Minimum S/N: In addition to the NB-excess significance, we impose a minimum signal-to-noise ratio of S/N > 6 for the NB where we identified the line detection.This ensures that the photometry in the selected filter is clean and reliable.
Lowering this threshold significantly increases the number of spurious detections due to random fluctuations of the photometric fluxes.-EW 0 cut: Ly α has a large intrinsic EW 0 in comparison to other galactic emission lines (Vanden Berk et al. 2001;Nakajima et al. 2018).Many past works have imposed a minimum EW 0 in order to reduce the number of contaminants (e.g., Fujita et al. 2003;Gronwall et al. 2007;Ouchi et al. 2008;Santos et al. 2016;Sobral et al. 2018;Spinoso et al. 2020).Following these approaches, we impose: EW 0 > EW min 0 .From the definition of EW we can derive where z NB is the Lyα redshift associated with the selected NB.We choose a cut at EW min 0 = 30 Å. Lowering the value of EW min 0 significantly increases contamination without a meaningful increase in completeness.
-Multiple line combinations: Some sources of our catalog show multiple NB excesses compatible with emission lines.The ratios between the observed wavelengths of the multiple lines in a given source can be used to identify contaminants or to confirm true positive LAE detections.Indeed, SFG LAEs are not expected to show relevant line emission features other than Ly α in the rest-frame UV (Nakajima et al. 2018) et al. 2001;Nakajima et al. 2018).Therefore, as shown in Fig. 3, both classes of LAEs are likely to present bluer broadband colours than the low-z galaxy contaminants.This allows us to define a set of colour cuts to remove part of these contaminants.We keep only sources with r −i < 0.6∧g−r < 0.6 when selecting candidates with z Ly α < 3.At z Ly α > 3 the Lyα forest affects the flux of the g band and this propagates into the expected colors.The color cut at z Ly α > 3 is defined as r − i < 0.6 ∧ g − r < 1.5.However, if a source has multiple line detection compatible with QSO lines, this color cut does not apply and the object is classified as a true QSO LAE.

Lyα luminosity estimation
The flux of a NB selected as a Lyα emission-line candidate contains the contribution of both the line flux and the continuum.Therefore, we estimate the Lyα integrated flux as: This equation implicitly assumes that the NB transmission curve can be reasonably approximated by a squared top-hat filter (as in the case of the J-PAS NBs, see Bonoli et al. 2021).Then, the Lyα luminosity is obtained as where d L is the luminosity distance corresponding to the Lyα redshift associated to the wavelength of the detection NB, according to our cosmology.
There are several factors that can affect the estimation of L Lyα : the variable width of the Lyα line, the uncertain position of the line center with respect to the NB transmission boundaries, the chosen photometric aperture and the uncertainty on the continuum estimate, among others.In addition to that, QSOs often show rather strong N v emission lines (λ 1240 Å) that contaminate the Lyα measurement.While in most spectroscopic surveys it is possible to resolve the Lyα and N v line profiles separately, both lines cannot be disentangled with NB imaging, thus N v significantly affects the Lyα flux measurement in QSOs.As a consequence, our NB-estimated Lyα line flux actually includes the sum of both contributions: F Lyα+N v .We account for these biases on our measured L Lyα by computing the median offset between the estimated and real values for our mock LAEs (L intrinsic Lyα ), as a function of L Lyα , This bias is computed in bins of log 10 (L Lyα /erg s −1 ) and subtracted from the L Lyα measurement.Fig. 4 shows the measured log 10 (L Lyα /erg s −1 ) distribution from the mock as a function of the intrinsic luminosity.Since there is no clear way to systematically disentangle QSOs from SFG LAEs in our sample, we apply the same correction indistinctly.

Purity and completeness
We compute the purity P of our mock sample as and the completeness C as where TP, FP and FN are the number of true positive, false positive and false negative detections, respectively.After applying the selection method to our mocks, we can estimate the purity and completeness curves of the selected sample for each filter, and for the whole set as a function of L Lyα .
In Fig. 5 we show the purity (top panel) and completeness (bottom panel) of our selection method as a function of the Lyα luminosity for the whole sample (r < 24, 2.05 < z < 3.75).We also show the purity and completeness for the 6 bins of redshift used to compute the Lyα LFs.The redshift intervals are composed of groups of 5 NBs, as listed in Table 2.All the redshift bins exhibit a similar behaviour: the completeness increases with L Lyα , reaching values of ≳ 75% for log 10 (L Lyα /erg s −1 ) ≥ 44 for 2 ≲ z ≲ 3.3, and for log 10 (L Lyα /erg s −1 ) ≥ 44.5 at 3.1 ≤ z ≤ 3.8.The sample purity also increases with L Lyα for all redshift bins, with a slight decline for the brightest luminosity in some intervals (see Fig. 5, top panel).The drop in purity at the bright-end can be explained by the overestimation of the line luminosity of the contaminants (for example, a C iv emitter at z = 1.7 with log 10 (L C iv /erg s −1 ) = 44 will appear to have log 10 (L C iv /erg s −1 ) = 44.4 if we assume its redshift to be z = 2.5).This effect is increased by the rather high uncertainties on the line flux measurements in combination with the Eddington bias (Eddington 1913).Interestingly, for z ≳ 2.8 the estimated purity reaches values very close to 1 for the brightest Lyα luminosity.This can be explained by the fact that the potential contaminants in this luminosity regime are QSOs with z > 2 for which the selected feature is the C iv.We note that most of these sources are classified as LAEs at their correct redshift by our selection pipeline.

