Euclid Data Research Articles

AMICO-COSMOS galaxy cluster and group catalogue up to z = 2: Sample properties and X-ray counterparts

Aims. We present the results of a new galaxy cluster search in the COSMOS field obtained using the Adaptive Matched Identifier of Clustered Objects (AMICO). Our aim was to produce a new cluster and group catalogue up to z = 2 by performing an innovative application of AMICO with respect to previous successful applications to wide-field surveys in terms of depth (down to r < 26.7), small area covered (∼1.69 deg2 of unmasked effective area), and redshift extent. This sample and the comparative analysis we performed with the X-rays, allowed for the calibration of mass-proxy scaling relations up to z = 2 and down to less than 1013 M⊙, and constitutes the basis for the refinement of the cluster model for future applications of AMICO, such as the analysis of upcoming Euclid data. Methods. The AMICO algorithm is based on an optimal linear matched filter and detects clusters in photometric galaxy catalogues using galaxy location, photometric redshift and, in the simplest case, one galaxy property. We chose to use a single magnitude as the galaxy property, avoiding the explicit use of galaxy colour for the selection of clusters. We used three different magnitudes by performing three independent runs in the r-, Y-, and H-bands using both COSMOS2020 and COSMOS2015 galaxy catalogues. We created a composite visibility mask and cluster models for the signal to detect, and we estimated the noise directly from the data. Results. We performed a matching of the catalogues resulting from the three runs and merged them to produce a final catalogue that contains 1269 and 666 candidate clusters and groups with S/N > 3.0 and > 3.5, respectively. A total of 490 candidates are detected in all three runs. Most of the detections unmatched between runs have S/N < 3.5, which can be set as a threshold for selecting a more robust sample. We assigned X-ray properties to our detections by matching the catalogue with a public X-ray selected group sample and by estimating, for unmatched detections, the X-ray properties at the location of AMICO candidates using Chandra+XMM-Newton data. There are in total 622 candidate clusters and groups with an X-ray flux estimate. This large sample of candidates with X-ray properties allowed the calibration of the scaling relations between two AMICO mass-proxies (richness and cluster amplitude) and X-ray mass and the study of their redshift dependence for the selection of the most stable photometric bands.

THE THREE HUNDRED: Contrasting cluster galaxy density in hydrodynamical and dark matter simulations

Cluster number counts at visible and IR wavelengths will be a key cosmological probe in the next decade thanks to the Euclid satellite mission. For this purpose, the performance of cluster detection algorithms, which at these wavelengths are sensitive to the spatial distributions of the cluster galaxy members and their luminosity functions, need to be accurately characterized. Using THE THREE HUNDRED hydrodynamical and dark-matter-only simulations, we studied a complete sample of massive clusters beyond 7 (5) × 1014 M⊙ at redshift 0 (1) on a (1.48 Gpc)3 volume. We find that the mass resolution of the current hydrodynamical simulations (1.5 × 109 M⊙) is not enough to characterize the luminosity function of the sample in the perspective of Euclid data. Nevertheless, these simulations are still useful to characterize the spatial distribution of the cluster substructures assuming a common relative mass threshold for the different flavours and resolutions. By comparing with the dark-matter-only version of these simulations, we demonstrate that baryonic physics preserves significantly low-mass subhalos (galaxies), as has also been observed in previous studies with less statistics. Furthermore, by comparing the hydro simulations with higher resolution dark-matter-only simulations of the same objects and taking the same limit in subhalo mass, we find galaxy density profiles that are significantly more cuspy towards the centre of the clusters, where the low-mass substructures tend to concentrate. We conclude that using a dark-matter-only simulation may lead to some biases on the spatial distribution and density of galaxy cluster members. Based on the preliminary analysis of few high-resolution hydro simulations we conclude that a mass resolution of 1.8 × 108h−1 M⊙ will be needed for THE THREE HUNDRED simulations to approach the expected magnitude limits for the Euclid survey. These simulations are currently under way.

