Free Access
Issue
A&A
Volume 654, October 2021
Article Number A101
Number of page(s) 24
Section Numerical methods and codes
DOI https://doi.org/10.1051/0004-6361/202141236
Published online 19 October 2021

© ESO 2021

1. Introduction

The idea of using multi-wavelength photometry to estimate the redshift of galaxies (photometric redshifts, photo-z in the following) was first proposed as a last-resort technique to obtain redshifts for sources that were deemed too faint for spectroscopy to be feasible or economical (Baum 1962; Couch et al. 1983). Photo-z became increasingly useful with the advent of deep multi-wavelength imaging surveys, starting with the Hubble Deep Field (e.g., Lanzetta et al. 1996; Mobasher et al. 1996; Fernández-Soto et al. 1999). The main advantage of photo-z over spectroscopic redshifts (spec-z) is the ability of obtaining redshifts for all the sources that are detected in an imaging survey without pre-selection. Combined with large CCD detectors, this implies an increase in the survey speed of several orders of magnitude compared to the most advanced multi-object spectrographs (Blake & Bridle 2005).

The main drawback of the photo-z method is the accuracy of its redshift estimates, which is typically much lower than spec-z and imposes hard constraints on their range of application. However, in the past few years, photo-z techniques have matured enough to promote a shift in the redshift strategy of many current and upcoming surveys, which now use photo-z as their primary method for distance determination. Spectroscopy is still essential for obtaining the calibration and validation samples needed to fine-tune the photo-z machinery, or to follow up on particularly interesting sources. However, relying on photo-z for an overwhelming majority of targets allows for complete, flux-limited samples containing many millions of galaxies, which opens up entirely new applications such as baryonic acoustic oscillation (BAO) measurements (Blake & Bridle 2005; Angulo et al. 2008; Chaves-Montero et al. 2018).

Essential to this rise to preeminence of photo-z has been the huge improvement in accuracy and reliability over time, in particular, on imaging surveys that were designed with photo-z in mind, which split the optical range into increasingly large numbers of ever narrower bandpasses. The first wide-area survey of the photo-z era was the Sloan Digital Sky Survey (SDSS; York et al. 2000), with only 5 (carefully designed) broad-band filters. COMBO-17 (Wolf et al. 2003) and Subaru COSMOS 20 (Taniguchi et al. 2007, 2015) increased the number of filters to 17 and 20, respectively, including broad- and medium- or narrow-band filters. The Advanced, Large, Homogeneous Area, Medium- Band Redshift Astronomical (ALHAMBRA) survey (Moles et al. 2008) observed ∼4 deg2 in 20 optical medium-band filters (full width at half maximum, FWHM ∼ 300 Å) combined with JHKs near-infrared imaging. The Survey for High-z Absorption Red and Dead Sources (SHARDS; Pérez-González et al. 2013) imaged the Hubble Deep Field in 25 contiguous optical filters with an FWHM ∼ 170 Å, and the Physics of the Accelerating Universe Survey (PAUS) observed the COSMOS field in 40 filters with an FWHM ∼ 130 Å (Eriksen et al. 2019).

A new landmark of the application of photo-z will be reached with the Javalambre-Physics of the Accelerating Universe Astrophysical Survey (J-PAS; Benítez et al. 2009, 2014), which was specifically designed to achieve the high-redshift accuracy required to perform BAO measurements over a wide redshift range. Using 54 narrow-band filters (FWHM ∼ 145 Å) complemented with two broad-band filters at the two extremes of the optical range, J-PAS imaging will effectively obtain a low-resolution spectrum (photo-spectrum) for every 0.46″ pixel in the sky over thousands of square degrees. The J-PAS survey will be performed by the 2.5 m Javalambre Survey Telescope (JST), equipped with a 1.2 Gigapixel camera (JPCam) with a field of view of 4.2 deg2.

To test the performance of JST and begin scientific operation prior to the installation of JPCam, a pathfinder camera (PF) with a single 9k × 9k CCD was installed. To prove the scientific potential of J-PAS, a small survey of ∼1 deg2 (miniJPAS) was carried out with PF on the AEGIS field using the 56 J-PAS filters as well as four broad-band filters (u, g, r, i). MiniJPAS observations span four overlapping pointings along the Extended Groth Strip (EGS), reaching the depth planned for J-PAS (5σ limits between ∼21.5 and 22.5 for the narrow-band filters and ∼24 for the broad-band filters in a 3″ aperture). A detailed description of the miniJPAS observations, data reduction, and calibration is presented in Bonoli et al. (2021, hereafter B21). Fully reduced images and source catalogues are publicly available at the CEFCA catalogues portal1.

In this paper, we present the photometric redshift catalogue for miniJPAS. Section 2 outlines the miniJPAS observations and data reduction, and describes the photometric measurements used for photo-z calculation and the spectroscopic redshifts. Section 3 discusses our photometric recalibration procedure. Section 4 offers an overview of the photo-z code, the templates used, and its outputs, while Sect. 5 discusses the sources of error in photo-z estimates. In Sect. 6 we present the main results of the redshift distribution and photo-z accuracy for miniJPAS galaxies and its dependence on multiple quantities. Finally, Sect. 7 summarises our conclusions. All magnitudes are presented in the AB system.

2. Data

2.1. Observations and data reduction

The observations and data reduction of miniJPAS are described in detail in Sects. 2 and 3 of B21. Here we provide a brief summary. The miniJPAS covers the EGS in four overlapping pointings for a total area of ∼1 deg2. Each pointing was observed with a minimum of four exposures per filter, with a dithering of 10″ along both CCD axes. The readout of the CCD was done in 2 × 2 binning mode for the narrow-band filters (0.46″ pix−1) and 1 × 1 for the broad-band filters (0.23″ pix−1). Individual exposure times were 120 s for the 56 narrow-band filters as well as the u filter, but only 30 s for the other broad-band filters to prevent saturation. Total exposure times range from 480 s to 3240 s, depending on the filter and pointing (see Table A.1 in B21 for details).

Data reduction for the individual images includes the standard bias and over-scan subtraction, trimming, flat fielding, and illumination correction. Some issues specific to the Pathfinder camera (which unlike JPCam was not designed specifically for the JST/T250) also required additional corrections for vignetting, background patterns, and fringing (see B21).

Astrometric calibration was performed with SCAMP (Bertin 2006) using the Gaia DR2 catalogue as reference. The astrometric solution for the individual images has an rms of ∼0.035″ with respect to Gaia. Coaddition of the individual images was performed with SWARP (Bertin et al. 2002), with all the images resampled to the fiducial pixel scale of the camera (0.23″).

The average 5σ depth of the coadded narrow-band images ranges from ∼21.5–22.0 AB magnitudes in the reddest filters to ∼22.5–23.5 in the bluest ones. For broad-band filters, it is u ∼ 22.8, g ∼ 24.0, r ∼ 23.8, and i ∼ 23.2.

The point spread funtion (PSF) FWHM of the coadded images ranges from ∼0.6″ to ∼2.0″, with most of them below the 1.5″ mark. The images for the reference band (r) have the lowest PSF FWHM, averaging 0.7″ in the four pointings.

2.2. Photometry

Source detection and extraction on the reduced miniJPAS images was performed with SEXTRACTOR (Bertin & Arnouts 1996). Aperture photometry was obtained in both dual-mode and single-mode for several types and aperture sizes and was calibrated using an adaptation of the method presented in López-Sanjuan et al. (2019b, see Sects. 3.3 and 3.4 in B21 for details).

In dual-mode, the extraction aperture is defined in a reference band (in our case, the detection band r) and is used to perform forced photometry on the images in all the other filters. SEXTRACTOR computes total magnitudes using the auto (MAG_AUTO), isophotal (MAG_ISO), and Petrosian (MAG_PETRO) apertures. These apertures are defined individually for each source based on the r band so that the fraction of the (estimated) total flux of the galaxy enclosed is constant, regardless of the galaxy size and surface brightness profile. A constant scaling factor then converts the integrated fluxes in the apertures into total fluxes.

However, accurate total fluxes are much less important than accurate colour indices for the purpose of photo-z estimation. Obtaining accurate colours requires maximising the signal-to-noise ratio (S/N) within the extraction aperture and to compensate for PSF variation among the images in different filters. In order to achieve this, we use PSF-corrected magnitudes (MAG_PSFCOR) obtained following the method presented in Molino et al. (2019), which is based on COLORPRO (Coe et al. 2006).

Very briefly, PSFCOR magnitudes are obtained by extracting the flux in a small aperture, defined as the Kron aperture (Kron 1980) with a semi-major axis equal to 1 Kron radius in the reference band. This is half the size of a standard AUTO aperture in SEXTRACTOR (2 Kron radii). The resulting magnitude is known as the “restricted AUTO” or just “restricted” magnitude (Molino et al. 2017, 2019). For the reference band, the PSFCOR magnitude is simply the restricted magnitude. For bands with a wider PSF than the reference band, a correction term for PSF broadening is applied as follows:

PSFCOR j = REST j + REST r REST ( j ) r , $$ \begin{aligned} \mathrm{PSFCOR}_j = \mathrm{REST}_j + \mathrm{REST}_r - \mathrm{REST}(j)_r , \end{aligned} $$(1)

where RESTj and RESTr are the magnitudes measured on the restricted aperture for the images in band j and the reference band, respectively, while REST(j)r is measured on the reference image after convolution to the same PSF of the image in band j.

If, in contrast, band j has a narrower PSF than the reference band, then the PSFCOR magnitude is simply the restricted magnitude measured on the image after convolution to the same PSF as the reference band. We emphasise that PSFCOR magnitudes are not total magnitudes. They underestimate the total flux of galaxies by ∼0.5 mag on average with respect to AUTO magnitudes (see also González Delgado et al. 2021).

Hereafter, we omit the explicit reference to the aperture type when discussing magnitudes, colours, or magnitude offsets. Unless otherwise stated, it is implied that AUTO magnitudes are used whenever the flux or luminosity in a single band is needed (e.g., selection of a flux-limited sample, redshift priors), while PSFCOR magnitudes are used to fit the spectral energy distribution (SED) and colour-dependent quantities.

The photometry is corrected for atmospheric extinction as part of the calibration process (see López-Sanjuan et al. 2019b, for details). We also correct for Galactic extinction using the Milky Way dust maps from Bayestar17 (Green et al. 2018) with extinction coefficients kλ computed using the prescription in Whitten et al. (2019) for the extinction law of Schlafly et al. (2016).

2.3. Flags

The miniJPAS catalogue includes the column FLAGS, which contains information on whether each source is affected in each of the bands by a number of issues that may impair or invalidate the photometry. The FLAGS value is an integer that encodes several binary flags (see B21 for the details), including the SEXTRACTOR flags (which alerts for close neighbours, blending, saturation, truncation, etc.) as well as two additional flags that mark sources that are duplicated in another tile or that are known to be variable. Sources that have no apparent issues in their photometry in a particular band have FLAGS = 0 for that band. Sources with FLAGS > 0 in at least one band represent ∼30% of the miniJPAS catalogue.

We compute photo-z for every source brighter than r < 24 and with FLAGS < 4 in the detection band (this removes saturated and truncated sources as well as those with incomplete or corrupted data in the extraction aperture). The FLAGS values are used to choose which bands are considered for the photo-z calculation. In the general case, we select only bands with FLAGS = 0 (meaning that none of the SEXTRACTOR flags or additional flags is raised). However, if a source has FLAGS > 0 in more than 50% of the bands, we relax this condition by requiring FLAGS < 4, which dismisses the values indicating close neighbours or blending.

The impact of the photometric issues signalled by the flags on the photo-z accuracy is hard to predict as it depends on many factors, including the specific bands that are affected, the error introduced in the photometric measurement, the SED of the source, and its redshift. In general, the photo-z accuracy is degraded in sources with flags, and in particular, the rate of catastrophic errors (outliers) is substantially higher.

Except for saturation, all the conditions signaled by the photometry flags mainly depend on the location of the source within the image, not on its intrinsic properties. As a consequence, which sources are flagged should not depend on their brightness, apparent size, redshift, or spectral type. Figure 1 confirms that this is the case for brightness: ∼30% of the sources are flagged regardless of their magnitude.

thumbnail Fig. 1.

Distribution of r-band magnitudes for the whole miniJPAS sample (solid black line), flagged sources (dot-dashed olive line), and non-flagged sources (dashed magenta line). The distribution for the whole sample scaled by a factor 0.7 is shown for reference (dotted black line).

Because of this, we consider the ∼70% of sources with no flags to be representative of the full miniJPAS sample. We use this sub-sample to discuss the properties of the population of miniJPAS sources throughout the paper.

