EDP Sciences logo
Subscriber Authentication Point
Search
Menu
Home All issues Volume 711 (July 2026) A&A, 711 (2026) A14 Full HTML
Issue
A&A
Volume 711, July 2026
Euclid Quick Data Release (Q1)
Article Number A14
Number of page(s) 18
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/202554576
Published online 30 June 2026

© The Authors 2026

Licence Creative CommonsOpen Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

This article is published in open access under the Subscribe to Open model. This email address is being protected from spambots. You need JavaScript enabled to view it. to support open access publication.

1. Introduction

The star-forming main-sequence (SFMS) is a relation between stellar masses (M*) and star-formation rates (SFRs) that is observed for star-forming galaxies (SFGs). It has been extensively studied in the last few decades (Brinchmann et al. 2004; Daddi et al. 2007; Elbaz et al. 2011), with investigations into its slope, normalisation, scatter, and evolution over time (see Speagle et al. 2014; Popesso et al. 2023, and references therein). The SFMS is observed across different redshifts and is already in place by z ∼ 6 (e.g., Clarke et al. 2024; Cole et al. 2025). It hosts the majority of star formation at each epoch (Rodighiero et al. 2011), suggesting that galaxies spend most of their lifetimes on the SFMS, undergoing secular evolution. The tightness of the relation, with a typical scatter between 0.2 dex and 0.4 dex, implies its universality as the main mode of galaxy growth (Schreiber et al. 2015; Donnari et al. 2019; Matthee & Schaye 2019).

This relation emerges from the interplay between the stellar content of galaxies and their cold gas reservoirs (i.e., the so-called Kennicutt–Schmidt relation from Schmidt 1959; Kennicutt 1998a, and the (resolved or integrated) molecular gas main-sequence, see e.g. Lin et al. 2019; Morselli et al. 2020; Ellison et al. 2021; Baker et al. 2023), and it has been shown to hold at sub-kiloparsec scales too (e.g., Wuyts et al. 2013; Hsieh et al. 2017; Lin et al. 2017; Abdurro’uf & Akiyama 2017; Ellison et al. 2018; Enia et al. 2020; Baker et al. 2022).

At masses of log10(M*/M⊙) > 10 at 0 < z < 1 and at the high-mass end log10(M*/M⊙) > 11 at z ∼ 2, the relation appears to exhibit a deviation from the linear trend, the so-called bending of the SFMS (Whitaker et al. 2014; Schreiber et al. 2015; Tomczak et al. 2016; Popesso et al. 2019; Leja et al. 2022; Daddi et al. 2022a; Leroy et al. 2024; Wang et al. 2024). The bending traces changes in cold-gas accretion (Kereš et al. 2005; Dekel & Birnboim 2006) and availability for star formation processes, and could be a consequence of the reduced availability of cold gas in halos entering the hot accretion mode phase (Daddi et al. 2022a), or feedback from active galactic nuclei (Fabian 2012), or both (Bower et al. 2017). Additionally, the reactivation of star formation in the disks of galaxies that are approaching quiescence or have already been quenched may also contribute to the bending of the SFMS (Mancini et al. 2019). This turnover mass can be linked with the host halo mass quenching threshold (Yang et al. 2007; Behroozi et al. 2019; Leslie et al. 2020; Popesso et al. 2023), defining the transition between an environment favourable to star formation to a regime where these processes are suppressed.

The Euclid Quick Release Q1 (2025) is the first release of Euclid survey data, corresponding to a single reference observing sequence (ROS, see Euclid Collaboration: Scaramella et al. 2022) of the Euclid Deep Fields (EDFs). This is a homogeneous view of a large area of the extragalactic sky (∼63 deg2) from optical to near-infrared (NIR), complemented with observations of the same fields at 3.6 μm and 4.5 μm with the Infrared Array Camera (IRAC, Fazio et al. 2004) on Spitzer (Werner et al. 2004). These fields have the potential to become the best-studied extragalactic fields of the coming decades. In this work, we illustrate the results obtained with the data and products of Q1 for the SFMS, investigating its evolution up to z = 3, and the distribution of physical and morphological parameters along the SFMS, as well as validating these results with the existing literature, a first demonstration of the potential of Euclid to investigate scaling relations and the baryon cycle.

This paper is structured as follows. In Sect. 2, we describe the data released for Q1. In Sect. 3, we describe the methods used to recover the photometric redshifts and physical parameters (PPs). In the same section, we validate the results, reporting the performance of our methods on simulations and the available sub-sample of spectroscopic redshifts and Hα-estimated SFRs. In Sect. 4, we report the results for the SFMS. In Sect. 5, we present our conclusions and perspectives for the upcoming Data Release 1.

Throughout this paper we adopt a flat Λ cold dark matter (ΛCDM) cosmology with H0 = 70 km s−1 Mpc−1, Ωm = 0.3, and ΩΛ = 0.7, and assume a Chabrier (2003) initial mass function (IMF). All magnitudes are given in the AB photometric system (Oke & Gunn 1983).

2. Data

A detailed description of the Q1 data release is presented in Euclid Collaboration: Aussel et al. (2026), Euclid Collaboration: McCracken et al. (2026), Euclid Collaboration: Polenta et al. (2026), and Euclid Collaboration: Romelli et al. (2026). A summary of the scientific objectives of the mission can be found in Euclid Collaboration: Mellier et al. (2025). In short, for Q1 Euclid observed ∼63 deg2 of the extragalactic sky, divided into EDF-North (EDF-N), EDF-Fornax (EDF-F), and EDF-South (EDF-S), in four photometric bands, one in the visible (IE, Euclid Collaboration: Cropper et al. 2025), and three in the NIR (YE, JE, and HE, Euclid Collaboration: Jahnke et al. 2025). These observations are complemented by ground-based observations carried out with multiple instruments to cover the wavelength range between 0.3 μm and 1.8 μm by the Ultraviolet Near-Infrared Optical Northern Survey (UNIONS, Gwyn et al. 2025) and the Dark Energy Survey (DES, Flaugher et al. 2015; Dark Energy Survey Collaboration 2016).

In order to obtain robust results and improve the quality of the recovered photometric redshifts and PPs (see Sect. 3.3), we also added to the Euclid photometry two available IRAC bands, at 3.6 μm and 4.5 μm, covering all the EDFs (Euclid Collaboration: Moneti et al. 2022; Euclid Collaboration: McPartland et al. 2025). More details on how IRAC photometry is measured can be found in Euclid Collaboration: Bisigello et al. (2026).

In Table 1 we report the filters used in this work, with the observed 10σ depths for an extended source in an aperture that is twice the full width at half maximum (FWHM, i.e., the one with the lowest resolution between the optical and Euclid bands, see Euclid Collaboration: Romelli et al. 2026, for further details). For this work, we started from the available Euclid catalogues and applied a series of selections to make our analysis more robust, removing compact or low-quality sources. These selections are:

  • SPURIOUS_FLAG = 0;

  • DET_QUALITY_FLAG < 4;

  • MUMAX_MINUS_MAG > −2.6.

For further details on the meaning of the flags, see Euclid Collaboration: Tucci et al. (2026). This selection skims the sample from stars and compact objects such as quasi-stellar objects (QSOs).

Table 1.

Filters used in this work, with associated observed depths.

We further cleaned our sample from these two classes of objects using the classification probability of the Q1 data products, imposing the following criteria:

  • PROB_QSO < 0.86;

  • PROB_STAR < 0.10.

See Sect. 4 of Euclid Collaboration: Tucci et al. (2026) for further details, and also Euclid Collaboration: Matamoro Zatarain et al. (2026) about the classification thresholds.

Finally, we benefited from the results of the morphological analysis for Q1 (Euclid Collaboration: Walmsley et al. 2026; Euclid Collaboration: Quilley et al. 2026), applying another set of cuts related to the morphological parameters and the size of the source. We kept sources with:

  • q > 0.05;

  • 0.01a < Re < 2a.

q is the Sérsic axis ratio, Re the Sérsic radius, and a the isophote semi-major axis, in units of VIS pixels. For further information see Sect. 4 and the left panel of Fig. 3 in Euclid Collaboration: Quilley et al. (2026). These further remove diffraction spikes, cosmic rays, or stars that survived the cuts described above.

The last cut that we applied was in magnitude, in order to work with a mass-complete sample, limiting our analysis to sources with observed HE < 24, corresponding to an average measured signal-to-noise ratio of five, measured from the 2 × FWHM aperture photometry. Our final sample is composed of 8 090 074 sources.

3. Physical properties and validation

We refer the reader to Euclid Collaboration: Tucci et al. (2026) for a description of how the Q1 data were processed to infer photometric redshifts and PPs. In this section, we briefly summarise the procedure.

Due to the large number of sources detected (of the order of tens of millions) in the EDFs, machine learning (ML) methods have been developed to speed up the computational process while achieving a comparable performance of template fitting methods (see e.g., Euclid Collaboration: Desprez et al. 2020; Euclid Collaboration: Enia et al. 2024). Data products produced for Q1 have been obtained with a nearest-neighbours (NNs) algorithm, nnpz, which finds a k number of NNs (30 in the Euclid pipeline, 80 for this work) in the template space (i.e., magnitude and colour) for each target galaxy from a reference sample, and infers the photometric redshifts and PPs from those.

The reference sample differs from the one used to produce the Q1 data products, the reason for which is explained below. It was built from a grid of templates (Bruzual & Charlot 2003, 2016 version1), using the MILES stellar library, which adopts the Kroupa (2001) IMF, which we therefore converted to Chabrier (2003) taking into account a difference of about 0.03 dex for PPs. The models were built with exponentially delayed star formation histories:

SFR ( t ) ∝ ( t − T 0 ) e − ( t − T 0 ) / τ , Mathematical equation: $$ \begin{aligned} \mathrm{SFR}(t) \propto (t-T_0)\,\mathrm{e}^{-(t-T_0)/\tau }, \end{aligned} $$(1)

drawn from a Halton (1964) grid2 in a six-dimensional space with the following free parameters:

  • redshifts: 0 < z < 7;

  • ages: 8 < log10(T0/yr) < 10.138;

  • e-folding timescale: 8 < log10(τ/yr) < 10.5;

  • ionisation parameter: −4 < log10(U) <  − 2;

  • metallicities: 0.1 < Z/Z⊙ < 2.

