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

The entropy of elliptical galaxies in Coma: a clue for a distance indicator

We have fitted the surface brightness of a sample of 79 elliptical galaxies pertaining to the Coma cluster of galaxies using the Sersic profile. This model is defined through three primary parameters: scale length (a), intensity (\Sigma_0), and a shape parameter (\nu); physical and astrophysical quantities may be computed from these parameters. We show that correlations are stronger among primary parameters than the classical astrophysical ones. In particular, the galaxies follow a high correlation in \nu and a parameters. We show that the \nu and a correlation satisfies a constant specific entropy condition. We propose to use this entropy relation as distance indicator for clusters.Comment: 5 pages, 3 figures, submitted to MNRAS Letter

The rich cluster of galaxies ABCG 85. II. X-ray analysis using the ROSAT HRI

We present a new X-ray analysis mainly based on ROSAT HRI data. The HRI spatial resolution combined with an improved wavelet analysis method and with complementary radio and optical data provides new results compared to a previous paper based on ROSAT PSPC data (Pislar et al. 1997). We use also redshift data in order to identify galaxies dynamically belonging to the main body of the cluster and/or to superimposed substructures. Various kinds of emission are superimposed on a mean thermal X-ray emission due to the intra-cluster gas: a) an X-ray flux excess in the centre; b) a south blob, partially generated by individual galaxies. The mean velocity and velocity dispersion of the galaxies located in this region are the same as those of the cluster as a whole: it therefore does not seem to be a bound subgroup; c) West emission due to a foreground group with self-emission from a Seyfert galaxy located at the north-west; d) emission in the south-west due to inverse Compton emission associated to a very steep radio source (the remnant of an active galactic nucleus). We have examined the possibility for the central peak to be an "unusual" galaxy, as assumed for the central galaxy of J2310-43 (Tananbaum et al. 1997). We conclude on the existence of a cooling flow region, in which the presence of at least three small features certainly related to cooler blobs is revealed by the wavelet analysis. We have performed a pixel-to-pixel modelling of the double X-ray emission. The large scale emission component is comparable to those derived from by the PSPC data and the small scale one is interpreted as a cooling-flow. A multiphase gas model analysis leads to a mass deposit of 50-150 M_\odot/yr.Comment: 11 pages, 6 figures, 3 tables, LaTeX Accepted for publication in Astronomy & Astrophysics main journa

The rich cluster of galaxies ABCG 85.I. X-ray analysis

We present an X-ray analysis of the rich cluster ABCG 85 based on ROSAT PSPC data. By applying an improved wavelet analysis, we show that our view of this cluster is notably changed from what was previously believed (a main region and a south blob). The main emission comes from the central part of the main body of the cluster on which is superimposed that of a foreground group of galaxies. The foreground group and the main cluster are separated (if redshifts are cosmological) by 46 1/h_50 Mpc. The southern blob is clearly not a group: it is resolved into X-ray emitting galaxies (in particular the second more luminous galaxy of the main cluster). Several X-ray features are identified with bright galaxies. We performed a spectral analysis and derived the temperature (T), metallicity (Z) and hydrogen column density NH. The global quantities are: T=4keV (in agreement with the velocity dispersion of 760km/s) and $Z=0.2Z_\odot$. We cannot derive accurate gradients for these quantities with our data, but there is strong evidence that the temperature is lower ($\sim 2.8 keV$) and the metallicity much higher (Z $\sim 0.8 Z_\odot$) in the very centre (within about 50 1/h_50 kpc). We present a pixel by pixel method to model the physical properties of the X-ray gas and derive its density distribution. We apply classical methods to estimate the dynamical, gas and stellar masses, as well as the cooling time and cooling flow characteristics. At the limiting radius of the image (1.4 1/h_50 Mpc), we find $M_{\rm Dyn}\sim (2.1-2.9)10^{14} 1/h_50 M$_{\odot}$,$M_{gas}/M_{Dyn}\sim 0.18 h_{50}^{-1.5}$. The stellar mass is$6.7\ 10^{12}M_{\odot}$, giving a mass to light ratio of$M/L_{V}\sim 300$. The cooling time is estimated for different models, leading to a cooling radius of 30-80 kpc depending on theComment: 14 pages incl 16 postscript figures available, 4 tables, corrected stellar mass. Accepted for publication in Astronomy & Astrophysic

