The Ks-band Luminosity and Stellar Mass Functions of Galaxies in z~1 Clusters

We present the near-infrared (Ks-band) luminosity function of galaxies in two z~1 cluster candidates, 3C336 and Q1335+28. A third cluster, 3C289, was observed but found to be contaminated by a foreground system. Our wide field imaging data reach to Ks=20.5 (5sigma), corresponding to ~M*+2.7 with respect to the passive evolution. The near-infrared luminosity traces the stellar mass of a galaxy due to its small sensitivity to the recent star formation history. Thus the luminosity function can be transformed to the stellar mass function of galaxies using the $J-K$ colours with only a small correction (factor<2) for the effects of on-going star formation. The derived stellar mass function spans a wide range in mass from ~3 x 10^{11}Msun down to ~6 x 10^{9}Msun (set by the magnitude limit). The form of the mass function is very similar to lower redshift counterparts such as that from 2MASS/LCRS clusters (Balogh et al. 2001) and the z=0.31 clusters (Barger et al. 1998). This indicates little evolution of galaxy masses from z=1 to the present-day. Combined with colour data that suggest star formation is completed early (z>>1) in the cluster core, it seems that the galaxy formation processes (both star formation and mass assembly) are strongly accerelated in dense environments and has been largely completed by z=1. We investigate whether the epoch of mass assembly of massive cluster galaxies is earlier than that predicted by the hierarchical galaxy formation models. These models predict the increase of characteristic mass by more than factor ~3 between z=1 and the present day. This seems incompatible with our data.Comment: 12 pages, including 12 figures, uses mn.sty and epsf.sty. Accepted for publication in MNRAS Main Journa

Homogeneity of Stellar Populations in Early-Type Galaxies with Different X-ray Properties

We have found the stellar populations of early-type galaxies are homogeneous with no significant difference in color or Mg2 index, despite the dichotomy between X-ray extended early-type galaxies and X-ray compact ones. Since the X-ray properties reflect the potential gravitational structure and hence the process of galaxy formation, the homogeneity of the stellar populations implies that the formation of stars in early-type galaxies predat es the epoch when the dichotomy of the potential structure was established.Comment: 6 pages, 5 figures, accepted for publication in Ap

Reconstructing the History of Star Formation in Rich Cluster Cores

We address the current crucial issues on the formation and evolution of cluster galaxies: ie., connection between the Butcher-Oemler effect, assembly of cluster galaxies, truncation of star formation, and the origin of S0 galaxies. We construct the field corrected colour-magnitude (CM) diagrams for 7 CNOC clusters (0.23<z<0.43) and Coma, and illustrate the evolution of the complete cluster population down to the present-day based on the model in which star formation is truncated when the galaxies infall from the surrounding field. We show that the blue galaxies are incorporated into the present-day tight CM relation as they fade and become redder after the truncation, which is possibly responsible for producing faint S0's (>M*+1). Truncation of star formation is, however, found to be relatively milder (with a time scale of 1 Gyr) than suggested by the viorent processes such as ram-pressure stripping and/or mergers/harassment. The BO effect is after all found to be a combination of three effects, namely, increasing field star formation activity, increasing galaxy infall rate, and the truncatin of star formation after the accretion. Our approach naturally leads to the history of galaxy assembly and `global' star foramtion for `cluster' galaxies.Comment: 20 pages, 12 figures, Accepted for Publication in MNRAS (first submitted on 9th Feb 2000

Perturbative analysis of wave interactions in nonlinear systems

This work proposes a new way for handling obstacles to asymptotic integrability in perturbed nonlinear PDEs within the method of Normal Forms - NF - for the case of multi-wave solutions. Instead of including the whole obstacle in the NF, only its resonant part is included, and the remainder is assigned to the homological equation. This leaves the NF intergable and its solutons retain the character of the solutions of the unperturbed equation. We exploit the freedom in the expansion to construct canonical obstacles which are confined to te interaction region of the waves. Fo soliton solutions, e.g., in the KdV equation, the interaction region is a finite domain around the origin; the canonical obstacles then do not generate secular terms in the homological equation. When the interaction region is infifnite, or semi-infinite, e.g., in wave-front solutions of the Burgers equation, the obstacles may contain resonant terms. The obstacles generate waves of a new type, which cannot be written as functionals of the solutions of the NF. When an obstacle contributes a resonant term to the NF, this leads to a non-standard update of th wave velocity.Comment: 13 pages, including 6 figure