For dust attenuation, we generated models with both Calzetti et al. (2000) and SMC (Prevot et al. 1984) laws, with V-band attenuation, AV, between 0 and 5. Stellar masses and SFRs were inferred from the amplitude of the observed spectral energy distribution (SED), as a scaling parameter recovered by nnpz. Metallicities and ionisation parameters are distributed uniformly within the given ranges; the same for τ, but on a logarithmic scale. The redshifts are distributed with a linear scaling in (1 + z) steps, while ages and AV scale logarithmically from the lowest value to the highest. For these last three parameters, their distribution in the reference sample is shown in black in the first three panels of Fig. 1. We then generated the noise-free observed-frame photometry associated with each model. In the end, the reference sample consists of 1 490 150 objects.

Thumbnail: Fig. 1. Refer to the following caption and surrounding text. Fig. 1.

Left panels: Distribution of redshifts, z, attenuations, AV, and ages, T0 for the reference sample used in this work. Right panels: Two priors adopted in this work – volume and age – as multiplicative weights on the reference galaxies, depending on their redshifts or ages.

nnpz then finds the 80 NNs for every target galaxy, based on the observed magnitudes and colours. Each of these NNs will have its own weight – measured from the χ2 distance between the reference and the target – and scaling parameter from the SED amplitude. By combining them, we measure the median (or the mode) of the distribution of NNs, which ultimately are the inferred photo-zs, PPs, and absolute magnitudes of the target galaxies.

Unlike what has been done in the Euclid pipeline, we added two more photometric points to the reference sample, accounting for the IRAC1 and IRAC2 channels (see Sect. 2). Moreover, having access to the nnpz results – that is, the set of NNs for each target galaxy – we can impose whatever physically motivated condition (i.e. a prior) directly on the NNs, either by measuring the output, zphot or PPs, only on the set of NNs that satisfy the condition, or by differently re-weighting the NNs in the reference sample in order to penalise unphysical solutions.

As is reported in Sect. 6.1.1 of Euclid Collaboration: Tucci et al. (2026), the Q1 pipeline results (obtained without the application of any condition to the NNs) contain an artificially high number of low-z galaxies with extremely young ages – log10(T0/yr) starts from 7 in the pipeline – observed at the peak of their star-forming activity, and thus at the limit of specific star-formation rate (sSFR) inherent to parametric models (log10sSFR/yr−1 ≃ −7.8, see Fig. 8 of Ciesla et al. 2017). The resulting redshift distribution is ultimately skewed towards non-physically high number counts at low z, creating an artefact straight line at the sSFR saturation limit (see Fig. 14 in Euclid Collaboration: Tucci et al. 2026). In principle, this issue could be addressed in the Q1 pipeline data product by imposing an age prior on the NNs; for example, ignoring those with ages < 0.1 Gyr. This would significantly reduce the impact of artefacts, but at the cost of reducing the Q1 sample by about 40%, excluding from the sample all sources without even a single NN that satisfies the prior. Losing these sources would introduce systematic biases into our analysis. To avoid this, we took some precautions that deviate from what has been done in the pipeline, in order to reduce the impact of those artefact sources without losing a significant fraction of the sample: the boundaries for ages and AV mentioned above used to generate the reference sample for this work are different from those reported in Euclid Collaboration: Tucci et al. (2026), with 0 < AV < 3 and 7 < log10(T0/yr) < 10.138. We also increased the k number of NNs to 80. Finally, we imposed both a volume and an age prior on the NNs in the reference sample.

With the volume prior, we increased the weights of NNs at higher redshifts compared to the ones at lower redshifts, where the volume of the Universe sampled by the survey is smaller and fewer galaxies are expected to be observed. This prior was implemented as a multiplicative weight assigned to each object in the reference sample, and only depends on the redshift as

WGT ( z ) ∝ d V c ( z ) d z , Mathematical equation: $$ \begin{aligned} \mathcal{WGT} (z) \propto \frac{\mathrm{d}V_{\rm c}(z)}{\mathrm{d}z}, \end{aligned} $$(2)

where dVc(z) is the comoving volume shell in the interval [z,  z + dz]. This prior is shown in red in the centre-right panel of Fig. 1.

The age prior is once again a multiplicative weight, 𝒲𝒢𝒯(T0), to apply to NNs. This takes into account the fact that younger galaxies could be observed at higher redshifts, while this possibility should be reduced at low redshifts. In building the prior, we looked at the distribution of ages in different redshift bins in the 2 deg2 of the Cosmic Evolution Survey (COSMOS, Weaver et al. 2022), finding that these can be modelled as normal distributions with the peak age decreasing while moving at a higher redshift. This weight is then constructed as a truncated normal distribution centred on two thirds the age of the Universe at any given z, with width 0.7 in log10(T0/yr). A weight equal to zero is assigned for those sources with an age greater than the age of the Universe at the given z. The shape of the age prior is reported in the rightmost panel of Fig. 1 for four indicative redshift values.

This procedure makes us sensitive to the bulk of the population of SFGs, while reducing our ability to properly identify and describe outliers (e.g., the starburst galaxies, as the presence of a star-forming burst is not directly accounted for in the reference sample). Given the main scopes of this work, this is acceptable, since it has been found that the exponentially delayed τ model is an accurate description of the star formation histories of the main population of SFMS galaxies, at least at z < 2 (see e.g., Speagle et al. 2014; Ciesla et al. 2017). Recently, studies focussing on non-parametric models of star formation histories have found how these models could better recover the complex events that arise during the evolution of a galaxy (Iyer et al. 2019; Leja et al. 2019; Baes et al. 2020). In the future, for Data Release 1, models will better account for starburst galaxies, with the possibility of exploring other regions of the parameter space, even accounting for complex star formation histories (see for example Euclid Collaboration: Corcho-Caballero et al. 2026).

We validated our results both on the available state-of-the-art simulations adapted to reproduce as closely as possible Euclid observations (i.e., the Flagship2 simulation, FS2, see Euclid Collaboration: Castander et al. 2025), and on a compilation of the available spectroscopic redshifts and Hα measured SFRs in the EDFs. Although the latter is fundamental to assess the quality of recovered parameters with what can be interpreted as the closest possible thing to a ‘ground truth’ value, the former is necessary to put a degree of confidence in all the other recovered quantities that have no such ‘ground truth’ to compare with.

3.1. Metrics for quality assessment

The metrics used to quantify the quality of the results are defined differently when referring to redshifts or PPs. We refer the reader to Euclid Collaboration: Enia et al. (2024) for a full discussion of thresholds and catastrophic outlier definitions; here, we simply report the definitions.

We first defined a set of true values, ztest and ytest (on a logarithmic scale for PPs), to confront with the predicted values, zpred and ypred. We then defined the normalised median absolute deviation as

NMAD = 1.48 × median { | z pred − z test | 1 + z test − b , for redshifts , | y pred − y test | − b , for PPs , Mathematical equation: $$ \begin{aligned} \mathrm{NMAD} = 1.48 \times \mathrm{median} {\left\{ \begin{array}{ll} \,\dfrac{|z_{\rm pred} - z_{\rm test}|}{1+z_{\rm test}} - b,&\mathrm{for\,redshifts,} \\ \,|y_{\rm pred} - y_{\rm test}| - b,&\mathrm{for\,PPs,} \end{array}\right.} \end{aligned} $$(3)

with b being the model bias (see below).

Then, we defined the outlier fraction,

f out = { | z pred − z test | 1 + z test > 0.15 , for redshifts , | y pred − y test | > t out , for PPs , Mathematical equation: $$ \begin{aligned} f_{\rm out} = {\left\{ \begin{array}{ll} \,\dfrac{|z_{\rm pred} - z_{\rm test}|}{1+z_{\rm test}} > 0.15,&\mathrm{for\,redshifts,} \\ \,|y_{\rm pred} - y_{\rm test}| > t_{\rm out},&\mathrm{for\,PPs,} \end{array}\right.} \end{aligned} $$(4)

with tout = 0.4 for stellar masses and tout = 0.8 for SFRs.

Finally, we defined the bias,

b = median { ( z pred − z test 1 + z test ) , for redshifts , ( y pred − y test ) , for PPs . Mathematical equation: $$ \begin{aligned} b = \mathrm{median} {\left\{ \begin{array}{ll} \,\left(\dfrac{z_{\rm pred} - z_{\rm test}}{1+z_{\rm test}}\right),&\mathrm{for\,redshifts,} \\ \,(y_{\rm pred} - y_{\rm test}),&\mathrm{for\,PPs.} \end{array}\right.} \end{aligned} $$(5)

3.2. Validation on simulations

We randomly selected about 70 k sources from a complete octant of the FS2 simulation (Euclid Collaboration: Castander et al. 2025). We checked that the selection does not skew the ground-truth values with respect to the full distribution. These mock sources are, by construction, distributed in the redshift range 0 < z < 3, with 6.4 < log10(M*/M⊙) < 12 and −4 < log10 (SFR/M⊙ yr−1) < 3.1. We then followed the same procedure described in Sect. 2 of Euclid Collaboration: Enia et al. (2024) to produce a realistic catalogue of mock sources that reproduces as closely as possible what is observed in Q1. We perturbed the intrinsic fluxes with the noise level found in Q1 in the same set of filters (see Table 1), and cut at observed magnitudes HE < 24. Instead of IRAC, in the FS2 simulation these wavelength ranges are covered by mock observations with WISE bands, W1 and W2 (Wright et al. 2010). Given the similar range covered, we ensured that the resulting performance is comparable if not exactly the same.

We then ran nnpz with the same reference sample described in Sect. 3, one run with the WISE filters and one without, and produced the recovered results as the median of the 80 NNs. The results are shown in Fig. 2, where we report the recovered versus true relation without (top panel) and with (bottom panel) the two WISE filters. These results follow closely what has already been described in Euclid Collaboration: Enia et al. (2024), at least at the order-of-magnitude level. It is immediately noticeable how the addition of the two filters at 3.6 μm and 4.5 μm improves parameter estimation, with photo-z NMADs and the outlier fraction decreasing from 0.048 to 0.035 and from 15% to 7%, respectively. The same holds for stellar masses (NMAD decreasing from 0.206 to 0.170 and the outlier fraction from 17% to 12%) and especially for SFRs (NMAD decreasing from 0.643 to 0.446 and the outlier fraction from 25% to 11%). As was expected, the recovery of SFMS improves with respect to the case without the two filters in NIR, with a much better recovery of the slope and normalisation of the SFMS relation.