2D purity and number counts correction maps
We apply our selection method (see Sect. 4.1) to the mock in order to characterize its performance as a function of r magnitude and measured L Lyα , in terms of purity and number count correction.We build 2D maps of these two quantities over a grid of (r, log 10 (L Lyα /erg s −1 )) values, that will be used in the Lyα LF computation.
Table 2: Groups of NBs used in this work for the computation of the Lyα LF, their associated redshift coverage of Lyα, and the comoving volume of the Universe sampled by those redshift intervals for an area of 1.14 deg 2 .Each batch is composed by 5 contiguous NBs.Two subsequent batches have 2 NBs in common, thus their redshift coverage is partially overlapped.
Fig. 5: Purity and completeness as a function of L Lyα of the full retrieved sample at 2.05 < z < 3.75.We show the values of purity and completeness for the whole redshift range in black solid lines, and for each redshift interval used in colored solid lines.We represent an additional redshift interval to show the trend beyond the redshift range probed by this work (dashed line).
As a first step, we compute the purity (P 2D ) of the sample in bins of (∆r, ∆ log 10 L Lyα ), according to Eq. 12.We consider as true positives the objects detected inside a given interval of (∆r, ∆ log 10 L Lyα ) with a minimum Lyα EW 0 = 30 Å, whose redshift measurement is correct within a confidence interval of ∆z = 0.12 3 .As a second step, we define the number counts correction (w 2D ) as the ratio between the number of eligible LAEs inside a given interval of r and log 10 (L Lyα /erg s −1 ) and the number of true positives retrieved by the selection inside that interval.This number-counts correction can be seen as the inverse of the completeness as a function of measured L Lyα , defined in Eq. 13.Due to the uncertainties on the estimation of L Lyα , some bins of this map contain values below 1, meaning that in some regimes we might get a larger number of true positives than the intrinsic number of LAEs.
We show an example of these correction maps in Appendix B. In general terms, the purity of the sample increases with L Lyα and r.This is because for a fixed value of L Lyα , fainter magnitudes mean larger equivalent widths and therefore, our selection method is more successful in retrieving true LAEs at these regimes.For the brightest magnitudes the purity increases again due to the low relative errors of the photometry, which allow to reliably discern between true positives and contaminants.

Computation of the Lyα luminosity function
We compute our Lyα LF through several realizations in order to take into account the various sources of uncertainty and variability.At each realization, we perturb the estimated values of L Lyα assuming Gaussian errors.Then, every selected LAE candidate is included in the current sub-sample with a probability based on the 2D purity, that is inferred from the r magnitude and the perturbed log 10 (L Lyα /erg s −1 ) (see Sect. 4.4).For the candidate j, let us define p j as where ξ j is a random number drawn from a uniform distribution in the interval Next, each source is weighted with a value w j , computed as where w 2D is the number count correction (as defined in Sect.4.4) and C int the intrinsic completeness of the survey.The value of C int is computed for point-like and extended sources separately in miniJPAS (see Bonoli et al. 2021).This process is done equivalently for J-NEP (see Hernán-Caballero et al. 2023).We assign every LAE candidate a value of C int using the mini-JPAS and J-NEP completeness curves, in terms of r magnitude and the field in which the object was detected.Our target population are LAEs at z > 2, these objects are expected to appear point-like in the BB images of miniJPAS&J-NEP.Hence, we use the intrinsic completeness curves for point-like objects.
Each NB can probe Ly α in an effective range of redshift equal to (λ NB ± 0.5 • FWHM NB )/λ 0 − 1.The volume (V) considered for the LF is the comoving volume comprised between those redshifts in the survey area, according to our cosmology.Given that the number count of candidates is not large enough to accurately estimate the LF at each NB independently, we combine several NBs to build the LF.The associated redshift range of each group of NBs goes from the minimum z of the bluest filter to the maximum z of the reddest.Adjacent miniJPAS NBs show significant overlap (∼ 45 Å).As explained in Sect.4.1.3,in case of multiple line detections in adjacent NBs, we assign the Lyα line to the NB with the highest measured flux.Therefore, the effective volume probed by a single NB in the wavelengths of the overlaps is halved.
The ith iteration of the LF Φ i is computed as follows: where the sum extends to all the objects with a perturbed L Lyα falling inside a given luminosity bin.After performing 1000 realizations, our final LF (Φ) is built with the median values of Φ i for each luminosity bin.
For estimating the Φ uncertainties we have to take into account the contribution of: (i) the spatial variance of the candidates in the surveyed area (commonly referred to as "cosmic variance"), (ii) the uncertainty of L Lyα estimation and (iii) the shot noise of the candidate sample.In order to estimate the contribution of (i), we divide our candidate sample in 5 sub-samples.First, we split the miniJPAS footprint in 4 regions of equal angular area.Then, the candidates are assigned to 4 different subsamples according to the split region they belong.The 5th subsample is that of the J-NEP candidates.After that, we perform 1000 realizations of Φ i , each time using the candidates of 5 random sub-samples with repetition.On each realization, we resample the candidates of each sub-sample using the bootstrap technique and we also perturb L Lyα as explained above.The final uncertainties on our LFs are inferred via the 16th and 84th percentiles of the Φ i distribution.

