A non commutative sewing lemma

In a preceding paper [E.J.ofProb.34,860-892,(2006)], we proved a sewing lemma which was a key result for the study of Holder continuous functions. In this paper we give a non-commutative version of this lemma with some applications.Comment: 11 page

Joint signal extraction from galaxy clusters in X-ray and SZ surveys: A matched-filter approach

The hot ionized gas of the intra-cluster medium emits thermal radiation in the X-ray band and also distorts the cosmic microwave radiation through the Sunyaev-Zel'dovich (SZ) effect. Combining these two complementary sources of information through innovative techniques can therefore potentially improve the cluster detection rate when compared to using only one of the probes. Our aim is to build such a joint X-ray-SZ analysis tool, which will allow us to detect fainter or more distant clusters while maintaining high catalogue purity. We present a method based on matched multifrequency filters (MMF) for extracting cluster catalogues from SZ and X-ray surveys. We first designed an X-ray matched-filter method, analogous to the classical MMF developed for SZ observations. Then, we built our joint X-ray-SZ algorithm by combining our X-ray matched filter with the classical SZ-MMF, for which we used the physical relation between SZ and X-ray observations. We show that the proposed X-ray matched filter provides correct photometry results, and that the joint matched filter also provides correct photometry when the $F_{\rm X}/Y_{500}$ relation of the clusters is known. Moreover, the proposed joint algorithm provides a better signal-to-noise ratio than single-map extractions, which improves the detection rate even if we do not exactly know the $F_{\rm X}/Y_{500}$ relation. The proposed methods were tested using data from the ROSAT all-sky survey and from the Planck survey.Comment: 22 pages (before appendices), 19 figures, 3 tables, 5 appendices. Accepted for publication in A&

The stellar mass function of galaxies in Planck-selected clusters at 0.5 < z < 0.7: new constraints on the timescale and location of satellite quenching

We study the abundance of star-forming and quiescent galaxies in a sample of 21 massive clusters at 0.5<z<0.7, detected with the Planck satellite. We measure the cluster galaxy stellar mass function (SMF), which is a fundamental observable to study and constrain the formation and evolution of galaxies. Our measurements are based on homogeneous and deep multi-band photometry spanning u- to the Ks-band for each cluster and are supported by spectroscopic data from different programs. The galaxy population is separated between quiescent and star-forming galaxies based on their rest-frame U-V and V-J colours. The SMF is compared to that of field galaxies at the same redshifts, using data from the COSMOS/UltraVISTA survey. We find that the shape of the SMF of star-forming galaxies does not depend on environment, while the SMF of quiescent galaxies has a significantly steeper low-mass slope in the clusters compared to the field. We estimate the environmental quenching efficiency (f_EQ), i.e. the probability for a galaxy that would normally be star forming in the field, to be quenched due to its environment. The f_EQ shows no stellar-mass dependence in any environment, but it increases from 40% in the cluster outskirts to ~90% in the cluster centres. The radial signature of f_EQ provides constraints on where the dominant quenching mechanism operates in these clusters and on what timescale. Exploring these using a simple model based on galaxy orbits obtained from an N-body simulation, we find a clear degeneracy between both parameters. For example, the quenching process may either be triggered on a long (~3 Gyr) time scale at large radii (r~8R_500), or happen well within 1 Gyr at r<R_500. The radius where quenching is triggered is at least r_quench> 0.67R_500 (95%CL). The ICM density at this location suggests that ram-pressure stripping of the cold gas is a likely cause of quenching. [Abridged]Comment: 16 pages, 12 figures, accepted for publication in A&

Peut-on donner d’une clause et reprendre de l’autre? Essai sur la cause comme instrument de contrôle de la cohérence matérielle du contrat