Dark Energy Survey Deep Field photometric redshift performance and training incompleteness assessment

Context. The determination of accurate photometric redshifts (photo-zs) in large imaging galaxy surveys is key for cosmological studies. One of the most common approaches is machine learning techniques. These methods require a spectroscopic or reference sample to train the algorithms. Attention has to be paid to the quality and properties of these samples since they are key factors in the estimation of reliable photo-zs. Aims. The goal of this work is to calculate the photo-zs for the Year 3 (Y3) Dark Energy Survey (DES) Deep Fields catalogue using the Directional Neighborhood Fitting (DNF) machine learning algorithm. Moreover, we want to develop techniques to assess the incompleteness of the training sample and metrics to study how incompleteness affects the quality of photometric redshifts. Finally, we are interested in comparing the performance obtained by DNF on the Y3 DES Deep Fields catalogue with that of the EAzY template fitting approach. Methods. We emulated – at a brighter magnitude – the training incompleteness with a spectroscopic sample whose redshifts are known to have a measurable view of the problem. We used a principal component analysis to graphically assess the incompleteness and relate it with the performance parameters provided by DNF. Finally, we applied the results on the incompleteness to the photo-z computation on the Y3 DES Deep Fields with DNF and estimated its performance. Results. The photo-zs of the galaxies in the DES deep fields were computed with the DNF algorithm and added to the Y3 DES Deep Fields catalogue. We have developed some techniques to evaluate the performance in the absence of “true” redshift and to assess the completeness. We have studied the tradeoff in the training sample between the highest spectroscopic redshift quality versus completeness. We found some advantages in relaxing the highest-quality spectroscopic redshift requirements at fainter magnitudes in favour of completeness. The results achieved by DNF on the Y3 Deep Fields are competitive with the ones provided by EAzY, showing notable stability at high redshifts. It should be noted that the good results obtained by DNF in the estimation of photo-zs in deep field catalogues make DNF suitable for the future Legacy Survey of Space and Time (LSST) and Euclid data, which will have similar depths to the Y3 DES Deep Fields.

Euclid view of the dusty star-forming galaxies at ≳ detected in wide area submillimetre surveys

ABSTRACT We investigate the constraints provided by the Euclid space observatory on the physical properties of dusty star-forming galaxies (DSFGs) at $z\gtrsim 1.5$ detected in wide area submillimetre surveys with Herschel. We adopt a physical model for the high-z progenitors of spheroidal galaxies, which form the bulk of DSFGs at $z\gtrsim 1.5$. We improve the model by combining the output of the equations of the model with a formalism for the spectral energy distribution (SED). After optimizing the SED parameters to reproduce the measured infrared luminosity function and number counts of DFSGs, we simulated a sample of DSFGs over 100 $\hbox{deg}^2$ and then applied a $5\, \sigma$ detection limit of $37\,$ mJy at 250 $\mu$m. We estimated the redshifts from the Euclid data and then fitted the Euclid+Herschel photometry with the code CIGALE to extract the physical parameters. We found that 100 per cent of the Herschel galaxies are detected in all 4 Euclid bands above $3\, \sigma$. For 87 per cent of these sources the accuracy on $1 + z$ is better than 15 per cent. The sample comprises mostly massive, i.e. $\log (M_{\star }/{\rm M}_{\odot })\sim 10.5{\!-\!}12.9$, highly star forming, i.e. $\log (\hbox{SFR}/{\rm M}_{\odot }\hbox{yr}^{-1})\sim 1.5{\!-\!}4$, dusty, i.e. $\log (M_{\rm dust}/{\rm M}_{\odot })\sim 7.5{\!-\!}9.9$, galaxies. The measured stellar masses have a dispersion of 0.19 dex around the true value, thus showing that Euclid will provide reliable stellar mass estimates for the majority of the bright DSFGs at $z\gtrsim 1.5$ detected by Herschel. We also explored the effect of complementing the Euclid photometry with that from the Vera C. Rubin Observatory/LSST.

Euclid preparation

Aims. We derived galaxy colour selections from Euclid and ground-based photometry, aiming to accurately define background galaxy samples in cluster weak-lensing analyses. These selections have been implemented in the Euclid data analysis pipelines for galaxy clusters. Methods. Given any set of photometric bands, we developed a method for the calibration of optimal galaxy colour selections that maximises the selection completeness, given a threshold on purity. Such colour selections are expressed as a function of the lens redshift. Results. We calibrated galaxy selections using simulated ground-based griz and EuclidYEJEHE photometry. Both selections produce a purity higher than 97%. The griz selection completeness ranges from 30% to 84% in the lens redshift range zl ∈ [0.2, 0.8]. With the full grizYEJEHE selection, the completeness improves by up to 25 percentage points, and the zl range extends up to zl = 1.5. The calibrated colour selections are stable to changes in the sample limiting magnitudes and redshift, and the selection based on griz bands provides excellent results on real external datasets. Furthermore, the calibrated selections provide stable results using alternative photometric aperture definitions obtained from different ground-based telescopes. The griz selection is also purer at high redshift and more complete at low redshift compared to colour selections found in the literature. We find excellent agreement in terms of purity and completeness between the analysis of an independent, simulated Euclid galaxy catalogue and our calibration sample, except for galaxies at high redshifts, for which we obtain up to 50 percentage points higher completeness. The combination of colour and photo-z selections applied to simulated Euclid data yields up to 95% completeness, while the purity decreases down to 92% at high zl. We show that the calibrated colour selections provide robust results even when observations from a single band are missing from the ground-based data. Finally, we show that colour selections do not disrupt the shear calibration for stage III surveys. The first Euclid data releases will provide further insights into the impact of background selections on the shear calibration.