Lyα emitters candidate sample
The result of the preliminary selection is a sample of 135 candidates (38,19,22,14 and 34 in AEGIS001, AEGIS002, AEGIS003, AEGIS004 and J-NEP, respectively) with redshifts between 2.05 and 3.75.Eight of these selected candidates were removed immediately after a first visual inspection, because their NB images were clearly affected by cosmic rays or artifacts, leaving a sample of 127 candidates.
In Fig. 6 we show examples of miniJPAS&J-NEP sources in order to illustrate the populations retrieved by our selection method.The five objects on the left column (1-5) are examples of genuine QSO LAEs.Three of them have SDSS/HETDEX spectroscopic confirmation.Candidates 1-4 have secondary QSO line detections that support the Lyα redshift estimation (see Sect. 4.1.3).Candidate 5 lacks spectroscopical confirmation or other QSO line detection, however, through visual inspection we determined the presence of spectral features consistent with QSO emission lines, given the estimated Lyα redshift (O vi+Ly β, Si iv+O iv, C iv). Candidates 6-9 are examples of QSO contaminants selected because of their strong C iv or C iii] emission.In the particular case of candidate 9, our method detects a secondary line consistent with Mg ii, given that the selected NB is spectroscopically identified as C iii] at z = 1.03.Hence, candidate 9 is effectively not selected by our pipeline.Finally, candidate 10 is an example of a contaminant [O ii] emitter.A visual inspection reveals that this candidate shows a relevant feature consistent with H β and [O iii] emission lines, if we assume the selected NB is [O ii] at z = 0.54.Moreover, candidate 10 shows significant emission at bluer wavelengths than its strong emission line at λ obs ≈ 5800Å.Therefore, it is unlikely that this line is Lyα, due to the absence of the expected decrease of flux due to the Lyα forest, and beyond the Lyman limit break at λ 0 < 912 Å (λ obs ≪ 5800Å for the assumed Lyα redshift of z Lyα = 3.69; see the photometric drop at λ obs < 4200Å in the photospectrum of candidate 3, in the central left panel of Fig. 6).

Sample contamination
As discussed in Sect.3, we expect the interlopers of our selection to be mainly low-z galaxies and z < 2 QSOs.Through the analysis of the selected sample in our mock, we can describe the predicted populations of contaminants.
Due to its typically high intrinsic luminosity, the C iv line is the QSO feature which mainly contributes to the contamination of our samples (see Vanden Berk et al. 2001), followed by C iii], and in a lesser amount, Mg ii and O vi.This can be clearly seen in Fig. 7, which presents the number of objects in the mock classified as LAEs by our method, as a function of the rest-frame wavelength of the selected feature.This is in line with the results of the spectroscopic follow-up presented in Spinoso et al. (2020), which show that C iv is the main source of contamination for samples of bright, NB-selected, LAE candidates.The contaminants whose NB wavelength does not correspond to any relevant QSO spectral feature are selected because of the scatter of NB fluxes due to random fluctuations.This causes either: (i) the flux of a NB to incidentally exceed our 3σ detection limit or (ii) produce an under-estimation of the continuum.
Regarding low-z galaxy interlopers, Fig. 7 shows that several galaxies are selected as LAE candidates at a redshift which is not associated to any specific emission line, with the exception of a small peak at the [O ii] wavelength.Therefore, most of the low-z galaxy contamination can be explained as false line detections caused by noise.On the other hand, many candidates in our observational sample might show extended BB emission, which classifies them as low-z galaxies.These wrongly selected candidates can be easily removed via a posterior visual inspection (see Sect. 4.11).

Spectroscopic counterparts
We cross-match the miniJPAS&J-NEP catalogs with the spectroscopic catalogs of SDSS DR16 and HETDEX in order to characterize our candidate sample.

Cross-match with SDSS DR16
We cross-match with the SDSS DR16 source catalog (Lyke et al. 2020), using a search radius of 1.5 ′′ among the whole catalog of miniJPAS.As a result, 32 (17 with log 10 (L Lyα /erg s −1 ) > 44) sources are identified as QSO LAEs by SDSS (i.e. sources with redshift in the range z spec = 2.1-4, no redshift warnings and a significant Lyα measurement).Among these 32 sources, 17 are selected by our method (53%), and 13 out of 17 (76.5%)within the ones with log 10 (L Lyα /erg s −1 ) > 44.This retrieval rate is in agreement with the completeness estimated by our mock (see Fig. 5), considering the statistical uncertainties and cosmic variance.

Cross-match with HETDEX Public Source Catalog 1
We also cross-match the miniJPAS catalog with the HETDEX Public Source Catalog 1 (Mentuch Cooper et al. 2023).This catalog contains the spectra of 232 650 sources observed by the HETDEX program (Gebhardt et al. 2021) over 25 deg 2 .The footprint of the HETDEX catalog partly overlaps with mini-JPAS.We find 158 objects within a radius of 1.5 ′′ of any miniJPAS source with a reliable spectroscopic redshift measure according to the HETDEX catalog (z_hetdex_conf > 0.9).Among these objects, 22 are labeled as AGNs by HETDEX and 12 have z spec > 2. Within our selection, 10 objects have a HET-DEX identification: 9 AGNs and one [O ii] emitter.Finally, 5 of the 9 spectroscopically confirmed AGNs have z > 2 and clear Lyα emission line measurements.This numbers translate into a ∼ (41 ± 22)% recovery rate of AGNs with z > 2, and a purity of ∼ (56 ± 30)%.
Moreover, the cross-match with HETDEX reveals the presence of 17 SFG LAEs (z_hetdex_conf > 0.9) in the dual mode catalogs of miniJPAS.However, none of them is detected in our  sample.This is because all these SFG LAEs are too faint both in Lyα luminosity and r magnitude to be selected by our method.Indeed, they all show log 10 (L Lyα /erg s −1 ) ≲ 43.2 and rSDSS magnitudes close or below the miniJPAS nominal depth (see Table 1).Hence, the signal-to-noise of these sources photometry is overall too low for them to be detected by our selection pipeline.

