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

Mass formula for T=0 and T=1 ground states of N=Z nuclei

An algebraic model is developed to calculate the T=0 and T=1 ground state binding energies for N=Z nuclei. The method is tested in the sd shell and is then extended to 28-50 shell which is currently the object of many experimental studies.Comment: 5 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

An XMM-Newton view of the cluster of galaxies Abell 85

We have observed the cluster of galaxies Abell 85 with XMM-Newton. These data have allowed us to confirm in a previous paper the existence of the extended 4 Mpc filament detected by the ROSAT PSPC in the neighbourhood of this cluster, and to determine an X-ray temperature of about about 2 keV. We now present a thorough analysis of the properties of the X-ray gas in the cluster itself, including temperature and metallicity maps for the entire cluster. These results show that Abell 85 had intense merging activity in the past and is not fully relaxed, even in the central region. We have also determined the individual abundances for some iron-group metals and alpha-elements in various regions; the ratios of these metallicities to the iron abundance show that both supernova types Ia and II must be involved in the intra-cluster gas enrichment. Spectral analysis of the central region suggests a different redshift of the X-ray emitting gas compared to the mean cluster velocity derived from galaxy member redshifts. We discuss the implications of the difference between the cD galaxy redshift, the mean galaxy redshift and the hot gas redshift, as well as the possibility of several groups being accreted on to Abell 85. Finally, we obtain the dynamical mass profile and baryon fraction taking into account the new determined temperature profile. The dynamical mass in Abell 85 has a steep density profile, similar to the ones found in N-body simulations.Comment: Accepted for publication in Astronomy & Astrophysic

New observational constraints on interacting dark energy using galaxy clusters virial equilibrium states

As the dark sector remains unknown in composition and interaction between dark energy and dark matter stand out as natural, observations of galaxy clusters out of equilibrium abound, opening a promising window on these questions. We continue here the exploration of dark sector interaction detection via clusters virial equilibrium state for all clusters configurations. The dynamics of clusters is evaluated with the Layzer-Irvine equation, a simple model of an interacting dark sector and some simplifying assumptions to obtain the time-dependent part of the virial dynamics. The clusters' data are concentrated in optical weak lensing and X-ray observations that evaluate, respectively, the clusters' mass profiles and temperatures. The global inconsistency of available X-ray data led us to constitute `gold' cluster samples. Through a Bayesian analysis, they are processed to obtain consistent interaction detected up to 3$\sigma$, in compounded interaction strength for 11 clusters at $-0.027 \pm 0.009$ that translate in compounded universal equilibrium virial ratio of $-0.61^{+0.04}_{-0.03}$. The level of detection and inconsistency of X-ray data call for caution, although future instruments promise a clearer detection soon.Comment: 8 page

The Effect of Recency to Human Mobility

In recent years, we have seen scientists attempt to model and explain human dynamics and, in particular, human movement. Many aspects of our complex life are affected by human movements such as disease spread and epidemics modeling, city planning, wireless network development, and disaster relief, to name a few. Given the myriad of applications it is clear that a complete understanding of how people move in space can lead to huge benefits to our society. In most of the recent works, scientists have focused on the idea that people movements are biased towards frequently-visited locations. According to them, human movement is based on an exploration/exploitation dichotomy in which individuals choose new locations (exploration) or return to frequently-visited locations (exploitation). In this work, we focus on the concept of recency. We propose a model in which exploitation in human movement also considers recently-visited locations and not solely frequently-visited locations. We test our hypothesis against different empirical data of human mobility and show that our proposed model is able to better explain the human trajectories in these datasets

Simulations of the merging galaxy cluster Abell 3376

Observed galaxy clusters often exhibit X-ray morphologies suggestive of recent interaction with an infalling subcluster. Abell 3376 is a nearby (z=0.046) massive galaxy cluster whose bullet-shaped X-ray emission indicates that it may have undergone a recent collision. It displays a pair of Mpc-scale radio relics and its brightest cluster galaxy is located 970 h_70^-1 kpc away from the peak of X-ray emission, where the second brightest galaxy lies. We attempt to recover the dynamical history of Abell 3376. We perform a set of N-body adiabatic hydrodynamical simulations using the SPH code Gadget-2. These simulations of binary cluster collisions are aimed at exploring the parameter space of possible initial configurations. By attempting to match X-ray morphology, temperature, virial mass and X-ray luminosity, we set approximate constraints on some merger parameters. Our best models suggest a collision of clusters with mass ratio in the range 1/6-1/8, and having a subcluster with central gas density four times higher than that of the major cluster. Models with small impact parameter (b<150 kpc), if any, are preferred. We estimate that Abell 3376 is observed approximately 0.5 Gyr after core passage, and that the collision axis is inclined by i~40 degrees with respect to the plane of the sky. The infalling subcluster drives a supersonic shock wave that propagates at almost 2600 km/s, implying a Mach number as high as M~4; but we show how it would have been underestimated as M~3 due to projection effects.Comment: 12 pages, 7 figures, accepted for publication in MNRA