Gravo-thermal properties and formation of elliptical galaxies

We have analyzed a sample of galaxies belonging to three clusters: Coma, Abell 85, and Abell 496 (real galaxies) and a sample of simulated elliptical galaxies formed in a hierarchical merging scheme (virtual galaxies). We use the Sersic law to describe their light profile. The specific entropy (Boltzmann-Gibbs definition) is then calculated supposing that the galaxies behave as spherical, isotropic, one-component systems. We find that, to a good approximation (about 10%), both real and virtual galaxies have an almost unique specific entropy. Within this approximation the galaxies are distributed in a thin plane in the space defined by the three Sersic law parameters, which we call the Entropic Plane. A further analysis shows that both real and virtual galaxies are in fact located on a thin line, therefore indicating the existence of another - and yet unknown - physical property, besides the uniqueness of the specific entropy. A more careful examination of the virtual galaxies sample indicates a very small increase of their specific entropy with merging generation. In a hierarchical scenario, this implies a correlation between the specific entropy and the total mass, which is indeed seen in our data. The scatter and tilt of the Entropic Line, defined by Lima Neto et al. (1999a), are reduced when this correlation is taken into account. Although one cannot distinguish between various generations for real galaxies, the distribution of their specific entropy is similar to that in the virtual sample, suggesting that hierarchical merging processes could be an important mechanism in the building of elliptical galaxies

Dynamic Phase Transitions in Cell Spreading

We monitored isotropic spreading of mouse embryonic fibroblasts on fibronectin-coated substrates. Cell adhesion area versus time was measured via total internal reflection fluorescence microscopy. Spreading proceeds in well-defined phases. We found a power-law area growth with distinct exponents a_i in three sequential phases, which we denote basal (a_1=0.4+-0.2), continous (a_2=1.6+-0.9) and contractile (a_3=0.3+-0.2) spreading. High resolution differential interference contrast microscopy was used to characterize local membrane dynamics at the spreading front. Fourier power spectra of membrane velocity reveal the sudden development of periodic membrane retractions at the transition from continous to contractile spreading. We propose that the classification of cell spreading into phases with distinct functional characteristics and protein activity patterns serves as a paradigm for a general program of a phase classification of cellular phenotype. Biological variability is drastically reduced when only the corresponding phases are used for comparison across species/different cell lines.Comment: 4 pages, 5 figure

Model of Dark Matter and Dark Energy Based on Gravitational Polarization

A model of dark matter and dark energy based on the concept of gravitational polarization is investigated. We propose an action in standard general relativity for describing, at some effective or phenomenological level, the dynamics of a dipolar medium, i.e. one endowed with a dipole moment vector, and polarizable in a gravitational field. Using first-order cosmological perturbations, we show that the dipolar fluid is undistinguishable from standard dark energy (a cosmological constant Lambda) plus standard dark matter (a pressureless perfect fluid), and therefore benefits from the successes of the Lambda-CDM (Lambda-cold dark matter) scenario at cosmological scales. Invoking an argument of "weak clusterisation" of the mass distribution of dipole moments, we find that the dipolar dark matter reproduces the phenomenology of the modified Newtonian dynamics (MOND) at galactic scales. The dipolar medium action naturally contains a cosmological constant, and we show that if the model is to come from some fundamental underlying physics, the cosmological constant Lambda should be of the order of a0^2/c^4, where a0 denotes the MOND constant acceleration scale, in good agreement with observations.Comment: 38 pages, 4 figures; to appear in Phys. Rev.

Energy, entropy and mass scaling relations for elliptical galaxies. Towards a physical understanding of their photometric properties

In the present paper, we show that elliptical galaxies (Es) obey a scaling relation between potential energy and mass. Since they are relaxed systems in a post violent-relaxation stage, they are quasi-equilibrium gravitational systems and therefore they also have a quasi-constant specific entropy. Assuming that light traces mass, these two laws imply that in the space defined by the three S\'ersic law parameters (intensity Sigma_0, scale a and shape nu), elliptical galaxies are distributed on two intersecting 2-manifolds: the Entropic Surface and the Energy-Mass Surface. Using a sample of 132 galaxies belonging to three nearby clusters, we have verified that ellipticals indeed follow these laws. This also implies that they are distributed along the intersection line (the Energy-Entropy line), thus they constitute a one-parameter family. These two physical laws (separately or combined), allow to find the theoretical origin of several observed photometrical relations, such as the correlation between absolute magnitude and effective surface brightness, and the fact that ellipticals are located on a surface in the [log R_eff, -2.5 log Sigma_0, log nu] space. The fact that elliptical galaxies are a one-parameter family has important implications for cosmology and galaxy formation and evolution models. Moreover, the Energy-Entropy line could be used as a distance indicator.Comment: Revised version (considering non constant M/L), accepted by A&A on 10/03/0