2.4. Star and galaxy classification

The miniJPAS catalogue includes the results of different methods for separating stars from galaxies. The most basic approach is the CLASS_STAR parameter from SEXTRACTOR, which compares the spatial profile of the source with the expectation for a point source. A more realistic morphological classification is given by MORPH_PROB_STAR, which gives the probability that a source is a star based on its spatial profile and a prior probability based on its r-band magnitude (see López-Sanjuan et al. 2019a, for details). TOTAL_PROB_STAR combines MORPH_PROB_STAR with parallax information from Gaia for a more robust determination. Finally, ERT_PROB_STAR provides a classification using the extremely randomised trees machine-learning method, which uses morphological and photometric parameters (Baqui et al. 2021).

Although ERT_PROB_STAR has the highest success rate in separating stars from galaxies (Bonoli et al. 2021; Baqui et al. 2021), we chose TOTAL_PROB_STAR as the preferred measurement of the probability of being a star, PS, throughout the paper. This is because TOTAL_PROB_STAR has the advantage that it does not rely on the SED of the galaxy, which is important for obtaining the redshift distribution of galaxies in a consistent way, as we show below.

The distribution of PS is strongly bimodal. Most sources are concentrated near the extremes of its range, at PS ∼ 0 (very likely to be a galaxy) or PS ∼ 1 (star, see Fig. 2). In particular, 96.8% of the sources brighter than r = 22 have either PS < 0.01 or PS > 0.99. However, the distinction becomes more uncertain at faint magnitudes, where many sources take intermediate values of PS. As a consequence, applying a cut in PS to distinguish galaxies from stars results in contamination and incompleteness in both samples. Any determination of the statistical properties of miniJPAS galaxies based on this partitioning, (including the redshift distribution) would be biased at faint magnitudes.

thumbnail Fig. 2.

Distribution of the probability of being a star, PS, for miniJPAS sources as a function of the (colour-coded) limiting magnitude of the sample. The spike at PS = 0.5 is due to sources with insufficient S/N for a classification in the detection band, which are assigned PS = 0.5 by default.

To solve this issue, we compute photo-z for all miniJPAS sources regardless of the morphological classification. For each source we obtain P(z|G), the redshift probability distribution conditional to the source being a galaxy, which depends on its SED alone. If a source is known to be a star or quasar (PS = 1) then the value of P(z|G) is meaningless. However, by computing P(z|G) independently of any morphological information and applying the morphological classification as a posterior, we can easily estimate redshift-dependent statistics for the population of miniJPAS galaxies that account for the uncertainty in the classification of individual sources (see Sect. 6).

2.5. Spectroscopic redshifts

The Deep Extragalactic Evolutionary Probe 2 (DEEP2) and 3 (DEEP3) galaxy redshift surveys (Davis et al. 2003; Cooper et al. 2011; Newman et al. 2013) cover about half of the area of the miniJPAS survey (Fig. 3). Both surveys were performed with the DEIMOS multi-object spectrograph on the Keck II telescope. DEEP2 spectra were obtained with the 1200 lines/mm grating, covering the ∼6500–9100 Å range with a spectral resolution of R ∼ 5000, while DEEP3 used the 600 lines/mm grating, allowing for a wider spectral coverage (∼4550–9900 Å) at R ∼ 2500.

thumbnail Fig. 3.

Footprint of the miniJPAS and DEEP2/DEEP3 spectroscopic observations. Grey dots represent miniJPAS sources with r < 23, and blue and red dots represent sources that were targeted for spectroscopy by the DEEP2 and DEEP3 surveys, respectively.

We retrieved the combined DEEP2/3 redshift catalogue for the EGS2, which contains a total of 23 822 unique sources. Targets for DEEP2 observations were selected at random from the R < 24.1 flux-limited catalogue of Coil et al. (2004), which covers the entirety of the EGS. By contrast, DEEP3 covers only the central part of the EGS. While most DEEP3 targets were also selected from the R < 24.1 sample, additional sources were targeted based on detection at other wavelengths, such as far-infrared or X-rays, including some R > 24.1 sources. We removed these sources from the catalogue to keep the spectroscopic sample representative of the population of R < 24.1 sources. We also required that sources have secure redshifts (ZQUALITY > = 3) and a spectral classification as galaxy. These criteria were met by 15 222 sources.

We performed a match by coordinates between this sample and the miniJPAS catalogue using a search radius of 1.5″. We found spectroscopic counterparts for 4825 out of 20 962 miniJPAS sources brighter than r = 23 at an average matching distance of 0.12″.

We also matched the miniJPAS catalogue with the spectroscopic redshift catalogue from SDSS DR12, which covers the entirety of the miniJPAS footprint. Again, we kept only matches for sources with secure spectroscopic redshifts (zwarning = 0) and spectroscopic classification as galaxy. These criteria are met by 564 sources, including 123 that also have redshifts from DEEP. In all the galaxies in common between SDSS and DEEP, the redshift measurements agree to within |δz| < 0.001, the median |δz| being 0.00012.

Figure 4 shows the distribution of sources of all types, galaxies, and galaxies with spectroscopic redshifts as a function of the r-band magnitude in the miniJPAS catalogue. The distribution for all sources is computed without taking the morphological classification into account, and it is dominated by stars at r < 19.5. The distributions for stars and galaxies were obtained by weighting each source with its PS and PG. Finally, the distribution for galaxies with spectroscopic redshifts was computed from the subsample with matches in our spectroscopic catalogue.

thumbnail Fig. 4.

Distribution of miniJPAS sources as a function of r-band magnitude for all sources (solid black lines), stars (dashed green lines), galaxies (dot-dashed red lines), and galaxies with spectroscopic redshifts (dotted blue lines). Smooth lines show cumulative counts, and histograms show counts in bins of 0.1 magnitudes.

The fraction of miniJPAS galaxies with spectroscopic redshifts is roughly constant at ∼25% within the range 19 < r < 23. This fraction increases to ∼50% when we consider only sources within the DEEP footprint (the number of SDSS spectra for r > 19 galaxies is negligible).

3. Recalibration

The observed colours of galaxies may be affected by systematics in the photometry that originates from errors in the absolute flux calibration of the images, in the correction for Galactic extinction, or aperture effects introduced by PSF variation among images in different bands. Because accurate galaxy colours are essential for photometric redshifts, many SED-fitting photo-z codes include a pre-processing stage dedicated to computing magnitude offsets for each band that minimises the average colour differences between the observed photometry and synthetic photometry extracted from the spectral templates (e.g., Ilbert et al. 2006; Molino et al. 2014; Eriksen et al. 2019). We call this process zero-point recalibration, or recalibration for short. Because the spectral templates are also affected by calibration uncertainties, this procedure has the advantage of placing the observed photometry and the templates in the same “photometric system”.

A great shortcoming of this approach is that the template set usually contains only a few “archetype” templates that are representative of the broad spectral types expected to be found in the sample. For datasets such as miniJPAS, which have observations in many bands, this implies that poor fits (high χ2 values) are obtained for many sources (in particular, those with highest S/N) even after the recalibration offsets have converged because the template set is not large and diverse enough to reproduce the entire variety of spectral features that are found in individual galaxies. Discrepancies between the best-fitting template and the actual spectrum of the galaxy increase the dispersion in the magnitude offsets calculated from different galaxies for each band, implying a more uncertain correction.

To overcome this issue, we instructed the photo-z code to skip the recalibration step3 and instead performed the recalibration separately using a custom routine. This allowed us to use a very large grid of spectral templates, built from stellar population synthesis models, which can reproduce the SED of miniJPAS galaxies to much higher accuracy.

3.1. Grid of models

We generated a grid of 90 720 synthetic spectra with the python implementation of CIGALE, which is described in Boquien et al. (2019). Each spectrum represents the theoretical spectrum of a galaxy composed of two stellar populations (namely ‘young’ and ‘old’). The old population is assumed to have a delayed-exponential star formation history (SFH), with an age between 2 and 10 Gyr and an e-folding timescale between 0.5 and 2 Gyr. The SFH for the young population is also a delayed-exponential, with an age between 0.1 and 1 Gyr and an e-folding timescale between 50 and 200 Myr. The fractional contribution of the young population to the total stellar mass of the galaxy may take values from 0% to 10%.

The synthetic spectrum for each population was generated by integration over time of a library of simple stellar populations (SSPs). We chose the high spectral resolution version of the library of Bruzual & Charlot (2003), with a Chabrier (2003) initial mass function (IMF), and stellar metallicities Z/Z = 0.2, 0.4, and 1.0. The nebular emission was modelled with the grid of nebular templates from Inoue (2011), which were generated using CLOUDY 13.01 (Ferland et al. 1998, 2013). The metallicity of the gas was assumed to be the same as that of the stellar component. To keep the total number of models manageable, we restricted values of the ionisation parameter to the range log U = [ − 3, −1] in steps of 0.5. The fraction of Lyman continuum photons reprocessed into nebular emission (i.e. not absorbed by dust or escaping into the intergalactic medium) ranged from 5% to 100%. The attenuation law was that of Calzetti et al. (2000), and the colour excess E(B − V) of both stellar components was fixed at 0.44 times that of the nebular component (which takes values from 0 to 0.5 mag in steps of 0.1).

3.2. Computation of offsets

We performed the recalibration using miniJPAS galaxies with secure spectroscopic redshifts and spectroscopic classification as “galaxy” from either SDSS or DEEP. Because complete and accurate SEDs are essential for the recalibration procedure, we excluded sources fainter than r = 22 or with flags in the photometry of any of the 60 bands.

We obtained recalibration offsets independently for each of the four pointings of the miniJPAS survey using ∼500 galaxies per pointing. For each galaxy, the model rest-frame spectra in the grid were redshifted to the observed frame of the galaxy. Then synthetic photometry was obtained by convolving the redshifted spectra with the transmission curves of the filters, and a scaling factor was found that provides the best fit (minimum χ2) between the observed and synthetic SEDs. We selected as the best model for each galaxy the one that produced the absolute minimum χ2 of the 90 720 models in the grid. For every pointing, we then computed the systematic offset in the photometry for band j as

δ m ( j ) = median { m i obs ( j ) m i synth ( j ) } , $$ \begin{aligned} \delta m(j) = \mathrm{median} \left\{ m_i^\mathrm{obs}(j) - m_i^\mathrm{synth}(j) \right\} , \end{aligned} $$(2)

where m i obs (j) $ m_i^{\rm obs}(j) $ and m i synth (j) $ m_i^{\rm synth}(j) $ are the observed and synthetic magnitudes in band j for the ith galaxy, respectively. The observed photometry was adjusted by subtracting the offsets that were just computed,

m i corr ( j ) = m i obs ( j ) δ m ( j ) . $$ \begin{aligned} m_i^\mathrm{corr}(j) = m_i^\mathrm{obs}(j) - \delta m(j) . \end{aligned} $$(3)

We repeated the SED-fitting with the grid of models for the updated photometry and recomputed the offsets iteratively, until all new additional offsets were smaller than 0.001 magnitudes, which in practice happened after three or four iterations (Fig. 5). The cumulative offsets resulting from the addition of the successive offsets in all the iterations, Δm(j) = δm(j) + δm′(j) +⋯+ δmn(j), are the final recalibration corrections that we applied to the original photometry for all the sources in the pointing.

thumbnail Fig. 5.

Magnitude residuals between the observed and synthetic photometry after the first (top) and third (bottom) iterations of the recalibration procedure. Symbols indicate the median residual, and error bars enclose the 16th to 84th percentile ranges. Small symbols correspond to photometry in the narrow-band J-PAS filters, and large symbols represent broad-band filters (uJAVA, uSDSS, gSDSS, rSDSS, and iSDSS) and the long-pass J1007 filter.

We estimated the uncertainty in the recalibration offsets as the uncertainty in the median of the residuals after the last iteration, assuming a normal distribution,

σ ( Δ m ( j ) ) = π 2 N σ { m i obs ( j ) Δ m ( j ) m i synth ( j ) } , $$ \begin{aligned} \sigma \left(\Delta m(j)\right) = \sqrt{\frac{\pi }{2N}} \sigma \left\{ m_i^\mathrm{obs}(j) - \Delta m(j) - m_i^\mathrm{synth}(j) \right\} , \end{aligned} $$(4)

where N is the number of galaxies used and m i obs (j) $ m_i^{\rm obs}(j) $ − Δm(j) is the magnitude in band j of the ith galaxy after recalibration.

