The Hi content of compact groups of galaxies

The Hi content of Hickson Compact Groups in the southern hemisphere is measured using data from the Hi Parkes All-Sky Survey (HIPASS), and dedicated observations using the narrow band filter on the Multibeam instrument on the Parkes telescope. The expected Hi mass of these groups was estimated using the luminosity, diameter, and morphological types of the member galaxies, calibrated from published data. Taking careful account of non-detection limits, the results show that the compact group population that has been detected by these observations has an Hi content similar to that of galaxies in the reference field sample. The upper limits for the undetected groups lie within the normal range; improvement of these limits will require a large increase in sensitivity.

Compact groups of galaxies selected by stellar mass: the 2MASS compact group catalogue

We present a photometric catalogue of compact groups of galaxies (p2MCGs) automatically extracted from the Two-Micron All Sky Survey (2MASS) extended source catalogue. A total of 262 p2MCGs are identified, following the criteria defined by Hickson, of which 230 survive visual inspection (given occasional galaxy fragmentation and blends in the 2MASS parent catalogue). Only one quarter of these 230 groups were previously known compact groups (CGs). Among the 144 p2MCGs that have all their galaxies with known redshifts, 85 (59?per cent) have four or more accordant galaxies. This v2MCG sample of velocity-filtered p2MCGs constitutes the largest sample of CGs (with N = 4) catalogued to date, with both well-defined selection criteria and velocity filtering, and is the first CG sample selected by stellar mass. It is fairly complete up to Kgroup similar to 9 and radial velocity of similar to 6000?km?s-1. We compared the properties of the 78 v2MCGs with median velocities greater than 3000?km?s-1 with the properties of other CG samples, as well as those (mvCGs) extracted from the semi-analytical model (SAM) of Guo et al. run on the high-resolution Millennium-II simulation. This mvCG sample is similar (i.e. with 2/3 of physically dense CGs) to those we had previously extracted on three other SAMs run on the Millennium simulation with 125 times worse spatial and mass resolutions. The space density of v2MCGs within 6000?km?s-1 is 8.0 X 10-5?h3?Mpc-3, i.e. four times that of the Hickson sample [Hickson Compact Group (HCG)] up to the same distance and with the same criteria used in this work, but still 40?per cent less than that of mvCGs. The v2MCG constitutes the first group catalogue to show a statistically large firstsecond ranked galaxy magnitude gap according to TremaineRichstone statistics, as expected if the first ranked group members tend to be the products of galaxy mergers, and as confirmed in the mvCGs. The v2MCG is also the first observed sample to show that first-ranked galaxies tend to be centrally located, again consistent with the predictions obtained from mvCGs. We found no significant correlation of group apparent elongation and velocity dispersion in the quartets among the v2MCGs, and the velocity dispersions of apparently round quartets are not significantly larger than those of chain-like ones, in contrast to what has been previously reported in HCGs. By virtue of its automatic selection with the popular Hickson criteria, its size, its selection on stellar mass, and its statistical signs of mergers and centrally located brightest galaxies, the v2MCG catalogue appears to be the laboratory of choice to study physically dense groups of four or more galaxies of comparable luminosity.

Sets of p-multiplicity in locally compact groups

We initiate the study of sets of p-multiplicity in locally compact groups and their operator versions. We show that a closed subset E of a second countable locally compact group G is a set of p-multiplicity if and only if E∗={(s,t):ts−1∈E} is a set of operator p-multiplicity. We exhibit examples of sets of p-multiplicity, establish preservation properties for unions and direct products, and prove a p-version of the Stone–von Neumann Theorem.