Thumbnail: Fig. 2. Refer to the following caption and surrounding text. Fig. 2.

Results for the nnpz run on the 70 k simulated FS2 galaxies, without (top panels) and with the first two WISE filters (bottom panels). The black line is the 1:1 relation; the shaded area is the region beyond which a prediction is an outlier. In every panel, the contours are the area containing 86%, 39% (corresponding to the 2σ and 1σ levels for a 2D histogram), and 20% of the sample. For SFMS (right panel), the true distribution is reported in red (dashed) and the predicted one in blue (solid). The lines are the orthogonal distance regression (ODR) best fit to the distribution with passive galaxies removed. The reported metrics are NMAD (purple), the outlier fraction, fout (blue), and the bias (green) for the photometric redshifts and physical parameters, and the slope, m, scatter, σ, and fraction of passive galaxies, fp, for the SFMS, all defined in Sect. 3.1.

3.3. Photometric redshifts and PPs validation

Quality assessment for the redshifts was performed by looking at how they compare with respect to the observed spectroscopic ones. The EDFs cover regions of the sky where there is a plethora of coverage from other spectroscopic surveys. In total, we successfully matched 63 504 galaxies with a reliable spectroscopic redshift; that is, with a redshift quality flag of 3 or 4 (see description in Sect. 5.2 of Euclid Collaboration: Tucci et al. 2026). These zspec values are from: the Dark Energy Spectroscopic Instrument (DESI, DESI Collaboration 2016, 2024); the 16th Data Release of the Sloan Digital Sky Survey (SDSS, Ahumada et al. 2020); the 2MASS Redshift Survey (2MRS, Huchra et al. 2012); the PRIsm MUlti-object Survey (PRIMUS, Coil et al. 2011); the Australian Dark Energy Survey (OzDES, Yuan et al. 2015; Childress et al. 2017; Lidman et al. 2020); 3dHST (Brammer et al. 2012); the 2-degree Field Galaxy Redshift Survey (2dFGRS, Colless et al. 2001); the 6-degree Field Galaxy Redshift Survey (6dFGS, Jones et al. 2009); the MOSFIRE Deep Evolution Field Survey (MOSDEF, Kriek et al. 2015); the VANDELS ESO public spectroscopic survey (Pentericci et al. 2018; Talia et al. 2023); the JWST Advanced Deep Extragalactic Survey DR3 (JADES, D’Eugenio et al. 2025); the 2-degree Field Lensing Survey (2dFLens, Blake et al. 2016); and the VIMOS VLT deep survey (VVDS, Le Fèvre et al. 2005).

The results are reported in Fig. 3. In the left panel, we compare the photometric and spectroscopic redshifts for the subset of reliable spectroscopic redshifts in our sample. These are almost equally divided between EDF-F and EDF-N, with only a select number (123) of objects in EDF-S. The trend we find using Euclid real data is similar to what is shown in the previous section, with a non-negligible improvement when adding the two IRAC bands. To put it in quantitive terms, compared to the same analysis performed without the two IRAC bands (not shown in Fig. 3) the NMAD decreases from 0.06 to 0.04 and the fraction of outliers decreases from 26% to 13%. In the central panels, we show the normalised difference between spectroscopic and photometric redshifts, as a function of the stellar masses and the SFRs. We do not observe any troubling systematic trend, with the exception of the (expected) behaviour in which galaxies mistakenly placed at higher redshift – mostly those with (zspec − zphot)/(1 + zspec) >  − 1 – are found with an incorrect higher SFRs, so some caution must be taken when dealing with those high-z galaxies, or with log10 (SFR/M⊙ yr−1) > 2.4. In terms of observed bias, we find a negligible value of +0.01, well below the typical uncertainties associated with photo-zs (see below).

Thumbnail: Fig. 3. Refer to the following caption and surrounding text. Fig. 3.

Left: Comparison between the measured photometric redshifts and a compilation of all the available and reliable spectroscopic redshifts, colour-coded by the density of objects in each bin. The black line is the 1:1 relation, while the shaded grey area is the region beyond which a prediction is considered to be an outlier. The reported metrics are NMAD (purple), the outlier fraction, fout (blue), and the bias (green), all defined in Sect. 3.1. Middle: Normalised redshift difference as a function of stellar masses (top) and SFRs (bottom). The black contours are at the same levels as in Fig. 2. Right: Normalised distributions of photometric redshifts (top), stellar masses (centre), and SFRs (bottom) for our full sample (dashed red lines), compared with the results coming from the Q1 data products (PHZ, in dotted blue lines), and COSMOS2020 (in solid grey lines), at the same magnitude cuts applied in this work (see Sect. 2).

When looking at the full sample of objects – not just spectroscopic ones – there are no ground-truth values to compare with, but we can still investigate how our results agree with the full distribution of photometric redshifts, stellar masses, and SFRs, especially when compared with other surveys. This is done in the right panels in Fig. 3, where we compare our results for the full sample (the dashed red lines) with what is observed in the LePhare run from the classic catalog of COSMOS 2020 (the solid grey lines), and with the inferred PPs from the Q1 data products (PHZ, the dotted blue lines), both at the same magnitude cut applied in this work (i.e. HE < 24). The first two distributions in redshift are comparable, with the main differences observed in a slightly lower fraction of 0.6 < z < 1.2 objects in our sample (and conversely, a few more z > 3 galaxies), while the Q1 data products exhibit a significantly greater number of z < 0.2 objects. As for the stellar masses, our results improve with respect to the almost flat at 8 < log10(M*/M⊙) < 9 distributions of Q1 data products; however, we find fewer objects in the 10.2 < log10(M*/M⊙) < 11.2 range and conversely more in the 9.2 < log10(M*/M⊙) < 10.2 range with respect to COSMOS. The biggest differences are observed in terms of SFRs, with more galaxies in our sample in the 0 < log10 (SFR/M⊙ yr−1) < 1 range with respect to COSMOS, and conversely slightly fewer galaxies per SFR bin in our sample at 1 < log10 (SFR/M⊙ yr−1) < 2.

In Fig. 4, we report all this information in the M*–SFR plane, where the SFMS is observed. For the sub-sample of sources with a reliable spectroscopic redshift, we show the median value of the normalised redshift difference in each bin, with red colours highlighting sources mistakenly placed at a higher redshift, and blue colours the opposite. While the latter catastrophic outliers are a small issue only visible in the first redshift interval (with 0.2 < z < 0.5), the former becomes more and more prominent at higher redshifts (i.e., z > 1.5), introducing a non-negligible bias in the estimates of M* and SFR in the highest mass and SFR regimes, with these skewed towards higher values due to the wrong redshift attribution.

Thumbnail: Fig. 4. Refer to the following caption and surrounding text. Fig. 4.

M*–SFR plane at four different redshift intervals, only for the sources with a reliable zspec described in Sect. 3.3, colour-coded by the median normalised redshift difference in each bin. To give an idea of the density of objects in each redshift interval, we superimposed the contours in grey, with the same levels as in Fig. 2.

We compare the measured PPs with the ones in the value-added catalogue of PPs in DESI (Siudek et al. 2024), although for a limited number of sources (∼5 k) in the interval 0 < z < 0.6. In particular, we confront the SFRs with the ones obtained from both Hα and Hβ line measurement – not exactly ‘ground truth’ values, but close – while the stellar masses are compared to their SED fitting results, even though, given how it has been performed on fewer and shallower filters (see Table 1 in Siudek et al. 2024), we expect our stellar masses to be more reliable. The IMF is the same as the one adopted for this work (Chabrier 2003), and SFRs were obtained from Hα following Kennicutt (1998b). The results are shown in Fig. 5, where the result for each PP is colour-coded as a function of the median value of (zspec − zphot)/(1 + zspec) in each bin. Despite the limited sample, the performance is in line with what is expected from the simulations. It is immediately clear how the vast majority of catastrophic outliers (i.e. where PPs fall outside of the defined thresholds) are a consequence of sources with an incorrect photometric redshift estimate. Again, the observed bias in stellar masses and SFR is still below the typical uncertainties associated with each PPs.

Thumbnail: Fig. 5. Refer to the following caption and surrounding text. Fig. 5.

Comparison between the stellar masses and SFRs measured in this work and a sample of objects from DESI with stellar masses from SED fitting (left) and SFRs from Hα (right), colour-coded as a function of the median normalised redshift difference in each bin. The black line is the 1:1 relation, while the shaded area is the region beyond which a prediction is an outlier. The contours are the same as in Fig. 2. The reported metrics are defined in Sect. 3.1.

Finally, we used these SFRs from Hα and the reliable spectroscopic redshift sample to place some constraints on the estimated uncertainties in the photo-zs and SFRs. Uncertainties were measured from the 16th and 84th percentiles of the weighted distribution of NNs (see Sect. 3). To account for the possibility of an under- (or over-) estimation of those uncertainties, we looked at the cumulative distribution of (zphot − zspec)/zerr – and similarly (SFR − SFRHα)/SFRerr – where we expect 68% of these to fall below 1 if the uncertainties are well estimated. In contrast, an underestimate would lead to fewer sources within the 1σ limit, and the opposite would be true for an overestimate. These cumulative distributions (‘normalised residuals’, red for redshifts and blue for SFRs) are reported in Fig. 6. We find that our uncertainties are slightly underestimated for redshifts (1σ level reached for 55% of the sample) and almost spot on for SFRs. We estimate the underestimation of the uncertainties of the photometric redshifts to be a factor of about 1.5.

Thumbnail: Fig. 6. Refer to the following caption and surrounding text. Fig. 6.

Cumulative distribution of the normalised residuals for photometric redshifts (red) and SFRs (blue). For comparison, we also show in grey the cumulative of a normal distribution with σ = 1. Dashed black lines highlight the position where 68% of the distributions are, and the 1σ level for the residuals.

We take the mode of the distribution of uncertainties as the typical values for each parameter, which are 0.05 for redshifts, 0.11 for stellar masses, and 0.08 for SFRs (on a logarithmic scale). The typical uncertainty on SFRs are used in the following section for the fit of the SFMS.