Spectroscopic characterization of the LAE candidate sample
Within our candidate sub-sample, we find an SDSS counterpart for 41 out of 127 LAE candidates, all of which are identified as QSOs at any redshift by SDSS.HETDEX counterpart, confirming that z < 2 AGN emitting C iv or C iii] (misclassified as Lyα) are the main source of contamination for our pipeline results.There are no spectroscopically confirmed contaminants at z Lyα ≥ 3, which is in line with the high-purity we estimate for our samples at these high redshifts (Fig. 5).In the bottom panel of Fig. 8 we show the offsets between the NB Lyα redshift of our candidates and the SDSS spectroscopic redshift.For LAEs at z ∼ 2, the observed Lyα wavelength could lay slightly below the lower limits of our survey.In some of those cases, we still detect the redmost part of the line, often affected by the N v flux.For this reason, we notice a small bias in the measured redshift for LAEs with z spec ≲ 2.1 (see the bottom panel of Fig. 8).At higher redshifts, z NB is a good esti- ).We show spectroscopically confirmed LAEs (green filled circles) and contaminants (red empty circles), objects with extended morphology (morph_star_prob<0.1;blue empty squares), and sources without any spectral or morphology identification (gray crosses).The dashed lines mark the confusion between Lyα and typical galactic emission lines.
mator within the interval of confidence given by the width of the NBs.The mean offset of z NB with respect to z spec is |∆z| ≈ 0.013, about a 20% of the z NB uncertainty.
In Fig. 4 we show the comparison between the measured and spectroscopic log 10 (L Lyα /erg s −1 ) from SDSS DR16Q, compared to mock distributions.This figure shows that the estimation of log 10 (L Lyα /erg s −1 ) in the spectroscopic subsample of our candidates is consistent with the results in the mock.

Photometric redshifts
The miniJPAS and J-NEP dual-mode catalogs provide accurate photometric redshifts for galaxies in the interval z = 0-1.5 (Hernán-Caballero et al. 2021, 2023).These photo-z have been obtained using a template-fitting method which employs a sample of 50 galaxy templates.Fig. 9 shows the photo-z of the LAE candidates as compared to the redshifts obtained from the NB central wavelengths, assuming that the detected line of a candidate is Lyα.From this figure it is not evident any clear pattern which may help to identify a systematic source of contamination; this is in agreement with the results of the contamination analysis of the mocks, that predicts a rather flat distribution in the selected rest-frame wavelengths of the galactic contaminants, with a small peak in the [O ii] line (Fig. 7).On the other hand, the current photo-z code does not account for QSOs, hence they are not useful to confirm QSO LAEs or contaminants; most of the sources with z phot = 1.5 are likely to be QSOs with bad fit of the photo-z.For the same reason, the photo-z values exhibit arbitrary correspondence with the redshifts of our candidates having spectroscopic counterparts.(green filled circles in Fig. 9).Analogously, the photo-z are not useful to confirm SFG LAEs because their redshift (z > 2) is far out of the working range of the miniJPAS photo-z code.

Morphology cut
We notice that some of our candidates have visually evident extended emission in their BB images.The population of LAEs at z > 2 is expected to appear point-like given the the expected observed size of either high-z QSOs or SFG LAEs, and the average PSF of miniJPAS&J-NEP.Hence, the candidates clearly showing BB extended morphologies are very likely to be lowz contaminants.In order to remove this kind of objects from the Lyα LF estimation, we make use of the star-galaxy estimator morph_prob_star (López-Sanjuan et al. 2019), available in the miniJPAS&J-NEP catalogs.We only keep objects with morph_prob_star > 0.1.With this cut we remove 36 extended objects (28.3% of the selected sample), leaving a sample of 91 LAE candidates.To perform such morphology cut in the mock sample is not possible due to the lack of photometric images for the mock sources.However, the corrections for the Lyα LF can be recomputed taking into account the morphology cut, and other posterior catalog cuts (see Sect. 4.11).
On the other hand, LAEs often present NB extended emission in the Lyα observed wavelength (see, e.g., Haardt & Madau 1996;Borisova et al. 2016;Arrigoni Battaia et al. 2016) -not to be confused with extended BB continuum emission-.The recent work of Rahna et al. (2022) presented the Lyα extended emission of two miniJPAS QSOs showing double-core Lyα emission (z = 3.218, 3.287); both objects are detected by our pipeline and included in our catalog.

Visual inspection
We perform a visual inspection of the images and photospectra of the 127 initial candidates.We identify 39 objects in our sample as nearby galaxies either by their extended BB morphology or by their spectral features (e. g. emission lines not detected by our method, the presence of a 4000 Å break etc.), 36 of which are already systematically removed by a cut in morph_prob_star > 0.1 (see Sect. 4.10).Another 21 objects are clearly identified as contaminant QSOs at z < 2. Finally, 32 objects are visually classified as secure QSOs with Lyα emission.The remaining 35 objects do not have a secure classification due to having very noisy continua and/or unclear BB images.We remove the visually confirmed contaminants, leaving a sample of 67 objects.The visual inspection of the candidates is aided by the spectroscopic counterparts of SDSS and HETDEX (Sect.4.8).
After removing the visually selected contaminants, the purity of the final sample increases.Our mock selection predicts number counts of 53, 23, 59 and 4 deg −2 for QSO LAEs, contaminant QSOs, low-z galaxies and SFG LAEs, respectively, in the effective area of miniJPAS&J-NEP.Hence, we conclude that after a visual inspection, we are able to remove ∼ 80% of the QSO contaminants and ∼ 58% of the low-z galactic contaminants.The 35 unidentified objects are consistent with the remaining ∼ 42% galaxies and the visually unidentified LAEs predicted by our mock selection.These purity estimates are reasonable within the sampling error of our method.We recompute the 2D purity and number count (see Sect. 4.4) of the remaining sample assuming the above fractions of removed galaxy and QSO contaminants.We underline that the Lyα LFs we present in Sect.5.2 are estimated using the sample of 67 candidates obtained after our visual inspection of the photospectra and NB images.

miniJPAS&J-NEP LAEs catalog
In Table 3 we show the number of candidates after applying every cut described in Sect.4.1.3.The last three columns of this table display the number of candidates in three relevant subsamples for this work with, respectively: 127, 91 and 67 candidates.The first sub-sample is the direct result of applying the selection method to the miniJPAS&J-NEP catalogs, before the morphology cut.This first sub-sample will be used throughout Sect. 5 to compare with the mock results.The second subsample, composed of 91 candidates, is obtained after applying the morphology cut to the previous one.In Table A.1 we provide the catalog of sources in this sub-sample.Finally, we obtain the third sub-sample of 67 candidates, after performing a crossmatch with available spectroscopic surveys and a visual inspection for further contamination removal.Nonetheless, in future J-PAS observations the available spectroscopic data can be limited.Also the volume of data can be large enough to make a visual inspection of all the candidates not feasible.The sample presented in Table A.1 could therefore be intended as representative of what can be statistically obtained from any J-PAS data set.

