The definability criterions for convex projective polyhedral reflection groups

Following Vinberg, we find the criterions for a subgroup generated by reflections \Gamma \subset \SL^{\pm}(n+1,\mathbb{R}) and its finite-index subgroups to be definable over $\mathbb{A}$ where $\mathbb{A}$ is an integrally closed Noetherian ring in the field $\mathbb{R}$. We apply the criterions for groups generated by reflections that act cocompactly on irreducible properly convex open subdomains of the $n$-dimensional projective sphere. This gives a method for constructing injective group homomorphisms from such Coxeter groups to \SL^{\pm}(n+1,\mathbb{Z}). Finally we provide some examples of \SL^{\pm}(n+1,\mathbb{Z})-representations of such Coxeter groups. In particular, we consider simplicial reflection groups that are isomorphic to hyperbolic simplicial groups and classify all the conjugacy classes of the reflection subgroups in \SL^{\pm}(n+1,\mathbb{R}) that are definable over $\mathbb{Z}$. These were known by Goldman, Benoist, and so on previously.Comment: 31 pages, 8 figure

On compatibility between isogenies and polarisations of abelian varieties

We discuss the notion of polarised isogenies of abelian varieties, that is, isogenies which are compatible with given principal polarisations. This is motivated by problems of unlikely intersections in Shimura varieties. Our aim is to show that certain questions about polarised isogenies can be reduced to questions about unpolarised isogenies or vice versa. Our main theorem concerns abelian varieties B which are isogenous to a fixed abelian variety A. It establishes the existence of a polarised isogeny A to B whose degree is polynomially bounded in n, if there exist both an unpolarised isogeny A to B of degree n and a polarised isogeny A to B of unknown degree. As a further result, we prove that given any two principally polarised abelian varieties related by an unpolarised isogeny, there exists a polarised isogeny between their fourth powers. The proofs of both theorems involve calculations in the endomorphism algebras of the abelian varieties, using the Albert classification of these endomorphism algebras and the classification of Hermitian forms over division algebras

Building a Sample of Distant Clusters of Galaxies

Candidate clusters of galaxies drawn from the sample identified from the moderately deep I-band data of the ESO Imaging Survey (EIS), have been used for follow-up optical/infrared imaging and spectroscopic observations. The observations were conducted to assess the nature of these candidates over a large range of redshifts. Currently, 163 EIS candidates have (V-I) colors, 15 have (I-K) and 65 cluster fields have been observed spectroscopically. From a preliminary analysis of these data, we find that > 65% of the candidates studied show strong evidence of being real physical associations, over the redshift range 0.2<z<1.1. The evidence in some cases comes directly from spectroscopic measurements, in others indirectly from the detection of overdensities of objects with either the same color or the same photometric redshift, or from a combination of color and spectroscopic information. Preliminary results also suggest that the redshift derived from the matched-filter algorithm is a reasonable measure of the cluster's redshift, possibly overestimating it by Delta z ~0.1, at least for systems at z<0.7. Overdensities of red objects have been detected in over 100 candidates, 38 of which with estimated redshifts >0.6, and six candidates in the interval 0.45<z<0.81 have either been identified directly from measured redshifts or have been confirmed by the measurement of at least one redshift for galaxies located along a red-sequence typical of cluster early-type galaxies. Lastly, five candidates among those already observed in the infrared have (I-Ks) colors consistent with them being in the redshift interval 0.8<z<1.1. The sample of "confirmed" clusters, already the largest of its kind in the southern hemisphere, will be further enlarged by ongoing observations.Comment: To appear in "Large Scale Structure in the X-ray Universe", ed. M. Plionis and I. Georgantopoulos (Paris: Editions Frontieres), in pres

Spectroscopic confirmation of clusters from the ESO imaging survey

We measure redshifts for 67 galaxies in the field of six cluster candidates from the ESO Imaging Survey (EIS). The cluster candidates are selected in the EIS patches C and D among those with estimated mean redshifts between 0.5 and 0.7. The observations were made with EFOSC2 at the 3.6m ESO telescope. In the six candidate cluster fields, we identify 19 possible sets of 2 to 7 galaxies in redshift space. In order to establish which of the 19 sets are likely to correspond to real dense systems we compare our counts with those expected from a uniform distribution of galaxies with given luminosity function. In order to take into account the effect of the Large Scale Structure, we modulate the probability computed from the luminosity function with random samplings of the Canada-France Redshift Survey. We find that four out of six candidate EIS clusters are likely to correspond to real systems in redshift space (> 95 % confidence level). Two of these systems have mean redshift in agreement with the redshift estimate given by the matched filter algorithm. The other two systems have significantly lower redshifts. We discuss the implications of our results in the context of our ongoing research projects aimed at defining high-redshift optically-selected cluster samples.Comment: To appear in A&A, main journal -- 12 pages, 9 figure

