We provide an early assessment of the imaging capabilities of the Euclid space mission to probe deeply into nearby star-forming regions and associated very young open clusters, and in particular to check to what extent it can shed light on the new-born free-floating planet population. This paper focuses on a low-reddening region observed in just one Euclid pointing where the dust and gas has been cleared out by the hot sigma Orionis star. One late-M and six known spectroscopically confirmed L-type substellar members in the sigma Orionis cluster are used as benchmarks to provide a high-purity procedure to select new candidate members with Euclid. The exquisite angular resolution and depth delivered by the Euclid instruments allow us to focus on bona-fide point sources. A cleaned sample of sigma Orionis cluster substellar members has been produced and the initial mass function (IMF) has been estimated by combining Euclid and Gaia data. Our sigma Orionis substellar IMF is consistent with a power-law distribution with no significant steepening at the planetary-mass end. No evidence of a low-mass cutoff is found down to about 4 Jupiter masses at the young age (3 Myr) of the sigma Orionis open cluster.

The Euclid Early Release Observations (ERO) showcase Euclid's capabilities in advance of its main mission by targeting 17 astronomical objects, including galaxy clusters, nearby galaxies, globular clusters, and star-forming regions. A total of 24 hours of observing time was allocated in the early months of operation, and the scientific community was engaged through an early public data release. We describe the development of the ERO pipeline to create visually compelling images while simultaneously meeting the scientific demands within months of launch by leveraging a pragmatic data-driven development strategy. The pipeline's key requirements are to preserve the image quality and to provide flux calibration and photometry for compact and extended sources. The pipeline's five pillars are removal of instrumental signatures, astrometric calibration, photometric calibration, image stacking, and the production of science-ready catalogues for both the VIS and NISP instruments. We report a point spread function (PSF) with a full width at half maximum of 0.'' 16 in the optical I-E-band and 0.'' 49 in the near-infrared (NIR) bands Y-E, J(E), and H-E. Our VIS mean absolute flux calibration is accurate to about 1%, and the accuracy is 10% for NISP due to a limited calibration set; both instruments have considerable colour terms for individual sources. The median depth is 25.3 and 23.2 AB mag with a signal-to-noise ratio (S/N) of ten for galaxies, while it is 27.1 and 24.5 AB mag at an S/N of five for point sources for VIS and NISP, respectively. Euclid's ability to observe diffuse emission is exceptional due to its extended PSF nearly matching a pure diffraction halo, the best ever achieved by a wide-field high-resolution imaging telescope. Euclid offers unparalleled capabilities for exploring the low-surface brightness (LSB) Universe across all scales, providing high precision within a wide field of view (FoV), and opening a new observational window in the NIR. Median surface-brightness levels of 29.5 and 27.9, AB mag arcsec(-2) are achieved for VIS and NISP, respectively, for detecting a 10 '' x 10 '' extended feature at the 1 sigma level.

We present an analysis of Euclid observations of a 0.5 deg$^2$ field in the central region of the Fornax galaxy cluster that were acquired during the performance verification phase. With these data, we investigate the potential of Euclid for identifying GCs at 20 Mpc, and validate the search methods using artificial GCs and known GCs within the field from the literature. Our analysis of artificial GCs injected into the data shows that Euclid's data in $I_{\rm E}$ band is 80% complete at about $I_{\rm E} \sim 26.0$ mag ($M_{V\rm } \sim -5.0$ mag), and resolves GCs as small as $r_{\rm h} = 2.5$ pc. In the $I_{\rm E}$ band, we detect more than 95% of the known GCs from previous spectroscopic surveys and GC candidates of the ACS Fornax Cluster Survey, of which more than 80% are resolved. We identify more than 5000 new GC candidates within the field of view down to $I_{\rm E}$ mag, about 1.5 mag fainter than the typical GC luminosity function turn-over magnitude, and investigate their spatial distribution within the intracluster field. We then focus on the GC candidates around dwarf galaxies and investigate their numbers, stacked luminosity distribution and stacked radial distribution. While the overall GC properties are consistent with those in the literature, an interesting over-representation of relatively bright candidates is found within a small number of relatively GC-rich dwarf galaxies. Our work confirms the capabilities of Euclid data in detecting GCs and separating them from foreground and background contaminants at a distance of 20 Mpc, particularly for low-GC count systems such as dwarf galaxies.