4. Results

We started from the sample described in Sect. 2, and limited our analysis to the redshift range between 0.2 and 3.0. This is motivated by the need to obtain a statistically reliable sample in terms of mass completeness and the quality of the recovered photometric redshifts and physical properties. In Euclid Collaboration: Enia et al. (2024), it is shown how the main source of biases in the analysis of SFMS during cosmic time – apart from the inherent dispersions in determining the correct PPs – arises from the photo-z estimation, whereby typically some low-z (i.e. z < 0.5) objects are placed at high z (up to around 10% of catastrophic outliers) with increased stellar masses and SFRs. The net effect is a steepening of the SFMS at lower redshifts, and the opposite at higher z (see Fig. 11 of Euclid Collaboration: Enia et al. 2024). This is also observed in the validation tests that we performed with simulations and reported in Sect. 3.3 (see Fig. 4).

We performed our subsequent analysis in the following redshift bins: [0.2, 0.5], [0.5, 0.8], [0.8, 1.5], [1.5, 3.0], with the exception of the morphological analysis, where we stopped at z = 1.5, since for higher redshifts the quality of the recovered morphological parameters is limited by the sizes of the sources reaching the resolution limit of the survey. Based on the results shown in Fig. 4, we can place a certain degree of confidence in the highest-mass end of the first two redshift intervals, while greater caution is required for the last two. In each redshift bin, we limited our analysis – and the reported values – to log10(M*/M⊙) < 11.5.

4.1. Mass completeness

We estimated the mass completeness of the sample limited to HE < 24 following the method described in Pozzetti et al. (2010). We selected galaxies close to the limiting magnitude of our sample; that is, those with 23 < HE < 24 (with identical results of choosing the faintest 20% as in Pozzetti et al. 2010), and measured for each galaxy

log 10 ( M lim / M ⊙ ) = log 10 ( M ∗ / M ⊙ ) − 0.4 ( H E − 24 ) , Mathematical equation: $$ \begin{aligned} \log _{10}(M_{\rm lim}/M_\odot ) = \log _{10}(M_{*}/M_\odot ) - 0.4(H_{\scriptscriptstyle \mathrm E} - 24), \end{aligned} $$(6)

representing the mass the galaxies would have at the limiting magnitude. We then measured the 95th percentile of the distribution of Mlim(z) for each redshift bin. This is reported in Fig. 7. The classification into star-forming (dashed blue line) and passive galaxies (dash-dotted red line) was done with the selection criteria based on the NUV − r+ − J diagram (as is explained below).

Thumbnail: Fig. 7. Refer to the following caption and surrounding text. Fig. 7.

The stellar mass completeness for the sample used in this work (Pozzetti et al. 2010), with a cut at HE < 24, shown as the density of galaxies in the photometric redshifts vs. stellar masses plane. The solid grey line is the 95% stellar mass completeness limit, red dashed-dotted line for passive galaxies, and blue dashed line for SFGs.

The sample is around 95% complete for M*, which increases from log10(M*/M⊙)∼7 (at z ∼ 0.1) to ∼9 (at z ∼ 1), and increases from log10(M*/M⊙)∼9.5 to log10(M*/M⊙)∼10, while going to higher redshifts, from z = 1.5 to 2.5. For passive galaxies, the limit is 0.3 − 0.4 dex higher up to z ∼ 1.8, and about 0.7 dex higher at z > 2. Up to z = 3, there are 4 654 430 galaxies over the 95% stellar mass completeness limit.

4.2. Star-forming and passive galaxy classification

Colour-based classifications of galaxies use the principle of separating red and blue galaxies and distinguish between dusty and intrinsically red ones (e.g. the U − V versus V − J colour diagram Labbé et al. 2005; Wuyts et al. 2007; Williams et al. 2010). In this work, we use the NUV − r+, r+ − J colours (Ilbert et al. 2010), whereby star-forming and passive galaxies are discriminated based on their absolute NUV, r+, and J magnitudes, with quiescent galaxies satisfying the following relations:

NUV − r + > 3 ( r + − J ) + 1 ; NUV − r + > 3.1 . Mathematical equation: $$ \begin{aligned} \mathrm{NUV}-r^+&>3(r^+-J)+1; \nonumber \\ \mathrm{NUV}-r^+&>3.1. \end{aligned} $$(7)

This combination of criteria works in a similar fashion to the UVJ diagram, but it has been widely used in recent literature as it is more sensitive to recent star formation via the NUV − r+ colour, which separates passive (redder) and star-forming (bluer) galaxies (Ilbert et al. 2013; Arnouts et al. 2013). Truly passive galaxies are then distinguished from dusty, star-forming objects via the r+ − J colour, ensuring a proper separation between the two different populations.

The colours NUV − r+ versus r+ − J of our sample are shown in Fig. 8, colour-coded as a function of the number density of objects with certain colours (top panels) and the median T0/τ (middle panels) and sSFR in each bin (bottom panels), in the four different redshift bins. Only objects whose mass is higher than the Mlim(z) value at the zmin of the redshift bin are shown, to account for sample incompleteness (see Fig. 7). To be consistent with the selection criteria reported above, the adopted absolute magnitude, J, is not the one estimated in the rest frame Euclid JE filter but in the JUltraVISTA filter (Euclid Collaboration: Schirmer et al. 2022); similarly, we adopted the r+ band as in Ilbert et al. (2010).

Thumbnail: Fig. 8. Refer to the following caption and surrounding text. Fig. 8.

NUV − r+ versus r+ − J rest-frame colours for the sources above the 95% mass completeness limit, in four redshift bins, colour-coded with the density of objects (upper panels), the ratio between T0 and τ (middle panels), and the sSFR (bottom panels). Dash-dotted lines divide the regions between star-forming and quiescent galaxies, following the criteria presented in Ilbert et al. (2013).

We recover the well-known increase in the fraction of passive galaxies while going to later cosmic times, highlighting the assembly of the population of quiescent galaxies observed in the Universe. When checking the colour diagrams against the measured values of sSFR, we notice the presence of a small fraction of objects (∼3%) outside the boundaries for quiescent galaxies in the NUV − r+ − J diagram, but with a median value of log10(sSFR/yr−1) <  − 11 (and T0/τ > 8); that is, in a region of the M*–SFR plane where we would expect only quiescent galaxies. This is a small, negligible number of interlopers, which is reassuring with regard to the goodness of the classification based on the rest-frame colours.

4.3. The SFR–M* relation in the EDFs

The M*–SFR plane for the sample of SFGs selected with the NUV − r+ − J colours is shown in Fig. 9, in four redshift bins, colour-coded in terms of the logarithmic density of objects per bin. The SFMS is observed up to the highest redshift bin (z < 3). In the figure, we report three previously published SFMS relations for comparison: Eq. (15) of Popesso et al. (2023, black dashed line), that is, a comprehensive compilation of 27 literature SFMS relations fitted to the same functional form, in the mass range 8.5 < log10(M*/M⊙) < 11.5; Schreiber et al. (2015, dotted grey line), obtained from ∼10 k galaxies with the deepest Herschel observations of the GOODS and CANDELS-Herschel programme, with 9.5 < log10(M*/M⊙) < 11.5; and Daddi et al. (2022a, dash-dotted blue line), obtained from a stacking analysis of ∼400 k colour-selected SFGs in COSMOS (Delvecchio et al. 2021), here too in the mass range 8.5 < log10(M*/M⊙) < 11.5).

Thumbnail: Fig. 9. Refer to the following caption and surrounding text. Fig. 9.

SFR–M* relation for SFGs, selected with the NUV − r+ versus r+ − J condition, coloured by the density of objects in each redshift bin. Within the coloured bins is 99.9% of the sample of SFGs, while the grey contours are the lines enclosing 95%, 50%, and 10% of it. The red line is the fitted SFMS presented in this work, starting from the completeness limit mass at the start of the z-bin. The other SFMSs are from Popesso et al. (2023, dashed black line), Schreiber et al. (2015, dotted grey line), and Daddi et al. (2022a, dashed-dotted blue line), all evaluated at the median redshift of each redshift bin (or to the closest reported value). The shaded purple regions highlight where the mass is below the completeness limit at the start (hatched) and at the end of the redshift bin. Dashed grey lines highlight the region of constant sSFR.

All these SFMS forms include the presence of a bending of the relation at the high-mass end. Having enough statistics in terms of the number of objects per bin, we can significantly constrain the deviation from the linear form at high masses. For example, in each redshift interval Delvecchio et al. (2021) and Daddi et al. (2022a) found no more than 838 SFGs at log10(M*/M⊙) > 11, and in the same mass range the stacking analysis in Schreiber et al. (2015) has < 15 galaxies per bin. Analogously, most of the studies in the compilation of Popesso et al. (2023) stop at log10(M*/M⊙) = 11, and those that extend further never reach more than 103 galaxies per bin in comparable redshift ranges. Due to the large area observed in Q1, the minimum number of galaxies we have at log10(M*/M⊙) > 11 is 875, in the [0.2, 0.5] redshift bin. This number increases to 7640 (for 0.5 < z < 0.8), 18 951 (for 0.8 < z < 1.5), and 8165 (for 1.5 < z < 3.0), one or two orders of magnitude higher than the former reported statistics. These numbers are more than enough to subdivide the log10(M*/M⊙) > 11 region into two different bins at z > 0.8, to better constrain the part of the SFMS where the SFR appears to saturate. The same reasoning, scaled by an order of magnitude, applies if we consider log10(M*/M⊙) > 10.5.

Our fit to the observed data is the red line in Fig. 9. Overall, the fits in Popesso et al. (2023) and Daddi et al. (2022a) closely resemble our results, while Schreiber et al. (2015) find systematically higher SFRs at the highest mass end. The functional form that we fit these data to, first proposed by Lee et al. (2015), is the same as in Eq. (15) of Popesso et al. (2023) or Eq. (1) of Daddi et al. (2022a),

SFR = SFR max 1 + ( M 0 / M ∗ ) γ ; Mathematical equation: $$ \begin{aligned} \mathrm{SFR} = \frac{\mathrm{SFR}_{\rm max}}{1+(M_0/M_*)^{\gamma }}; \end{aligned} $$(8)

that is, a parameterisation where the SFR is linked to the stellar mass through three parameters – the bending mass after which the relation deviates from the linear behaviour (M0), the maximum SFR for M* ≫ M0 (SFRmax), and the slope of the linear relation when M* ≪ M0 (γ). These parameters have been shown to be directly linked to fundamental properties in models of gas accretion (e.g. the bending mass M0 is directly linked to the ratio between Mshock and Mstream, see Daddi et al. 2022a,b). For each fit, we kept γ fixed at 1.0, as it has been shown to be a representative value around which almost every fit converges at different redshifts (see Lee et al. 2015; Popesso et al. 2023; Daddi et al. 2022a). This also makes it possible to make a direct comparison with these works in terms of bending mass and the maximum SFR.