Peut-on donner d’une clause et reprendre de l’autre? Si deux siècles de décisions et de commentaires contradictoires empêchent de répondre à cette question avec la certitude et l’assurance auxquelles nous a habitué la doctrine civiliste, il est tout de même possible d’affirmer que le droit civil prohibe la clause qui permet à un contractant de se dédire totalement de son engagement. Privant l’engagement de son cocontractant de toute raison, et le contrat dans lequel elle se trouve de toute fonction, cette clause contracticide se heurte en effet à une notion fondamentale du droit commun des contrats : la cause. C’est pour éviter que ne soient validés les contrats qui ne présentent aucun intérêt pour l’une ou l’autre des parties que le législateur québécois a choisi d’importer – et de conserver, dans son article introductif du Livre des obligations, cette notion que l’on dit la plus symbolique du droit français des obligations. En effet, bien que son rôle soit fréquemment assumé par d’autres mécanismes, la cause demeure la gardienne des fonctions du contrat synallagmatique. À ce titre, elle permet non seulement d’annuler les contrats qui ne codifient aucun échange, mais également, et surtout, de contrôler ceux dont le contenu ne permet pas de matérialiser les avantages négociés. Octroyant au juge le pouvoir d’assurer que le contrat contienne les outils nécessaires et adaptés à la réalisation de l’opération qu’il a pour fonction de mettre en œuvre, la cause lui offre donc le moyen de garantir l’adéquation entre la fin et ses moyens, bref de contrôler la cohérence matérielle du contrat.Can one provision take away what another has given? While two hundred years of contradictory decisions and commentaries renders this question difficult to answer with certainty and confidenc – two things we’ve grown accustomed to from civil law doctrine, we can safely assert that civil law prohibits provisions allowing a contracting party to completely renege on his obligations. By depriving the co-contractor’s undertaking of all reasons, and the contract of its purpose, such “contract-killing” provision runs counter to a fundamental concept of general contract law: “la cause”. This notion, which constitutes the first article of the “Obligations” book and which is said to be one of the most important of French contract law, was imported and kept by Quebec legislature to ensure that contracts providing no benefits to one of the parties would not be validated. Although its role is often fulfilled by other mechanisms, “la cause” remains the “guardian” of synallagmatic contracts. As such, it can not only nullify contracts without valuable consideration, but it can also, and especially, control those whose content can’t form the negotiated benefits. By giving judges the power to ensure that contracts contain the tools needed to achieve its objectives, “la cause” offers them the best way to guarantee the alignment of end and means. In other words, it offers judges a way to control the material coherence of contracts

An analysis of electron distributions in galaxy clusters by means of the flux ratio of iron lines FeXXV and XXVI

The interpretation of hard X-ray emission from galaxy clusters is still ambiguous and different models proposed can be probed using various observational methods. Here we explore a new method based on Fe line observations. Spectral line emissivities have usually been calculated for a Maxwellian electron distribution. In this paper a generalized approach to calculate the iron line flux for a modified Maxwellian distribution is considered. We have calculated the flux ratio of iron lines for the various possible populations of electrons that have been proposed to account for measurements of hard X-ray excess emission from the clusters A2199 and Coma. We found that the influence of the suprathermal electron population on the flux ratio is more prominent in low temperature clusters (as Abell 2199) than in high temperature clusters (as Coma).Comment: 6 pages, 3 figures, accepted for publication in A&

X-ray He-like ions diagnostics: New Computations for Photoionized Plasmas: I. preliminary considerations

Using the new version of the photoionization code Titan designed for plane-parallel photoionized thick hot media, which is unprecedented from the point of view of line transfer, we have undertaken a study of the influence of different parameters on the He-like and H-like emission of a medium photoionized by an X-ray source. We explain why in modelling the emitting medium it is important to solve in a self-consistent way the thermal and ionization equilibria and to take into account the interconnection between the different ions. We give the equivalent widths of the sum of the He-like triplets and the triplet intensity ratios $G$ and $R$, for the most important He-like ions, for a range of density, column density, and ionization parameter, in the case of constant density media. We show that the line intensities from a given ion can be accounted for, either by small values of both the column density and of the ionization parameter, or by large values of both quantities, and it is necessary to take into account several ions to disentangle these possibilities. We show also that a "pure recombination spectrum" almost never exists in a photoionized medium: either it is thin, and resonance lines are formed by radiative excitation, or it is thick, and free-bound absorption destroys the resonance photons as they undergo resonant diffusion.Comment: 19 pages, 14 figures, accepted in A &

Hardware and Arithmetic for Hyperelliptic Curves Cryptography

International audiencePresentation of the HAH project main results for IRISA partner at CominLabs Days November 2016

X-Ray Photoabsorption in KLL Resonances of O VI And Abundance Analysis

It is shown that photoabsorption via autoionizing resonances may be appreciable and used for abundance analysis. Analogous to spectral lines, the `resonance oscillator strength' f_r may be defined and evaluated in terms of the differential oscillator strength df/d(epsilon) that relates bound and continuum absorption. X-ray photoabsorption in KLL (1s2s2p) resonances of O VI is investigated using highly resolved relativistic photoionization cross sections with fine structure. It is found that f_r is comparable to that for UV dipole transition in O VI (2s - 2p) and the X-ray (1s^2 ^1S_0 - 1s2p ^1P^o_1) transition in O VII. The dominant O VI(KLL) components lie at 22.05 and 21.87 Angstroms. These predicted absorption features should be detectable by the Chandra X-Ray Observatory (CXO) and the X-Ray Multi-Mirror Mission (XMM). The combined UV/X-ray spectra of O VI/O VII should yield valuable information on the ionization structure and abundances in sources such as the `warm absorber' region of active galactic nuclei and the hot intergalactic medium. Some general implications of resonant photoabsorption are addressed.Comment: Astrophys. J. Letters (in press), 9 pages, 3 figure