21,884 research outputs found
The specific entropy of elliptical galaxies: an explanation for profile-shape distance indicators?
Dynamical systems in equilibrium have a stationary entropy; we suggest that
elliptical galaxies, as stellar systems in a stage of quasi-equilibrium, may
have a unique specific entropy. This uniqueness, a priori unknown, should be
reflected in correlations between the parameters describing the mass (light)
distribution in galaxies. Following recent photometrical work (Caon et al.
1993; Graham & Colless 1997; Prugniel & Simien 1997), we use the Sersic law to
describe the light profile of elliptical galaxies and an analytical
approximation to its three dimensional deprojection. The specific entropy is
calculated supposing that the galaxy behaves as a spherical, isotropic,
one-component system in hydrostatic equilibrium, obeying the ideal gas state
equations. We predict a relation between the 3 parameters of the Sersic,
defining a surface in the parameter space, an `Entropic Plane', by analogy with
the well-known Fundamental Plane. We have analysed elliptical galaxies in Coma
and ABCG 85 clusters and a group of galaxies (associated with NGC 4839). We
show that the galaxies in clusters follow closely a relation predicted by the
constant specific entropy hypothesis with a one-sigma dispersion of 9.5% around
the mean value of the specific entropy. Assuming that the specific entropy is
also the same for galaxies of different clusters, we are able to derive
relative distances between the studied clusters. If the errors are only due to
the determination of the specific entropy (about 10%), then the error in the
relative distance determination should be less than 20% for rich clusters. We
suggest that the unique specific entropy may provide a physical explanation for
the distance indicators based on the Sersic profile put forward by Young &
Currie (1994, 1995) and discussed by Binggeli & Jerjen (1998).Comment: Submitted to MNRAS (05/05/99), 15 pages, 10 figure
On Useful Conformal Tranformations In General Relativity
Local conformal transformations are known as a useful tool in various
applications of the gravitational theory, especially in cosmology. We describe
some new aspects of these transformations, in particular using them for
derivation of Einstein equations for the cosmological and Schwarzschild
metrics. Furthermore, the conformal transformation is applied for the
dimensional reduction of the Gauss-Bonnet topological invariant in to the
spaces of lower dimensions.Comment: 17 pages, LaTeX. The paper is intended mainly for pedagogical
purposes and represents a collection of exercises concerning local conformal
transformations and dimensional reduction. To be published in "Gravitation
and Cosmology
Persistence in the zero-temperature dynamics of the -states Potts model on undirected-directed Barab\'asi-Albert networks and Erd\"os-R\'enyi random graphs
The zero-temperature Glauber dynamics is used to investigate the persistence
probability in the Potts model with , ,..., states on {\it directed} and {\it
undirected} Barab\'asi-Albert networks and Erd\"os-R\'enyi random graphs. In
this model it is found that decays exponentially to zero in short times
for {\it directed} and {\it undirected} Erd\"os-R\'enyi random graphs. For {\it
directed} and {\it undirected} Barab\'asi-Albert networks, in contrast it
decays exponentially to a constant value for long times, i.e, is
different from zero for all values (here studied) from ; this shows "blocking" for all these values. Except that for
in the {\it undirected} case tends exponentially to zero;
this could be just a finite-size effect since in the other "blocking" cases you
may have only a few unchanged spins.Comment: 14 pages, 8 figures for IJM
The cluster of galaxies Abell 376
We present a dynamical analysis of the galaxy cluster Abell 376 based on a
set of 73 velocities, most of them measured at Pic du Midi and Haute-Provence
observatories and completed with data from the literature. Data on individual
galaxies are presented and the accuracy of the determined velocities is
discussed as well as some properties of the cluster. We obtained an improved
mean redshift value z=0.0478^{+0.005}_{-0.006} and velocity dispersion
sigma=852^{+120}_{-76}km/s. Our analysis indicates that inside a radius of
900h_{70}^{-1}kpc (15 arcmin) the cluster is well relaxed without any
remarkable feature and the X-ray emission traces fairly well the galaxy
distribution. A possible substructure is seen at 20 arcmin from the centre
towards the Southwest direction, but is not confirmed by the velocity field.
This SW clump is, however, kinematically bound to the main structure of Abell
376. A dense condensation of galaxies is detected at 46 arcmin (projected
distance 2.6h_{70}^{-1}Mpc) from the centre towards the Northwest and analysis
of the apparent luminosity distribution of its galaxies suggests that this
clump is part of the large scale structure of Abell 376. X-ray spectroscopic
analysis of ASCA data resulted in a temperature kT = 4.3+/-0.4 keV and metal
abundance Z = 0.32+/-0.08 Z_solar. The velocity dispersion corresponding to
this temperature using the T_X-sigma scaling relation is in agreement with the
measured galaxies velocities.Comment: 11 pages, 10 figures, accepted for publication in A&
Knizhnik-Zamolodchikov-Bernard equations connected with the eight-vertex model
Using quasiclassical limit of Baxter's 8 - vertex R - matrix, an elliptic
generalization of the Knizhnik-Zamolodchikov equation is constructed. Via
Off-Shell Bethe ansatz an integrable representation for this equation is
obtained. It is shown that there exists a gauge transformation connecting this
equation with Knizhnik-Zamolodchikov-Bernard equation for SU(2)-WZNW model on
torus.Comment: 20 pages latex, macro: tcilate
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