Intragroup diffuse light in compact groups of galaxies - II. HCG 15, 35 and 51

This continuing study of intragroup light in compact groups of galaxies aims to establish new constraints to models of formation and evolution of galaxy groups, specially of compact groups, which are a key part in the evolution of larger structures, such as clusters. In this paper we present three additional groups (HCG 15, 35 and 51) using deep wide-field B- and R-band images observed with the LAICA camera at the 3.5-m telescope at the Calar Alto observatory (CAHA). This instrument provides us with very stable flat-fielding, a mandatory condition for reliably measuring intragroup diffuse light. The images were analysed with the OV_WAV package, a wavelet technique that allows us to uncover the intragroup component in an unprecedented way. We have detected that 19, 15 and 26 per cent of the total light of HCG 15, 35 and 51, respectively, are in the diffuse component, with colours that are compatible with old stellar populations and with mean surface brightness that can be its low as 28.4 B mag arcsec(-2). Dynamical masses, crossing times and mass-to-light ratios were recalculated using the new group parameters. Also tidal features were analysed using the wavelet technique.

Almost p-compact groups

We show that if p is a selective ultrafilter, then for each cardinal alpha <= omega(1), there exists a topological group G such that G(beta) is almost p-compact (in particular, countably compact), for beta < alpha, but G(alpha) is not countably compact. If in addition, we assume Martin's Axiom, then the result above holds for every alpha < c. (C) 2012 Elsevier By. All rights reserved.

Galaxy triplets in Sloan Digital Sky Survey Data Release 7: II. A connection with compact groups?

We analyse a sample of 71 triplets of luminous galaxies derived from the work of O’Mill et al. We compare the properties of triplets and their members with those of control samples of compact groups, the 10 brightest members of rich clusters and galaxies in pairs. The triplets are restricted to have members with spectroscopic redshifts in the range 0.01 ≤ z ≤ 0.14 and absolute r-band luminosities brighter than Mr = −20.5. For these member galaxies, we analyse the stellar mass content, the star formation rates, the Dn(4000) parameter and (Mg − Mr) colour index. Since galaxies in triplets may finally merge in a single system, we analyse different global properties of these systems. We calculate the probability that the properties of galaxies in triplets are strongly correlated. We also study total star formation activity and global colours, and define the triplet compactness as a measure of the percentage of the system total area that is filled by the light of member galaxies. We concentrate in the comparison of our results with those of compact groups to assess how the triplets are a natural extension of these compact systems. Our analysis suggests that triplet galaxy members behave similarly to compact group members and galaxies in rich clusters. We also find that systems comprising three blue, star-forming, young stellar population galaxies (blue triplets) are most probably real systems and not a chance configuration of interloping galaxies. The same holds for triplets composed of three red, non-star-forming galaxies, showing the correlation of galaxy properties in these systems. From the analysis of the triplet as a whole, we conclude that, at a given total stellar mass content, triplets show a total star formation activity and global colours similar to compact groups. However, blue triplets show a high total star formation activity with a lower stellar mass content. From an analysis of the compactness parameter of the systems we find that light is even more concentrated in triplets than in compact groups. We propose that triplets composed of three luminous galaxies, should not be considered as an analogous of galaxy pairs with a third extra member, but rather they are a natural extension of compact groups.