Euclid preparation

Material outgassing in a vacuum leads to molecular contamination, a well-known problem in spaceflight. Water is the most common contaminant in cryogenic spacecraft, altering numerous properties of optical systems. Too much ice means that Euclid’s calibration requirements cannot be met anymore. Euclid must then be thermally decontaminated, which is a month-long risky operation. We need to understand how ice affects our data to build adequate calibration and survey plans. A comprehensive analysis in the context of an astrophysical space survey has not been done before. In this paper we look at other spacecraft with well-documented outgassing records. We then review the formation of thin ice films, and find that for Euclid a mix of amorphous and crystalline ices is expected. Their surface topography – and thus optical properties – depend on the competing energetic needs of the substrate-water and the water-water interfaces, and they are hard to predict with current theories. We illustrate that with scanning-tunnelling and atomic-force microscope images of thin ice films. Sophisticated tools exist to compute contamination rates, and we must understand their underlying physical principles and uncertainties. We find considerable knowledge errors on the diffusion and sublimation coefficients, limiting the accuracy of outgassing estimates. We developed a water transport model to compute contamination rates in Euclid, and find agreement with industry estimates within the uncertainties. Tests of the Euclid flight hardware in space simulators did not pick up significant contamination signals, but they were also not geared towards this purpose; our in-flight calibration observations will be much more sensitive. To derive a calibration and decontamination strategy, we need to understand the link between the amount of ice in the optics and its effect on the data. There is little research about this, possibly because other spacecraft can decontaminate more easily, quenching the need for a deeper understanding. In our second paper, we quantify the impact of iced optics on Euclid’s data.

The cosmic web of X-ray active galactic nuclei seen through the eROSITA Final Equatorial Depth Survey (eFEDS)

Which galaxies in the general population turn into active galactic nuclei (AGNs) is a keystone of galaxy formation and evolution. Thanks to SRG/eROSITA’s contiguous 140 square degree pilot survey field, we constructed a large, complete, and unbiased soft X-ray flux-limited (FX > 6.5 × 10−15 erg s−1 cm−2) AGN sample at low redshift, 0.05 < z < 0.55. Two summary statistics, the clustering using spectra from SDSS-V and galaxy-galaxy lensing with imaging from HSC, are measured and interpreted with halo occupation distribution and abundance matching models. Both models successfully account for the observations. We obtain an exceptionally complete view of the AGN halo occupation distribution. The population of AGNs is broadly distributed among halos with a mean mass of 3.9−2.4+2.0 × 1012 M⊙. This corresponds to a large-scale halo bias of b(z = 0.34) = 0.99−0.10+0.08. The central occupation has a large transition parameter, σlog10(M) = 1.28 ± 0.2. The satellite occupation distribution is characterized by a shallow slope, αsat = 0.73 ± 0.38. We find that AGNs in satellites are rare, with fsat < 20%. Most soft X-ray-selected AGNs are hosted by central galaxies in their dark matter halo. A weak correlation between soft X-ray luminosity and large-scale halo bias is confirmed (3.3σ). We discuss the implications of environmental-dependent AGN triggering. This study paves the way toward fully charting, in the coming decade, the coevolution of X-ray AGNs, their host galaxies, and dark matter halos by combining eROSITA with SDSS-V, 4MOST, DESI, LSST, and Euclid data.