When fitting the SFMS, we must take into account the fact that for each redshift bin there are two possible values for the mass completeness limit, depending on whether consider the mass at the lower limit of the redshift bin, zstart, or at the higher limit, zend. Depending on the width of the redshift bin, these two masses can differ significantly, of the order of 0.4 − 0.6 dex (see Fig. 9). When M* > Mlim(zend), we are dealing with a complete sample; in this case, we fit the points measured as the median stellar masses and SFRs of the distribution of SFGs in each bin of mass, with the associated uncertainty as the quadrature sum of the standard deviation of the median in each bin and the typical uncertainty on the SFRs (see Sect. 3.3). These are shown as stars in the bottom panel of Fig. 10, coloured as a function of the redshift bin to which they belong. When M* < Mlim(zstart) we consider the sample to be incomplete, and these galaxies are excluded from the fit. In the mass bins where Mlim(zstart) < M* < Mlim(zend), we are preferentially missing lower-mass galaxies, which tend to have lower SFRs. As a result, we treat the SFR data points in these bins as upper limits, as is indicated by the arrows in the bottom panel of Fig. 10.

Thumbnail: Fig. 10. Refer to the following caption and surrounding text. Fig. 10.

Lower panel: Our fit of the SFMS, in the four redshift bins (stars with error bars and arrows) and best-fit model (dashed lines). The reported redshift is the median z of the bin. Upper panels: Best-fit (red stars) and reported (squares for Popesso et al. 2023; circles for Daddi et al. 2022a) values for the bending mass and maximum SFR, defined as ℳ0 ≡ log10(M0/M⊙) and 𝒮ℱℛmax ≡ log10(SFRmax/M⊙ yr−1), as a function of redshift.

The SFR–mass bins were obtained by binning the distribution of stellar mass to uniformly cover the stellar masses space with a similar number of sources to make these statistically significant. The bins start from where the stellar mass is higher than the 95% completeness limit at the lower limit of the redshift bin; that is, log10(M*/M⊙)∼8.1 at z = 0.37, log10(M*/M⊙)∼8.6 at z = 0.67, log10(M*/M⊙)∼9.0 at z = 1.15, and log10(M*/M⊙)∼9.5 at z = 1.83. The results of the fit are reported in Table 2, and shown in Fig. 10 as dashed lines colour-coded by redshift bin. The bending mass and maximum SFR are reported as a function of redshift in the upper panels of Fig. 10, as red stars and solid lines. We also show, for comparison, the same parameters found in Daddi et al. (2022a, as blue circles and dashed dotted line) and Popesso et al. (2023, black edged squares and dashed line) as a function of z. As an internal check, we also fitted the same points with a linear relation (e.g., Eq. (10) in Popesso et al. 2023), obtaining worse χ2 for each redshift bin with respect to the relation including the bending at the high-mass end.

Table 2.

Fitted values for log10(M0/M⊙), log10(SFRmax/M⊙ yr−1), and the relation scatter σSFMS for each redshift bin, with the median redshift in bin reported in the first column.

Our recovered bending masses M0 increase with redshift. We find results similar to those of Daddi et al. (2022a), with the main difference in the [0.8, 1.5] bin, with a higher log10(M0/M⊙) = 10.62 ± 0.05 (similar to what was found in Popesso et al. 2023). In the [1.5, 3.0] bin, our bending mass is more in line with Daddi et al. (2022a) at log10(M0/M⊙) = 11.10 ± 0.09, (0.6 dex higher than the one in Popesso et al. 2023). However, for this redshift bin, we must again warn the reader about the caveats highlighted in Sect. 3.3 and Fig. 4; that is, at 11 < log10(M*/M⊙) < 11.5 any wrong redshift attribution will introduce an important source of systematic biases, skewing the fitted bins at higher values of M* and SFR, and therefore the recovered M0 and SFRmax. In any case, the observed agreement and evolution with redshift are remarkable, when taking into account the fact that our SFRs have been evaluated with photometry ranging from the g band (the u band is available only in one field) up to 4.5 μm, and thus without properly accounting for dust-obscured star formation processes, which are disentangled from quiescence only when photometry from the far-IR up to radio is available.

Trying to find the best-fit parameters of the SFMS with the functional form in Eq. (8), we also measured the scatter in the relation σSFMS, fitting the difference between the observed set of galaxy stellar masses and SFRs and the model as a normal distribution, 𝒩(σSFMS). We find the same tight scatter, σSFMS ≃ 0.3, observed in previous studies (e.g. Clarke et al. 2024, for a SED-fitting derived SFMS), consistent in all redshift intervals within the uncertainties (Table 2). We also investigated whether there is any correlation between σSFMS and stellar masses. The topic is still highly debated, from both theoretical and observational points of view. Simulations find either a mass dependence (e.g. Ceverino et al. 2018; Katsianis et al. 2019; Legrand et al. 2022) or no dependence at all (e.g. Donnari et al. 2019; Pallottini & Ferrara 2023). The same is true for observational studies, with reported cases of no trend (e.g. Schreiber et al. 2015; Shivaei et al. 2015; Clarke et al. 2024), a monotonically increasing trend (Popesso et al. 2019; Sherman et al. 2021; Cole et al. 2025), or even a decrease with stellar mass (Willett et al. 2015). In each redshift interval, we measured the SFMS scatter in seven different mass bins as was previously done, starting from the mass limit completeness at the end of the interval (or at the start, for 1.5 < z < 3.0) in order to reduce any systematic effect arising from mass incompleteness. To account for the uncertainties in redshift, stellar mass, and SFR, we measured σSFMS in each mass bin ten times, each time on a sample generated perturbing the best-fit redshifts and PPs with the measured uncertainties. We then took every measure of σSFMS as the median of all iterations, with associated uncertainties as the 16th and 84th percentile of the distributions. The results are reported in Fig. 11. Even though caution must be taken given the various sources of uncertainties, we observe an increase in σSFMS with stellar mass, or at least an overall increasing trend.

Thumbnail: Fig. 11. Refer to the following caption and surrounding text. Fig. 11.

Scatter of the SFR–M* relation, σSFMS, in different mass bins. The purple shaded regions highlight where the mass is below the completeness limit at the start (hatched) and end of the redshift bin.

The SFMS dependence on the absorption, AV, and the ratio between the age and the e-folding time, τ, is shown in the first two rows of Fig. 12, where the colours correspond to the median of AV and T0/τ values of the sources within each bin, with the SFMS contours superimposed in grey. In this case, we have not limited the sample to SFGs only (i.e. we have not removed the sources identified as quiescent in the NUV − r+ − J diagram), highlighting a bin when the number of sources within the bin is greater than 20. In this way, we can explore less populated regions of the M*–SFR plane, where passive galaxies are expected to appear. The location of galaxies in the plane below a certain limiting sSFR (e.g. 0.01 Gyr−1) should not be considered as absolute, but rather as indicative that those objects are passive galaxies and could lie anywhere below that line. As was expected, maximum extinction values (AV > 2.0) are associated with the most massive and star-forming galaxies of the SFMS, with 1 < sSFR/Gyr−1 < 10, while low or zero dust extinction values are observed at lower sSFRs. The typical AV of SFMS galaxies decreases slightly from AV ∼ 1.0 to AV ∼ 0.5 with increasing redshift. Looking at the distribution of fitted AV, we recover only a small fraction of objects (∼1%) with a high extinction of AV > 2.5, with the AV distribution peaking at 0.5 < AV < 1.0. This could be due to the particular limitations and caveats of the recovered sample (see Sect. 3), especially in the range of wavelengths covered. Lower sSFR galaxies are associated with stellar populations with older ages, in particular at low redshift, and high age/τ ratios, while younger ages are found in the upper part of the SFMS and at high redshift (Nersesian et al. 2025).

Thumbnail: Fig. 12. Refer to the following caption and surrounding text. Fig. 12.

SFR–M* relation, colour-coded by the median AV (top), T0/τ (middle-top), Sérsic index (middle-bottom), and Sérsic radius (bottom) of objects in each bin. A bin is coloured only when the number of sources falling within the bin is higher than 20. The contours in grey contain 90%, 50%, and 10% of the full sample. The literature SFMS are the same as the ones shown in Fig. 9 and reported in Sect. 4. Dashed lines highlight the loci of equal sSFR.

The morphological parameters of all the Euclid-detected sources were measured by running the SourceXtractor++ code (Bertin et al. 2020; Kümmel et al. 2022), fitting the detections as two-dimensional Sérsic profiles (see Euclid Collaboration: Romelli et al. 2026 and Euclid Collaboration: Quilley et al. 2026, for further details). Here, we focus on the Sérsic radius, Re, and the Sérsic index, nS. In order to be more conservative, following what was found in Euclid Collaboration: Quilley et al. (2026, see their Fig. 2), in addition to the cuts described in Sect. 2, we also removed the sources whose fit did not converge on a solution. In these cases, the Sérsic axis ratio is exactly equal to one, and the Sérsic index nS < 0.302 or nS > 5.45. These cuts reduce our sample for morphological analysis by 17%, leaving a total of 6 702 811 sources.

In the two bottom rows of Fig. 12, we report the SFMS, colour-coded for the median values of nS (middle-bottom row) and Re (bottom row), converted from arcseconds to kiloparsecs for the predicted photo-z). We note that the higher values of nS > 3 are associated with the most massive, low-sSFR objects, and the radii, Re, increase with stellar mass at all redshifts. The combination of the limited volume of Universe sampled at low z with the increasing difficulty of properly identifying smaller galaxies at higher redshifts due to the fixed Euclid resolution (roughly translating into a limit in measured effective radiuses, Re, lim ≃ 2 − 3 kpc, in the redshift interval [0.5, 3.0]) results in an apparent decrease in Re with cosmic time, as the distributions of galaxies falling within each stellar mass–SFR bin suffer from this size incompleteness.