The recalibration offset computed for a given band differs significantly from one pointing to the next, mostly because of differences in the PSF FWHM of the images. Table A.1 indicates the offsets and their uncertainties for PSFCOR magnitudes in the 60 bands for the four miniJPAS pointings.

3.3. Validation of recalibration offsets

The recalibration procedure may raise some legitimate concerns about its robustness. One possible source of problems is that systematic errors in the spectral templates can also result in systematic offsets between the observed and synthetic photometry. If most of the galaxies in the recalibration sample are within a small redshift range, any given spectral feature will appear most of the time in only a few bands. This might bias the recalibration if the best-fitting models for these galaxies systematically under- or over-predict the intensity of the feature. Emission lines, whose intensity is particularly hard to predict from the observed continuum, are one clear example.

In order to determine whether this degeneracy is an issue for the miniJPAS sample, we split the recalibration sample for each pointing into two subsamples, one containing all the galaxies with a redshift below the median of the sample, and the other with those above the median. We performed the recalibration separately for the two subsamples and compared the resulting offsets. We find that the offsets calculated for the two subsamples are consistent within their uncertainties.

Another sensible concern is the unicity of the results from the recalibration procedure. To test whether the recalibration converges to the same corrected photometry regardless of the systematic offsets, we modified the observed photometry by applying random shifts between −0.2 and +0.2 magnitudes (selected from a uniform distribution). The same shift x(j) was applied to all galaxies for each band j to simulate a systematic offset.

We computed recalibration corrections, Δm*(j), for this modified photometry using the exact same method as before. If the recalibration can compensate for these additional systematic shifts, then we expect the difference between the original and the new recalibration offsets to match the shift applied to the photometry,

Δ m ( j ) Δ m ( j ) x ( j ) . $$ \begin{aligned} \Delta m(j) - \Delta m^*(j) \approx x(j). \end{aligned} $$(5)

Figure 6 compares the random shifts we introduced, x(j), with the resulting change in the recalibration offsets, Δm(j)−Δm*(j), for all the bands and pointings. The dispersion around the 1:1 relation is ∼0.01 mag (except for pointing AEGIS-3, which has σ ∼0.03 mag), which is an order of magnitude smaller than the shifts we introduced and also comparable to or smaller than the uncertainties we calculated for the original recalibration offsets (see Table A.1).

thumbnail Fig. 6.

Comparison between the arbitrary shifts introduced in the input photometry for individual bands (X-axis) and the resulting change in the recalibration offsets obtained (Y-axis). Symbols are the same as in Fig. 5. The dashed line marks the 1:1 relation that is expected when the recalibration process perfectly compensates for systematic offsets in the photometry.

This suggests that the recalibration procedure converges to the same or very similar stellar population models for most galaxies, regardless of any systematic shifts in the photometry. Therefore we conclude that the offsets Δm(j) obtained in the recalibration remove real systematics in the photometry, which are probably associated with imperfect aperture corrections.

We emphasise that the Δm(j) in Table A.1 are valid only for the PSFCOR aperture. We also caution about the systematic errors that could be introduced if these recalibration offsets were used in the spectral analysis of miniJPAS sources. Their values may still be model dependent with regard to the specific choice of the stellar library, the extinction law, or other model parameters. However, this is not a problem for our photo-z calculation because the template library we use is a subset of the model grid (see Sect. 4.2).

4. Computation of photometric redshifts

4.1. Photo-z code

We compute photo-z for miniJPAS sources using JPHOTOZ, a python package that is part of JYPE, the data reduction pipeline for J-PAS. JPHOTOZ acts as an interface between the database and the actual photo-z computing code(s) and also handles all the pre- and post-processing of the data, including application of Galactic extinction correction and recalibration offsets to the photometry, filtering of flagged photometric measurements, contrast-correction of the redshift probability distribution function (zPDF; see Sect. 4.3), and computation of the odds parameter as well as other parameters derived from the zPDF (Sect. 4.4).

The photo-z code we used for miniJPAS is a customised version of LEPHARE (Arnouts & Ilbert 2011), modified to remove a limitation in the maximum number of bands in the photometric catalogue (32 in the original LEPHARE), as well as to allow for higher resolution in redshift with a finer sampling of the redshift search range (in miniJPAS, from z = 0 to z = 1.5 in constant steps of δz = 0.002). LEPHARE computes photo-z using the template-fitting method (see Salvato et al. 2019, for a recent review of the different photo-z techniques). Template fitting photo-z works by evaluating a goodness-of-fit estimator (typically χ2) between the observed photometry and synthetic photometry generated from each of the templates as a function of z. The corresponding χ2 values sample the (assumed Gaussian) log-likelihood distribution, logL(z) χ min 2 (z)/2 $ \log \mathcal{L}(z) \propto -\chi^2_{\rm min}(z)/2 $. Most modern photo-z codes (including LEPHARE) compute the zPDF by weighting ℒ(z) with a redshift prior that summarises our a priori knowledge of the underlying redshift distribution as a function of the galaxy magnitude and/or colour (see Ilbert et al. 2006 for details and Benítez 2000 for a general description of the method).

We used the default redshift prior in LEPHARE, which is obtained from the spectroscopic redshift distribution of galaxies in the VIMOS VLT Deep Survey (VVDS; Le Fèvre et al. 2005), and contains the probability density function P(z, T|m) of the redshift and spectral type as a function of the i-band magnitude. Figure 7 shows P(z, T|m) for the broad spectral types elliptical (E/S0), spiral (Sp), and irregular (Irr), defined according to the rest-frame g − i colour of the templates (see Ilbert et al. 2006 for details), and for magnitudes i = 21, 22, and 23. For galaxies brighter than i = 20, LEPHARE replaces the empirical prior with a step function that takes the value 1 at z ≤ 1 and 0 at z > 1, regardless of the spectral type. While such a prior is not a realistic model for the actual redshift distribution of bright galaxies, this fact is unimportant in practice because i < 20 miniJPAS galaxies have high S/N photometry and their logℒ(z) presents a very sharp peak. The prior also prevents i < 20 sources from finding solutions at z > 1. This is not an issue for miniJPAS given its small volume (the brightest galaxy with zspec > 1 has i = 20.6), but a more realistic prior will be needed for J-PAS in order to obtain accurate photo-z for the most luminous z > 1 galaxies.

thumbnail Fig. 7.

Prior probability redshift distributions used by LEPHARE for the broad spectral types elliptical (solid line), spiral (dotted line), and irregular (dot-dashed line), with colour coding for the magnitude (see text for details).

LEPHARE also separately calculates the minimum χ2 obtained with a set of stellar and quasar templates, which could help to classify sources. However, we find it more convenient to exclude these templates and to interpret the zPDF from LEPHARE as the redshift probability distribution conditional to the source being a galaxy, P(z|G).

4.2. CEFCA_MINIJPAS library of templates

A key aspect of the template-fitting method for photo-z determination is that it generally does not require a good fit between the template and the observed photometry; it suffices that the best fit is obtained at the true redshift. In particular, only a few templates (broadly corresponding to the major spectral types) are needed to obtain good photo-z from broadband photometry (e.g., Benítez 2000), where the photo-z accuracy depends on the correct detection of broad spectral features such as the Lyman break or the 4000 Å break.

The requirements are different when narrow-band photo-spectra are used because narrow spectral features such as emission and absorption lines have a much stronger impact on the photometry (the effect of a spectral feature on the photometry is proportional to its equivalent width and inversely proportional to the bandpass). Multiple works have shown that photo-z for narrow-band datasets improve significantly when emission lines are taken into account (e.g., Molino et al. 2014; Eriksen et al. 2019; Alarcon et al. 2021).

LEPHARE can add emission lines to the templates with intensities individually adjusted for each galaxy to match the photometry in the affected bands. However, this often results in too much freedom, as it allows unphysical models that lead to spurious solutions. Because of this, we prefer to switch off the emission line adjustment capability in LEPHARE and instead provide templates that include both the stellar and nebular emission (lines and continuum).

In the past, template libraries were conditioned by the availability of spectral templates, which were often based on the observed spectra of archetypal galaxies or composites from multiple galaxies of the same type, often extrapolated with models or photometry beyond the range of the spectroscopic observations. An alternative approach that has gained popularity thanks to improvements in the stellar libraries and stellar evolution models is the generation of synthetic galaxy spectra with SPS models (e.g., Brammer et al. 2008; Eriksen et al. 2019).

To build the CEFCA_MINIJPAS library of templates, we started from the grid of 90 720 SPS models that we used for the recalibration. Because we wished to use templates that represent real galaxies, we chose only those that provide the best fit for one (or more) of the miniJPAS galaxies using the recalibrated PSFCOR photometry. We excluded sources fainter than r = 22 to guarantee a good S/N in all the bands, and also considered only sources with secure spectroscopic redshifts. We ensured that the best-fitting template was consistent with the observed photometry by requiring a reduced chi-squared χ r 2 $ \chi^2_r $ < 1. We also imposed a constraint on the coefficient of variation of the RMS error,

CV RMSE = n = 1 N ( f obs ( λ n ) f model ( λ n ) ) 2 / N n = 1 N f obs ( λ n ) / N , $$ \begin{aligned} \mathrm{CV}_{\rm RMSE} = \frac{\sqrt{\sum _{n=1}^N \left(f_{\rm obs}(\lambda _n) - f_{\rm model}(\lambda _n)\right)^2/N}}{\sum _{n=1}^N f_{\rm obs}(\lambda _n)/N} , \end{aligned} $$(6)

which represents the ratio of the typical residual to the mean flux. We required CVRMSE< 0.04 because selecting for low χ r 2 $ \chi^2_r $ alone favours the sources with lower S/N (see e.g., Hernán-Caballero et al. 2015), for which a wider range of models is consistent with the observed photometry. These criteria were met by 455 SPS models.

We further reduced the number of templates by iteratively performing a photo-z calculation with multiple combinations of these 455 models to select those that provide the best results in the spectroscopic subsample. This method for optimisation of the template set is the subject of an upcoming paper (Hernán-Caballero et al., in prep.). Very briefly, a score was associated with each combination of templates that summarised the quality of the photo-z obtained on a test sample with these templates. Starting from random selections of templates, each set of templates was modified by removing some and adding new ones at random (selected from the population of 455 candidates). The score was computed for every new set. Those with a higher score were then taken as the basis for new sets with higher probability. We iterated until the score of the best-performing set stabilised and no further increases were obtained in a predetermined number of iterations. We took the set with the highest score as the final selection and used it to compute the photo-z for the whole miniJPAS sample.

We repeated this procedure multiple times with different random initial sets. While the final selection changed from one run to another, the score converged to the same maximum value in all the runs, and the photo-z of the whole miniJPAS sample in two different runs are identical for ∼98% of the sources. Some particular templates always reached the final selection, others appeared interchangeable, and the large majority was never selected.

The final set we used to compute the published photo-z of miniJPAS contains 50 templates (the number for which the precision saturates) and is shown in Fig. 8. The values of the main parameters we used to build these models are listed in Table A.2, and common observables measured on the models are presented in Table A.3.

thumbnail Fig. 8.

Set of fifty galaxy templates used for computing the photo-z for miniJPAS sources, sorted by their rest-frame UV-to-optical spectral index and shifted in the Y-axis for clarity.

4.3. Contrast correction of the zPDF

The probabilistic nature of the zPDF implies that for individual sources, it is often impossible to determine whether they are realistic or not because any P(z|G) that verifies P(zspec|G) > 0 is consistent with the spectroscopic redshift. However, when large groups of sources are considered, some statistical tests can determine whether the zPDF are well behaved. One powerful test is the calculation of the fraction of galaxies in which zspec falls within a given confidence interval (CI) of the zPDF (e.g., Fernández-Soto et al. 2002; Dahlen et al. 2013; Schmidt & Thorman 2013). If the zPDF describes the actual redshift probability distribution, we can expect 10% of galaxies to fall within any 10% CI, 20% in a 20% CI, and so on. Out of the many possible definitions of a CI, the most useful is the highest probability density (HPD) CI, as proposed initially by Fernández-Soto et al. (2002) and illustrated by Wittman et al. (2016). The HPD CI is the shortest redshift interval (or union of disjoint intervals) that contains a given fraction of the total area under the zPDF distribution. Therefore it always encloses the main peak of the zPDF.

We computed the fraction (c) of miniJPAS galaxies with zspec inside the HPD CI at a confidence level c using the algorithm presented in Wittman et al. (2016). We separated the galaxies into groups according to their r-band magnitude. The results (left panel in Fig. 9) show that in general, there are more zspec values inside the HPD CI than expected, indicating that the zPDF has too much weight at redshifts far from the main peak (or peaks). This effect is increasingly stronger at fainter magnitudes. For bright sources (r < 19), the opposite is true: too much weight is placed at the main peak of the zPDF, causing (c) < c.

thumbnail Fig. 9.