Groups of unstable Adams operations on p-local compact groups

Peer reviewed

Automorphisms of p-local compact groups

Peer reviewed

Groups of unstable Adams operations on p-local compact groups

Peer reviewed

GALAXY EVOLUTION IN A COMPLEX ENVIRONMENT: A MULTI-WAVELENGTH STUDY OF HCG 7

The environment where galaxies are found heavily influences their evolution. Close groupings, like the ones in the cores of galaxy clusters or compact groups, evolve in ways far more dramatic than their isolated counterparts. We have conducted a multi-wavelength study of Hickson Compact Group 7 (HCG 7), consisting of four giant galaxies: three spirals and one lenticular. We use Hubble Space Telescope (HST) imaging to identify and characterize the young and old star cluster populations. We find young massive clusters (YMCs) mostly in the three spirals, while the lenticular features a large, unimodal population of globular clusters (GCs) but no detectable clusters with ages less than a few Gyr. The spatial and approximate age distributions of the similar to 300 YMCs and similar to 150 GCs thus hint at a regular star formation history in the group over a Hubble time. While at first glance the HST data show the galaxies as undisturbed, our deep ground-based, wide-field imaging that extends the HST coverage reveals faint signatures of stellar material in the intragroup medium (IGM). We do not, however, detect the IGM in H I or Chandra X-ray observations, signatures that would be expected to arise from major mergers. Despite this fact, we find that the H I gas content of the individual galaxies and the group as a whole are a third of the expected abundance. The appearance of quiescence is challenged by spectroscopy that reveals an intense ionization continuum in one galaxy nucleus, and post-burst characteristics in another. Our spectroscopic survey of dwarf galaxy members yields a single dwarf elliptical galaxy in an apparent stellar tidal feature. Based on all this information, we suggest an evolutionary scenario for HCG 7, whereby the galaxies convert most of their available gas into stars without the influence of major mergers and ultimately result in a dry merger. As the conditions governing compact groups are reminiscent of galaxies at intermediate redshift, we propose that HCGs are appropriate for studying galaxy evolution at z similar to 1-2.

Star formation in H I tails: HCG 92, HCG 100 and six interacting systems

We present new Gemini spectra of 14 new objects found within the H?i tails of Hickson Compact Groups (HCGs) 92 and 100. Nine of them are Galaxy Evolution Explorer (GALEX) far-ultraviolet (FUV) and near-ultraviolet (NUV) sources. The spectra confirm that these objects are members of the compact groups and have metallicities close to solar, with an average value of 12+log(O/H) similar to 8.5. They have average FUV luminosities 7 x 10(40)?erg?s-1 and very young ages (<100?Myr), and two of them resemble tidal dwarf galaxy (TDG) candidates. We suggest that they were created within gas clouds that were ejected during galaxygalaxy interactions into the intergalactic medium, which would explain the high metallicities of the objects, inherited from the parent galaxies from which the gas originated. We conduct a search for similar objects in six interacting systems with extended H?i tails: NGC 2623, NGC 3079, NGC 3359, NGC 3627, NGC 3718 and NGC 4656. We found 35 ultraviolet (UV) sources with ages < 100?Myr; however, most of them are on average less luminous/massive than the UV sources found around HCG 92 and HCG 100. We speculate that this might be an environmental effect and that compact groups of galaxies are more favourable to TDG formation than other interacting systems.

Abelian torsion groups with a countably compact group topology

Comfort and Remus [W.W. Comfort, D. Remus, Abelian torsion groups with a pseudo-compact group topology, Forum Math. 6 (3) (1994) 323-337] characterized algebraically the Abelian torsion groups that admit a pseudocompact group topology using the Ulm-Kaplansky invariants. We show, under a condition weaker than the Generalized Continuum Hypothesis, that an Abelian torsion group (of any cardinality) admits a pseudocompact group topology if and only if it admits a countably compact group topology. Dikranjan and Tkachenko [D. Dikranjan. M. Tkachenko, Algebraic structure of small countably compact Abelian groups, Forum Math. 15 (6) (2003) 811-837], and Dikranjan and Shakhmatov [D. Dikranjan. D. Shakhmatov, Forcing hereditarily separable compact-like group topologies on Abelian groups, Topology Appl. 151 (1-3) (2005) 2-54] showed this equivalence for groups of cardinality not greater than 2(c). We also show, from the existence of a selective ultrafilter, that there are countably compact groups without non-trivial convergent sequences of cardinality kappa(omega), for any infinite cardinal kappa. In particular, it is consistent that for every cardinal kappa there are countably compact groups without non-trivial convergent sequences whose weight lambda has countable cofinality and lambda > kappa. (C) 2009 Elsevier B.V. All rights reserved.