Crossing the Phantom Divide

We consider fluid perturbations close to the "phantom divide" characterised by p = -rho and discuss the conditions under which divergencies in the perturbations can be avoided. We find that the behaviour of the perturbations depends crucially on the prescription for the pressure perturbation delta-p. The pressure perturbation is usually defined using the dark energy rest-frame, but we show that this frame becomes unphysical at the divide. If the pressure perturbation is kept finite in any other frame, then the phantom divide can be crossed. Our findings are important for generalised fluid dark energy used in data analysis (since current cosmological data sets indicate that the dark energy is characterised by p ~ -rho so that p < -rho cannot be excluded) as well as for any models crossing the phantom divide, like some modified gravity, coupled dark energy and braneworld models. We also illustrate the results by an explicit calculation for the "Quintom" case with two scalar fields.Comment: 14 pages, 10 figures, v2: updated to agree with published version: more readable figures, slightly expanded discussion on modified gravity models and the interpolation across w=-1, results and conclusions unchange

Thermodynamics of four-dimensional black objects in the warped compactification

We reinvestigate the thermodynamics of black objects (holes and strings) in four-dimensional braneworld models that are originally constructed by Emparan, Horowitz and Myers based on the anti-de Sitter (AdS) C-metric. After proving the uniqueness of slicing the AdS C-metric, we derive thermodynamic quantities of the black objects by means of the Euclidean formulation and find that we have no necessity of requiring any regularization to calculate their classical action. We show that there exist the Bekenstein-Hawking law and the thermodynamic first law. The thermodynamic mass of the localized black hole on a flat brane is negative, and it differs from the one previously derived. We discuss the thermodynamic stabilities and show that the BTZ black string is more stable than the localized black holes in a canonical ensemble, except for an extreme case. We also find a braneworld analogue of the Hawking-Page transition between the BTZ black string and thermal AdS branes. The localized black holes on a de Sitter brane is discussed by considering Nariai instanton, comparing the study of "black cigar" in the five-dimensional braneworld model.Comment: 15 pages, 4 figures, RevTex4, typos fixed, minor correction

Multiple-Time Higher-Order Perturbation Analysis of the Regularized Long-Wavelength Equation

By considering the long-wave limit of the regularized long wave (RLW) equation, we study its multiple-time higher-order evolution equations. As a first result, the equations of the Korteweg-de Vries hierarchy are shown to play a crucial role in providing a secularity-free perturbation theory in the specific case of a solitary-wave solution. Then, as a consequence, we show that the related perturbative series can be summed and gives exactly the solitary-wave solution of the RLW equation. Finally, some comments and considerations are made on the N-soliton solution, as well as on the limitations of applicability of the multiple scale method in obtaining uniform perturbative series.Comment: 15 pages, RevTex, no figures (to appear in Phys. Rev. E

Coarse graining scale and effectiveness of hydrodynamic modeling

Some basic questions about the hydrodynamical approach to relativistic heavy ion collisions are discussed aiming to clarify how far we can go with such an approach to extract useful information on the properties and dynamics of the QCD matter created. We emphasize the importance of the coarse-graining scale required for the hydrodynamic modeling which determines the space-time resolution and the associated limitations of collective flow observables. We show that certain kinds of observables can indicate the degree of inhomogeneity of the initial condition under less stringent condition than the local thermal equilibrium subjected to the coarse-graining scale compatible to the scenario.Comment: 12 pages, 4 figures, Quark Matter 201

Linearizability of the Perturbed Burgers Equation

We show in this letter that the perturbed Burgers equation $u_t = 2uu_x + u_{xx} + \epsilon ( 3 \alpha_1 u^2 u_x + 3\alpha_2 uu_{xx} + 3\alpha_3 u_x^2 + \alpha_4 u_{xxx} )$ is equivalent, through a near-identity transformation and up to order \epsilon, to a linearizable equation if the condition $3\alpha_1 - 3\alpha_3 - 3/2 \alpha_2 + 3/2 \alpha_4 = 0$ is satisfied. In the case this condition is not fulfilled, a normal form for the equation under consideration is given. Then, to illustrate our results, we make a linearizability analysis of the equations governing the dynamics of a one-dimensional gas.Comment: 10 pages, RevTeX, no figure

New X-ray Clusters in the EMSS II: Optical Properties

We present optical images for 9 new clusters of galaxies we have found in a reanalysis of the Einstein IPC images comprising the Extended Medium Sensitivity Survey (EMSS). Based on the presence of a red sequence of galaxies in a color-magnitude (CM) diagram, a redshift is estimated for each cluster. Galaxy overdensities (cluster richnesses) are measured in each field using the B_gc statistic which allows their plausible identification with the X-ray emission. The nature of our X-ray detection algorithm suggests that most of these clusters have low X-ray surface brightness (LSB) compared to the previously known EMSS clusters. We compare the optical and X-ray observations of these clusters with the well-studied Canadian Network for Observational Cosmology (CNOC) subsample of the EMSS, and conclude that the new clusters exhibit a similar range of optical richnesses, X-ray luminosities, and, somewhat surprisingly, galaxy populations as the predominantly rich, relaxed EMSS/CNOC clusters.Comment: Accepted to ApJ, 17 pages, 14 figures, uses emulateapj5.st