Fraction of galaxies with zspec within the highest probability density confidence interval as a function of the confidence level before (left) and after (right) the contrast correction of the zPDF. Galaxies are grouped by their r-band flux in bins of 0.5 magnitudes. The diagonal line marks the (c) = c relation that is expected if the zPDF represents the actual redshift uncertainty. Values above (below) this line imply under- (over-)confidence in the zbest estimate.

This type of inaccuracies in the zPDF is a common issue of photo-z codes, which causes an under- (or over-)estimation of the actual redshift uncertainty (e.g., Hildebrandt et al. 2008; Dahlen et al. 2013; Mundy et al. 2017). Several factors may contribute to these trends, including over- (or under-) estimation of photometric errors and the sparse sampling of the parameter space of the models that results from using only a few templates. The latter implies that the best-fitting template is often substantially different from the actual spectrum of the source. This sparseness of the models is particularly relevant for miniJPAS, where the high number of narrow-band filters allows resolving many spectral features. Because of this, most galaxies achieve poor fits ( χ min 2 $ \chi^2_{\rm min} $ ≫ 1) even at the spectroscopic redshift, in particular those with higher S/N photometry.

Modelling the impact on the zPDF of all the factors described above is overly complex and ultimately unnecessary. An empirical correction of the contrast of the zPDF (the difference between the value at peaks and valleys) suffices to restore the expected relation between (c) and c. To do this, JPHOTOZ implements a variation of the method described by Dahlen et al. (2013), which corrects the zPDF in two steps. First, a discrete convolution of the zPDF and a Lorentzian kernel is performed,

P [ n ] = ( P k ) [ n ] = m = 2 2 P [ n m ] k [ m ] , $$ \begin{aligned} P^\prime [n] = (P * k)[n] = \sum \limits _{m=-2}^{2} P[n-m]k[m], \end{aligned} $$(7)

where P[n] is the value of the zPDF for the nth element in which it is sampled (corresponding to the redshift z[n] = 0.002n), and k[m] = 1/(m2 + γ2), with γ = 1.18. This convolution is particularly important for bright sources, which sometimes have P[n] = 0 for all elements except for the one corresponding to the peak. The contrast of the convolved zPDF is then adjusted with the transformation P″[n] = P′[n]1/α, with α = 0.54. The values of α and γ are calculated by minimising over the whole sample the function

D ( α , γ ) = i | F ̂ ( c i ) c i | . $$ \begin{aligned} D(\alpha ,\gamma ) = \sum _i | \hat{F}(c_i)-c_i|. \end{aligned} $$(8)

The right panel in Fig. 9 shows the relation between (c) and c for the same magnitude cuts after the contrast correction.

4.4. Scalar parameters

While the zPDF provides the most complete description of our knowledge of the redshift of a source, it is often more convenient to use scalar parameters that condense its main properties. The table PhotoZLephare_updated in the miniJPAS database4 contains several of them:

– Z_ML (Z_ML in LEPHARE) is the median redshift of the zPDF (50% of the total area is on either side).

– PHOTOZ (Z_BEST in LEPHARE, hereafter zbest) is the redshift corresponding to the absolute maximum of the zPDF. We consider this the most useful point estimate of the photo-z, as it is more robust than Z_ML for asymmetric or multi-peaked zPDF profiles.

– CHI_BEST (CHI_BEST in LEPHARE) is the χ2 of the best-fitting galaxy model at zbest.

– Z_BEST68_LOW (Z_BEST68_LOW in LEPHARE) the low-z limit of the 68% confidence interval for zbest, computed using the Δχ2 method (e.g., Avni 1976; Bolzonella et al. 2000).

– Z_BEST68_HIGH (Z_BEST68_HIGH in LEPHARE) the high-z limit of the 68% confidence interval for zbest, computed using the Δχ2 method.

– PHOTOZ_ERR is the 1σ uncertainty in zbest, computed as PHOTOZ_ERR = 0.5(Z_BEST68_HIGH - Z_BEST68_LOW). We used a related quantity, the relative 1σ uncertainty,

z err = Z _ BEST 68 _ HIGH Z _ BEST 68 _ LOW 2 ( 1 + Z _ BEST ) . $$ \begin{aligned} z_{\rm err} = \frac{\mathrm{Z\_BEST68\_HIGH} - \mathrm{Z\_BEST68\_LOW}}{2(1 + \mathrm{Z\_BEST})} .\end{aligned} $$(9)

– ODDS (hereafter odds) is the probability of the relative error in zbest being smaller than 3% (|Δz|=|zbest − zspec|/(1 + zspec) < 0.03). Unlike all the others, this is not a direct output from LEPHARE, but is computed by JPHOTOZ from the contrast-corrected zPDF, using the formula

o d d s = z best d z best + d P ( z | G ) d z , d = 0.03 ( 1 + z best ) . $$ \begin{aligned} odds = \int _{z_{\rm {best}} - d}^{z_{\rm {best}} + d} P(z \vert \mathrm{G}) dz, \quad d = 0.03(1+z_{\rm {best}}) .\end{aligned} $$(10)

5. Quantifying the photo-z accuracy

5.1. Origin of errors in photo-z

Taking the spectroscopic value as the true redshift of the galaxy, the error in zbest is often defined as Δz = (zbest − zspec)/(1 + zspec), where the 1 + zspec factor conveniently compensates for the stretching of spectral features with redshift. The value of Δz is determined by two main types of error, which differ substantially in their prevalence and impact on the resulting photo-z. Broadly speaking, we can describe them as “inaccuracies” and “catastrophic errors”.

The former are the cumulative effect of small systematic and random errors in the photometry, flux calibration, and wavelength calibration, as well as the uncertainty introduced by the limited spectral resolution of the photo-spectra, the finite number of templates, and the discretisation of the redshift search range, to name a few. Each of these factors affects the shape and peak redshift of the zPDF. Combined, they result in a small, largely random shift in zbest relative to the true redshift of the galaxy.

On the other hand, catastrophic errors are mainly caused by the non-linearity of the transformation between colour space and redshift, which implies that galaxies with very different spectral types and redshifts may have similar observed colours. The importance of this degeneracy increases at faint magnitudes because larger photometric errors imply more uncertain observed colours, which can be consistent with more combinations of template and redshift. The result is a zPDF with two or more peaks of comparable strength at different redshifts, often far apart. When the strongest peak is not the peak that corresponds to the actual redshift, Δz can be an order of magnitude or more larger than typical inaccuracies. The use of redshift priors mitigates this issue, at least in the aggregate, by favouring the most likely redshift given the magnitude of the galaxy. However, for some galaxies with unusually high or low luminosity, the prior may exacerbate the risk of a catastrophic error by favouring the wrong redshift solution (see Sect. 6.5).

Another cause for catastrophic errors is large errors in the photometry that are not accounted for by the nominal flux uncertainties, such as contamination by nearby sources or artefacts in the images that may drastically alter the photometry in one or more bands. The result is often spikes or jumps in the photo-spectra that the photo-z code tries to match to legitimate spectral features. Fortunately, in the case of miniJPAS the photometry flags identify most of these sources, and the affected bands are masked for photo-z computation. However, a small number of galaxies is likely to be affected by yet undetected issues. Finally, galaxies with “exotic” spectra that do not resemble any of the galaxy templates in the library may also get wrong redshift estimates.

Figure 10 shows the distribution of |Δz| for the miniJPAS galaxies with r < 23 and with spectroscopic redshifts. The binning is uniform in log |Δz| to highlight the bimodality of the distribution caused by the two types of error. The main peak at |Δz| ∼ 0.004 corresponds to the typical error due to inaccuracies, while the peak at |Δz| ∼ 0.04 represents the catastrophic errors. The first peak and the tail at very small |Δz| are well reproduced by a Gaussian or a Lorentzian distribution. The second peak requires a Lorentzian because the slope of the Gaussian at large |Δz| is too steep. Moreover, the combination of two Lorentzians fits the distribution of |Δz| slightly better than the combination Gaussian+Lorentzian.

thumbnail Fig. 10.

Distribution of redshift errors for the spectroscopic subsample of miniJPAS (histogram) and best-fitting model combining one Gaussian and one Lorentzian profile (dotted line) or two Lorentzians (dashed line).

As we show in the next sections, the relative importance of inaccuracies and catastrophic errors in shaping the distribution of Δz varies with properties of the galaxies such as the brightness and redshift, and can be predicted (to some extent) from parameters derived from the zPDF such as zerr and odds.

5.2. Summary statistics

Similarly to the scalar parameters derived from the zPDF, it is often very convenient to rely on summary statistics of the distribution of Δz in the analysis of the dependence of photo-z accuracy with one or more galaxy properties, or for easy comparison between samples. In most cases, the distribution of Δz is far from Gaussian, therefore the mean and standard deviation are often replaced by more robust analogues: the median and the normalised median absolute deviation, σNMAD. The latter is defined as

σ NMAD = 1.48 × median | Δ z i median ( Δ z i ) | , $$ \begin{aligned} \sigma _{\rm {NMAD}} = 1.48 \times \mathrm{median}|\Delta z_i - \mathrm{median}(\Delta z_i)|, \end{aligned} $$(11)

where the factor 1.48 is used to match the standard deviation for a Gaussian distribution. Like the standard deviation, σNMAD is insensitive to a systematic offset in zbest, but unlike the former, it is also insensitive to the tail of the distribution for high values of |Δz|.

A complementary statistic to σNMAD is the outlier rate, η, which represents the fraction of galaxies with redshift errors larger than a given threshold X,

η = N ( | Δ z | > X ) N tot , $$ \begin{aligned} \eta = \frac{N(| \Delta z | > X)}{N_{\rm tot}}, \end{aligned} $$(12)

where X is set at several times the σNMAD (we chose X = 0.03) to ensure that only values far from the main peak of the distribution are identified as outliers. As a consequence, η is a good approximation for the frequency of catastrophic errors.

While σNMAD and η are aggregate statistics that describe the redshift errors of samples, not individual galaxies, their values can also help validate uncertainty estimates for individual sources. In particular, if redshift uncertainties obtained with the Δχ2 method are accurate, we can expect σNMAD ∼ ⟨zerr⟩ for a sample of galaxies that are selected to have similar values of zerr. Furthermore, in a sample of galaxies with comparable odds, the expected outlier rate is η ∼ 1 − ⟨odds⟩. In Sects. 6.4 and 6.5 we apply these tests to the miniJPAS sample.

6. Results

We computed photo-z for nearly all r < 24 sources in the dual-mode photometric catalogue of miniJPAS. However, we restricted the analysis to r < 23 sources because fainter sources are undetected in most or all of the narrow-band images, and the completeness of miniJPAS for extended sources also drops quickly at r > 23 (see Fig. 16 in B21).

Out of 20,962 miniJPAS sources with r < 23, 186 (0.9%) were not selected for photo-z calculation because they failed the FLAGS < 4 condition in the selection band (these sources have PHOTOZ = −1 in the redshift catalogue). For another 87 (0.4%), LEPHARE could not obtain a photo-z measurement due to non-detections in all but one non-flagged bands (PHOTOZ = −99 in the catalogue).

Additionally, we considered as invalid the redshift solutions for all sources where zbest is at one of the extremes of the redshift search range (zbest = 0 or zbest = 1.5) because we cannot determine whether a minimum of χ2(z) found at one of the extremes is a local minimum, and the actual number of miniJPAS galaxies at z = 0 or z = 1.5 must be very small in any case. Out of 203 sources with zbest = 0, 200 are clearly stars (PS > 0.99), while the remaining 3 are spurious sources in the halo of a bright star. Forty out of 69 sources with zbest = 1.5 are also point sources, most of them known quasars.

The final number of miniJPAS sources with r < 23 and valid photo-z is 20 417. Out of these, 15 719 have FLAGS = 0 in all bands. In this section we use the latter to characterise the photo-z of miniJPAS.

6.1. Redshift distribution of miniJPAS galaxies

Figure 11 shows the distribution of zbest for miniJPAS sources brighter than r < 23. The black histogram was obtained by assigning the same weight w = 1 to every source regardless of its morphology, while the green and red histograms weight each source by the probability of being a star (w = PS) or a galaxy (w = PG = 1 − PS), respectively.

thumbnail Fig. 11.

Distribution of the most likely redshift (zbest) for all miniJPAS sources brighter than r = 23 (solid black line), as well as for galaxies (dot-dashed red line), stars (dashed green line), and galaxies with spectroscopic redshifts (dotted blue line).