Results and discussion
In this section, we describe the relevant features of the LAE candidate sample and we present the Lyα LF.We also fit our Lyα LF to a Schechter function and a power-law and give an estimation of the AGN/SFG fraction as a function of Lyα luminosity.Finally, we discuss the expected performance of the method described through this work in future data releases of J-PAS.

EW 0 distribution
We obtain the rest-frame Lyα EW from the measured F Lyα , following Eq. 3. As stated in Sect.4.1.3,one of the criteria of our candidates selection is a cut in Lyα EW 0 > 30 Å.However, the additional conditions on the NB-photometry S/N and on the line-excess significance (see Sect. 4.1.3)can override the condition on EW 0 , effectively forcing a higher EW 0 limit (especially for faint sources and shallow NBs).
The distribution of EW 0 retrieved from our 127 candidates sample (before applying the morphology cut, in order to match the mock; see Sect.4.12) is shown in Fig. 10.The miniJPAS&J-NEP Lyα EW 0 distribution ( orange dashed line) is in good agreement with the one resulting from applying our selection pipeline to our mock data ( gray dashed line).
Fig. 10 also shows that the selected objects with log 10 (EW Lyα 0 /Å) > 2, are likely to be genuine LAEs, as the distribution of mock-LAEs ( black solid line) becomes closely comparable to the whole mock sample.Moreover, the EW 0 distribution of the selected LAEs in our mock is remarkably close to that of the observational sources visually classified as LAEs.Our retrieved Lyα EW 0 distribution is also compatible with the determinations of Spinoso et al. (2020) and Liu et al. (2022a) for Lyα lines of QSOs with z ∼ 2-3.5.All of our candidates are inside the range EW 0 = 30-400 Å except for one candidate with an extremely large EW 0 of 2379 ± 278 Å.However, this candidate has r = 23.8,very close to the detection limit and the estimation of its continuum flux under the Lyα line is likely to be underestimated (and its error overestimated).Furthermore, despite being in our selection, the purity assigned to this candidate by our method is P 2D = 0, making it irrelevant for the Lyα LF estimation.

Lyα Luminosity Functions
We compute the Lyα LF for every redshift interval listed in Table 2 through the procedure explained in Sect.4.5.We use the candidate sample of 67 objects obtained after the visual inspection (see Sect. 4.11).Using this configuration, the full redshift range at which we probe the Lyα LF is 2.05 < z < 3.75.For z ≳ 3.8, the available QSO data in the SDSS DR16 starts to become scarce, thus limiting the effectiveness of our mock to compute the LF corrections (see Sect. 3.3).Furthermore, the completeness of our sample drops drastically for z ≳ 3.5 (see Fig. 5).With the miniJPAS&J-NEP dataset we are able to estimate the Lyα LF in the intermediate luminosity regime ( 43.5 ≳ log 10 (L Lyα /erg s −1 ) ≲ 44.5).This is the regime where the contribution of Lyα emitting AGN begins to produce a clear deviation from a Schechter exponential decay of the Lyα LF (see e.g., Konno et al. 2016;Sobral et al. 2018;Zhang et al. 2021).Our analysis at the faint end of the LF is limited by the depth of miniJPAS&J-NEP (i.e., r ∼ 24 at 5σ), while at the bright-end (log 10 (L Lyα /erg s −1 ) ∼ 45) our results are limited by low number counts and cosmic variance.In this regime, the determinations of Zhang et al. (2021) and Liu et al. (2022b) present an exponential decay.
As we explained in Sect.4.11, we confidently remove ∼ 75% and ∼ 100% of the contaminants coming from low-z galaxies and QSOs, respectively.For the estimation of the Lyα LFs, we remove the securely identified contaminants from the candidate sample, and correct the 2D purity estimates according to the fraction of contaminants withdrawn after visual inspection.

Evolution of the Lyα LF with redshift
We stress that our necessity to group NBs in order to increase the number counts in each z bin is only due to the small area surveyed by miniJPAS.On the other hand, we expect that our method will be able to produce a reliable LF determination for each NB as soon as a wide-enough area of the J-PAS survey will be observed.This upcoming possibility will allow to study the Lyα LF evolution with an unprecedented redshift detail.Therefore, the results presented in the following may be regarded as a proof-of-concept for these kind of tomographic analysis of the Lyα LF (further discussion in Sect.5.4).
In Fig. 11 we show the Lyα luminosity functions for different bins of redshift, ranging from z = 2.05 to z = 3.75.We compare our Lyα LF estimates to previous determinations in the literature.Several works explore the faint and intermediate regime of the Lyα LF (43.3 < log 10 (L Lyα /erg s −1 ) < 44), at the transition between the population of SFG and AGN LAEs (Ouchi et al. 2008;Blanc et al. 2011;Konno et al. 2016;Sobral et al. 2017;Matthee et al. 2017).Our measurements of the Lyα LF at every redshift interval is compatible with all of these works.
Our data does not show evidence of evolution with redshift of the Lyα LF within the given uncertainties.In Fig. 12 we show the integral in the range 43.6 < log 10 (L Lyα /erg s −1 ) < 44.8 of the Lyα LFs estimated for each of the six intervals in redshift.The integral is computed as the sum of the LF bins multiplied by the width of the bins.
We also estimate the Lyα LF in the full redshift range covered by our selection.Fig. 13 shows the Lyα LF computed through the usual procedure (see Sect. 4.5) but using all the realizations of the LF of every redshift bin.We compare our results to three past realizations of the Lyα LF which cover similar redshift ranges (i.e. Blanc et al. 2011;Zhang et al. 2021;Liu et al. 2022b).

