Euclide | EPFL Graph Search

Euclide (en Eukleídês), dit parfois Euclide d'Alexandrie, est un mathématicien de la Grèce antique, auteur d’un traité de mathématiques, qui constitue l'un des textes fondateurs de cette discipline en Occident. Aucune information fiable n'est parvenue sur la vie ou la mort d'Euclide ; il est possible qu'il ait vécu vers 300 avant notre ère. Son ouvrage le plus célèbre, les Éléments, est un des plus anciens traités connus présentant de manière systématique, à partir d'axiomes et de postulats, un large ensemble de théorèmes accompagnés de leurs démonstrations. Il porte sur la géométrie, tant plane que solide, et l’arithmétique théorique. L'ouvrage a connu des centaines d’éditions en toutes langues et ses thèmes restent à la base de l’enseignement des mathématiques au niveau secondaire dans de nombreux pays. Du nom d’Euclide dérivent en particulier l’algorithme d'Euclide, la géométrie euclidienne, la géométrie non euclidienne et la division euclidienne. Biographie Il n’exist

A 7 deg(2) survey for galaxy-scale gravitational lenses with the HST imaging archive(star)

Frédéric Courbin, Georges Meylan, Ravindra Pawase

We present the results of a visual search for galaxy-scale gravitational lenses in similar to 7 deg(2) of Hubble Space Telescope (HST) images. The data set comprises the whole imaging data ever taken with the Advanced Camera for Surveys (ACS) in the filter F814W (I-band) up to 2011 August 31, i.e. 6.03 deg(2) excluding the field of the Cosmic Evolution Survey which has been the subject of a separate visual search. In addition, we have searched for lenses in the whole Wide Field Camera 3 (WFC3) near-IR imaging data set in all filters (1.01 deg(2)) up to the same date. Our primary goal is to provide a sample of lenses with a broad range of different morphologies and lens-source brightness contrast in order to estimate a lower limit to the number of galaxy-scale strong lenses in the future Euclid survey in its VIS band. Our criteria to select lenses are purely morphological as we do not use any colour or redshift information. The final candidate selection is very conservative hence leading to a nearly pure but incomplete sample. We find 49 new lens candidates: 40 in the ACS images and 9 in the WFC3 images. Out of these, 16 candidates are secure lenses owing to their striking morphology, 21 more are very good candidates and 12 more have morphologies compatible with gravitational lensing but also compatible with other astrophysical objects such as ring and chain galaxies or mergers. Interestingly, some lens galaxies include low surface brightness galaxies, compact groups and mergers. The imaging data set is heterogeneous in depth and spans a broad range of galactic latitudes. It is therefore insensitive to cosmic variance and allows us to estimate the number of galaxy-scale strong lenses on the sky for a putative survey depth, which is the main result of this work. Because of the incompleteness of the sample, the estimated lensing rates should be taken as lower limits. Using these, we anticipate that a 15 000 deg(2) space survey such as Euclid will find at least 60 000 galaxy-scale strong lenses down to a limiting AB magnitude of I = 24.5 (10 Sigma) or I = 25.8 (3 Sigma).

Wiley-Blackwell2014

Euclid : Effects of sample covariance on the number counts of galaxy clusters

Richard Massey, Georges Meylan, Yi Wang

Aims. We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey. Methods. By analysing 1000 Euclid-like light cones, produced with the PINOCCHIO approximate method, we validated the analytical model of Hu & Kravtsov (2003, ApJ, 584, 702) for the covariance matrix, which takes into account both sources of statistical error. Then, we used such a covariance to define the likelihood function that is better equipped to extract cosmological information from cluster number counts at the level of precision that will be reached by the future Euclid photometric catalogs of galaxy clusters. We also studied the impact of the cosmology dependence of the covariance matrix on the parameter constraints. Results. The analytical covariance matrix reproduces the variance measured from simulations within the 10 percent; such a difference has no sizeable effect on the error of cosmological parameter constraints at this level of statistics. Also, we find that the Gaussian likelihood with full covariance is the only model that provides an unbiased inference of cosmological parameters without underestimating the errors, and that the cosmology-dependence of the covariance must be taken into account.

EDP SCIENCES S A2021

Euclid preparation V. Predicted yield of redshift 7 < z < 9 quasars from the wide survey

Richard Massey, Georges Meylan, Yi Wang

We provide predictions of the yield of 7 < z < 9 quasars from the Euclid wide survey, updating the calculation presented in the Euclid Red Book in several ways. We account for revisions to the Euclid near-infrared filter wavelengths; we adopt steeper rates of decline of the quasar luminosity function (QLF; Phi) with redshift, Phi proportional to 10(k(z-6)), k = 0:72, and a further steeper rate of decline, k = 0:92; we use better models of the contaminating populations (MLT dwarfs and compact early-type galaxies); and we make use of an improved Bayesian selection method, compared to the colour cuts used for the Red Book calculation, allowing the identification of fainter quasars, down to J(AB) similar to 23. Quasars at z > 8 may be selected from Euclid OYJH photometry alone, but selection over the redshift interval 7 < z < 8 is greatly improved by the addition of z-band data from, e.g., Pan-STARRS and LSST. We calculate predicted quasar yields for the assumed values of the rate of decline of the QLF beyond z = 6. If the decline of the QLF accelerates beyond z = 6, with k = 0.92, Euclid should nevertheless find over 100 quasars with 7.0 < z < 7.5, and similar to 25 quasars beyond the current record of z = 7.5, including similar to 8 beyond z = 8.0. The first Euclid quasars at z > 7.5 should be found in the DR1 data release, expected in 2024. It will be possible to determine the bright-end slope of the QLF, 7 < z < 8, M-1450 < 25, using 8m class telescopes to confirm candidates, but follow-up with JWST or E-ELT will be required to measure the faint-end slope. Contamination of the candidate lists is predicted to be modest even at J(AB) similar to 23. The precision with which k can be determined over 7 < z < 8 depends on the value of k, but assuming k = 0.72 it can be measured to a 1 sigma uncertainty of 0.07.

EDP SCIENCES S A2019

A 7 deg(2) survey for galaxy-scale gravitational lenses with the HST imaging archive(star)

Frédéric Courbin, Georges Meylan, Ravindra Pawase

Wiley-Blackwell2014