We forecast the expected population of active galactic nuclei (AGN) observable in the Euclid Wide Survey (EWS) and Euclid Deep Survey (EDS). Starting from an X-ray luminosity function (XLF) we generate volume-limited samples of the AGN expected in the survey footprints. Each AGN is assigned an SED appropriate for its X-ray luminosity and redshift, with perturbations sampled from empirical distributions. The photometric detectability of each AGN is assessed via mock observation of the assigned SED. We estimate 40 million AGN will be detectable in at least one band in the EWS and 0.24 million in the EDS, corresponding to surface densities of 2.8$\times$10$^{3}$ deg$^{-2}$ and 4.7$\times$10$^{3}$ deg$^{-2}$. Employing colour selection criteria on our simulated data we select a sample of 4.8$\times$10$^{6}$ (331 deg$^{-2}$) AGN in the EWS and 1.7$\times$10$^{4}$ (346 deg$^{-2}$) in the EDS, amounting to 10% and 8% of the AGN detectable in the EWS and EDS. Including ancillary Rubin/LSST bands improves the completeness and purity of AGN selection. These data roughly double the total number of selected AGN to comprise 21% and 15% of the detectable AGN in the EWS and EDS. The total expected sample of colour-selected AGN contains 6.0$\times$10$^{6}$ (74%) unobscured AGN and 2.1$\times$10$^{6}$ (26%) obscured AGN, covering $0.02 \leq z \lesssim 5.2$ and $43 \leq \log_{10} (L_{bol} / erg s^{-1}) \leq 47$. With this simple colour selection, expected surface densities are already comparable to the yield of modern X-ray and mid-infrared surveys of similar area. The relative uncertainty on our expectation for detectable AGN is 6.7% for the EWS and 12.5% for the EDS, driven by the uncertainty of the XLF.

Extragalactic globular clusters (EGCs) are an abundant and powerful tracer of galaxy dynamics and formation, and their own formation and evolution is also a matter of extensive debate. The compact nature of globular clusters means that they are hard to spatially resolve and thus study outside the Local Group. In this work we have examined how well EGCs will be detectable in images from the Euclid telescope, using both simulated pre-launch images and the first early-release observations of the Fornax galaxy cluster. The Euclid Wide Survey will provide high-spatial resolution VIS imaging in the broad IE band as well as near-infrared photometry (YE, JE, and HE). We estimate that the galaxies within 100 Mpc in the footprint of the Euclid survey host around 830 000 EGCs of which about 350 000 are within the survey's detection limits. For about half of these EGCs, three infrared colours will be available as well. For any galaxy within 50Mpc the brighter half of its GC luminosity function will be detectable by the Euclid Wide Survey. The detectability of EGCs is mainly driven by the residual surface brightness of their host galaxy. We find that an automated machine-learning EGC-classification method based on real Euclid data of the Fornax galaxy cluster provides an efficient method to generate high purity and high completeness GC candidate catalogues. We confirm that EGCs are spatially resolved compared to pure point sources in VIS images of Fornax. Our analysis of both simulated and first on-sky data show that Euclid will increase the number of GCs accessible with high-resolution imaging substantially compared to previous surveys, and will permit the study of GCs in the outskirts of their hosts. Euclid is unique in enabling systematic studies of EGCs in a spatially unbiased and homogeneous manner and is primed to improve our understanding of many understudied aspects of GC astrophysics.