Maximal Subgroups of Compact Lie Groups

This report aims at giving a general overview on the classification of the maximal subgroups of compact Lie groups (not necessarily connected). In the first part, it is shown that these fall naturally into three types: (1) those of trivial type, which are simply defined as inverse images of maximal subgroups of the corresponding component group under the canonical projection and whose classification constitutes a problem in finite group theory, (2) those of normal type, whose connected one-component is a normal subgroup, and (3) those of normalizer type, which are the normalizers of their own connected one-component. It is also shown how to reduce the classification of maximal subgroups of the last two types to: (2) the classification of the finite maximal Sigma-invariant subgroups of centerfree connected compact simple Lie groups and (3) the classification of the Sigma-primitive subalgebras of compact simple Lie algebras, where Sigma is a subgroup of the corresponding outer automorphism group. In the second part, we explicitly compute the normalizers of the primitive subalgebras of the compact classical Lie algebras (in the corresponding classical groups), thus arriving at the complete classification of all (non-discrete) maximal subgroups of the compact classical Lie groups.

The operator algebra approach to quantum groups

A relatively simple definition of a locally compact quantum group in the C*-algebra setting will be explained as it was recently obtained by the authors. At the same time, we put this definition in the historical and mathematical context of locally compact groups, compact quantum groups, Kac algebras, multiplicative unitaries, and duality theory.

On the Geometry of Infinite-Dimensional Grassmannian Manifolds and Gauge Theory

This PhD Thesis is about certain infinite-dimensional Grassmannian manifolds that arise naturally in geometry, representation theory and mathematical physics. From the physics point of view one encounters these infinite-dimensional manifolds when trying to understand the second quantization of fermions. The many particle Hilbert space of the second quantized fermions is called the fermionic Fock space. A typical element of the fermionic Fock space can be thought to be a linear combination of the configurations m particles and n anti-particles . Geometrically the fermionic Fock space can be constructed as holomorphic sections of a certain (dual)determinant line bundle lying over the so called restricted Grassmannian manifold, which is a typical example of an infinite-dimensional Grassmannian manifold one encounters in QFT. The construction should be compared with its well-known finite-dimensional analogue, where one realizes an exterior power of a finite-dimensional vector space as the space of holomorphic sections of a determinant line bundle lying over a finite-dimensional Grassmannian manifold. The connection with infinite-dimensional representation theory stems from the fact that the restricted Grassmannian manifold is an infinite-dimensional homogeneous (Kähler) manifold, i.e. it is of the form G/H where G is a certain infinite-dimensional Lie group and H its subgroup. A central extension of G acts on the total space of the dual determinant line bundle and also on the space its holomorphic sections; thus G admits a (projective) representation on the fermionic Fock space. This construction also induces the so called basic representation for loop groups (of compact groups), which in turn are vitally important in string theory / conformal field theory. The Thesis consists of three chapters: the first chapter is an introduction to the backround material and the other two chapters are individually written research articles. The first article deals in a new way with the well-known question in Yang-Mills theory, when can one lift the action of the gauge transformation group on the space of connection one forms to the total space of the Fock bundle in a compatible way with the second quantized Dirac operator. In general there is an obstruction to this (called the Mickelsson-Faddeev anomaly) and various geometric interpretations for this anomaly, using such things as group extensions and bundle gerbes, have been given earlier. In this work we give a new geometric interpretation for the Faddeev-Mickelsson anomaly in terms of differentiable gerbes (certain sheaves of categories) and central extensions of Lie groupoids. The second research article deals with the question how to define a Dirac-like operator on the restricted Grassmannian manifold, which is an infinite-dimensional space and hence not in the landscape of standard Dirac operator theory. The construction relies heavily on infinite-dimensional representation theory and one of the most technically demanding challenges is to be able to introduce proper normal orderings for certain infinite sums of operators in such a way that all divergences will disappear and the infinite sum will make sense as a well-defined operator acting on a suitable Hilbert space of spinors. This research article was motivated by a more extensive ongoing project to construct twisted K-theory classes in Yang-Mills theory via a Dirac-like operator on the restricted Grassmannian manifold.