ESO Imaging Survey VII. Distant Cluster Candidates over 12 square degrees

In this paper the list of candidate clusters identified from the I-band data of the ESO Imaging Survey (EIS) is completed using the images obtained over a total area of about 12 square degrees. Together with the data reported earlier the total I-band coverage of EIS is 17 square degrees, which has yielded a sample of 252 cluster candidates in the redshift range 0.2 \lsim z \lsim 1.3. This is the largest optically-selected sample currently available in the Southern Hemisphere. It is also well distributed in the sky thus providing targets for a variety of VLT programs nearly year round.Comment: 5 pages, 3 figures, submitted to Astronomy & Astrophysic

A2163: Merger events in the hottest Abell galaxy cluster II. Subcluster accretion with galaxy-gas separation

Located at z = 0.203, A2163 is a rich galaxy cluster with an intra-cluster medium (ICM) that exhibits extraordinary properties, including an exceptionally high X-ray luminosity, average temperature, and a powerful and extended radio halo. The irregular and complex morphology of its gas and galaxy structure suggests that this cluster has recently undergone major merger events that involve two or more cluster components. In this paper, we study the gas structure and dynamics by means of spectral-imaging analysis of X-ray data obtained from XMM-Newton and Chandra observations. From the evidence of a cold front, we infer the westward motion of a cool core across the E-W elongated atmosphere of the main cluster A2163-A. Located close to a galaxy over-density, this gas 'bullet' appears to have been spatially separated from its galaxy (and presumably dark matter component) as a result of high-velocity accretion. From gas brightness and temperature profile analysis performed in two opposite regions of the main cluster, we show that the ICM has been adiabatically compressed behind the crossing 'bullet' possibly because of shock heating, leading to a strong departure of the ICM from hydrostatic equilibrium in this region. Assuming that the mass estimated from the Yx proxy best indicates the overall mass of the system and that the western cluster sector is in approximate hydrostatic equilibrium before subcluster accretion, we infer a merger scenario between two subunits of mass ratio 1:4, leading to a present total system mass of M500 $\propto 1.9 \times 1015 M_{\odot}$. The exceptional properties of A2163 present various similarities with those of 1E0657-56, the so-called 'bullet-cluster'. These similarities are likely to be related to a comparable merger scenario.Comment: A&A, in pres

On the Nature of the EIS Candidate Clusters: Confirmation of z<0.6 candidates

We use public V-band imaging data from the wide-angle surveys conducted by the ESO Imaging Survey project (EIS) to further investigate the nature of the EIS galaxy cluster candidates. These were originally identified by applying a matched-filter algorithm which used positional and photometric data of the galaxy sample extracted from the I-band survey images. In this paper, we apply the same technique to the galaxy sample extracted from V-band data and compare the new cluster detections with the original ones. We find that ~75% of the low-redshift cluster candidates (z<0.6) are detected in both passbands and their estimated redshifts show good agreement with the scatter in the redshift differences being consistent with the estimated errors of the method. For the ``robust'' I-band detections the matching frequency approaches ~85%. We also use the available (V-I) color to search for the red sequence of early-type galaxies observed in rich clusters over a broad range of redshifts. This is done by searching for a simultaneous overdensity in the three-dimensional color-projected distance space. We find significant overdensities for ~75% of the ``robust'' candidates with z_I<0.6. We find good agreement between the characteristic color associated to the detected "red sequence" and that predicted by passive evolution galaxy models for ellipticals at the redshift estimated by the matched-filter. The results presented in this paper show the usefulness of color data, even of two-band data, to both tentatively confirm cluster candidates and to select possible cluster members for spectroscopic observations. Based on the present results, we estimate that ~150 EIS clusters with z_I<0.6 are real, making it one of the largest samples of galaxy clusters in this redshift range currently available in the southern hemisphere.Comment: 11 pages, 10 figures, accepted for publication in A&

The First VLT FORS1 spectra of Lyman-break candidates in the HDF-S and AXAF Deep Field

We report on low-resolution multi-object spectroscopy of 30 faint targets (R \~ 24-25) in the HDF-S and AXAF deep field obtained with the VLT Focal Reducer/low dispersion Spectrograph (FORS1). Eight high-redshift galaxies with 2.75< z < 4 have been identified. The spectroscopic redshifts are in good agreement with the photometric ones with a dispersion $\sigma_z = 0.07$ at z<2 and $\sigma_z = 0.16$ at z>2. The inferred star formation rates of the individual objects are moderate, ranging from a few to a few tens solar masses per year. Five out of the eight high-z objects do not show prominent emission lines. One object has a spectrum typical of an AGN. In the AXAF field two relatively close pairs of galaxies have been identified, with separations of 8.7 and 3.1 proper Mpc and mean redshifts of 3.11 and 3.93, respectively.Comment: 5 pages Latex, with 2 PostScript figures. Astronomy and Astrophysics, in pres