Schechter function and power-law fits
We use an MCMC algorithm in order to constrain the three parameters of a Schechter function, namely: the normalization Φ * , the characteristic Lyα luminosity L * and the faint-end slope α.As already discussed in Sect.5.2, our ability to reliably sample the bright-end of the Lyα LF is limited by the surveyed area.Our data can measure the Lyα LF up to log 10 (L Lyα /erg s −1 ) ∼ 44.5.Past works have shown that at higher luminosity than this, the Lyα LF shows significant deviations from a simple power-law, either in the form of a Schechter exponential decay, or a "broken power law" (see Spinoso et al. 2020;Zhang et al. 2021;Liu et al. 2022b).Due to this limitation, we use a gaussian with µ = 44.65 and σ = 0.7 as prior distribution for L * , based on the results of Spinoso et al. (2020) and Zhang et al. (2021).We use wide, flat priors for the parameters Φ * and α.We obtain a best fitting Schechter function with log 10 (Φ * /Mpc −3 ) = −6.30+0.48 −0.70 , log 10 (L * /erg s −1 ) = 44.85+0.50 −0.32 and α = −1.65 +0.29 −0.27 .Our constraints on the Schechter parameters are compatible within 1σ to those found by Spinoso et al. (2020) (see Table 4).Our results are as well compatible within 1σ with the analog values obtained by Zhang et al. (2021) fitting the AGN/QSO Lyα LF to a double power-law (DPL).In left panel of Fig. 14 we show our Schechter fit and compare it to the fits in Spinoso et al. (2020) for four NBs of J-PLUS.
The LF estimated by our data in the full redshift range is better described by a power-law.This can be interpreted as our data representing the faint-end of a Schechter function for the QSO/AGN component of the global Lyα LF4 .We fit our Lyα LF for log 10 (L Lyα /erg s −1 ) < 44.5 to a power-law of the form:  We obtain the following results for the power-law fit: A = −0.70+0.25 −0.25 , B = −5.07+0.14 −0.13 .Past works that have fitted a powerlaw in the same regime of the AGN Lyα LF: A = −0.74± 0.17 Matthee et al. (2017); A = −0.75 ± 0.17 Sobral et al. (2018).Our estimation of the power-law slope A, is consistent with these past realizations.

QSO/AGN fraction
Fig. 15 shows the fraction of AGN within the sample of sources with r < 23 extracted from our mock data (blue solid line).At log 10 (L Lyα /erg s −1 ) ≳ 43.75 the fraction of AGN is greater than ∼ 90%.This is in line with past works which analyzed high-z samples of bright LAEs and found that the AGN fraction approaches to 100% at log 10 (L Lyα /erg s −1 ) ≳ 44 (e.g., Matthee et al. 2017;Wold et al. 2014;Sobral et al. 2018;Calhau et al. 2020).By considering the depth of the miniJPAS and J-NEP observations, we conclude that our analysis can primarily focus on the luminosity range log 10 (L Lyα /erg s −1 ) > 43, where the class of AGN/QSOs is expected to be numerically dominant.Hence, if we assume that our power-law fit (see Sect. 5.2.2) describes a regime of the Lyα LF populated entirely by QSOs, we can compute the intrinsic QSO fraction assuming that the SFG population is well described by the Lyα LF presented in Sobral et al. (2018), which is measured in the range 42.5 < log 10 (L Lyα /erg s −1 ) < 44 using a sample of ∼ 3700 LAEs showing no X-ray emission.This result is shown as the green solid line in Fig. 15.The estimated intrinsic QSO fraction drops faster than the fraction in our candidate sample at log 10 (L Lyα /erg s −1 ) ∼ 43.75.This happens because SFGs typically have fainter continua, thus their detection is limited by the magnitude cut of our selection pipeline (r = 24).
Nevertheless, our results can also populate the intermediate luminosity regime of 43.5 ≲ log 10 (L Lyα /erg s −1 ) ≲ 44.5 which, to date, it is yet relatively unexplored (see e. g.Zhang et al. 2021;Liu et al. 2022b).At this "intermediate" luminosity, bright SFG LAEs may still produce some minor contribution to the Lyα LF.Consequently, we can speculate that our candidate samples contain a small fraction of SFGs.Nevertheless, systematic spectroscopic confirmation of our selected sources would be necessary to draw a definitive conclusion about this point.