Euclid is poised to make significant advances in the study of nearby galaxies in the local Universe. Here we present a first look at 6 galaxies observed for the Nearby Galaxy Showcase as part of the Euclid Early Release Observations acquired between August and November, 2023. These targets, 3 dwarf galaxies (HolmbergII, IC10, NGC6822) and 3 spirals (IC342, NGC2403, NGC6744), range in distance from about 0.5 Mpc to 8.8 Mpc. Our assessment of the surface brightness depths in the stacked Euclid images confirms previous estimates in 100 arcsec^2 regions of 1sigma=30.5 mag/arcsec^2 for VIS, but slightly deeper than previous estimates for NISP with 1sigma=29.2-29.4 mag/arcsec^2. By combining Euclid HE, YE, and IE into RGB images, we illustrate the large field-of-view covered by a single Reference Observing Sequence, together with exquisite detail on parsec scales in these nearby galaxies. Radial surface brightness and color profiles demonstrate galaxy colors in agreement with stellar population synthesis models. Standard stellar photometry selection techniques find approximately 1.3 million stars across the 6 galaxy fields. Euclid's resolved stellar photometry allows us to constrain the star-formation histories of these galaxies, by disentangling the distributions of young stars, as well as asymptotic giant branch and red giant branch stellar populations. We finally examine 2 galaxies individually for surrounding satellite systems. Our analysis of the ensemble of dwarf satellites around NGC6744 reveals a new galaxy, EDwC1, a nucleated dwarf spheroidal at the end of a spiral arm. Our new census of the globular clusters around NGC2403 yields 9 new star-cluster candidates, 8 of which with colors indicative of evolved stellar populations. In summary, our investigation of the 6 Showcase galaxies demonstrates that Euclid is a powerful probe of the anatomy of nearby galaxies [abridged].

The Euclid ERO programme targeted the Perseus cluster of galaxies, gathering deep data in the central region of the cluster over 0.7 square degree, corresponding to approximately 0.25 r_200. The data set reaches a point-source depth of IE=28.0 (YE, JE, HE = 25.3) AB magnitudes at 5 sigma with a 0.16" and 0.48" FWHM, and a surface brightness limit of 30.1 (29.2) mag per square arcsec. The exceptional depth and spatial resolution of this wide-field multi-band data enable the simultaneous detection and characterisation of both bright and low surface brightness galaxies, along with their globular cluster systems, from the optical to the NIR. This study advances beyond previous analyses of the cluster and enables a range of scientific investigations summarised here. We derive the luminosity and stellar mass functions (LF and SMF) of the Perseus cluster in the Euclid IE band, thanks to supplementary u,g,r,i,z and Halpha data from the CFHT. We adopt a catalogue of 1100 dwarf galaxies, detailed in the corresponding ERO paper. We identify all other sources in the Euclid images and obtain accurate photometric measurements using AutoProf or AstroPhot for 138 bright cluster galaxies, and SourceExtractor for half a million compact sources. Cluster membership for the bright sample is determined by calculating photometric redshifts with Phosphoros. Our LF and SMF are the deepest recorded for the Perseus cluster, highlighting the groundbreaking capabilities of the Euclid telescope. Both the LF and SMF fit a Schechter plus Gaussian model. The LF features a dip at M(IE)=-19 and a faint-end slope of alpha_S = -1.2 to -1.3. The SMF displays a low-mass-end slope of alpha_S = -1.2 to -1.35. These observed slopes are flatter than those predicted for dark matter halos in cosmological simulations, offering significant insights for models of galaxy formation and evolution.

The Near-Infrared Spectrometer and Photometer (NISP) on board the satellite provides multiband photometry and $R slitless grism spectroscopy in the 950--2020\,nm wavelength range. In this reference article, we illuminate the background of NISP's functional and calibration requirements, describe the instrument's integral components, and provide all its key properties. We also sketch the processes needed to understand how NISP operates and is calibrated as well as its technical potentials and limitations. Links to articles providing more details and the technical background are included. The NISP's 16 H2RG detectors with a plate scale of $ deliver a field of view of 0.57\,deg$^2$. In photometric mode, NISP reaches a limiting magnitude of sim \,24.5\,AB\,mag in three photometric exposures of about 100\,s in exposure time for point sources and with a S/N of five. For spectroscopy, NISP's point-source sensitivity is a SNR = 3.5 detection of an emission line with flux sim \,$2 $ integrated over two resolution elements of 13.4\ in 3times 560\,s grism exposures at 1.6\ (redshifted Halpha ). Our calibration includes on-ground and in-flight characterisation and monitoring of the pixel-based detector baseline, dark current, non-linearity, and sensitivity to guarantee a relative photometric accuracy better than 1.5 and a relative spectrophotometry better than 0.7. The wavelength calibration must be accurate to 5\ or better. The NISP is the state-of-the-art instrument in the near-infrared for all science beyond small areas available from HST and JWST -- and it represents an enormous advance from any existing instrumentation due to its combination of field size and high throughput of telescope and instrument. During six-year survey covering 14\,000\,deg$^2$ of extragalactic sky, NISP will be the backbone in determining distances of more than a billion galaxies. Its near-infrared data will become a rich reference imaging and spectroscopy data set for the coming decades.

