How non-linear scaling relations unify dwarf and giant elliptical galaxies

Dwarf elliptical galaxies are frequently excluded from bright galaxy samples because they do not follow the same linear relations in diagrams involving effective half light radii R_e or mean effective surface brightnesses _e. However, using two linear relations which unite dwarf and bright elliptical galaxies we explain how these lead to curved relations when one introduces either the half light radius or the associated surface brightness. In particular, the curved _e - R_e relation is derived here. This and other previously misunderstood curved relations, once heralded as evidence for a discontinuity between faint and bright elliptical galaxies at M_B ~ -18 mag, actually support the unification of such galaxies as a single population whose structure (i.e. stellar concentration) varies continuously with stellar luminosity and mass.Comment: 4 pages including 2 figures, to appear in "A Universe of dwarf galaxies", Conf. Proc. (Lyon, June 14-18, 2010

Subleading corrections to the Double Coset Ansatz preserve integrability

In this article we compute the anomalous dimensions for a class of operators, belonging to the SU(3) sector of the theory, that have a bare dimension of order N. For these operators the large N limit and the planar limit are distinct and summing only the planar diagrams will not capture the large N dynamics. Although the spectrum of anomalous dimensions has been computed for this class of operators, previous studies have neglected certain terms which were argued to be small. After dropping these terms diagonalizing the dilatation operator reduces to diagonalizing a set of decoupled oscillators. In this article we explicitly compute the terms which were neglected previously and show that diagonalizing the dilatation operator still reduces to diagonalizing a set of decoupled oscillators.Comment: 1 + 39 pages; v2: references adde

The Casimir Effect for Fermions in One Dimension

We study the Casimir problem for a fermion coupled to a static background field in one space dimension. We examine the relationship between interactions and boundary conditions for the Dirac field. In the limit that the background becomes concentrated at a point (a ``Dirac spike'') and couples strongly, it implements a confining boundary condition. We compute the Casimir energy for a masslike background and show that it is finite for a stepwise continuous background field. However the total Casimir energy diverges for the Dirac spike. The divergence cannot be removed by standard renormalization methods. We compute the Casimir energy density of configurations where the background field consists of one or two sharp spikes and show that the energy density is finite except at the spikes. Finally we define and compute an interaction energy density and the force between two Dirac spikes as a function of the strength and separation of the spikes.Comment: 18 pages, 6 figure

Updated Mass Scaling Relations for Nuclear Star Clusters and a Comparison to Supermassive Black Holes

We investigate whether nuclear star clusters and supermassive black holes follow a common set of mass scaling relations with their host galaxy's properties, and hence can be considered to form a single class of central massive object. We have compiled a large sample of galaxies with measured nuclear star cluster masses and host galaxy properties from the literature and fit log-linear scaling relations. We find that nuclear star cluster mass, M_{NC}, correlates most tightly with the host galaxy's velocity dispersion: log M_{NC} = (2.11 \pm 0.31) log (\sigma/54) + (6.63 \pm 0.09), but has a slope dramatically shallower than the relation defined by supermassive black holes. We find that the nuclear star cluster mass relations involving host galaxy (and spheroid) luminosity and stellar and dynamical mass, intercept with but are in general shallower than the corresponding black hole scaling relations. In particular M_{NC} \propto {M}_{Gal,dyn}^{0.55 \pm 0.15}; the nuclear cluster mass is not a constant fraction of its host galaxy or spheroid mass. We conclude that nuclear stellar clusters and supermassive black holes do not form a single family of central massive objects.Comment: 8 pages, 3 figure

Extending the M_(bh)-sigma diagram with dense nuclear star clusters

Abridged: Four new nuclear star cluster masses, M_nc, plus seven upper limits, are provided for galaxies with previously determined black hole masses, M_bh. Together with a sample of 64 galaxies with direct M_bh measurements, 13 of which additionally now have M_nc measurements rather than only upper limits, plus an additional 29 dwarf galaxies with available M_nc measurements and velocity dispersions sigma, an (M_bh + M_nc)-sigma diagram is constructed. Given that major dry galaxy merger events preserve the M_bh/L ratio, and given that L ~ sigma^5 for luminous galaxies, it is first noted that the observation M_bh ~ sigma^5 is consistent with expectations. For the fainter elliptical galaxies it is known that L ~ sigma^2, and assuming a constant M_nc/L ratio (Ferrarese et al.), the expectation that M_nc ~ sigma^2 is in broad agreement with our new observational result that M_nc ~ sigma^{1.57\pm0.24}. This exponent is however in contrast to the value of ~4 which has been reported previously and interpreted in terms of a regulating feedback mechanism from stellar winds.Comment: 6 pages, 2 figures. Submitted 08/08/2011 to MNRAS, first referee report received 19/01/2012, accepted 10/02/201

Book review: access to justice for disadvantaged communities by Marjorie Mayo, Gerald Koessl, Matthew Scott, Imogen Slater

The basic human right of access to justice for all has come under threat through wider processes of restructuring, with an increasingly market-led approach to the provision of welfare. Graham de Barra recommends the book to students interested in public policy, law, sociology and access to justice. The insights provided by the study of qualitative interviews make this book a unique read from beginning to end

Loewner equations on complete hyperbolic domains

We prove that, on a complete hyperbolic domain D\subset C^q, any Loewner PDE associated with a Herglotz vector field of the form H(z,t)=A(z)+O(|z|^2), where the eigenvalues of A have strictly negative real part, admits a solution given by a family of univalent mappings (f_t: D\to C^q) such that the union of the images f_t(D) is the whole C^q. If no real resonance occurs among the eigenvalues of A, then the family (e^{At}\circ f_t) is uniformly bounded in a neighborhood of the origin. We also give a generalization of Pommerenke's univalence criterion on complete hyperbolic domains.Comment: 19 pages, revised exposition, improved results, added reference