In all redshift intervals, the concurrent presence of the SFMS and the prominence of exponential disks with nS ≃ 1 (in blue) is immediately visible, while at lower sSFR, close to the limit where measuring SFRs becomes difficult, we note a crowding of sources with de Vaucoulers profiles of nS ≃ 4 (in red). Between those, there is an intermediate region of profiles with 2 < nS < 3 (the white strip) at about sSFR ∼ 0.05 Gyr−1, which indicates an evolutionary trend in the structural parameters while moving in the stellar mass–SFR plane, in agreement with what has been observed previously in other samples (Kauffmann et al. 2003; Wuyts et al. 2011; Whitaker et al. 2015; McPartland et al. 2019; Cooke et al. 2023; Martorano et al. 2025). This kind of transition is observed only at the medium-to-high-mass end log10(M*/M⊙) > 10, and appears to show only a weak redshift dependence. Interestingly, the mass over which the sequence of passive nS ≃ 4 profiles is observed is almost coincident with the fitted bending mass, M0, a trend that has already been observed in the literature (e.g. Leslie et al. 2020).

Euclid combines a large sample area with a uniform multi-wavelength view, which has great potential for environmental studies. Despite that, here we do not focus on how the environment shapes SFMS, as this is the main scope of other Q1 works (Euclid Collaboration: Cleland et al. 2025; Euclid Collaboration: Mai et al. 2025). The soon-to-be-available DR1 observations of the EDFs are expected to have at least ten ROSs, which corresponds to 1.25 magnitude-deeper data. Combining the DR1 data, along with other multi-wavelength observations and the Euclid spectroscopy sample, will allow for a thorough investigation of the environmental effects on the SFMS.

5. Conclusions

The Euclid Q1 data release, with its first look at the EDFs, is already a good test of the capabilities of the mission to investigate the formation and evolution of galaxies, especially in terms of the enhanced statistics of such a large area of the extragalactic sky. In this work, we have investigated the relation between stellar masses and SFRs, the SFMS, and how it relates to the other well-constrained PPs and morphological parameters, comparing the results with the existing literature, as a fair validation of the Euclid results and a first exploration of the mission capabilities to return a statistically robust sample. Even a single ROS of the EDFs is able to yield reliable measurements for the photometric redshifts, stellar masses, and SFRs – which in this work have been improved due to the addition of the first two channels of IRAC – for more than eight million galaxies at a magnitude cut of HE < 24. In particular, more than ∼30 k galaxies are found with log10(M*/M⊙) > 11, a substantial improvement over all the other extragalactic surveys limited to a few square degrees of the sky.

The recovered scaling relation between stellar mass and SFR is consistent with what is known from previous studies on the SFMS. The data show a similar tight dispersion, between 0.26 and 0.40 dex, with an increase in σSFMS occurring at higher masses, and are in excellent agreement with the functional forms reported in Popesso et al. (2023), Daddi et al. (2022a), and Schreiber et al. (2015). These works fit SFMS with a non-linear term that translates into a bending of the relation, becoming more pronounced at high masses. We fit the relation with the same parameterisation – that is, linking the SFR directly to the bending mass, M0, and the SFR maximum, SFRmax – recovering the same statistical agreement with the previous studies. M0 increases almost monotonically with redshift, starting from log10(M0/M*)≃10.3 at z = 0.37, up to 11.1 at cosmic noon. Our results are in accord with the presence of this reduction in SFR in massive galaxies, with a better χ2 with respect to a linear one. At the same time, when correlating our results with the catalogue of morphological properties, we recover the well-known bimodality between exponential and smaller star-forming disks and de Vaucoulers profiles for passive and bigger galaxies.

Acknowledgments

AnEn, LuPo, MiBo, EmDa, ViAl, FaGe, SaQu, MaTa, MaSc, and BeGr acknowledge support from the ELSA project. “ELSA: Euclid Legacy Science Advanced analysis tools” (Grant Agreement no. 101135203) is funded by the European Union. Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or Innovate UK. Neither the European Union nor the granting authority can be held responsible for them. UK participation is funded through the UK HORIZON guarantee scheme under Innovate UK grant 10093177. AnEn, MiBo, StCa, ElZu acknowledge support from the INAF MiniGrant 2023 “ADIEU: Anomaly Detections In EUclid”. This work has been partially funded by Italian MUR Premiale MITiC 2017. The Euclid Consortium acknowledges the European Space Agency and a number of agencies and institutes that have supported the development of Euclid, in particular the Agenzia Spaziale Italiana, the Austrian Forschungsförderungsgesellschaft funded through BMK, the Belgian Science Policy, the Canadian Euclid Consortium, the Deutsches Zentrum für Luft-und Raumfahrt, the DTU Space and the Niels Bohr Institute in Denmark, the French Centre National d’Etudes Spatiales, the Fundação para a Ciência e a Tecnologia, the Hungarian Academy of Sciences, the Ministerio de Ciencia, Innovación y Universidades, the National Aeronautics and Space Administration, the National Astronomical Observatory of Japan, the Netherlandse Onderzoekschool Voor Astronomie, the Norwegian Space Agency, the Research Council of Finland, the Romanian Space Agency, the State Secretariat for Education, Research, and Innovation (SERI) at the Swiss Space Office (SSO), and the United Kingdom Space Agency. A complete and detailed list is available on the Euclid website (www.euclid-ec.org). This work has made use of the Euclid Quick Release Q1 data from the Euclid mission of the European Space Agency (ESA), 2025, https://doi.org/10.57780/esa-2853f3b. This work has made use of CosmoHub, developed by PIC (maintained by IFAE and CIEMAT) in collaboration with ICE-CSIC. CosmoHub received funding from the Spanish government (MCIN/AEI/10.13039/501100011033), the EU NextGeneration/PRTR (PRTRC17. I1), and the Generalitat de Catalunya. Based on data from UNIONS, a scientific collaboration using three Hawaii-based telescopes: CFHT, Pan-STARRS, and Subaru www.skysurvey.cc. Based on data from the Dark Energy Camera (DECam) on the Blanco 4-m Telescope at CTIO in Chile https://www.darkenergysurvey.org. In preparation for this work, we used the following codes for Python: Numpy (Harris et al. 2020), Scipy (Virtanen et al. 2020), Pandas (McKinney 2010), nnpz (Tanaka et al. 2018).