While all stars are obviously at z = 0, their zbest estimates span the entire 0 < z < 1.5 search range. Stars dominate the number counts at the extremes (zbest < 0.2 and zbest > 1.4) because fewer galaxies are detected at these redshifts. The very strong peak at zbest ∼ 0.82 is caused by M-type stars, which find their best fit at this particular redshift. Other weaker peaks in the distribution of zbest for stars are also evident in Fig. 11.

Because galaxies represent ∼80% of the r < 23 sample, their redshift distribution is very similar to that for all sources, except at the two ends of the redshift range, where the galaxy counts decrease steeply. The distribution of zbest for galaxies is not smooth, but changes from one redshift bin to the next by more than is expected from shot noise. Interestingly, these peaks are mirrored in the distribution of zspec, indicating that miniJPAS can trace over-densities and voids in the radial direction at least up to z ∼ 0.8. It is unclear if structure in zbest at z ≳ 1 also corresponds to real over- or under-densities because the spectroscopic counts are too low in this range. In any case, the general trend remains consistent between zbest and zspec within the uncertainties up to the photo-z search range limit of z = 1.5.

The redshift distribution depends strongly on the magnitude of the sources because higher-redshift galaxies are typically fainter. The top panel in Fig. 12 shows the distribution of zbest as a function of the limiting r-band magnitude of the selection. Nearly all zbest > 1 galaxies are faint (r ≳ 22), implying a low S/N in the narrow bands. This makes their zbest estimates unreliable (low odds, see bottom panel in Fig. 12). However, the decrease in the odds at high redshift is steeper than expected from the increase in the average magnitude alone.

thumbnail Fig. 12.

Redshift distribution of miniJPAS galaxies as a function of the magnitude cut (top panel) or odds cut (bottom panel) applied on the sample.

Figure 13 shows that at constant magnitude, the mean odds even increases slightly from z ∼ 0.5 to z ∼ 0.8, but decreases abruptly at z > 0.8. This is probably caused by the spectral features with the highest contrast (in particular, Hα and the 4000 Å break), which shift into redder bands (where the depth is shallower, see Fig. 4 in B21) and ultimately beyond the range of miniJPAS.

thumbnail Fig. 13.

Mean value of the odds parameter for galaxies as a function of redshift and brightness. Each symbol indicates the average odds for galaxies in bins of width equal to 0.1 in zbest and 0.5 in r-band magnitude. Symbol areas are proportional to the effective number of galaxies contributing to each bin.

6.2. Accuracy of zbest estimates

In this section, we use the subsample of miniJPAS galaxies with spectroscopic redshifts to evaluate the accuracy of photo-z determinations using the most probable value (the mode of the zPDF), zbest. Figure 14 shows the usual comparison between photometric and spectroscopic redshifts. In the case of miniJPAS, a normal scatter plot is not very informative because most of the dots clump in a very narrow band around the diagonal line that marks the 1:1 relation. To give a realistic impression of the actual density of dots along this line, we generated a density map from the scatter plot by convolving with a Gaussian kernel (note that the pixelation and convolution performed to generate the density map cause some broadening of the distribution compared to the original scatter plot).

thumbnail Fig. 14.

Comparison between photometric and spectroscopic redshifts for individual miniJPAS galaxies in the spectroscopic sample. The left panel includes all r < 23 galaxies with valid photo-z estimates, and the right panel contains only half the sample (those with higher odds). The bottom panels show the redshift errors, Δz. A 2D Gaussian smoothing is applied to the data to improve the visualisation of the density of points. The solid line marks the zbest = zspec relation, and the dotted lines indicate the |Δz| = 0.03 threshold we used to define outliers.

The dark blue areas indicate the regions with the highest density of dots. These correspond to the over-densities found in the distribution of zspec in Fig. 11. The dotted lines enclosing the |Δz| < 0.03 region contain 64% of the whole r < 23 sample (left panel) and 87% of the sub-sample with odds > 0.61 (right panel).

Comparison of the left and right panels in Fig. 11 shows that most of the dispersion in the zbest vs. zspec relation is due to galaxies with low odds. At faint magnitudes, the shape of the zPDF is increasingly dominated by the redshift prior, which favours zbest values close to the peak probability defined by the prior at each magnitude (see Fig. 7). This implies large errors in zbest for sources whose true redshift is far from the z ∼ 0.7 peak of the prior.

The distribution of Δz is noticeably shifted from the origin (Fig. 15), indicating a small positive systematic bias in zbest. The shift is evident in all the four AEGIS pointings when they are considered separately.

thumbnail Fig. 15.

Distribution of the error in zbest, Δz, for the galaxies in the spectroscopic sample. The tails of the distribution at |Δz| > 0.03 are truncated to emphasise the shape of the central peak. Only sources with odds > 0.61 are shown. Each colour represents the distribution for an individual pointing. The black histogram represents the combined distribution for all four pointings.

To estimate the magnitude of the systematic bias in zbest, Δzsys, we calculated the median Δz among the galaxies with odds > 0.65 and |Δz| < 0.03. These constraints help to decrease the dispersion introduced by outliers and galaxies with a broad zPDF. We obtain Δzsys = 1.4 ± 0.1 × 10−3. The shift is also detected at high significance for other cuts in odds or r-band magnitude and for no cuts at all.

We find no dependence of Δzsys on the spectral type of the galaxies (see Sect. 6.6 for the details of our classification method). We also searched for a dependence of Δzsys on the r-band magnitude and redshift of the galaxies in Fig. 16. We find tentative evidence for an increase in the median Δz with r, and a decrease with zspec. This is striking because r and zspec have a positive correlation. The decrease from Δzsys ∼ 0.002 at z ∼ 0 to Δzsys ∼ 0.001 at z ∼ 0.8 is consistent with a constant offset in zbest instead of zbest/(1 + zspec). To prove this, we show with open red symbols the median value of Δz* = zbest − zspec, which revolves around ∼0.002 for the entire redshift range. While an offset of ∼0.002 matches the redshift step we used in the photo-z calculation and the zPDF, it is unlikely that Δzsys is related to the discretisation of the redshift range because we find comparable values for a redshift step of 0.001.

thumbnail Fig. 16.

Median error in zbest as a function of the r-band magnitude (left) and redshift (right) for the galaxies in the spectroscopic sample verifying |Δz| < 0.03 and odds > 0.65. Solid black symbols and open red symbols represent two different definitions of Δz (see text for details). Error bars indicate the 16–84th percentile confidence interval obtained with bootstrap resampling.

The systematic bias affects not only the zbest values, but the entire zPDFs, as evidenced by the slope of the distribution of the probability integral transform (PIT) of the zPDFs (Fig. 17). PIT values for individual sources are computed as the cumulative distribution function of the zPDF evaluated at the spectroscopic redshift (e.g., Schmidt et al. 2020) and represent the probability P(z < zspec). Well-calibrated zPDFs result in a flat distribution of PIT values, while a tilted distribution indicates a bias (Polsterer et al. 2016). Shifting the zPDFs in redshift by Δzsys ∼ 0.0014 or Δzsys ∼ 0.002/(1 + z) largely removes this bias. The excess frequency in the first and last bins of the PIT distribution are the consequence of catastrophic redshift errors (Schmidt et al. 2020).

thumbnail Fig. 17.

Distribution of the PIT values for the zPDFs of galaxies in the spectroscopic sample with odds > 0.65. Black circles and red squares represent the PIT distributions after correcting the individual zPDFs assuming a systematic offset of Δzsys ∼ 0.0014 and Δzsys ∼ 0.002/(1 + z), respectively. Grey bars show the PIT distribution without correction for systematic offset.

The origin of this bias is uncertain. Systematic errors in the wavelength calibration of the JPAS filters is one possibility, as are errors in the characterisation of the spectral response of the detector or the telescope throughput. However, to produce a shift of Δzsys = 1.4 × 10−3, the effective wavelength of the filters would have to be redshifted by ∼9 Å on average, which is more than an order of magnitude larger than the precision of the transmission curves. The same bias could be obtained if the spectral templates are blueshifted by a similar amount, but this is also highly unlikely as the main emission lines are all found at the expected wavelengths. The redshift prior can, in principle, bias zbest values if the width of the prior is comparable to the width of the zPDF. However, our redshift prior is flat for r < 20 galaxies and broad for fainter ones, and the bias is also found for sources with high odds that typically have very narrow zPDFs. Finally, the existence of a bug in the code of LEPHARE is conceivable, but this possibility has been ruled out because roughly the same Δzsys is obtained independently with the TOPZ code (Laur et al., in prep.). Because Δzsys is significantly smaller than the nominal uncertainty of most zbest estimates and its origin remains unknown, we chose not to correct zbest values for this bias.

6.3. Best predictor of the photo-z accuracy

The distributions of |Δz| and Δz shown in Figs. 10 and 15 do not reflect the dependence of the photo-z accuracy on many galaxy properties, such as the magnitude of the sources (which determines the S/N of the photometry), the redshift (which conditions the spectral features within the observed spectral range), and the spectral type (which determines the strength of the spectral features). In addition, some parameters derived from the zPDF such as zerr and odds are not real galaxy properties, but clearly depend on them, and in practice, they summarise our knowledge about the multiple factors that impact photo-z performance. All these quantities are correlated to some extent with each other and with |Δz|. In this section, we examine how the distribution of errors in zbest depends on the r-band magnitude, zbest, zerr, and odds, and analyse which quantity is most useful as a predictor of the photo-z accuracy for individual sources.

Figure 18 shows the cumulative distribution of |Δz| for subsamples of the spectroscopic sample, selected according to the value of one of these four quantities. We split the range of variation for each of them into same-width intervals. The relative number of galaxies in every interval is shown in the small bar histograms. For reference, we plot with dashed lines the cumulative distributions of |Δz| that would result from Gaussian errors with standard deviations of σz) = 0.003, 0.01, and 0.03.

thumbnail Fig. 18.

Cumulative distributions of |Δz| for subsets of the spectroscopic sample within specific intervals of (from top to bottom) the r-band magnitude, zbest, odds, and zerr. Dashed lines represent predictions for a Gaussian distribution of Δz centred at Δzsys = 0.001 and with standard deviations of 0.003, 0.01, and 0.03, and solid lines show the actual distributions for galaxies inside each bin. The inset plots on the right of the panels represent the relative number of galaxies contributing to each bin, coloured according to the central value of the bin. Cumulative distributions for bins containing fewer than 50 galaxies are not shown.

All four quantities present the same general trend: in the most favourable cases (left-most lines, corresponding respectively to bright r-band magnitude, low z, high odds, or low zerr), the distributions of |Δz| are nearly Gaussian, with departure from Gaussianity only at the high |Δz| tail. However, at less favourable values of the quantities, the distributions shift to higher |Δz| at any given value of the normalised counts. They also become less Gaussian, with flatter slopes and heavier tails at high |Δz|. The reason for this change in the shape of the |Δz| distributions is an increase in the rate of catastrophic errors as we progress from left to right.

To identify which of these four quantities is more effective in separating the good from the bad photo-z, we cannot rely on Fig. 18 because the distribution of each of these quantities in the miniJPAS sample is different. Instead, we calculated the correlation of these quantities with |Δz| for individual sources (Fig. 19). Because of the different ranges that each of these quantities span and the non-linearity of their relation with |Δz|, we computed correlations between ranks, instead of correlation of their values. That is, for each quantity (including |Δz|), we sorted the galaxies in ascending order and computed the Spearman rank correlation coefficient (ρ). We find ρ = 0.285, 0.466, 0.551, and −0.602 for zbest, r-mag, zerr, and odds, respectively. In the case of the odds parameter, ρ is negative because the average |Δz| decreases at higher odds. According to this, the odds parameter has the strongest correlation with |Δz|, closely followed by zerr and then r, while zbest has the weakest correlation.

thumbnail Fig. 19.

Comparison of the predictive power for the error in zbest of four quantities: r-band magnitude, the value of zbest, the odds parameter, and zerr. Each plot shows the correlation between the ranks of individual galaxies when sorted by each of this quantities and the rank when sorted by |Δz|. The Spearman rank correlation coefficient (ρ) is quoted for each case.

This suggests that the best way to select a subsample of N galaxies with the most accurate photo-z is not to pick the N brightest galaxies in the sample (a cut in magnitude) or the N with smallest zerr, but the N with higher odds. The high dispersion in all panels of Fig. 19 implies that for individual galaxies or small samples, this may not always be the case, but for large enough N, odds should have a clear advantage.