Expected results in J-PAS
With the eventual release of the full J-PAS dataset, there will be a significantly larger source catalog available with very similar features to the one of miniJPAS&J-NEP.Therefore, an analogous method to the one described in this work could be applied to the complete J-PAS dataset to build the Lyα LF.The target depth for J-PAS is expected to be slightly shallower than miniJ-PAS and J-NEP, yet a much larger dataset will allow to describe the SFG-AGN/QSO transition of the Lyα LF with better statistics.As to the bright-end, in this work we are limited by the intrinsic scarcity of extremely bright objects in Lyα.In other words, due to the small area sampled by miniJPAS and J-NEP, our LF at log 10 (L Lyα /erg s −1 ) > 44.5 is dominated by shot noise and cosmic variance.On the other hand, a larger dataset will allow to estimate the Lyα LF for every individual NB of the filter set.This has the potential to provide a precise and tomographic analysis of the Lyα LF evolution with redshift.
Our work provides the means to infer the expected results for the first hundreds of square degrees of observed J-PAS data.By integrating the power-law fit of our Lyα LF (see Sect. 5.2.2), we obtain a predicted number count of 72 ± 25 deg −2 of LAEs in the range 43.5 < log 10 (L Lyα /erg s −1 ) < 44.5 at 2.05 < z < 3.75.The mean recovery rate of our method in this range is C ∼ 60%.This results translate into ∼ 4300 recovered LAEs for the first 100 deg 2 , and ∼ 3.7 • 10 5 in the full 8500 deg 2 expected at the completion of the J-PAS survey.On the other hand, our work cannot reliably provide a direct estimate for the number count of objects with log 10 (L Lyα /erg s −1 ) > 44.5.Therefore, for the analysis of the Lyα LF bright-end, we integrate the best Schechter fit of Spinoso et al. (2020).At this bright regime, the exponential decay component of the Schechter function dominates, rapidly decreasing the number of available candidates with increasing L Lyα .The predicted number count of QSOs with Lyα emission is ∼ 24.5 deg −2 for log 10 (L Lyα /erg s −1 ) > 44.5 and ∼ 1.7 deg −2 for log 10 (L Lyα /erg s −1 ) > 45.We define the upper limit L max Lyα as the maximum Lyα luminosity for which the predicted average number of candidates with log 10 (L Lyα /erg s −1 ) > log 10 (L max Lyα /erg s −1 ) in a given survey area is > 1 (at 2.05 < z < 3.75).For 1 deg 2 , this limit is log 10 (L max Lyα /erg s −1 ) ∼ 45.07, consistent with our candidate sample.This limit increases to log 10 (L max Lyα /erg s −1 ) ∼ 45.44 over 100 deg 2 , log 10 (L max Lyα /erg s −1 ) ∼ 45.56 over 1000 deg 2 , and log 10 (L max Lyα /erg s −1 ) ∼ 45.65 over 8500 deg 2 .At this bright-end regime, the estimated completeness of our method is C ≳ 80% (see Sect. 4.3).
Furthermore, as stated before, an increase in the volume of data will allow to measure the Lyα LF in smaller bins of redshift.For example, with the release of the first 100 deg 2 of J-PAS, it will be possible to estimate the Lyα LF for each individual NB up to z ∼ 4 (in intervals of ∆z ∼ 0.12) with log 10 (L max Lyα /erg s −1 ) ∼ 45.2 (log 10 (L max Lyα /erg s −1 ) ∼ 45.54 for 8500 deg 2 ).This will provide a remarkable measurement of the Lyα LF evolution with redshift.

Summary
In this work we developed a method to detect sources with Lyα emission within the J-PAS filter system, and applied it to the J-PAS Pathfinder surveys: miniJPAS and J-NEP in order to estimate the Lyα LF in the redshift range 2.05 < z < 3.75.We summarize here our main results.
First, we build a mock catalog of LAEs and their contaminants in order to test and calibrate the accuracy of our LAE selection method, as well as to compute the corrections needed to estimate the Lyα LF.The mock is composed of four populations: (i) QSOs with z > 2, which are potential LAE candidates; (ii) QSO interlopers, that is, z < 2 QSOs detected via strong emission lines different than Lyα; (iii) SFG LAEs at z > 2 and (iv) low-z galaxies (0 < z < 2).By studying the performance Fig. 14: Schechter and power-law fits of the 2.05 < z < 3.75 Lyα LF.Left panel: Schechter best fit and 1σ confidence region for the fit of the full z range of this work (blue solid line and shaded area).We compare our result with the Schechter fits in Spinoso et al. (2020) for 4 NBs of J-PLUS.Our Schechter fit is in line with the fits in Spinoso et al. (2020) for z = 2.2, 2.5 and 3.2 at the faintest bins of our LF.We advise some caution when considering our results at the brightest luminosity (i.e., log 10 (L Lyα /erg s −1 ) > 45.5).Indeed our results in this regime are limited by our survey area.Right panel: Power-law fit to our Lyα LF at log 10 (L Lyα /erg s −1 ) < 44.5.The bins of the LF represented with empty squares are not used in this fit in particular.We compare to the power-law fits in Matthee et al. (2017); Sobral et al. (2018) in the same L Lyα regime.The shaded blue area marks the 1σ confidence region.Our constraint on the power-law slope A for the faint-end of the AGN/QSO Lyα LF is consistent with the other realizations shown in this plot within a 1σ confidence interval.Fig. 15: Fraction of QSOs in the candidate sample from the mock at 2.05 < z < 3.75.We represent our estimation of the QSO fraction (green solid line and green shaded area for 1σ uncertainty) based on the power-law fit to our Lyα LF and the SFG Lyα LF of Sobral et al. (2018).We also show the QSO fraction extracted from our mocks (blue solid line).We compare our results to previous realizations from past works.of our selection method on our mock, we are able to build 2D maps of purity and number count corrections in terms of L Lyα and r band magnitude (see Fig. B.1).These 2D maps are used in order to compute the corrections for the Lyα LF estimate.
Our method retrieves a sample of 127 LAE candidates with 2.05 < z < 3.75.From our mock, we show that our sample is > 75% complete and > 60% pure at log 10 (L Lyα /erg s −1 ) ≳ 43.75.This sample was obtained from a total effective area of ∼ 1.14 deg 2 .Through a visual inspection of the NB images and photospectra, we confirm 32 candidates as QSO LAEs, 39 as low-z galaxies, 21 as QSOs with z < 2. The remaining 35 candidates are left with no visual classification.
Using the data from our LAE candidate sample (32 visually confirmed QSO LAEs and 35 candidates with no clear visual identification) we are able to determine the Lyα LF in the intermediate-bright luminosity range (43.5 ≲ log 10 (L Lyα /erg s −1 ) ≲ 45).At the faint end of this regime, we are limited by the depth of our survey (r ∼ 24 at 5σ), while at the brightest end we are limited by the survey area.
Finally, we give predictions about the performance of the method in the eventual release of the J-PAS data.With the completion of the first hundreds of square degrees of J-PAS, it will already be possible to resolve the Lyα LF in redshift bins of ∆z = 0.12 in the luminosity interval 43.5 ≲ log 10 (L Lyα /erg s −1 ) ≲ 45.This achievement will allow to study the evolution of the Lyα AGN LF with redshift with unprecedented precision.

