Cluster luminosity function and n^th ranked magnitude as a distance indicator

We define here a standard candle to determine the distance of clusters of galaxies and to investigate their peculiar velocities by using the n^{th} rank galaxy (magnitude m$_n$). We address the question of the universality of the luminosity function for a sample of 28 rich clusters of galaxies ($cz \simeq 20000 km/s$) in order to model the influence on $m_n$ of cluster richness. This luminosity function is found to be universal and the fit of a Schechter profile gives $\alpha = -1.50 \pm 0.11$ and $M_{bj}* = -19.91 \pm 0.21$ in the range [-21,-17]. The uncorrected distance indicator $m_n$ is more efficient for the first ranks n. With n=5, we have a dispersion of 0.61 magnitude for the (m$_n$,5log(cz)) relation. When we correct for the richness effect and subtract the background galaxies we reduce the uncertainty to 0.21 magnitude with n=15. Simulations show that a large part of this dispersion originates from the intrinsic scatter of the standard candle itself. These provide upper bounds on the amplitude $\sigma_v$ of cluster radial peculiar motions. At a confidence level of 90%, the dispersion is 0.13 magnitude and $\sigma_v$ is limited to 1200 km/s for our sample of clusters.Comment: 9 pages, 7 postscript figures, LateX A&A, accepted in A&

A robust method for measuring the Hubble parameter

We obtain a robust, non-parametric, estimate of the Hubble constant from galaxy linear diameters calibrated using HST Cepheid distances. Our method is independent of the parametric form of the diameter function and the spatial distribution of galaxies and is insensitive to Malmquist bias. We include information on the galaxy rotation velocities; unlike Tully-Fisher, however, we retain a fully non-parametric treatment. We find $H_0=66\pm6$ km/s/Mpc, somewhat larger than previous results using galaxy diameters.Comment: 4 pages, 1 figure, Cosmic Flows Workshop, Victoria B.C. Canada, July 1999, ed. S. Courteau, M. Strauss & J. Willick, ASP conf. serie

A robust method for fitting peculiar velocity field models

We present a new method for fitting peculiar velocity models to complete flux limited magnitude-redshifts catalogues, using the luminosity function of the sources as a distance indicator.The method is characterised by its robustness. In particular, no assumptions are made concerning the spatial distribution of sources and their luminosity function. Moreover, selection effects in redshift are allowed. Furthermore the inclusion of additional observables correlated with the absolute magnitude -- such as for example rotation velocity information as described by the Tully-Fisher relation -- is straightforward. As an illustration of the method, the predicted IRAS peculiar velocity model characterised by the density parameter beta is tested on two samples. The application of our method to the Tully-Fisher MarkIII MAT sample leads to a value of beta=0.6 \pm 0.125, fully consistent with the results obtained previously by the VELMOD and ITF methods on similar datasets. Unlike these methods however, we make a very conservative use of the Tully-Fisher information. Specifically, we require to assume neither the linearity of the Tully-Fisher relation nor a gaussian distribution of its residuals. Moreover, the robustness of the method implies that no Malmquist corrections are required. A second application is carried out, using the fluxes of the IRAS 1.2 Jy sample as the distance indicator. In this case the effective depth of the volume in which the velocity model is compared to the data is almost twice the effective depth of the MarkIII MAT sample. The results suggest that the predicted IRAS velocity model, while successful in reproducing locally the cosmic flow, fails to describe the kinematics on larger scales.Comment: 10 pages, 14 figures, MNRAS in pres

Describing the set of words generated by interval exchange transformation

Let $W$ be an infinite word over finite alphabet $A$. We get combinatorial criteria of existence of interval exchange transformations that generate the word W.Comment: 17 pages, this paper was submitted at scientific council of MSU, date: September 21, 200

A physical distance indicator for spiral galaxies

In this paper we derive a Tully Fisher relation from measured I band photometry and H$\alpha$ rotation curves of a large survey of southern sky spiral galaxies, obtained in Persic \& Salucci (1995) by deprojecting and folding the raw H$\alpha$ data of Mathewson, Ford \& Buchhorn (1992). We calibrate the relation by combining several of the largest clusters in the survey, using an iterative maximum likelihood procedure to account for observational selection effects and Malmquist bias. We also incorporate a simple model for the line of sight depth of each cluster. Our results indicate a Tully Fisher relation of intrinsic dispersion $\sim0.3$ mag, corresponding to a distance error dispersion of $13\%$. Application of this relation to mapping the large scale velocity field is underway.Comment: Plain TeX Version 3.0, 4 pages, to appear in `Astrophysical Letters and Communications' - proceedings of the international workshop on observational cosmology: `From Galaxies to Galaxy Systems', Sesto, July 199