References

  1. Abdurro’uf, & Akiyama, M. 2017, MNRAS, 469, 2806 [CrossRef] [Google Scholar]
  2. Ahumada, R., Allende Prieto, C., Almeida, A., et al. 2020, ApJS, 249, 3 [NASA ADS] [CrossRef] [Google Scholar]
  3. Arnouts, S., Le Floc’h, E., Chevallard, J., et al. 2013, A&A, 558, A67 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  4. Baes, M., Nersesian, A., Casasola, V., et al. 2020, A&A, 641, A119 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  5. Baker, W. M., Maiolino, R., Bluck, A. F. L., et al. 2022, MNRAS, 510, 3622 [NASA ADS] [CrossRef] [Google Scholar]
  6. Baker, W. M., Maiolino, R., Belfiore, F., et al. 2023, MNRAS, 518, 4767 [Google Scholar]
  7. Behroozi, P., Wechsler, R. H., Hearin, A. P., & Conroy, C. 2019, MNRAS, 488, 3143 [NASA ADS] [CrossRef] [Google Scholar]
  8. Bertin, E., Schefer, M., Apostolakos, N., et al. 2020, ASP Conf. Ser., 527, 461 [NASA ADS] [Google Scholar]
  9. Blake, C., Amon, A., Childress, M., et al. 2016, MNRAS, 462, 4240 [NASA ADS] [CrossRef] [Google Scholar]
  10. Bower, R. G., Schaye, J., Frenk, C. S., et al. 2017, MNRAS, 465, 32 [NASA ADS] [CrossRef] [Google Scholar]
  11. Brammer, G. B., Sánchez-Janssen, R., Labbé, I., et al. 2012, ApJ, 758, L17 [NASA ADS] [CrossRef] [Google Scholar]
  12. Brinchmann, J., Charlot, S., White, S. D. M., et al. 2004, MNRAS, 351, 1151 [Google Scholar]
  13. Bruzual, G., & Charlot, S. 2003, MNRAS, 344, 1000 [NASA ADS] [CrossRef] [Google Scholar]
  14. Calzetti, D., Armus, L., Bohlin, R. C., et al. 2000, ApJ, 533, 682 [NASA ADS] [CrossRef] [Google Scholar]
  15. Ceverino, D., Klessen, R. S., & Glover, S. C. O. 2018, MNRAS, 480, 4842 [NASA ADS] [Google Scholar]
  16. Chabrier, G. 2003, PASP, 115, 763 [Google Scholar]
  17. Childress, M. J., Lidman, C., Davis, T. M., et al. 2017, MNRAS, 472, 273 [Google Scholar]
  18. Ciesla, L., Elbaz, D., & Fensch, J. 2017, A&A, 608, A41 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  19. Clarke, L., Shapley, A. E., Sanders, R. L., et al. 2024, ApJ, 977, 133 [NASA ADS] [CrossRef] [Google Scholar]
  20. Coil, A. L., Blanton, M. R., Burles, S. M., et al. 2011, ApJ, 741, 8 [Google Scholar]
  21. Cole, J. W., Papovich, C., Finkelstein, S. L., et al. 2025, ApJ, 979, 193 [Google Scholar]
  22. Colless, M., Dalton, G., Maddox, S., et al. 2001, MNRAS, 328, 1039 [Google Scholar]
  23. Cooke, K. C., Kartaltepe, J. S., Rose, C., et al. 2023, ApJ, 942, 49 [NASA ADS] [CrossRef] [Google Scholar]
  24. Daddi, E., Dickinson, M., Morrison, G., et al. 2007, ApJ, 670, 156 [NASA ADS] [CrossRef] [Google Scholar]
  25. Daddi, E., Delvecchio, I., Dimauro, P., et al. 2022a, A&A, 661, L7 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  26. Daddi, E., Rich, R. M., Valentino, F., et al. 2022b, ApJ, 926, L21 [NASA ADS] [CrossRef] [Google Scholar]
  27. Dark Energy Survey Collaboration (Abbott, T., et al.) 2016, MNRAS, 460, 1270 [Google Scholar]
  28. Dekel, A., & Birnboim, Y. 2006, MNRAS, 368, 2 [NASA ADS] [CrossRef] [Google Scholar]
  29. Delvecchio, I., Daddi, E., Sargent, M. T., et al. 2021, A&A, 647, A123 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  30. DESI Collaboration (Aghamousa, A., et al.) 2016, ArXiv e-prints [arXiv:1611.00036] [Google Scholar]
  31. DESI Collaboration (Adame, A. G., et al.) 2024, AJ, 168, 58 [NASA ADS] [CrossRef] [Google Scholar]
  32. D’Eugenio, F., Cameron, A. J., Scholtz, J., et al. 2025, ApJS, 277, 4 [Google Scholar]
  33. Donnari, M., Pillepich, A., Nelson, D., et al. 2019, MNRAS, 485, 4817 [Google Scholar]
  34. Elbaz, D., Dickinson, M., Hwang, H. S., et al. 2011, A&A, 533, A119 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  35. Ellison, S. L., Sánchez, S. F., Ibarra-Medel, H., et al. 2018, MNRAS, 474, 2039 [Google Scholar]
  36. Ellison, S. L., Lin, L., Thorp, M. D., et al. 2021, MNRAS, 501, 4777 [NASA ADS] [CrossRef] [Google Scholar]
  37. Enia, A., Rodighiero, G., Morselli, L., et al. 2020, MNRAS, 493, 4107 [NASA ADS] [CrossRef] [Google Scholar]
  38. Euclid Collaboration (Desprez, G., et al.) 2020, A&A, 644, A31 [EDP Sciences] [Google Scholar]
  39. Euclid Collaboration (Moneti, A., et al.) 2022, A&A, 658, A126 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  40. Euclid Collaboration (Scaramella, R., et al.) 2022, A&A, 662, A112 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  41. Euclid Collaboration (Schirmer, M., et al.) 2022, A&A, 662, A92 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  42. Euclid Collaboration (Enia, A., et al.) 2024, A&A, 691, A175 [NASA ADS] [Google Scholar]
  43. Euclid Collaboration (Castander, F., et al.) 2025, A&A, 697, A5 [Google Scholar]
  44. Euclid Collaboration (Cleland, C., et al.) 2025, A&A, submitted [arXiv:2503.15313] [Google Scholar]
  45. Euclid Collaboration (Cropper, M., et al.) 2025, A&A, 697, A2 [Google Scholar]
  46. Euclid Collaboration (Jahnke, K., et al.) 2025, A&A, 697, A3 [Google Scholar]
  47. Euclid Collaboration (Mai, N., et al.) 2025, ArXiv e-prints [arXiv:2503.15331] [Google Scholar]
  48. Euclid Collaboration (McPartland, C. J. R., et al.) 2025, A&A, 695, A259 [Google Scholar]
  49. Euclid Collaboration (Mellier, Y., et al.) 2025, A&A, 697, A1 [Google Scholar]
  50. Euclid Collaboration (Aussel, H., et al.) 2026, A&A, 711, A1 (Euclid Q1 SI) [Google Scholar]
  51. Euclid Collaboration (Bisigello, L., et al.) 2026, A&A, 711, A24 (Euclid Q1 SI) [Google Scholar]
  52. Euclid Collaboration (Corcho-Caballero, P., et al.) 2026, A&A, 711, A15 (Euclid Q1 SI) [Google Scholar]
  53. Euclid Collaboration (Matamoro Zatarain, T., et al.) 2026, A&A, 711, A20 (Euclid Q1 SI) [Google Scholar]
  54. Euclid Collaboration (McCracken, H. J., et al.) 2026, A&A, 711, A2 (Euclid Q1 SI) [Google Scholar]
  55. Euclid Collaboration (Polenta, G., et al.) 2026, A&A, 711, A3 (Euclid Q1 SI) [Google Scholar]
  56. Euclid Collaboration (Quilley, L., et al.) 2026, A&A, 711, A8 (Euclid Q1 SI) [Google Scholar]
  57. Euclid Collaboration (Romelli, E., et al.) 2026, A&A, 711, A4 (Euclid Q1 SI) [Google Scholar]
  58. Euclid Collaboration (Tucci, M., et al.) 2026, A&A, 711, A5 (Euclid Q1 SI) [Google Scholar]
  59. Euclid Collaboration (Walmsley, M., et al.) 2026, A&A, 711, A9 (Euclid Q1 SI) [Google Scholar]
  60. Euclid Quick Release Q1 2025, https://doi.org/10.57780/esa-2853f3b [Google Scholar]
  61. Fabian, A. C. 2012, ARA&A, 50, 455 [Google Scholar]
  62. Fazio, G. G., Hora, J. L., Allen, L. E., et al. 2004, ApJS, 154, 10 [Google Scholar]
  63. Flaugher, B., Diehl, H. T., Honscheid, K., et al. 2015, AJ, 150, 150 [Google Scholar]
  64. Gwyn, S., McConnachie, A. W., Cuillandre, J. C., et al. 2025, AJ, 170, 324 [Google Scholar]
  65. Halton, J. H. 1964, Commun. ACM, 7, 701 [Google Scholar]
  66. Harris, C. R., Millman, K. J., van der Walt, S. J., et al. 2020, Nature, 585, 357 [NASA ADS] [CrossRef] [Google Scholar]
  67. Hsieh, B. C., Lin, L., Lin, J. H., et al. 2017, ApJ, 851, L24 [Google Scholar]
  68. Huchra, J. P., Macri, L. M., Masters, K. L., et al. 2012, ApJS, 199, 26 [Google Scholar]
  69. Ilbert, O., Salvato, M., Le Floc’h, E., et al. 2010, ApJ, 709, 644 [Google Scholar]
  70. Ilbert, O., McCracken, H. J., Le Fèvre, O., et al. 2013, A&A, 556, A55 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  71. Iyer, K. G., Gawiser, E., Faber, S. M., et al. 2019, ApJ, 879, 116 [NASA ADS] [CrossRef] [Google Scholar]
  72. Jones, D. H., Read, M. A., Saunders, W., et al. 2009, MNRAS, 399, 683 [Google Scholar]
  73. Katsianis, A., Zheng, X., Gonzalez, V., et al. 2019, ApJ, 879, 11 [Google Scholar]
  74. Kauffmann, G., Heckman, T. M., White, S. D. M., et al. 2003, MNRAS, 341, 54 [Google Scholar]
  75. Kennicutt, R. C. 1998a, ARA&A, 36, 189 [NASA ADS] [CrossRef] [Google Scholar]
  76. Kennicutt, R. C. 1998b, ApJ, 498, 541 [NASA ADS] [CrossRef] [Google Scholar]
  77. Kereš, D., Katz, N., Weinberg, D. H., & Davé, R. 2005, MNRAS, 363, 2 [Google Scholar]
  78. Kriek, M., Shapley, A. E., Reddy, N. A., et al. 2015, ApJS, 218, 15 [NASA ADS] [CrossRef] [Google Scholar]
  79. Kroupa, P. 2001, MNRAS, 322, 231 [NASA ADS] [CrossRef] [Google Scholar]
  80. Kümmel, M., Vassallo, T., Dabin, C., & Gracia Carpio, J. 2022, ASP Conf. Ser., 532, 329 [Google Scholar]
  81. Labbé, I., Huang, J., Franx, M., et al. 2005, ApJ, 624, L81 [Google Scholar]
  82. Le Fèvre, O., Vettolani, G., Garilli, B., et al. 2005, A&A, 439, 845 [Google Scholar]
  83. Lee, N., Sanders, D. B., Casey, C. M., et al. 2015, ApJ, 801, 80 [Google Scholar]
  84. Legrand, L., Hutter, A., Dayal, P., et al. 2022, MNRAS, 509, 595 [Google Scholar]
  85. Leja, J., Carnall, A. C., Johnson, B. D., Conroy, C., & Speagle, J. S. 2019, ApJ, 876, 3 [Google Scholar]
  86. Leja, J., Speagle, J. S., Ting, Y.-S., et al. 2022, ApJ, 936, 165 [NASA ADS] [CrossRef] [Google Scholar]
  87. Leroy, L., Elbaz, D., Magnelli, B., et al. 2024, A&A, 691, A248 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  88. Leslie, S. K., Schinnerer, E., Liu, D., et al. 2020, ApJ, 899, 58 [Google Scholar]
  89. Lidman, C., Tucker, B. E., Davis, T. M., et al. 2020, MNRAS, 496, 19 [NASA ADS] [CrossRef] [Google Scholar]
  90. Lin, L., Belfiore, F., Pan, H.-A., et al. 2017, ApJ, 851, 18 [Google Scholar]
  91. Lin, L., Pan, H.-A., Ellison, S. L., et al. 2019, ApJ, 884, L33 [NASA ADS] [CrossRef] [Google Scholar]
  92. Mancini, C., Daddi, E., Juneau, S., et al. 2019, MNRAS, 489, 1265 [Google Scholar]
  93. Martorano, M., van der Wel, A., Baes, M., et al. 2025, A&A, 694, A76 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  94. Matthee, J., & Schaye, J. 2019, MNRAS, 484, 915 [CrossRef] [Google Scholar]
  95. McKinney, W. 2010, in Proceedings of the 9th Python in Science Conference, eds. S. van der Walt, & J. Millman, 56 [Google Scholar]
  96. McPartland, C., Sanders, D. B., Kewley, L. J., & Leslie, S. K. 2019, MNRAS, 482, L129 [CrossRef] [Google Scholar]
  97. Morselli, L., Rodighiero, G., Enia, A., et al. 2020, MNRAS, 496, 4606 [NASA ADS] [CrossRef] [Google Scholar]
  98. Nersesian, A., van der Wel, A., Gallazzi, A. R., et al. 2025, A&A, 695, A86 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  99. Oke, J. B., & Gunn, J. E. 1983, ApJ, 266, 713 [NASA ADS] [CrossRef] [Google Scholar]
  100. Pallottini, A., & Ferrara, A. 2023, A&A, 677, L4 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  101. Pentericci, L., McLure, R. J., Franzetti, P., Garilli, B., & the VANDELS team 2018, ArXiv e-prints [arXiv:1811.05298] [Google Scholar]
  102. Popesso, P., Concas, A., Morselli, L., et al. 2019, MNRAS, 483, 3213 [Google Scholar]
  103. Popesso, P., Concas, A., Cresci, G., et al. 2023, MNRAS, 519, 1526 [Google Scholar]
  104. Pozzetti, L., Bolzonella, M., Zucca, E., et al. 2010, A&A, 523, A13 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  105. Prevot, M. L., Lequeux, J., Maurice, E., Prevot, L., & Rocca-Volmerange, B. 1984, A&A, 132, 389 [Google Scholar]
  106. Rodighiero, G., Daddi, E., Baronchelli, I., et al. 2011, ApJ, 739, L40 [Google Scholar]
  107. Schmidt, M. 1959, ApJ, 129, 243 [NASA ADS] [CrossRef] [Google Scholar]
  108. Schreiber, C., Pannella, M., Elbaz, D., et al. 2015, A&A, 575, A74 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  109. Sherman, S., Jogee, S., Florez, J., et al. 2021, MNRAS, 505, 947 [CrossRef] [Google Scholar]
  110. Shivaei, I., Reddy, N. A., Shapley, A. E., et al. 2015, ApJ, 815, 98 [NASA ADS] [CrossRef] [Google Scholar]
  111. Siudek, M., Pucha, R., Mezcua, M., et al. 2024, A&A, 691, A308 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  112. Speagle, J. S., Steinhardt, C. L., Capak, P. L., & Silverman, J. D. 2014, ApJS, 214, 15 [Google Scholar]
  113. Talia, M., Schreiber, C., Garilli, B., et al. 2023, A&A, 678, A25 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  114. Tanaka, M., Coupon, J., Hsieh, B.-C., et al. 2018, PASJ, 70, S9 [Google Scholar]
  115. Tomczak, A. R., Quadri, R. F., Tran, K.-V. H., et al. 2016, ApJ, 817, 118 [Google Scholar]
  116. Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nat. Meth., 17, 261 [Google Scholar]
  117. Wang, T.-M., Magnelli, B., Schinnerer, E., et al. 2024, A&A, 681, A110 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  118. Weaver, J. R., Kauffmann, O. B., Ilbert, O., et al. 2022, ApJS, 258, 11 [NASA ADS] [CrossRef] [Google Scholar]
  119. Werner, M. W., Roellig, T. L., Low, F. J., et al. 2004, ApJS, 154, 1 [NASA ADS] [CrossRef] [Google Scholar]
  120. Whitaker, K. E., Franx, M., Leja, J., et al. 2014, ApJ, 795, 104 [NASA ADS] [CrossRef] [Google Scholar]
  121. Whitaker, K. E., Franx, M., Bezanson, R., et al. 2015, ApJ, 811, L12 [NASA ADS] [CrossRef] [Google Scholar]
  122. Willett, K. W., Schawinski, K., Simmons, B. D., et al. 2015, MNRAS, 449, 820 [NASA ADS] [CrossRef] [Google Scholar]
  123. Williams, R. J., Quadri, R. F., Franx, M., et al. 2010, ApJ, 713, 738 [NASA ADS] [CrossRef] [Google Scholar]
  124. Wright, E. L., Eisenhardt, P. R. M., Mainzer, A. K., et al. 2010, AJ, 140, 1868 [Google Scholar]
  125. Wuyts, S., Labbé, I., Franx, M., et al. 2007, ApJ, 655, 51 [NASA ADS] [CrossRef] [Google Scholar]
  126. Wuyts, S., Förster Schreiber, N. M., van der Wel, A., et al. 2011, ApJ, 742, 96 [NASA ADS] [CrossRef] [Google Scholar]
  127. Wuyts, S., Förster Schreiber, N. M., Nelson, E. J., et al. 2013, ApJ, 779, 135 [Google Scholar]
  128. Yang, X., Mo, H. J., van den Bosch, F. C., et al. 2007, ApJ, 671, 153 [Google Scholar]
  129. Yuan, F., Lidman, C., Davis, T. M., et al. 2015, MNRAS, 452, 3047 [Google Scholar]
2