Euclid: Testing the Copernican principle with next-generation surveys

Context.The Copernican principle, the notion that we are not at a special location in the Universe, is one of the cornerstones of modern cosmology. Its violation would invalidate the Friedmann-Lemaître-Robertson-Walker metric, causing a major change in our understanding of the Universe. Thus, it is of fundamental importance to perform observational tests of this principle.Aims.We determine the precision with which future surveys will be able to test the Copernican principle and their ability to detect any possible violations.Methods.We forecast constraints on the inhomogeneous Lemaître-Tolman-Bondi (LTB) model with a cosmological constant Λ, basically a cosmological constant Λ and cold dark matter (CDM) model but endowed with a spherical inhomogeneity. We consider combinations of currently available data and simulatedEucliddata, together with external data products, based on both ΛCDM and ΛLTB fiducial models. These constraints are compared to the expectations from the Copernican principle.Results.When considering the ΛCDM fiducial model, we find thatEucliddata, in combination with other current and forthcoming surveys, will improve the constraints on the Copernican principle by about 30%, with ±10% variations depending on the observables and scales considered. On the other hand, when considering a ΛLTB fiducial model, we find that futureEucliddata, combined with other current and forthcoming datasets, will be able to detect gigaparsec-scale inhomogeneities of contrast −0.1.Conclusions.Next-generation surveys, such asEuclid, will thoroughly test homogeneity at large scales, tightening the constraints on possible violations of the Copernican principle.

Euclid preparation

The European Space Agency's Euclid mission will provide high-quality imaging for about 1.5 billion galaxies. A software pipeline to automatically process and analyse such a huge amount of data in real time is being developed by the Science Ground Segment of the Euclid Consortium; this pipeline will include a model-fitting algorithm, which will provide photometric and morphological estimates of paramount importance for the core science goals of the mission and for legacy science. The Euclid Morphology Challenge is a comparative investigation of the performance of five model-fitting software packages on simulated Euclid data, aimed at providing the baseline to identify the best-suited algorithm to be implemented in the pipeline. In this paper we describe the simulated dataset, and we discuss the photometry results. A companion paper is focussed on the structural and morphological estimates. We created mock Euclid images simulating five fields of view of 0.48 deg2 each in the IE band of the VIS instrument, containing a total of about one and a half million galaxies (of which 350 000 have a nominal signal-to-noise ratio above 5), each with three realisations of galaxy profiles (single and double Sérsic, and 'realistic' profiles obtained with a neural network); for one of the fields in the double Sérsic realisation, we also simulated images for the three near-infrared YE, JE, and HE bands of the NISP-P instrument, and five Rubin/LSST optical complementary bands (u, g, r, i, and z), which together form a typical dataset for an Euclid observation. The images were simulated at the expected Euclid Wide Survey depths. To analyse the results, we created diagnostic plots and defined metrics to take into account the completeness of the provided catalogues, as well as the median biases, dispersions, and outlier fractions of their measured flux distributions. Five model-fitting software packages (DeepLeGATo, Galapagos-2, Morfometryka, ProFit, and SourceXtractor++) were compared, all typically providing good results. Of the differences among them, some were at least partly due to the distinct strategies adopted to perform the measurements. In the best-case scenario, the median bias of the measured fluxes in the analytical profile realisations is below 1% at a signal-to-noise ratio above 5 in IE, and above 10 in all the other bands; the dispersion of the distribution is typically comparable to the theoretically expected one, with a small fraction of catastrophic outliers. However, we can expect that real observations will prove to be more demanding, since the results were found to be less accurate for the most realistic realisation. We conclude that existing model-fitting software can provide accurate photometric measurements on Euclid datasets. The results of the challenge are fully available and reproducible through an online plotting tool.

