On the 3D Velocity Reconstruction of Clusters of Galaxies

The problem of reconstruction of the 3D velocities of clusters of galaxies from the redshift distribution of galaxies of the cluster is formulated. Though numerical simulations show the impossibility of direct use of Ambartsumian's formula derived for the stellar systems because of the small number of objects in the clusters, an additional physical assumption on the form of the searched velocity distribution can lead to the possibility of obtaining the transverse velocity of the cluster. The accuracy of the proposed reconstruction procedure is estimated.Comment: to appear in Astrofizika, vol.40, 1997; LaTex, 4 pages, 1 figure, *.ps figure can be obtained from the author

On the motion of the Local Group and its substructures

The problem of the relative motion of the substructures of the Local Group of galaxies revealed via S-tree method, as well as of the velocity of the Local Group itself, is considered. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via 3D reconstruction procedure, which uses the information on the radial velocities of the galaxies, but not on their distances. Once the bulk motion of substructures is estimated, in combination with the observed CMB dipole we also consider the mean velocity of the Local Group itself. Assigning the Local Group the mean motion of its main substructures we evaluate its peculiar velocity in Milky Way frame V(LG->MW)= (-7 \pm 303,-15 \pm 155 ,+177 \pm 144) or 178 km/s toward galactic coordinates l=245 and b=+85. Combined with CMB dipole V(MW->CMB), we obtain Local Group velocity in CMB frame: V(LG->CMB) = (-41\pm 303,-497\pm 155,445 \pm 144) or 668 km/s towards l=265 and b=42. This estimation is in good agreement, within 1 sigma level, with the estimation of Yahil et al (1977).Comment: To be published in MNRA

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

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

An algorithm to identify automorphisms which arise from self-induced interval exchange transformations

We give an algorithm to determine if the dynamical system generated by a positive automorphism of the free group can also be generated by a self-induced interval exchange transformation. The algorithm effectively yields the interval exchange transformation in case of success.Comment: 26 pages, 8 figures. v2: the article has been reorganized to make for a more linear read. A few paragraphs have been added for clarit

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

Observational Mass-to-Light Ratio of Galaxy Systems: from Poor Groups to Rich Clusters

We study the mass-to-light ratio of galaxy systems from poor groups to rich clusters, and present for the first time a large database for useful comparisons with theoretical predictions. We extend a previous work, where B_j band luminosities and optical virial masses were analyzed for a sample of 89 clusters. Here we also consider a sample of 52 more clusters, 36 poor clusters, 7 rich groups, and two catalogs, of about 500 groups each, recently identified in the Nearby Optical Galaxy sample by using two different algorithms. We obtain the blue luminosity and virial mass for all systems considered. We devote a large effort to establishing the homogeneity of the resulting values, as well as to considering comparable physical regions, i.e. those included within the virial radius. By analyzing a fiducial, combined sample of 294 systems we find that the mass increases faster than the luminosity: the linear fit gives M\propto L_B^{1.34 \pm 0.03}, with a tendency for a steeper increase in the low--mass range. In agreement with the previous work, our present results are superior owing to the much higher statistical significance and the wider dynamical range covered (about 10^{12}-10^{15} M_solar). We present a comparison between our results and the theoretical predictions on the relation between M/L_B and halo mass, obtained by combining cosmological numerical simulations and semianalytic modeling of galaxy formation.Comment: 25 pages, 12 eps figures, accepted for publication in Ap

The Nearby Optical Galaxy Sample: The Local Galaxy Luminosity Function

In this paper we derive the galaxy luminosity function from the Nearby Optical Galaxy (NOG) sample, which is a nearly complete, magnitude-limited (B<14 mag), all-sky sample of nearby optical galaxies (~6400 galaxies with cz<5500 km/s). For this local sample, we use galaxy distance estimates based on different peculiar velocity models. Therefore, the derivation of the luminosity function is carried out using the locations of field and grouped galaxies in real distance space. The local field galaxy luminosity function in the B system is well described by a Schechter function. The exact values of the Schechter parameters slightly depend on the adopted peculiar velocity field models. The shape of the luminosity function of spiral galaxies does not differ significantly from that of E-S0 galaxies. On the other hand, the late-type spirals and irregulars have a very steeply rising luminosity function towards the faint end, whereas the ellipticals appreciably decrease in number towards low luminosities. The presence of galaxy systems in the NOG sample does not affect significantly the field galaxy luminosity function, since environmental effects on the total luminosity function appear to be marginal.Comment: 35 pages including 7 figures and 4 tables. Accepted for publication in Ap