Data from the Euclid space telescope will enable cosmic shear measurements with very small statistical errors, requiring corresponding systematic error control level. A common approach to correct for shear biases involves calibrating shape measurement methods using image simulations with known input shear. Given their high resolution, Hubble Space Telescope (HST) galaxies can, in principle, be utilised to emulate Euclid observations. In this work, we employ a GalSim-based testing environment to investigate whether uncertainties in the HST point spread function (PSF) model or in data processing techniques introduce significant biases in weak-lensing (WL) shear calibration. We used single Sérsic galaxy models to simulate both HST and Euclid observations. We then `Euclidised' our HST simulations and compared the results with the directly simulated Euclid-like images. For this comparison, we utilised a moment-based shape measurement algorithm and galaxy model fits. Through the Euclidisation procedure, we effectively reduced the residual multiplicative biases in shear measurements to sub-percent levels. This achievement was made possible by employing either the native pixel scales of the instruments, utilising the Lanczos15 interpolation kernel, correcting for noise correlations, and ensuring consistent galaxy signal-to-noise ratios between simulation branches. However, the Euclidisation procedure requires further analysis on the impact of the correlated noise, to estimate calibration bias. Additionally, we conducted an in-depth analysis of the accuracy of TinyTim HST PSF models using star fields observed in the F606W and F814W filters. We observe that F606W images exhibit a broader scatter in the recovered best-fit focus, compared to those in the F814W filter.

The current standard model of cosmology successfully describes a variety of measurements, but the nature of its main ingredients, dark matter and dark energy, remains unknown. Euclid is a medium-class mission in the Cosmic Vision 2015-2025 programme of the European Space Agency (ESA) that will provide high-resolution optical imaging, as well as near-infrared imaging and spectroscopy, over about 14,000 deg^2 of extragalactic sky. In addition to accurate weak lensing and clustering measurements that probe structure formation over half of the age of the Universe, its primary probes for cosmology, these exquisite data will enable a wide range of science. This paper provides a high-level overview of the mission, summarising the survey characteristics, the various data-processing steps, and data products. We also highlight the main science objectives and expected performance.

We study the intracluster light (ICL) and intracluster globular clusters (ICGCs) in the nearby Perseus cluster of galaxies using Euclid's Early Release Observations. By modelling the isophotal and iso-density contours, we mapped the distributions and properties of the ICL and ICGCs out to radii of 200-600 kpc (up to similar to 1/3 of the virial radius, depending on the parameter) from the brightest cluster galaxy (BCG). We find that the central 500 kpc of the Perseus cluster hosts 70 000 +/- 2800 globular clusters, and 1.7 x 10(12) L-circle dot of diffuse light from the BCG+ICL in the near-infrared H-E. This accounts for 38 +/- 6% of the cluster's total stellar luminosity within this radius. The ICL and ICGCs share a coherent spatial distribution which suggests that they have a common origin or that a common potential governs their distribution. Their contours on the largest scales (>200 kpc) are not centred on the BCG's core, but are instead offset westwards by 60 kpc towards several luminous cluster galaxies. This offset is opposite to the displacement observed in the gaseous intracluster medium. The radial surface brightness profile of the BCG+ICL is best described by a double S & eacute;rsic model, with 68 +/- 4% of the H-E light contained in the extended, outer component. The transition between these components occurs at approximate to 60 kpc, beyond which the isophotes become increasingly elliptical and off-centred. Furthermore, the radial ICGC number density profile closely follows the profile of the BCG+ICL only beyond this 60 kpc radius, where we find an average of 60-80 globular clusters per 10(9) M-circle dot of diffuse stellar mass. The BCG+ICL colour becomes increasingly blue with radius, consistent with the stellar populations in the ICL having subsolar metallicities [Fe/H] similar to -0.6 to -1.0. The colour of the ICL, and the specific frequency and luminosity function of the ICGCs suggest that the ICL+ICGCs were tidally stripped from the outskirts of massive satellites with masses of a few x10(10) M-circle dot, with an increasing contribution from dwarf galaxies at large radii.