We confirmed this hypothesis by computing σNMAD and η as a function of the fraction (f) of the spectroscopic sample that is selected by applying a threshold in any of these four quantities (Fig. 20). For f close to 1 (very few galaxies rejected), all four quantities yield almost the same σNMAD and η because the selected samples are also nearly identical. However, as f decreases due to more restrictive thresholds, the tracks diverge. If we target a specific σNMAD, the size of the sample selected with a threshold in zerr or odds is significantly larger than that from a selection in r-band magnitude (up to ∼50% larger for σNMAD ∼ 0.003). If, on the other hand, we target a specific sample size, the σNMAD obtained from the corresponding threshold in zerr or odds is also significantly smaller.

thumbnail Fig. 20.

Dependence of σNMAD and η on the fraction of the r < 23 sample that was selected using a threshold in any of four different quantities: r-band magnitude, zbest, zerr, and odds.

The curves of σNMAD(f) for zerr and odds are nearly identical. This is expected because the two parameters have a very strong anti-correlation (ρ = −0.856, Fig. 21), much stronger than any of them has with |Δz|.

thumbnail Fig. 21.

Correlation between zerr and odds for individual sources in the spectroscopic sample.

It is remarkable that zerr and odds obtain the same σNMAD in the whole range of f and that it is significantly better than that of the r-band magnitude. However, zerr performs more poorly when outliers are to be avoided, in particular at f < 0.4, where it is also outperformed by the r-band magnitude.

Our interpretation of these trends is as follows: for sources with a single significant peak in the zPDF, both zerr and odds depend on the width of the peak and produce similar ranks. However, in sources with multiple peaks in the zPDF, zerr underestimates the actual uncertainty in zbest because it is blind to all but the highest peak. On the other hand, the odds is affected (decreased) by these secondary peaks. The consequence is that galaxies with multiple peaks in the zPDF (which are more likely to have catastrophic redshift errors) are ranked higher by zerr compared to odds. This has almost no impact on σNMAD because it is insensitive to outliers, but it shows up in η, as many more outliers are ranked above the threshold in zerr compared to odds.

6.4. Validation of zerr estimates

We have shown that zerr and odds are the quantities with the stronger correlation to Δz and are therefore the best choices for the selection of subsamples with the most accurate photo-z. In this section, we test if zerr corresponds to the actual 1σ uncertainty in zbest for individual galaxies.

Figure 22 shows the distribution of Δz/zerr, which corresponds to the error in zbest in units of the predicted 1σ uncertainty for each galaxy. Under ideal circumstances, the expected distribution is a Gaussian with a standard deviation of 1 (black line). However, the actual distribution is far from Gaussian, with a pointy core and extended tails. Fifty-five percent of the galaxies are within the [−1,1] interval and 77% in [−2,2] compared to expectations of 68% and 95%, respectively. The colour-coding reveals that the core of the distribution is dominated by galaxies with high zerr values, while those with small zerr dominate in the tails. This suggests that sources with large (small) zerr overestimate (underestimate) the actual uncertainty in zbest.

thumbnail Fig. 22.

Distribution of the ratio between the actual redshift error, Δz, and the uncertainty predicted with the Δχ2 method, zerr, for individual galaxies in the spectroscopic sample with colour-coding for zerr.

Further evidence is presented in Fig. 23, which shows the fraction of galaxies with Δz < zerr as a function of zerr (grey histogram). If zerr estimates were accurate, this fraction should be constant around ∼0.68 regardless of zerr. Instead, we find a strong dependence on zerr for low zerr values, with a fraction much lower than the expected 68%, while the relation becomes flat (but still below the expectation, with f ∼ 55–60%) for zerr ≳ 0.003.

thumbnail Fig. 23.

Distribution of the fraction of galaxies with |Δz| < zerr as a function of zerr (grey histogram). The horizontal line marks a fraction of 68% expected if zerr estimates are accurate. Small dots indicate the zerr and |Δz| of individual galaxies (right scale). The dots are orange and green for |Δz| > zerr and |Δz| < zerr, respectively. The dotted red line marks the expected σNMAD as a function of zerr, while the connected dark blue squares with error bars indicate the observed σNMAD and the 16–84th percentiles of its confidence interval.

One reason for the strong underestimation of the actual redshift uncertainty in sources with low zerr is the assumption implicit in the Δχ2 method that the probability distribution for the minimum of χ2(z) is the χ2 distribution for n degrees of freedom (Press et al. 1992). For bright sources with high S/N photometry, this is not the case because differences between the intrinsic SED of the galaxy and the closest template in the library are much larger than the photometric errors, implying high values for the reduced χ2, χ r 2 $ \chi^2_r $ = χ2/(n − 1) ≫ 1 (see Hernán-Caballero 2012; Hernán-Caballero et al. 2015, for a discussion). By contrast, galaxies with low S/N photometry can easily reach χ r 2 $ \chi^2_r $ ≲ 1 with multiple redshift-template combinations due to the degeneracy in the colour space. Because the model is not linear in the fitting parameters (the redshift and spectral type), the χ2 distribution does not provide a realistic description of the actual redshift uncertainty (Oyaizu et al. 2008).

Another factor contributing to the general overconfidence in zerr is the lack of sensitivity in the Δχ2 method to secondary peaks in the distribution of χ2(z), and thus, to the probability of a catastrophic redshift error. This is evidenced by the close to 1:1 relation between σNMAD and zerr in the range 0.001–0.1 (blue squares), which shows that for zerr > 0.001, it is in fact a realistic prediction of the error in zbest if catastrophic errors are excluded.

6.5. Validation of odds estimates

Our definition of the odds parameter (see Sect. 4.4) implies that for an individual galaxy, the probability of an error |Δz| > 0.03 in zbest is P = 1 − odds. For a sufficiently large subsample, the outlier rate should therefore be η ≈ 1 − ⟨odds⟩.

Because the zPDF used to compute the odds is derived from χ2(z) and the redshift prior, it is affected by the same χ r 2 $ \chi^2_r $ ≫1 issue that we discussed for zerr. However, we compensated for this with the contrast correction applied to the zPDF in Sect. 4.3. Moreover, unlike zerr, the odds is sensitive to the presence of secondary peaks in the zPDF, meaning that it should accurately estimate the probability of being an outlier for individual galaxies. We test this in Fig. 24, which shows that the fraction of galaxies with |Δz| < 0.03 has the expected dependence with the odds in the whole range (note that f(|Δz| < 0.03) = 1 − η).

thumbnail Fig. 24.

Distribution of the fraction of sources with |Δz| < 0.03 as a function of odds (grey histogram). The diagonal line marks the 1:1 relation expected if odds estimates for individual galaxies are accurate. Small dots indicate the odds and |Δz| of individual galaxies (right scale). The dots are red for outliers (|Δz| > 0.03) and cyan otherwise.

To determine whether the magnitude or redshift of the galaxies has any impact on photo-z accuracy that is not already accounted for by the odds, we show in Fig. 25 the magnitude and redshift dependence of σNMAD at constant odds. There is no clear residual dependence of σNMAD on the r magnitude. However, there seems to be an increase in σNMAD at low z, in particular for sources with very low odds. This might be a consequence of the redshift prior favouring intermediate zbest values in faint sources with low S/N (the prior probability peaks at z ∼ 0.6 for r = 22 and z ∼ 0.75 for r = 23, see Fig. 7). Because only few galaxies have low z and low odds, we do not expect this to have a significant impact on our results.

thumbnail Fig. 25.

Dependence of σNMAD on the r-band magnitude (left) and zspec (right) for galaxies grouped in bins of odds. σNMAD is computed in steps of 0.5 (1 for r < 20) for the r-band magnitude and 0.1 for redshift. Only bins containing more than 15 sources are shown.

6.6. Dependence on the spectral type

Photo-z accuracy is also expected to depend on the spectral type of the galaxies, which determines the contrast of the spectral features that anchor the photo-z. The most important such features at the redshifts typical of miniJPAS galaxies are the 4000 Å break of the stellar continuum and the main optical emission lines (Hα, Hβ, [O II] 3727 Å, and [O III] 4959+5007 Å).

The combination of deep broad-band and shallower narrow-band photometry produces some interesting trends for miniJPAS galaxies: at relatively bright magnitudes, the narrow-band filters easily detect emission lines, if they are present, which increases the chances of a highly accurate photo-z in star-forming galaxies compared to quiescent ones. However, at fainter magnitudes, the emission lines become increasingly hard to detect, removing the advantage for star-forming galaxies. At magnitudes fainter than the detection limit in the narrow bands, quiescent galaxies often have an edge due to their stronger 4000 Å break, which is easily detected in the broad-band photometry.

To quantify the impact of the spectral type on σNMAD, we have classified all the galaxies in the spectroscopic sample into two broad categories of red and blue, loosely corresponding to quiescent and star-forming, respectively. We repeated the classification three times, according to the value of three different parameters from the best-fitting CIGALE model: (1) Dn(4000), which measures the strength of the 4000 Å break using the definition of Balogh et al. (1999) and is a proxy for the light-weighted age of the stellar population (e.g., Kauffmann et al. 2003a,b; Kriek et al. 2006; Hernán-Caballero et al. 2013), (2) the specific instantaneous star formation rate (sSFR) derived directly from the model star formation history, and (3) the equivalent width of the Hα line, EW(Hα), an observational proxy for the sSFR.

Because the boundary between the quiescent and star-forming classes is somewhat arbitrary (many galaxies have intermediate properties) and also depends on redshift and luminosity, we simplified the classification by splitting the sample into two same-sized subsamples. The first (second) subsample contains the 50% of galaxies with the highest (lowest) value of Dn(4000), sSFR, or EW(Hα). These criteria do not provide high purity in the resulting samples of quiescent and star-forming galaxies, but allow more easily comparing the results between the different selection criteria. They are also sufficient to determine whether the odds parameter accounts for the dependence on the spectral type.

Figure 26 shows the σNMAD for all sources brighter than a given r-band magnitude cut in the red and blue samples. The trends are similar regardless of the quantity that is used to split the sample, but there are some interesting differences: for a cut at very faint magnitudes (r ≲ 23), the red sample reaches lower σNMAD when the selection is made with Dn(4000) or sSFR, but not with EW(Hα). This indicates that a substantial number of galaxies switches between the red and blue classes depending on the parameter. Classifying with EW(Hα) places some high Dn(4000) galaxies (which for some reason, maybe active nuclei, also have Hα emission) in the blue sample, improving its σNMAD.

thumbnail Fig. 26.

Variation in σNMAD as a function of the cut applied in r-band magnitude separately for red and blue galaxies. Each panel shows results for a different way of classifying the galaxies, using the strength of the 4000 Å break (top), the specific instantaneous SFR (middle), and the equivalent width of Hα (bottom). Solid lines correspond to σNMAD values at 100% completeness (no cut in odds), and dotted lines indicate σNMAD values for a cut in odds corresponding to 50% completeness.

A consequence of this is that the photo-z accuracy at a given magnitude depends not only on the spectral type, but on how the spectral type is defined. In particular, more restrictive classification criteria are likely to improve the photo-z accuracy for both quiescent and star-forming galaxies because intermediate cases (where neither the 4000 Å break nor emission lines are strong) constitute the most difficult targets for photo-z calculation.

The factors responsible for the different photo-z accuracy in quiescent and star-forming galaxies are also reflected in the value of the odds parameter. Figure 27 shows that if the comparison is made between galaxies within a narrow range of odds, the difference in σNMAD between red and blue galaxies disappears. The similarity is even stronger for η, indicating that the odds parameter accurately predicts the probability of a catastrophic error for both quiescent and star-forming galaxies.

thumbnail Fig. 27.

Dependence of σNMAD and η on odds for quiescent (solid red symbols) and star-forming (open blue symbols) galaxies in the spectroscopic sample according to three different classification criteria (left, centre, and right panels; see text for details). The error bars represent 1σ confidence intervals calculated with bootstrap resampling.

6.7. Representativeness of the spectroscopic sample

The photo-z performance statistics presented so far refer only to the subsample of miniJPAS galaxies with spectroscopic redshifts (s-sample). We can expect these statistics to also predict the performance in the sources without spectroscopic redshifts (p-sample) only if the s- and p-sample are drawn from the same parent population.