Fig. 1 :
Fig. 1: Exponential fits of magnitude errors according to Eq. 1.For brevity, we show the magnitudes of 4 NBs and 2 BBs (colored dots) of J-NEP and their corresponding fits (dashed black lines).We get highly similar results for every filter in J-NEP and all pointings of miniJPAS.

Fig. 2 :
Fig. 2: Basic properties of the QSO mock.Top: Output Lyα LF of the QSO mock at z > 2. The measurement of the Lyα line can often be affected by the presence of the N v line, for this reason we also show the Ly α+N v LF.The bias correction in the L Lyα measurement caused by N v is addressed in Sect.4.2.We compare with the fits for the AGN/QSO Lyα LF in Spinoso et al. (2020) and Zhang et al. (2021), using a Schechter and a double power-law, respectively.Bottom: L Lyα as a function of r magnitude for the sources in the QSO mock (orange) and the QSOs of SDSS DR16Q with a L Lyα S/N > 5 (blue).The contour lines mark the regions containing the 68% and 95% of the objects.

Fig. 4 :
Fig. 4: Contours showing the areas encompassing the 68% and 95% of the LAEs in the mock showing the retrieved (observed) Lyα luminosity as a function of the real value in the catalog.The dotted and solid line contours show the values of L Lyα before and after applying the bias subtraction, respectively (see Sect. 4.2).Black dots represent the observational candidates from miniJ-PAS with a spectroscopic counterpart (see Sect. 4.8).

LLFig. 6 :
Fig. 6: Examples of miniJPAS&J-NEP LAE candidates.We show the fluxes of the 56 narrow medium (colored circles) and broad bands (colored squares) of the J-PAS filter set.The NB selected as Lyα by our pipeline is marked with a red dashed line.The detected secondary QSO lines are marked with green dashed lines (see Sect. 4.1.3).Spectroscopically or visually identified emission lines of the objects are shown with a gray dotted line.We also show the images of each source in r and the selected NB.The spectra of the SDSS DR16 (HETDEX) counterparts are shown in gray (orange) when available.The five objects in the left column are examples of LAEs identified by our method.The right column show five examples of possible contaminants.

Fig. 7 :Fig. 8 :
Fig.7: Rest-frame wavelength of the selected features in the QSO and low-z galaxy mock.The rest-frame wavelength is computed as λ 0 = λ NB /(1 + z), where λ NB is the central wavelength of the selected NB and z the true redshift of the mock object.

Fig. 9 :
Fig.9: Retrieved Lyα redshift of the candidates as compared to the miniJPAS photometric redshifts(Hernán-Caballero et al. 2021).We show spectroscopically confirmed LAEs (green filled circles) and contaminants (red empty circles), objects with extended morphology (morph_star_prob<0.1;blue empty squares), and sources without any spectral or morphology identification (gray crosses).The dashed lines mark the confusion between Lyα and typical galactic emission lines.

Fig. 10 :
Fig.10: Distribution of Lyα EW 0 of the candidate sample of miniJPAS&J-NEP.We compare the whole sample of candidates retrieved by our method in the mock (gray, dashed histogram) and in the observational data (orange, dashed histogram).We also compare the distribution of Lyα EW 0 for the mock subsample of true-positive LAEs (solid, black histogram) and the visually inspected subsample of miniJPAS&J-NEP (solid, red histogram) as defined in Sect.4.11.For log 10 [EW Lyα 0 /Å] > 2, more than a 90% of the sources retrieved from the mock are true LAEs.

Fig. 11 :
Fig.11: Lyα LFs for six intervals in redshift.We show the full redshift range power-law fit for reference (dashed red line).The redshift bins showed in this figure overlap and are therefore correlated.The Lyα LF shows no significant evolution with redshift within the given uncertainties.

Fig. 12 :Fig. 13 :
Fig. 12: Integrated LFs in 43.6 < log 10 (L Lyα /erg s −1 ) < 44.8 in the six intervals of redshift shown in Fig. 11.The chosen L Lyα interval is that where all six realizations of the Lyα LF are well defined.The horizontal error bars represent the width of the redshift interval.The dashed red line represents the integral of the best power-law fit presented in Sect.5.2.2

Table 1 :
Limit 5σ magnitudes of the BBs and NBs used to select LAEs.
Matthee et al. 2017;Spinoso et al. 2020)present extra emission lines which can only appear in specific combinations.After the Lyα line search, we check for other NBs with 5σ significant excesses, with an observed equivalent width EW obs > 100 Å.For the detection of these additional lines we estimate the spectral continuum without applying the IGM correction, which is only correct assuming the position of a Lyα line.In particular, we check if these additional flux excesses are compatible with the most prominent QSO lines: O vi, Si iv, C iv, C iii] or Mg ii (see, e.g.,Matthee et al. 2017;Spinoso et al. 2020).The sources showing multiple NB excesses which do not follow a compatible QSO emission pattern are discarded from our LAE candidate sample.-Colorcuts: In most cases, the continuum of both QSO and SFG LAEs can be well fitted by a power law (Vanden Berk

Table 3 :
Number of candidates after applying a first cut in 3-σ excess, and then the remaining candidates after applying every other cut described in section 4.1.3separately.The last column shows the number count in the final sample, after the visual inspection (VI), used to estimate the Lyα LF.

Table 4 :
Fit parameters obtained for the QSO/AGN Lyα LF in the literature.