To date, galaxy image simulations for weak lensing surveys usually approximate the light profiles of all galaxies as a single or double Sérsic profile, neglecting the influence of galaxy substructures and morphologies deviating from such a simplified parametric characterisation. While this approximation may be sufficient for previous data sets, the stringent cosmic shear calibration requirements and the high quality of the data in the upcoming survey demand a consideration of the effects that realistic galaxy substructures and irregular shapes have on shear measurement biases. Here we present a novel deep learning-based method to create such simulated galaxies directly from Hubble Space Telescope (HST) data. We first build and validate a convolutional neural network based on the wavelet scattering transform to learn noise-free representations independent of the point-spread function (PSF) of HST galaxy images. These can be injected into simulations of images from optical instrument VIS without introducing noise correlations during PSF convolution or shearing. Then, we demonstrate the generation of new galaxy images by sampling from the model randomly as well as conditionally. In the latter case, we fine-tune the interpolation between latent space vectors of sample galaxies to directly obtain new realistic objects following a specific Sérsic index and half-light radius distribution. Furthermore, we show that the distribution of galaxy structural and morphological parameters of our generative model matches the distribution of the input HST training data, proving the capability of the model to produce realistic shapes. Next, we quantify the cosmic shear bias from complex galaxy shapes in simulations by comparing the shear measurement biases between a sample of model objects and their best-fit double-Sérsic counterparts, thereby creating two separate branches that only differ in the complexity of their shapes. Using the Kaiser, Squires, and Broadhurst shape measurement algorithm, we find a multiplicative bias difference between these branches with realistic morphologies and parametric profiles on the order of $(6.9± 0.6) $ for a realistic magnitude-Sérsic index distribution. Moreover, we find clear detection bias differences between full image scenes simulated with parametric and realistic galaxies, leading to a bias difference of $(4.0± 0.9) $ independent of the shape measurement method. This makes complex morphology relevant for stage IV weak lensing surveys, exceeding the full error budget of the Euclid Wide Survey (Δμ_

We investigated the ability of the Euclid telescope to detect galaxy-scale gravitational lenses. To do so, we performed a systematic visual inspection of the 0.7 deg(2) Euclid Early Release Observations data towards the Perseus cluster using both the high-resolution IE band and the lower-resolution Y-E, J(E), and H-E bands. Each extended source brighter than magnitude 23 in I-E was inspected by 41 expert human classifiers. This amounts to 12086 stamps of 10 '' x 10 ''. We found 3 grade A and 13 grade B candidates. We assessed the validity of these 16 candidates by modelling them and checking that they are consistent with a single source lensed by a plausible mass distribution. Five of the candidates pass this check, five others are rejected by the modelling, and six are inconclusive. Extrapolating from the five successfully modelled candidates, we infer that the full 14 000 deg(2) of the Euclid Wide Survey should contain 100 000( -30 000)(+70 000) galaxy-galaxy lenses that are both discoverable through visual inspection and have valid lens models. This is consistent with theoretical forecasts of 170 000 discoverable galaxy-galaxy lenses in Euclid. Our five modelled lenses have Einstein radii in the range 0.'' 68 < theta(E)< 1.'' 24, but their Einstein radius distribution is on the higher side when compared to theoretical forecasts. This suggests that our methodology is likely missing small-Einstein-radius systems. Whilst it is implausible to visually inspect the full Euclid dataset, our results corroborate the promise that Euclid will ultimately deliver a sample of around 105 galaxy-scale lenses.

Habitable Worlds Observatory (HWO) will be NASA's flagship space telescope of the 2040s, designed to search for life on other planets and to transform broad areas of astrophysics. NASA are seeking international partners, and the UK is well-placed to lead the design and construction of its imaging camera - which is likely to produce the mission's most visible public impact. Early participation in the mission would return investment to UK industry, and bring generational leadership for the UK in space science, space technology, and astrophysics.