We already showed in Fig. 4 that the distribution of r-band magnitude in the s-sample reproduces that of the whole miniJPAS when every source is weighted with its probability of being a galaxy, PG. Figure 28 presents a more detailed comparison of the magnitude distribution in the s-sample and p-sample. Because the spectroscopic coverage and the depth of the miniJPAS images varies from one pointing to the next, we show the distributions for each pointing separately. We used the two-sample Kolmogorov-Smirnov test to calculate the probability p of the s-sample and p-sample being drawn from the same parent population. The difference between samples is significant (p < 0.01) only for pointing AEGIS-4. Unlike the other pointings, the spectroscopic counts in AEGIS-4 flatten at r > 21.5. Interestingly, the area covered by DEEP is the smallest in this pointing and the number of spectroscopic galaxies is the lowest. As a consequence, this pointing also has the highest counts of photo-z-only galaxies in almost every magnitude bin. The large galaxy cluster centred at RA = 213.6254, Dec = 51.9379 (see Fig. 28 in B21) may also boost the galaxy counts in AEGIS-4.

thumbnail Fig. 28.

Distribution of the observed r-band magnitude of miniJPAS galaxies for the photo-z-only sample (solid lines) and the spectroscopic sample (connected dots) for individual pointings. log p-values in the legend indicate the probability of the spectroscopic and photo-z-only samples being drawn from the same parent population.

In Fig. 29 we compare the distributions of four broad-band colours for galaxies in the p-sample and s-sample. For each colour index, only sources with > 3σ detection in both bands were considered. We show the distributions separately for three magnitude ranges. The magnitude-dependence of the colour distribution is small except for the ur colour, where the S/N > 3 requirement for the u band implies that most red objects are not selected at faint magnitudes, shifting the distribution towards bluer ur. The discrepancies between distributions for the s-sample and p-sample are highly significant, particularly for the ri colour in r > 20 sources (p < 0.0001). However, the range of colour indices that is covered is the same, and in all cases, the mean colour index of the distribution differs by less than 0.1 magnitudes (Table 1).

thumbnail Fig. 29.

Distribution of the observed broad-band colours in three bins of magnitude. Each plot only includes sources with > 3σ detections in the two bands defining the colour index and with valid photo-z estimates. Solid lines show the distributions measured for galaxies in the photo-z-only sample. Connected dots represent the distribution for galaxies in the spectroscopic sample (scaled by a factor 2 to facilitate the comparison).

Table 1.

Average colour indices by magnitude.

The distribution of zbest (left panel in Fig. 30) is slightly biased towards higher values for r > 20 sources in the s-sample compared to the p-sample. This is consistent with their redder gi and ri colours. For the odds parameter (right panel), the difference is significant only among the faintest galaxies (r > 22) and indicates that r > 22 galaxies have higher odds on average in the s-sample than in the p-sample. This may be a consequence of the requirement of a high confidence in the spectroscopic redshift for selection into the s-sample. At faint magnitudes, this confidence requires high-contrast spectral features (a strong 4000 Å break or emission lines) that also help increase the confidence in the photo-z estimate.

thumbnail Fig. 30.

Distribution of zbest and odds in bins of magnitude for the photo-z-only and spectroscopic samples. Symbols are the same as in Fig. 29.

As a result of this analysis, we conclude that the s-sample is slightly biased towards redder and more distant galaxies, but also with higher odds than same-magnitude galaxies in the p-sample. However, these small differences do not suggest the existence of a population of galaxies in the p-sample that is not represented in the s-sample. Accordingly, we consider the templates selected for the s-sample to be suitable for the p-sample as well, and we expect a similar performance.

The small but highly significant differences in the odds distributions are important because the strong correlation between odds and photo-z accuracy implies that for magnitude-limited subsamples, the σNMAD and η measured in the s-sample probably overestimate the actual accuracy in the p-sample. However, we have shown that odds is the best predictor of photo-z accuracy and that at constant odds, the residual dependence of photo-z accuracy on r, zspec, or the spectral type is small.

This implies that the distribution of |Δz| at a given odds obtained for the s-sample should also represent that of the p-sample. In the next section we show how this can be used to compensate for the different odds distributions in the s- and p-sample to obtain realistic photo-z performance statistics for the p-sample.

6.8. Extrapolation to the entire miniJPAS sample

The spectroscopic sample we used for the analysis up to this point excludes sources with flags in the photometry. In order to determine the impact of photometric flags in the photo-z accuracy, we compare in Fig. 31 the values of σNMAD and η as a function of odds for flagged and non-flagged galaxies in the spectroscopic sample. The differences in σNMAD are very small and largely consistent within the statistical errors, except at very low odds (odds < 0.4). This suggests that most flagged sources are barely affected in their photo-z accuracy by the photometric issue signalled by the flags. The trends for η are also very similar, except at odds > 0.9, where the outlier rate stays at η ∼ 0.1 for flagged sources but decreases to η ∼ 0.01 for non-flagged ones. This clear excess of outliers at very high odds is probably a consequence of strong spurious peaks in the zPDF caused by artefacts in the photometry of some of the flagged sources. Because flagged sources represent ∼30% of the miniJPAS sample, we consider that this small increase in the outlier rate relative to non-flagged sources does not justify purging flagged sources unless very high reliability (very low η) is required.

thumbnail Fig. 31.

Dependence of σNMAD (top) and η (bottom) on odds for sources in the spectroscopic sample without photometry flags in any band (solid symbols) and sources with flags in one or more bands (open symbols).

The strong dependence of the distribution of |Δz| on odds (Fig. 18) and the lack of a significant residual dependence on other quantities at constant odds allow us to estimate the number of galaxies with photo-z errors below a given threshold in any arbitrary sample of miniJPAS sources,

N ( | Δ z | < Δ z ) = i P G , i f S ( | Δ z | < Δ z | odds i ) , $$ \begin{aligned} N(| \Delta z | < \Delta z^\prime ) = {\sum _{i}} P_{G,i} \ f_S(| \Delta z | < \Delta z^\prime \ {|} \ {odds}_{i}) , \end{aligned} $$(13)

where PG, i is the probability of being a galaxy for source i (see Sect. 2.4) and fS(|Δz| < Δz′ | oddsi) is the frequency of |Δz| < Δz′ among galaxies with oddsoddsi in the spectroscopic sample. Table 2 lists the values of fS(|Δz|< Δz′ | odds) calculated for intervals of odds with several values of the threshold Δz′.

Table 2.

Fraction of sources with |Δz| < Δz′ per odds interval in the spectroscopic sample.

We used Eq. (13) to compute the number density n of galaxies in miniJPAS with r < 23 and |Δz| < Δz′ for several cuts in odds (Fig. 32). For this, we assumed that the effective area of miniJPAS (after taking the masked areas into account) is 0.895 deg2 (see B21). We repeated the calculation twice: first using the frequencies fS(|Δz|< Δz′ | odds) calculated on non-flagged sources for flagged and non-flagged sources indistinctly, second using their own fS(|Δz|< Δz′ | odds) for both flagged and non-flagged sources. The difference in number counts between the two methods is < 3% for any Δz′ and cut in odds.

thumbnail Fig. 32.

Predicted density of r < 23 miniJPAS galaxies with redshift errors |Δz| < Δz′ as a function of the threshold Δz′ for four different cuts in the odds parameter. The solid lines are generated by applying the same value of fS(|Δz| < Δz′ | oddsi) calculated in non-flagged sources to both flagged and non-flagged sources, and the dotted lines use separate values for flagged and non-flagged sources.

These distributions show that there are ∼17 500 galaxies per deg2 in miniJPAS at r < 23, of which ∼4200 have |Δz| < 0.003. However, selecting all of them requires placing no constraint on odds, which results in large average errors (σNMAD = 0.013) and a high rate of outliers (η = 0.39). The targeted photo-z accuracy for J-PAS (σNMAD = 0.003; Benítez et al. 2014) is achieved after imposing odds > 0.82, which implies selecting ∼5200 galaxies per deg2 (of which ∼2600 have |Δz| < 0.003 and only ∼5% are outliers).

7. Summary

This paper describes the procedures that we followed in order to generate the photo-z catalogue of miniJPAS, a ∼1 deg2 imaging survey in 60 optical bands encompassing the AEGIS field. We also provided a detailed analysis of the photo-z performance enabled by the exhaustive spectroscopic coverage of AEGIS by the SDSS and DEEP surveys.

We relied on forced (dual-mode) photometry obtained for an r-band selected catalogue with matched apertures corresponding to 1 Kron radius in the r band (restricted AUTO aperture), with corrections to compensate for the difference in the PSF of each band with respect to r (PSFCOR photometry). We used CIGALE to generate stellar population synthesis models matching the photo-spectra of all r < 22 galaxies with spectroscopic redshifts. Synthetic photometry obtained from these models was used to identify systematic offsets in the observed photometry with respect to the models. We showed that an iterative correction of these offsets converges to the same solution within ∼0.01 magnitudes, regardless of the initial offsets.

The photo-z were computed with a customised version of LEPHARE. The spectral templates we used were the best-fitting CIGALE models of 50 miniJPAS galaxies, selected from a larger set of 455 candidates as those that produce the most accurate photo-z in a test sample.

We showed that the zPDF generated by LEPHARE are slightly overconfident for r < 19 galaxies but severely underconfident at r > 20. A simple contrast correction of the zPDF compensates for this magnitude dependence.

Comparison between the mode of the zPDF (zbest) and the spectroscopic redshift (zspec) showed that the distribution of absolute redshift errors (|Δz|) is bimodal. The main peak at |Δz| ∼ 0.004 corresponds to the typical inaccuracy in photo-z estimates, and a second peak at |Δz| ∼ 0.04 represents catastrophic errors.

The distribution of zbest for the galaxies in miniJPAS closely follows the distribution of zspec in the spectroscopic subsample. This indicates that (1) the spectroscopic sample is representative of the redshift distribution of the whole sample and (2) we successfully detect variation in the density of galaxies along the redshift dimension, at least up to z ∼ 0.8.

We find zbest estimates are biased towards zbest > zspec by ∼0.10–0.14%. This bias is consistent among the four miniJPAS pointings and shows no clear dependence on either the magnitude or the redshift of the sources. In spite of our efforts to identify the origin of this bias, it remains uncertain and demands further analysis.

The odds parameter has the strongest correlation to |Δz| of any photo-z related quantities. In particular, its correlation is significantly stronger than obtained with the predicted 1σ redshift error (zerr) because the latter is insensitive to the probability of a catastrophic redshift error. This implies that applying a cut in odds is the most efficient way to select a fixed-size subsample with the best possible photo-z (or conversely, the largest sample within some photo-z quality constraints). We also showed that there is no clear residual dependence of the photo-z accuracy on r-band magnitude at constant odds, while there seems to be a redshift dependence for sources with very low odds, consistent with the expected effect of the redshift prior in low S/N photometry.

Comparison of zerr and |Δz| shows that the former increasingly underestimates the actual errors in zbest for lower zerr values. On the other hand, the odds parameter accurately represents the probability of a redshift outlier (|Δz| > 0.03).

The photo-z accuracy is dependent on the spectral type. Emission lines allow star-forming galaxies to obtain lower σNMAD than quiescent galaxies at bright magnitudes, but their advantage vanishes at faint magnitudes as the emission lines become increasingly hard to detect and the photo-z solution becomes dominated by the 4000 Å break. The dependence on the spectral type disappears if σNMAD or η are calculated for sources within narrow intervals of odds.

We confirm that the distribution of magnitudes and broadband colours in the spectroscopic sample is roughly consistent with the photo-z-only sample, but galaxies in the latter are slightly bluer (≲0.1 magnitudes) and have slightly lower zbest on average. The distribution of odds for r > 22 galaxies is also biased towards higher values in the spectroscopic sample. We took this into account to generate realistic estimates of the expected photo-z accuracy in the photo-z-only sample.

We conclude that at the depth of miniJPAS, there are ∼17 500 galaxies per deg2 with valid photo-z estimates, ∼4200 of which have |Δz| < 0.003. The typical error for r < 23 galaxies is σNMAD = 0.013 with an outlier rate η = 0.39. The target photo-z accuracy σNMAD = 0.003 is achieved after imposing odds > 0.82. Under these constraint, the density of the selected galaxies is reduced by 70% to n ∼ 5200 deg−2 (∼2600 of which have |Δz| < 0.003), and the outlier rate decreases to η = 0.05.


3

In LEPHARE, this is done by setting AUTO_ADAPT=NO in the configuration file.

