The most massive galaxies in clusters are already fully grown at z∼0.5z \sim 0.5

By constructing scaling relations for galaxies in the massive cluster MACSJ0717.5 at $z=0.545$ and comparing with those of Coma, we model the luminosity evolution of the stellar populations and the structural evolution of the galaxies. We calculate magnitudes, surface brightnesses and effective radii using HST/ACS images and velocity dispersions using Gemini/GMOS spectra, and present a catalogue of our measurements for 17 galaxies. We also generate photometric catalogues for $\sim 3000$ galaxies from the HST imaging. With these, we construct the colour-magnitude relation, the fundamental plane, the mass-to-light versus mass relation, the mass-size relation and the mass-velocity dispersion relation for both clusters. We present a new, coherent way of modelling these scaling relations simultaneously using a simple physical model in order to infer the evolution in luminosity, size and velocity dispersion as a function of redshift, and show that the data can be fully accounted for with this model. We find that (a) the evolution in size and velocity dispersion undergone by these galaxies between $z \sim 0.5$ and $z \sim 0$ is mild, with $R_e(z) \sim (1+z)^{-0.40\pm0.32}$ and $\sigma(z) \sim (1+z)^{0.09 \pm 0.27}$, and (b) the stellar populations are old, $\sim 10$ Gyr, with a $\sim 3$ Gyr dispersion in age, and are consistent with evolving purely passively since $z \sim 0.5$ with $\Delta \log M/L_B = -0.55_{-0.07}^{+0.15} z$. The implication is that these galaxies formed their stars early and subsequently grew dissipationlessly so as to have their mass already in place by $z \sim 0.5$, and suggests a dominant role for dry mergers, which may have accelerated the growth in these high-density cluster environments.Comment: 20 pages; accepted for publication in MNRA

Anomalous Rotational Relaxation: A Fractional Fokker-Planck Equation Approach

In this study we obtained analytically relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that rotational relaxation function has a fractional form for complex disordered systems, which indicates relaxation has non-exponential character obeys to Kohlrausch-William-Watts law, following the Mittag-Leffler decay.Comment: Revtex4, 9 pages. Paper was revised. References adde

Non-Markovian Levy diffusion in nonhomogeneous media

We study the diffusion equation with a position-dependent, power-law diffusion coefficient. The equation possesses the Riesz-Weyl fractional operator and includes a memory kernel. It is solved in the diffusion limit of small wave numbers. Two kernels are considered in detail: the exponential kernel, for which the problem resolves itself to the telegrapher's equation, and the power-law one. The resulting distributions have the form of the L\'evy process for any kernel. The renormalized fractional moment is introduced to compare different cases with respect to the diffusion properties of the system.Comment: 7 pages, 2 figure

Using the fractional interaction law to model the impact dynamics in arbitrary form of multiparticle collisions

Using the molecular dynamics method, we examine a discrete deterministic model for the motion of spherical particles in three-dimensional space. The model takes into account multiparticle collisions in arbitrary forms. Using fractional calculus we proposed an expression for the repulsive force, which is the so called fractional interaction law. We then illustrate and discuss how to control (correlate) the energy dissipation and the collisional time for an individual article within multiparticle collisions. In the multiparticle collisions we included the friction mechanism needed for the transition from coupled torsion-sliding friction through rolling friction to static friction. Analysing simple simulations we found that in the strong repulsive state binary collisions dominate. However, within multiparticle collisions weak repulsion is observed to be much stronger. The presented numerical results can be used to realistically model the impact dynamics of an individual particle in a group of colliding particles.Comment: 17 pages, 8 figures, 1 table; In review process of Physical Review

Measuring subdiffusion parameters

We propose a method to extract from experimental data the subdiffusion parameter $\alpha$ and subdiffusion coefficient $D_\alpha$ which are defined by means of the relation $=2D_\alpha/\Gamma(1+\alpha) t^\alpha$ where $$ denotes a mean square displacement of a random walker starting from $x=0$ at the initial time $t=0$. The method exploits a membrane system where a substance of interest is transported in a solvent from one vessel to another across a thin membrane which plays here only an auxiliary role. Using such a system, we experimentally study a diffusion of glucose and sucrose in a gel solvent. We find a fully analytic solution of the fractional subdiffusion equation with the initial and boundary conditions representing the system under study. Confronting the experimental data with the derived formulas, we show a subdiffusive character of the sugar transport in gel solvent. We precisely determine the parameter $\alpha$, which is smaller than 1, and the subdiffusion coefficient $D_\alpha$.Comment: 17 pages, 9 figures, revised, to appear in Phys. Rev.

The W51 Giant Molecular Cloud

We present 45"-47" angular resolution maps at 50" sampling of the 12CO and 13CO J=1-0 emission toward a 1.39 deg x 1.33 deg region in the W51 HII region complex. These data permit the spatial and kinematic separation of several spectral features observed along the line of sight to W51, and establish the presence of a massive (1.2 x 10^6 Mo), large (83 pc x 114 pc) giant molecular cloud (GMC), defined as the W51 GMC, centered at (l,b,V) = (49.5 deg, -0.2 deg, 61 km/s). A second massive (1.9 x 10^5 Mo), elongated (136 pc x 22 pc) molecular cloud is found at velocities of about 68 km/s along the southern edge of the W51 GMC. Of the five radio continuum sources that classically define the W51 region, the brightest source at lambda 6cm (G49.5-0.4) is spatially and kinematically coincident with the W51 GMC and three (G48.9-0.3, G49.1-0.4, and G49.2-0.4) are associated with the 68 km/s cloud. Published absorption line spectra indicate that the fifth prominent continuum source (G49.4-0.3) is located behind the W51 molecular cloud. The W51 GMC is among the upper 1% of clouds in the Galactic disk by size and the upper 5-10% by mass. While the W51 GMC is larger and more massive than any nearby molecular cloud, the average H2 column density is not unusual given its size and the mean H2 volume density is comparable to that in nearby clouds. The W51 GMC is also similar to other clouds in that most of the molecular mass is contained in a diffuse envelope that is not currently forming massive stars. We speculate that much of the massive star formation activity in this region has resulted from a collision between the 68 km/s cloud and the W51 GMC.Comment: Accepted for publication by the Astronomical Journal. 21 pages, plus 7 figures and 1 tabl