In this paper we present the framework for measuring angular power spectra in the Euclid mission. The observables in galaxy surveys, such as galaxy clustering and cosmic shear, are not continuous fields, but discrete sets of data, obtained only at the positions of galaxies. We show how to compute the angular power spectra of such discrete data sets, without treating observations as maps of an underlying continuous field that is overlaid with a noise component. This formalism allows us to compute the exact theoretical expectations for our measured spectra, under a number of assumptions that we track explicitly. In particular, we obtain exact expressions for the additive biases ('shot noise') in angular galaxy clustering and cosmic shear. For efficient practical computations, we introduce a spin-weighted spherical convolution with a well-defined convolution theorem, which allows us to apply exact theoretical predictions to finite-resolution maps, including HEALPix. When validating our methodology, we find that our measurements are biased by less than 1% of their statistical uncertainty in simulations of Euclid's first data release.

The Euclid Wide Survey (EWS) is predicted to find approximately 170 000 galaxy-galaxy strong lenses from its lifetime observation of 14 000 deg(2) of the sky. Detecting this many lenses by visual inspection with professional astronomers and citizen scientists alone is infeasible. As a result, machine learning algorithms, particularly convolutional neural networks (CNNs), have been used as an automated method of detecting strong lenses, and have proven fruitful in finding galaxy-galaxy strong lens candidates, such that the usage of CNNs in lens identification has increased. We identify the major challenge to be the automatic detection of galaxy-galaxy strong lenses while simultaneously maintaining a low false positive rate, thus producing a pure and complete sample of strong lens candidates from Euclid with a limited need for visual inspection. One aim of this research is to have a quantified starting point on the achieved purity and completeness with our current version of CNN-based detection pipelines for the VIS images of EWS. This work is vital in preparing our CNN-based detection pipelines to be able to produce a pure sample of the >100 000 strong gravitational lensing systems widely predicted for Euclid. We select all sources with VIS I-E < 23 mag from the Euclid Early Release Observation imaging of the Perseus field. We apply a range of CNN architectures to detect strong lenses in these cutouts. All our networks perform extremely well on simulated data sets and their respective validation sets. However, when applied to real Euclid imaging, the highest lens purity is just similar to 11%. Among all our networks, the false positives are typically identifiable by human volunteers as, for example, spiral galaxies, multiple sources, and artifacts, implying that improvements are still possible, perhaps via a second, more interpretable lens selection filtering stage. There is currently no alternative to human classification of CNN-selected lens candidates. Given the expected similar to 10(5) lensing systems in Euclid, this implies 10(6) objects for human classification, which while very large is not in principle intractable and not without precedent.

This paper presents the specification, design, and development of the Visible Camera (VIS) on the ESA Euclid mission. VIS is a large optical-band imager with a field of view of 0.54 deg^2 sampled at 0.1" with an array of 609 Megapixels and spatial resolution of 0.18". It will be used to survey approximately 14,000 deg^2 of extragalactic sky to measure the distortion of galaxies in the redshift range z=0.1-1.5 resulting from weak gravitational lensing, one of the two principal cosmology probes of Euclid. With photometric redshifts, the distribution of dark matter can be mapped in three dimensions, and, from how this has changed with look-back time, the nature of dark energy and theories of gravity can be constrained. The entire VIS focal plane will be transmitted to provide the largest images of the Universe from space to date, reaching m_AB>24.5 with S/N >10 in a single broad I_E~(r+i+z) band over a six year survey. The particularly challenging aspects of the instrument are the control and calibration of observational biases, which lead to stringent performance requirements and calibration regimes. With its combination of spatial resolution, calibration knowledge, depth, and area covering most of the extra-Galactic sky, VIS will also provide a legacy data set for many other fields. This paper discusses the rationale behind the VIS concept and describes the instrument design and development before reporting the pre-launch performance derived from ground calibrations and brief results from the in-orbit commissioning. VIS should reach fainter than m_AB=25 with S/N>10 for galaxies of full-width half-maximum of 0.3" in a 1.3" diameter aperture over the Wide Survey, and m_AB>26.4 for a Deep Survey that will cover more than 50 deg^2. The paper also describes how VIS works with the other Euclid components of survey, telescope, and science data processing to extract the cosmological information.