Acknowledgments

We thank the anonymous referee for useful comments and suggestions that helped improve this work. This paper has gone through internal review by the J-PAS collaboration. Based on observations made with the JST/T250 telescope at the Observatorio Astrofísico de Javalambre (OAJ), in Teruel, owned, managed, and operated by the Centro de Estudios de Física del Cosmos de Aragón (CEFCA). We acknowledge the OAJ Data Processing and Archiving Unit (UPAD) for reducing and calibrating the OAJ data used in this work. Funding for the J-PAS Project has been provided by the Governments of Spain and Aragón through the Fondo de Inversión de Teruel, European FEDER funding and the Spanish Ministry of Science, Innovation and Universities, and by the Brazilian agencies FINEP, FAPESP, FAPERJ and by the National Observatory of Brazil. Additional funding was also provided by the Tartu Observatory and by the J-PAS Chinese Astronomical Consortium. Funding for OAJ, UPAD, and CEFCA has been provided by the Governments of Spain and Aragón through the Fondo de Inversiones de Teruel; the Aragón Government through the Research Groups E96, E103, and E16_17R; the Spanish Ministry of Science, Innovation and Universities (MCIU/AEI/FEDER, UE) with grant PGC2018-097585-B-C21; the Spanish Ministry of Economy and Competitiveness (MINECO/FEDER, UE) under AYA2015-66211-C2-1-P, AYA2015-66211-C2-2, AYA2012-30789, and ICTS-2009-14; and European FEDER funding (FCDD10-4E-867, FCDD13-4E-2685). C. Q. acknowledges support from Brazilian agencies FAPESP and CAPES. E. S. C. acknowledges financial support from Brazilian agencies CNPq and FAPESP (process #2019/19687-2). L. D. G, R. G. D. and G. M. S. acknowledge support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709) and the projects PID2019-109067-GB100 and AYA2016-77846-P. Part of this work was supported by institutional research funding IUT40-2, JPUT907 and PRG1006 of the Estonian Ministry of Education and Research. We acknowledge the support by the Centre of Excellence “Dark side of the Universe” (TK133) financed by the European Union through the European Regional Development Fund.

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Appendix A: Additional tables

Table A.1.

Zero-point recalibration offsets [mag]

Table A.2.

Stellar population properties of the model templates

Table A.3.

Observables measured on the model templates

All Tables

Table 1.

Average colour indices by magnitude.

Table 2.

Fraction of sources with |Δz| < Δz′ per odds interval in the spectroscopic sample.

Table A.1.

Zero-point recalibration offsets [mag]

Table A.2.

Stellar population properties of the model templates

Table A.3.

Observables measured on the model templates

All Figures

thumbnail Fig. 1.

Distribution of r-band magnitudes for the whole miniJPAS sample (solid black line), flagged sources (dot-dashed olive line), and non-flagged sources (dashed magenta line). The distribution for the whole sample scaled by a factor 0.7 is shown for reference (dotted black line).

In the text
thumbnail Fig. 2.

Distribution of the probability of being a star, PS, for miniJPAS sources as a function of the (colour-coded) limiting magnitude of the sample. The spike at PS = 0.5 is due to sources with insufficient S/N for a classification in the detection band, which are assigned PS = 0.5 by default.

In the text
thumbnail Fig. 3.

Footprint of the miniJPAS and DEEP2/DEEP3 spectroscopic observations. Grey dots represent miniJPAS sources with r < 23, and blue and red dots represent sources that were targeted for spectroscopy by the DEEP2 and DEEP3 surveys, respectively.

In the text
thumbnail Fig. 4.

Distribution of miniJPAS sources as a function of r-band magnitude for all sources (solid black lines), stars (dashed green lines), galaxies (dot-dashed red lines), and galaxies with spectroscopic redshifts (dotted blue lines). Smooth lines show cumulative counts, and histograms show counts in bins of 0.1 magnitudes.

In the text
thumbnail Fig. 5.

Magnitude residuals between the observed and synthetic photometry after the first (top) and third (bottom) iterations of the recalibration procedure. Symbols indicate the median residual, and error bars enclose the 16th to 84th percentile ranges. Small symbols correspond to photometry in the narrow-band J-PAS filters, and large symbols represent broad-band filters (uJAVA, uSDSS, gSDSS, rSDSS, and iSDSS) and the long-pass J1007 filter.

In the text
thumbnail Fig. 6.

Comparison between the arbitrary shifts introduced in the input photometry for individual bands (X-axis) and the resulting change in the recalibration offsets obtained (Y-axis). Symbols are the same as in Fig. 5. The dashed line marks the 1:1 relation that is expected when the recalibration process perfectly compensates for systematic offsets in the photometry.

In the text
thumbnail Fig. 7.

Prior probability redshift distributions used by LEPHARE for the broad spectral types elliptical (solid line), spiral (dotted line), and irregular (dot-dashed line), with colour coding for the magnitude (see text for details).

In the text
thumbnail Fig. 8.

Set of fifty galaxy templates used for computing the photo-z for miniJPAS sources, sorted by their rest-frame UV-to-optical spectral index and shifted in the Y-axis for clarity.

In the text
thumbnail Fig. 9.

Fraction of galaxies with zspec within the highest probability density confidence interval as a function of the confidence level before (left) and after (right) the contrast correction of the zPDF. Galaxies are grouped by their r-band flux in bins of 0.5 magnitudes. The diagonal line marks the (c) = c relation that is expected if the zPDF represents the actual redshift uncertainty. Values above (below) this line imply under- (over-)confidence in the zbest estimate.

In the text
thumbnail Fig. 10.

Distribution of redshift errors for the spectroscopic subsample of miniJPAS (histogram) and best-fitting model combining one Gaussian and one Lorentzian profile (dotted line) or two Lorentzians (dashed line).

In the text
thumbnail Fig. 11.

Distribution of the most likely redshift (zbest) for all miniJPAS sources brighter than r = 23 (solid black line), as well as for galaxies (dot-dashed red line), stars (dashed green line), and galaxies with spectroscopic redshifts (dotted blue line).

In the text
thumbnail Fig. 12.

Redshift distribution of miniJPAS galaxies as a function of the magnitude cut (top panel) or odds cut (bottom panel) applied on the sample.

In the text
thumbnail Fig. 13.

Mean value of the odds parameter for galaxies as a function of redshift and brightness. Each symbol indicates the average odds for galaxies in bins of width equal to 0.1 in zbest and 0.5 in r-band magnitude. Symbol areas are proportional to the effective number of galaxies contributing to each bin.

In the text
thumbnail Fig. 14.

Comparison between photometric and spectroscopic redshifts for individual miniJPAS galaxies in the spectroscopic sample. The left panel includes all r < 23 galaxies with valid photo-z estimates, and the right panel contains only half the sample (those with higher odds). The bottom panels show the redshift errors, Δz. A 2D Gaussian smoothing is applied to the data to improve the visualisation of the density of points. The solid line marks the zbest = zspec relation, and the dotted lines indicate the |Δz| = 0.03 threshold we used to define outliers.

In the text
thumbnail Fig. 15.

Distribution of the error in zbest, Δz, for the galaxies in the spectroscopic sample. The tails of the distribution at |Δz| > 0.03 are truncated to emphasise the shape of the central peak. Only sources with odds > 0.61 are shown. Each colour represents the distribution for an individual pointing. The black histogram represents the combined distribution for all four pointings.

In the text
thumbnail Fig. 16.

Median error in zbest as a function of the r-band magnitude (left) and redshift (right) for the galaxies in the spectroscopic sample verifying |Δz| < 0.03 and odds > 0.65. Solid black symbols and open red symbols represent two different definitions of Δz (see text for details). Error bars indicate the 16–84th percentile confidence interval obtained with bootstrap resampling.

In the text
thumbnail Fig. 17.

Distribution of the PIT values for the zPDFs of galaxies in the spectroscopic sample with odds > 0.65. Black circles and red squares represent the PIT distributions after correcting the individual zPDFs assuming a systematic offset of Δzsys ∼ 0.0014 and Δzsys ∼ 0.002/(1 + z), respectively. Grey bars show the PIT distribution without correction for systematic offset.

In the text
thumbnail Fig. 18.

Cumulative distributions of |Δz| for subsets of the spectroscopic sample within specific intervals of (from top to bottom) the r-band magnitude, zbest, odds, and zerr. Dashed lines represent predictions for a Gaussian distribution of Δz centred at Δzsys = 0.001 and with standard deviations of 0.003, 0.01, and 0.03, and solid lines show the actual distributions for galaxies inside each bin. The inset plots on the right of the panels represent the relative number of galaxies contributing to each bin, coloured according to the central value of the bin. Cumulative distributions for bins containing fewer than 50 galaxies are not shown.

In the text
thumbnail Fig. 19.

Comparison of the predictive power for the error in zbest of four quantities: r-band magnitude, the value of zbest, the odds parameter, and zerr. Each plot shows the correlation between the ranks of individual galaxies when sorted by each of this quantities and the rank when sorted by |Δz|. The Spearman rank correlation coefficient (ρ) is quoted for each case.

In the text
thumbnail Fig. 20.

Dependence of σNMAD and η on the fraction of the r < 23 sample that was selected using a threshold in any of four different quantities: r-band magnitude, zbest, zerr, and odds.

In the text
thumbnail Fig. 21.

Correlation between zerr and odds for individual sources in the spectroscopic sample.

In the text
thumbnail Fig. 22.

Distribution of the ratio between the actual redshift error, Δz, and the uncertainty predicted with the Δχ2 method, zerr, for individual galaxies in the spectroscopic sample with colour-coding for zerr.

In the text
thumbnail Fig. 23.

Distribution of the fraction of galaxies with |Δz| < zerr as a function of zerr (grey histogram). The horizontal line marks a fraction of 68% expected if zerr estimates are accurate. Small dots indicate the zerr and |Δz| of individual galaxies (right scale). The dots are orange and green for |Δz| > zerr and |Δz| < zerr, respectively. The dotted red line marks the expected σNMAD as a function of zerr, while the connected dark blue squares with error bars indicate the observed σNMAD and the 16–84th percentiles of its confidence interval.

In the text
thumbnail Fig. 24.

Distribution of the fraction of sources with |Δz| < 0.03 as a function of odds (grey histogram). The diagonal line marks the 1:1 relation expected if odds estimates for individual galaxies are accurate. Small dots indicate the odds and |Δz| of individual galaxies (right scale). The dots are red for outliers (|Δz| > 0.03) and cyan otherwise.

In the text
thumbnail Fig. 25.

Dependence of σNMAD on the r-band magnitude (left) and zspec (right) for galaxies grouped in bins of odds. σNMAD is computed in steps of 0.5 (1 for r < 20) for the r-band magnitude and 0.1 for redshift. Only bins containing more than 15 sources are shown.

In the text
thumbnail Fig. 26.

Variation in σNMAD as a function of the cut applied in r-band magnitude separately for red and blue galaxies. Each panel shows results for a different way of classifying the galaxies, using the strength of the 4000 Å break (top), the specific instantaneous SFR (middle), and the equivalent width of Hα (bottom). Solid lines correspond to σNMAD values at 100% completeness (no cut in odds), and dotted lines indicate σNMAD values for a cut in odds corresponding to 50% completeness.

In the text
thumbnail Fig. 27.

Dependence of σNMAD and η on odds for quiescent (solid red symbols) and star-forming (open blue symbols) galaxies in the spectroscopic sample according to three different classification criteria (left, centre, and right panels; see text for details). The error bars represent 1σ confidence intervals calculated with bootstrap resampling.

In the text
thumbnail Fig. 28.

Distribution of the observed r-band magnitude of miniJPAS galaxies for the photo-z-only sample (solid lines) and the spectroscopic sample (connected dots) for individual pointings. log p-values in the legend indicate the probability of the spectroscopic and photo-z-only samples being drawn from the same parent population.

In the text
thumbnail Fig. 29.

Distribution of the observed broad-band colours in three bins of magnitude. Each plot only includes sources with > 3σ detections in the two bands defining the colour index and with valid photo-z estimates. Solid lines show the distributions measured for galaxies in the photo-z-only sample. Connected dots represent the distribution for galaxies in the spectroscopic sample (scaled by a factor 2 to facilitate the comparison).

In the text
thumbnail Fig. 30.

Distribution of zbest and odds in bins of magnitude for the photo-z-only and spectroscopic samples. Symbols are the same as in Fig. 29.

In the text
thumbnail Fig. 31.

Dependence of σNMAD (top) and η (bottom) on odds for sources in the spectroscopic sample without photometry flags in any band (solid symbols) and sources with flags in one or more bands (open symbols).

In the text
thumbnail Fig. 32.

Predicted density of r < 23 miniJPAS galaxies with redshift errors |Δz| < Δz′ as a function of the threshold Δz′ for four different cuts in the odds parameter. The solid lines are generated by applying the same value of fS(|Δz| < Δz′ | oddsi) calculated in non-flagged sources to both flagged and non-flagged sources, and the dotted lines use separate values for flagged and non-flagged sources.

In the text

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