Geometrical Models for Substitutions

International audienceWe consider a substitution associated with the Arnoux-Yoccoz interval exchange transformation (IET) related to the tribonacci substitution. We construct the so-called stepped lines associated with the fixed points of the substitution in the abelianization (symbolic) space. We analyze various projections of the stepped line, recovering the Rauzy fractal, a Peano curve related to work in [Arnoux 88], another Peano curve related to the work of [McMullen 09] and [Lowenstein et al. 07], and also the interval exchange transformation itself

A Study of Nine High-Redshift Clusters of Galaxies: IV. Photometry and Sp ectra of Clusters 1324+3011 and 1604+4321

New photometric and spectroscopic observations of galaxies in the directions of three distant clusters are presented as part of our on-going high-redshift cluster survey. The clusters are CL1324+3011 at z = 0.76, CL1604+4304 at z = 0.90, and CL1604+4321 at z = 0.92. The observed x-ray luminosities in these clusters are at least a factor of 3 smaller than those observed in clusters with similar velocity dispersions at z <= 0.4. These clusters contain a significant population of elliptical-like galaxies, although these galaxies are not nearly as dominant as in massive clusters at z <= 0.5. We also find a large population of blue cluster members. Defining an active galaxy as one in which the rest equivalent width of [OII] is greater than 15 Angstroms, the fraction of active cluster galaxies, within the central 1.0 Mpc, is 45%. In the field population, we find that 65% of the galaxies with redshifts between z = 0.40 and z = 0.85 are active, while the fraction is 79% for field galaxies at z > 0.85. The star formation rate normalized by the rest AB B-band magnitude, SFRN, increases as the redshift increases at a given evolving luminosity. At a given redshift, however, SFRN decreases linearly with increasing luminosity indicating a remarkable insensitivity of the star formation rate to the intrinsic luminosity of the galaxy over the range -18 >= ABB >= -22. Cluster galaxies in the central 1 Mpc regions exhibit depressed star formation rates. We are able to measure significant evolution in the B-band luminosity function over the range 0.1 <= z <= 1. The characteristic luminosity increases by a factor of 3 with increasing redshift over this range.Comment: 64 pages, 18 figures, accepted for publication in the Astronomical Journal on May 25, 2001. Scheduled to appear in Sept 2001 issu

K-band Properties of Well-Sampled Groups of Galaxies

We use a sample of 55 groups and 6 clusters of galaxies ranging in mass from 7 x 10^11 Msun to 1.5 x 10^15 Msun to examine the correlation of the Ks-band luminosity with mass discovered by Lin et al. (2003). We use the 2MASS catalog and published redshifts to construct complete magnitude limited redshift surveys of the groups. From these surveys we explore the IR photometric properties of groups members including their IR color distribution and luminosity function. Although we find no significant difference between the group Ks luminosity function and the general field, there is a difference between the color distribution of luminous group members and their counterparts (generally background) in the field. There is a significant population of luminous galaxies with H-Ks > 0.35 which are rarely, if ever, members of the groups in our sample. The most luminous galaxies which populate the groups have a very narrow range of IR color. Over the entire mass range covered by our sample, the Ks luminosity increases with mass as L ~ M^(0.64 +/- 0.06) implying that the mass-to-light ratio in the Ks-band increases with mass. The agreement between this result and earlier investigations of essentially non-overlapping sets of systems shows that this window in galaxy formation and evolution is insensitive to the selection of the systems and to the details of the mass and luminosity computations.Comment: 38 pages, 9 figures, 2 tables. Accepted for publication on Astronomical Journa

Generalized quasiperiodic Rauzy tilings

We present a geometrical description of new canonical $d$-dimensional codimension one quasiperiodic tilings based on generalized Fibonacci sequences. These tilings are made up of rhombi in 2d and rhombohedra in 3d as the usual Penrose and icosahedral tilings. Thanks to a natural indexing of the sites according to their local environment, we easily write down, for any approximant, the sites coordinates, the connectivity matrix and we compute the structure factor.Comment: 11 pages, 3 EPS figures, final version with minor change

Geometric representation of interval exchange maps over algebraic number fields

We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we call the drift vector. We exhibit some examples of renormalizable interval exchange maps with zero and non-zero drift vector, and carry out some investigations of their properties. In particular, we look for evidence of the finite decomposition property: each lattice is the union of finitely many orbits.Comment: 34 pages, 8 postscript figure