Euclid preparation

Context. The Euclid mission is expected to discover thousands of z > 6 galaxies in three deep fields, which together will cover a ∼50 deg2 area. However, the limited number of Euclid bands (four) and the low availability of ancillary data could make the identification of z > 6 galaxies challenging. Aims. In this work we assess the degree of contamination by intermediate-redshift galaxies (z = 1–5.8) expected for z > 6 galaxies within the Euclid Deep Survey. Methods. This study is based on ∼176 000 real galaxies at z = 1–8 in a ∼0.7 deg2 area selected from the UltraVISTA ultra-deep survey and ∼96 000 mock galaxies with 25.3 ≤ H < 27.0, which altogether cover the range of magnitudes to be probed in the Euclid Deep Survey. We simulate Euclid and ancillary photometry from fiducial 28-band photometry and fit spectral energy distributions to various combinations of these simulated data. Results. We demonstrate that identifying z > 6 galaxies with Euclid data alone will be very effective, with a z > 6 recovery of 91% (88%) for bright (faint) galaxies. For the UltraVISTA-like bright sample, the percentage of z = 1–5.8 contaminants amongst apparent z > 6 galaxies as observed with Euclid alone is 18%, which is reduced to 4% (13%) by including ultra-deep Rubin (Spitzer) photometry. Conversely, for the faint mock sample, the contamination fraction with Euclid alone is considerably higher at 39%, and minimised to 7% when including ultra-deep Rubin data. For UltraVISTA-like bright galaxies, we find that Euclid (IE − YE) > 2.8 and (YE − JE) < 1.4 colour criteria can separate contaminants from true z > 6 galaxies, although these are applicable to only 54% of the contaminants as many have unconstrained (IE − YE) colours. In the best scenario, these cuts reduce the contamination fraction to 1% whilst preserving 81% of the fiducial z > 6 sample. For the faint mock sample, colour cuts are infeasible; we find instead that a 5σ detection threshold requirement in at least one of the Euclid near-infrared bands reduces the contamination fraction to 25%.

Euclid preparation

The combination and cross-correlation of the upcoming Euclid data with cosmic microwave background (CMB) measurements is a source of great expectation since it will provide the largest lever arm of epochs, ranging from recombination to structure formation across the entire past light cone. In this work, we present forecasts for the joint analysis of Euclid and CMB data on the cosmological parameters of the standard cosmological model and some of its extensions. This work expands and complements the recently published forecasts based on Euclid-specific probes, namely galaxy clustering, weak lensing, and their cross-correlation. With some assumptions on the specifications of current and future CMB experiments, the predicted constraints are obtained from both a standard Fisher formalism and a posterior-fitting approach based on actual CMB data. Compared to a Euclid-only analysis, the addition of CMB data leads to a substantial impact on constraints for all cosmological parameters of the standard Λ-cold-dark-matter model, with improvements reaching up to a factor of ten. For the parameters of extended models, which include a redshift-dependent dark energy equation of state, non-zero curvature, and a phenomenological modification of gravity, improvements can be of the order of two to three, reaching higher than ten in some cases. The results highlight the crucial importance for cosmological constraints of the combination and cross-correlation of Euclid probes with CMB data.

Euclid: Constraining dark energy coupled to electromagnetism using astrophysical and laboratory data

In physically realistic, scalar-field-based dynamical dark energy models (including, e.g., quintessence), one naturally expects the scalar field to couple to the rest of the model’s degrees of freedom. In particular, a coupling to the electromagnetic sector leads to a time (redshift) dependence in the fine-structure constant and a violation of the weak equivalence principle. Here we extend the previous Euclid forecast constraints on dark energy models to this enlarged (but physically more realistic) parameter space, and forecast how well Euclid, together with high-resolution spectroscopic data and local experiments, can constrain these models. Our analysis combines simulated Euclid data products with astrophysical measurements of the fine-structure constant, α, and local experimental constraints, and it includes both parametric and non-parametric methods. For the astrophysical measurements of α, we consider both the currently available data and a simulated dataset representative of Extremely Large Telescope measurements that are expected to be available in the 2030s. Our parametric analysis shows that in the latter case, the inclusion of astrophysical and local data improves the Euclid dark energy figure of merit by between 8% and 26%, depending on the correct fiducial model, with the improvements being larger in the null case where the fiducial coupling to the electromagnetic sector is vanishing. These improvements would be smaller with the current astrophysical data. Moreover, we illustrate how a genetic algorithms based reconstruction provides a null test for the presence of the coupling. Our results highlight the importance of complementing surveys like Euclid with external data products, in order to accurately test the wider parameter spaces of physically motivated paradigms.

Determining the neutrino lifetime from cosmology

We explore the cosmological signals of theories in which the neutrinos decay into invisible dark radiation after becoming nonrelativistic. We show that, in this scenario, near-future large-scale structure measurements from the Euclid satellite, when combined with cosmic microwave background data from Planck, may allow an independent determination of both the lifetime of the neutrinos and the sum of their masses. These parameters can be independently determined, because the Euclid data will cover a range of redshifts, allowing the growth of structure over time to be tracked. If neutrinos are stable on cosmological timescales, these observations can improve the lower limit on the neutrino lifetime by 7 orders of magnitude, from $\mathcal{O}(10)$ to $2\ifmmode\times\else\texttimes\fi{}{10}^{8}\text{ }\text{ }\mathrm{yr}$ (95% C.L.), without significantly affecting the measurement of neutrino mass. On the other hand, if neutrinos decay after becoming nonrelativistic but on timescales less than $\mathcal{O}(100)$ million years, these observations may allow not just the first measurement of the sum of neutrino masses, but also the determination of the neutrino lifetime from cosmology.