We make use of the unprecedented depth, spatial resolution, and field of view of the Euclid Early Release Observations (EROs) of the Perseus galaxy cluster to detect and characterise the dwarf galaxy population in this massive system. Using a dedicated annotation tool, the Euclid high-resolution VIS and combined VIS+Near Infrared Spectrometer and Photometer (NISP) colour images were visually inspected and dwarf galaxy candidates were identified. Their morphologies, the presence of nuclei, and their globular cluster (GC) richness were visually assessed, complementing an automatic detection of the GC candidates. Structural and photometric parameters, including Euclid filter colours, were extracted from two-dimensional fitting. Based on this analysis, a total of 1100 dwarf candidates were found across the image; 606 of these appear to be new identifications. The majority (96%) are classified as dwarf ellipticals, 53% are nucleated, 26% are GC-rich, and 6% show disturbed morphologies. A relatively high fraction of galaxies, 8%, are categorised as ultra diffuse galaxies. The majority of the dwarfs follow the expected scaling relations of galaxies. Globally, the GC specific frequency, S-N, of the Perseus dwarf candidates is intermediate between those measured in the Virgo and Coma clusters. While the dwarf candidates with the largest GC counts are found throughout the Euclid field of view, the dwarfs located around the east-west strip, where most of the brightest cluster members are found, exhibit higher S-N values on average. The spatial distribution of the dwarfs, GCs, and intracluster light show a main iso-density and isophotal centre displaced to the west of the bright galaxy light distribution. The ERO imaging of the Perseus cluster demonstrates the unique capability of Euclid to concurrently detect and characterise large samples of dwarf galaxies, their nuclei, and their GC systems, allowing us to construct a detailed picture of the formation and evolution of galaxies over a wide range of mass scales and environments.

The instruments at the focus of the Euclid space observatory offer superb, diffraction-limited imaging over an unprecedented (from space) wide field of view of 0.57 deg^2. This exquisite image quality has the potential to produce high-precision astrometry for point sources once the undersampling of Euclid's cameras is taken into account by means of accurate, effective point spread function (ePSF) modelling. We present a complex, detailed workflow to simultaneously solve for the geometric distortion (GD) and model the undersampled ePSFs of the Euclid detectors. Our procedure was successfully developed and tested with data from the Early Release Observations (ERO) programme focused on the nearby globular cluster NGC 6397. Our final one-dimensional astrometric precision for a well-measured star just below saturation is 0.7 mas (0.007 pixel) for the Visible Instrument (VIS) and 3 mas (0.01 pixel) for the Near-Infrared Spectrometer and Photometer (NISP). Finally, we present a specific scientific application of this high-precision astrometry: the combination of Euclid and Gaia data to compute proper motions and study the internal kinematics of NGC 6397. Future work, when more data become available, will allow for a better characterisation of the ePSFs and GD corrections that are derived here, along with assessment of their temporal stability, and their dependencies on the spectral energy distribution of the sources as seen through the wide-band filters of Euclid.

Context. Strongly lensed quasars are fundamental sources for cosmology. The Gaia space mission covers the entire sky with the unprecedented resolution of $0.18$" in the optical, making it an ideal instrument to search for gravitational lenses down to the limiting magnitude of 21. Nevertheless, the previous Gaia Data Releases are known to be incomplete for small angular separations such as those expected for most lenses. Aims. We present the Data Processing and Analysis Consortium GravLens pipeline, which was built to analyse all Gaia detections around quasars and to cluster them into sources, thus producing a catalogue of secondary sources around each quasar. We analysed the resulting catalogue to produce scores that indicate source configurations that are compatible with strongly lensed quasars. Methods. GravLens uses the DBSCAN unsupervised clustering algorithm to detect sources around quasars. The resulting catalogue of multiplets is then analysed with several methods to identify potential gravitational lenses. We developed and applied an outlier scoring method, a comparison between the average BP and RP spectra of the components, and we also used an extremely randomised tree algorithm. These methods produce scores to identify the most probable configurations and to establish a list of lens candidates. Results. We analysed the environment of 3 760 032 quasars. A total of 4 760 920 sources, including the quasars, were found within 6" of the quasar positions. This list is given in the Gaia archive. In 87\% of cases, the quasar remains a single source, and in 501 385 cases neighbouring sources were detected. We propose a list of 381 lensed candidates, of which we identified 49 as the most promising. Beyond these candidates, the associate tables in this Focused Product Release allow the entire community to explore the unique Gaia data for strong lensing studies further.