A method to generate a quasi-random grid, which is evenly distributed across the parameter space, minimising the presence of gaps and clusters of points.

All Tables

Table 1.

Filters used in this work, with associated observed depths.

In the text
Table 2.

Fitted values for log10(M0/M⊙), log10(SFRmax/M⊙ yr−1), and the relation scatter σSFMS for each redshift bin, with the median redshift in bin reported in the first column.

In the text

All Figures

Thumbnail: Fig. 1. Refer to the following caption and surrounding text. Fig. 1.

Left panels: Distribution of redshifts, z, attenuations, AV, and ages, T0 for the reference sample used in this work. Right panels: Two priors adopted in this work – volume and age – as multiplicative weights on the reference galaxies, depending on their redshifts or ages.
In the text
Thumbnail: Fig. 2. Refer to the following caption and surrounding text. Fig. 2.

Results for the nnpz run on the 70 k simulated FS2 galaxies, without (top panels) and with the first two WISE filters (bottom panels). The black line is the 1:1 relation; the shaded area is the region beyond which a prediction is an outlier. In every panel, the contours are the area containing 86%, 39% (corresponding to the 2σ and 1σ levels for a 2D histogram), and 20% of the sample. For SFMS (right panel), the true distribution is reported in red (dashed) and the predicted one in blue (solid). The lines are the orthogonal distance regression (ODR) best fit to the distribution with passive galaxies removed. The reported metrics are NMAD (purple), the outlier fraction, fout (blue), and the bias (green) for the photometric redshifts and physical parameters, and the slope, m, scatter, σ, and fraction of passive galaxies, fp, for the SFMS, all defined in Sect. 3.1.
In the text
Thumbnail: Fig. 3. Refer to the following caption and surrounding text. Fig. 3.

Left: Comparison between the measured photometric redshifts and a compilation of all the available and reliable spectroscopic redshifts, colour-coded by the density of objects in each bin. The black line is the 1:1 relation, while the shaded grey area is the region beyond which a prediction is considered to be an outlier. The reported metrics are NMAD (purple), the outlier fraction, fout (blue), and the bias (green), all defined in Sect. 3.1. Middle: Normalised redshift difference as a function of stellar masses (top) and SFRs (bottom). The black contours are at the same levels as in Fig. 2. Right: Normalised distributions of photometric redshifts (top), stellar masses (centre), and SFRs (bottom) for our full sample (dashed red lines), compared with the results coming from the Q1 data products (PHZ, in dotted blue lines), and COSMOS2020 (in solid grey lines), at the same magnitude cuts applied in this work (see Sect. 2).
In the text
Thumbnail: Fig. 4. Refer to the following caption and surrounding text. Fig. 4.

M*–SFR plane at four different redshift intervals, only for the sources with a reliable zspec described in Sect. 3.3, colour-coded by the median normalised redshift difference in each bin. To give an idea of the density of objects in each redshift interval, we superimposed the contours in grey, with the same levels as in Fig. 2.
In the text
Thumbnail: Fig. 5. Refer to the following caption and surrounding text. Fig. 5.

Comparison between the stellar masses and SFRs measured in this work and a sample of objects from DESI with stellar masses from SED fitting (left) and SFRs from Hα (right), colour-coded as a function of the median normalised redshift difference in each bin. The black line is the 1:1 relation, while the shaded area is the region beyond which a prediction is an outlier. The contours are the same as in Fig. 2. The reported metrics are defined in Sect. 3.1.
In the text
Thumbnail: Fig. 6. Refer to the following caption and surrounding text. Fig. 6.

Cumulative distribution of the normalised residuals for photometric redshifts (red) and SFRs (blue). For comparison, we also show in grey the cumulative of a normal distribution with σ = 1. Dashed black lines highlight the position where 68% of the distributions are, and the 1σ level for the residuals.
In the text
Thumbnail: Fig. 7. Refer to the following caption and surrounding text. Fig. 7.

The stellar mass completeness for the sample used in this work (Pozzetti et al. 2010), with a cut at HE < 24, shown as the density of galaxies in the photometric redshifts vs. stellar masses plane. The solid grey line is the 95% stellar mass completeness limit, red dashed-dotted line for passive galaxies, and blue dashed line for SFGs.
In the text
Thumbnail: Fig. 8. Refer to the following caption and surrounding text. Fig. 8.

NUV − r+ versus r+ − J rest-frame colours for the sources above the 95% mass completeness limit, in four redshift bins, colour-coded with the density of objects (upper panels), the ratio between T0 and τ (middle panels), and the sSFR (bottom panels). Dash-dotted lines divide the regions between star-forming and quiescent galaxies, following the criteria presented in Ilbert et al. (2013).
In the text
Thumbnail: Fig. 9. Refer to the following caption and surrounding text. Fig. 9.

SFR–M* relation for SFGs, selected with the NUV − r+ versus r+ − J condition, coloured by the density of objects in each redshift bin. Within the coloured bins is 99.9% of the sample of SFGs, while the grey contours are the lines enclosing 95%, 50%, and 10% of it. The red line is the fitted SFMS presented in this work, starting from the completeness limit mass at the start of the z-bin. The other SFMSs are from Popesso et al. (2023, dashed black line), Schreiber et al. (2015, dotted grey line), and Daddi et al. (2022a, dashed-dotted blue line), all evaluated at the median redshift of each redshift bin (or to the closest reported value). The shaded purple regions highlight where the mass is below the completeness limit at the start (hatched) and at the end of the redshift bin. Dashed grey lines highlight the region of constant sSFR.
In the text
Thumbnail: Fig. 10. Refer to the following caption and surrounding text. Fig. 10.

Lower panel: Our fit of the SFMS, in the four redshift bins (stars with error bars and arrows) and best-fit model (dashed lines). The reported redshift is the median z of the bin. Upper panels: Best-fit (red stars) and reported (squares for Popesso et al. 2023; circles for Daddi et al. 2022a) values for the bending mass and maximum SFR, defined as ℳ0 ≡ log10(M0/M⊙) and 𝒮ℱℛmax ≡ log10(SFRmax/M⊙ yr−1), as a function of redshift.
In the text
Thumbnail: Fig. 11. Refer to the following caption and surrounding text. Fig. 11.

Scatter of the SFR–M* relation, σSFMS, in different mass bins. The purple shaded regions highlight where the mass is below the completeness limit at the start (hatched) and end of the redshift bin.
In the text
Thumbnail: Fig. 12. Refer to the following caption and surrounding text. Fig. 12.

SFR–M* relation, colour-coded by the median AV (top), T0/τ (middle-top), Sérsic index (middle-bottom), and Sérsic radius (bottom) of objects in each bin. A bin is coloured only when the number of sources falling within the bin is higher than 20. The contours in grey contain 90%, 50%, and 10% of the full sample. The literature SFMS are the same as the ones shown in Fig. 9 and reported in Sect. 4. Dashed lines highlight the loci of equal sSFR.
In the text

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.