Ultracool dwarfs in deep extragalactic surveys using the virtual observatory: ALHAMBRA and COSMOS

ABSTRACT Ultracool dwarfs (UCDs) encompass a wide variety of compact stellar-like objects with spectra classified as late-M, L, T, and Y. Most of them have been discovered using wide-field imaging surveys. The Virtual Observatory (VO) has proven to be of great utility to efficiently exploit these astronomical resources. We aim to validate a VO methodology designed to discover and characterize UCDs in deep extragalactic surveys like Advance Large Homogeneous Area Medium-Band Redshift Astronomical (ALHAMBRA) and Cosmological Evolution Survey (COSMOS). Three complimentary searches based on parallaxes, proper motions and colours, respectively, were carried out. A total of 897 candidate UCDs were found, with only 16 previously reported in SIMBAD. Most of the new UCDs reported here are likely late-M and L dwarfs because of the limitations imposed by the utilization of optical (Gaia DR2 and r-band) data. We complement ALHAMBRA and COSMOS photometry with other catalogues in the optical and infrared using VOSA, a VO tool that estimates effective temperatures from the spectral energy distribution fitting to collections of theoretical models. The agreement between the number of UCDs found in the COSMOS field and theoretical estimations together with the low false-negative rate (known UCDs not discovered in our search) validates the methodology proposed in this work, which will be used in the forthcoming wide and deep surveys provided by the Euclid space mission. Simulations of Euclid number counts for UCDs detectable in different photometric passbands are presented for a wide survey area of 15 000 deg2, and the limitations of applicability of Euclid data to detect UCDs using the methods employed in this paper are discussed.

Constraints on features in the inflationary potential from future Euclid data

ABSTRACT With Planck cosmic microwave background observations, we established the spectral amplitude and tilt of the primordial power spectrum. Evidence of a red spectral tilt (ns = 0.96) at 8σ provides strong support for the inflationary mechanism, especially the slow roll of the effective scalar field in its nearly flat potential as the generator of scalar primordial perturbations. With the next generation of large-scale structure surveys, we expect to probe primordial physics beyond the overall shape and amplitude of the main, smooth, and slowly changing part of the inflaton potential. Using the specifications for the upcoming Euclid survey, we investigate to what extent we can constrain the inflation potential beyond its established slow-roll behaviour. We provide robust forecasts with Euclid and Planck mock data from nine fiducial power spectra that contain suppression and wiggles at different cosmological scales, using the Wiggly Whipped Inflation (WWI) framework to generate these features in the primordial spectrum. We include both Euclid cosmic shear and galaxy clustering, with a conservative cut-off for non-linear scales. Using Markov chain Monte Carlo simulations, we obtain an improvement in constraints in the WWI potential, as well an improvement for the background cosmology parameters. We find that apart from improving the constraints on the overall scale of the inflationary potential by 40–50 per cent, we can also identify oscillations in the primordial spectrum that are present within intermediate to small scales ($k\sim 0.01\!-\!0.2\, \mathrm{Mpc^{-1}}$).

Naṣīr al-Dīn al-Ṭūsī's Comments on Euclid's Data

This paper is a study of Naṣīr al-Dīn al-Ṭūsī's comments on Euclid's Data. We produce a critical edition, translation and commentary of comments and marginal notes made by al-Ṭūsī in his Revision of the Euclidian text (Taḥrīr kitāb al-Muʿṭayāt li-Uqlīdis). The study results in some insight into what Ṭūsī thought was worth explaining from a mathematical perspective, some information about his manuscript sources, and, perhaps most importantly, some of his scholarly practices in producing his edition of this canonical mathematical text. Another result is that of two versions of this text that can be read in the manuscripts, one can be identified as the more polished draft.

Detecting Solar system objects with convolutional neural networks

In the preparation for ESA's Euclid mission and the large amount of data it will produce, we train deep convolutional neural networks on Euclid simulations classify solar system objects from other astronomical sources. Using transfer learning we are able to achieve a good performance despite our tiny dataset with as few as 7512 images. Our best model correctly identifies objects with a top accuracy of 94% and improves to 96% when Euclid's dither information is included. The neural network misses ~50% of the slowest moving asteroids (v < 10 arcsec/h) but is otherwise able to correctly classify asteroids even down to 26 mag. We show that the same model also performs well at classifying stars, galaxies and cosmic rays, and could potentially be applied to distinguish all types of objects in the Euclid data and other large optical surveys.

Weak-lensing shear measurement with machine learning

Cosmic shear, that is weak gravitational lensing by the large-scale matter structure of the Universe, is a primary cosmological probe for several present and upcoming surveys investigating dark matter and dark energy, such as Euclid or WFIRST. The probe requires an extremely accurate measurement of the shapes of millions of galaxies based on imaging data. Crucially, the shear measurement must address and compensate for a range of interwoven nuisance effects related to the instrument optics and detector, noise in the images, unknown galaxy morphologies, colors, blending of sources, and selection effects. This paper explores the use of supervised machine learning as a tool to solve this inverse problem. We present a simple architecture that learns to regress shear point estimates and weights via shallow artificial neural networks. The networks are trained on simulations of the forward observing process, and take combinations of moments of the galaxy images as inputs. A challenging peculiarity of the shear measurement task, in terms of machine learning applications, is the combination of the noisiness of the input features and the requirements on the statistical accuracy of the inverse regression. To address this issue, the proposed training algorithm minimizes bias over multiple realizations of individual source galaxies, reducing the sensitivity to properties of the overall sample of source galaxies. Importantly, an observational selection function of these source galaxies can be straightforwardly taken into account via the weights. We first introduce key aspects of our approach using toy-model simulations, and then demonstrate its potential on images mimicking Euclid data. Finally, we analyze images from the GREAT3 challenge, obtaining competitively low multiplicative and additive shear biases despite the use of a simple training set. We conclude that the further development of suited machine learning approaches is of high interest to meet the stringent requirements on the shear measurement in current and future surveys. We make a demonstration implementation of our technique publicly available.

Calibration of colour gradient bias in shear measurement using HST/CANDELS data

Accurate shape measurements are essential to infer cosmological parameters from large area weak gravitational lensing studies. The compact diffraction-limited point-spread function (PSF) in space-based observations is greatly beneficial, but its chromaticity for a broad band observation can lead to new subtle effects that could hitherto be ignored: the PSF of a galaxy is no longer uniquely defined and spatial variations in the colours of galaxies result in biases in the inferred lensing signal. Taking Euclid as a reference, we show that this colourgradient bias (CG bias) can be quantified with high accuracy using available multi-colour Hubble Space Telescope (HST) data. In particular we study how noise in the HST observations might impact such measurements and find this to be negligible. We determine the CG bias using HST observations in the F606W and F814W filters and observe a correlation with the colour, in line with expectations, whereas the dependence with redshift is weak. The biases for individual galaxies are generally well below 1%, which may be reduced further using morphological information from the Euclid data. Our results demonstrate that CG bias should not be ignored, but it is possible to determine its amplitude with sufficient precision, so that it will not significantly bias the weak lensing measurements using Euclid data.

Scientific Synergy between LSST and Euclid

Euclid and the Large Synoptic Survey Telescope (LSST) are poised to dramatically change the astronomy landscape early in the next decade. The combination of high cadence, deep, wide-field optical photometry from LSST with high resolution, wide-field optical photometry and near-infrared photometry and spectroscopy from Euclid will be powerful for addressing a wide range of astrophysical questions. We explore Euclid/LSST synergy, ignoring the political issues associated with data access to focus on the scientific, technical, and financial benefits of coordination. We focus primarily on dark energy cosmology, but also discuss galaxy evolution, transient objects, solar system science, and galaxy cluster studies. We concentrate on synergies that require coordination in cadence or survey overlap, or would benefit from pixel-level co-processing that is beyond the scope of what is currently planned, rather than scientific programs that could be accomplished only at the catalog level without coordination in data processing or survey strategies. We provide two quantitative examples of scientific synergies: the decrease in photo-z errors (benefitting many science cases) when high resolution Euclid data are used for LSST photo-z determination, and the resulting increase in weak lensing signal-to-noise ratio from smaller photo-z errors. We briefly discuss other areas of coordination, including high performance computing resources and calibration data. Finally, we address concerns about the loss of independence and potential cross-checks between the two missions and potential consequences of not collaborating.