Knot invariants in lens spaces

In this survey we summarize results regarding the Kauffman bracket, HOMFLYPT, Kauffman 2-variable and Dubrovnik skein modules, and the Alexander polynomial of links in lens spaces, which we represent as mixed link diagrams. These invariants generalize the corresponding knot polynomials in the classical case. We compare the invariants by means of the ability to distinguish between some difficult cases of knots with certain symmetries

An Evolving Entropy Floor in the Intracluster Gas?

Non-gravitational processes, such as feedback from galaxies and their active nuclei, are believed to have injected excess entropy into the intracluster gas, and therefore to have modified the density profiles in galaxy clusters during their formation. Here we study a simple model for this so-called preheating scenario, and ask (i) whether it can simultaneously explain both global X-ray scaling relations and number counts of galaxy clusters, and (ii) whether the amount of entropy required evolves with redshift. We adopt a baseline entropy profile that fits recent hydrodynamic simulations, modify the hydrostatic equilibrium condition for the gas by including approx. 20% non-thermal pressure support, and add an entropy floor K_0 that is allowed to vary with redshift. We find that the observed luminosity-temperature (L-T) relations of low-redshift (z=0.05) HIFLUGCS clusters and high-redshift (z=0.8) WARPS clusters are best simultaneously reproduced with an evolving entropy floor of K_0(z)=341(1+z)^{-0.83}h^{-1/3} keV cm^2. If we restrict our analysis to the subset of bright (kT > 3 keV) clusters, we find that the evolving entropy floor can mimic a self-similar evolution in the L-T scaling relation. This degeneracy with self-similar evolution is, however, broken when (0.5 < kT < 3 keV) clusters are also included. The approx. 60% entropy increase we find from z=0.8 to z=0.05 is roughly consistent with that expected if the heating is provided by the evolving global quasar population. Using the cosmological parameters from the WMAP 3-year data with sigma_8=0.76, our best-fit model underpredicts the number counts of the X-ray galaxy clusters compared to those derived from the 158 deg^2 ROSAT PSPC survey. Treating sigma_8 as a free parameter, we find a best-fit value of sigma_8=0.80+/- 0.02.Comment: 14 emulateapj pages with 9 figures, submitted to Ap

Three-dimensional Multi-probe Analysis of the Galaxy Cluster A1689

We perform a 3D multi-probe analysis of the rich galaxy cluster A1689 by combining improved weak-lensing data from new BVRi'z' Subaru/Suprime-Cam observations with strong-lensing, X-ray, and Sunyaev-Zel'dovich effect (SZE) data sets. We reconstruct the projected matter distribution from a joint weak-lensing analysis of 2D shear and azimuthally integrated magnification constraints, the combination of which allows us to break the mass-sheet degeneracy. The resulting mass distribution reveals elongation with axis ratio ~0.7 in projection. When assuming a spherical halo, our full weak-lensing analysis yields a projected concentration of $c_{200c}^{2D}=8.9\pm 1.1$ ($c_{vir}^{2D}\sim 11$), consistent with and improved from earlier weak-lensing work. We find excellent consistency between weak and strong lensing in the region of overlap. In a parametric triaxial framework, we constrain the intrinsic structure and geometry of the matter and gas distributions, by combining weak/strong lensing and X-ray/SZE data with minimal geometric assumptions. We show that the data favor a triaxial geometry with minor-major axis ratio 0.39+/-0.15 and major axis closely aligned with the line of sight (22+/-10 deg). We obtain $M_{200c}=(1.2\pm 0.2)\times 10^{15} M_{\odot}/h$ and $c_{200c}=8.4\pm 1.3$, which overlaps with the $>1\sigma$ tail of the predicted distribution. The shape of the gas is rounder than the underlying matter but quite elongated with minor-major axis ratio 0.60+/-0.14. The gas mass fraction within 0.9Mpc is 10^{+3}_{-2}%. The thermal gas pressure contributes to ~60% of the equilibrium pressure, indicating a significant level of non-thermal pressure support. When compared to Planck's hydrostatic mass estimate, our lensing measurements yield a spherical mass ratio of $M_{Planck}/M_{GL}=0.70\pm 0.15$ and $0.58\pm 0.10$ with and without corrections for lensing projection effects, respectively.Comment: Accepted by ApJ. Minor textual changes to improve clarity (e.g., 5. HST STRONG-LENSING ANALYSIS). 26 pages, 17 figures. A version with high-resolution figures is available at http://www.asiaa.sinica.edu.tw/~keiichi/upfiles/Umetsu15/umetsu15.pd

Application of a Self-Similar Pressure Profile to Sunyaev-Zel'dovich Effect Data from Galaxy Clusters

We investigate the utility of a new, self-similar pressure profile for fitting Sunyaev-Zel'dovich (SZ) effect observations of galaxy clusters. Current SZ imaging instruments - such as the Sunyaev-Zel'dovich Array (SZA) - are capable of probing clusters over a large range in physical scale. A model is therefore required that can accurately describe a cluster's pressure profile over a broad range of radii, from the core of the cluster out to a significant fraction of the virial radius. In the analysis presented here, we fit a radial pressure profile derived from simulations and detailed X-ray analysis of relaxed clusters to SZA observations of three clusters with exceptionally high quality X-ray data: A1835, A1914, and CL J1226.9+3332. From the joint analysis of the SZ and X-ray data, we derive physical properties such as gas mass, total mass, gas fraction and the intrinsic, integrated Compton y-parameter. We find that parameters derived from the joint fit to the SZ and X-ray data agree well with a detailed, independent X-ray-only analysis of the same clusters. In particular, we find that, when combined with X-ray imaging data, this new pressure profile yields an independent electron radial temperature profile that is in good agreement with spectroscopic X-ray measurements.Comment: 28 pages, 6 figures, accepted by ApJ for publication (probably April 2009

The Massive and Distant Clusters of WISE Survey: SZ effect Verification with the Atacama Compact Array -- Localization and Cluster Analysis

The Massive and Distant Clusters of WISE Survey (MaDCoWS) provides a catalog of high-redshift ($0.7\lesssim z\lesssim 1.5$) infrared-selected galaxy clusters. However, the verification of the ionized intracluster medium, indicative of a collapsed and nearly virialized system, is made challenging by the high redshifts of the sample members. The main goal of this work is to test the capabilities of the Atacama Compact Array (ACA; also known as the Morita Array) Band 3 observations, centered at about 97.5 GHz, to provide robust validation of cluster detections via the thermal Sunyaev-Zeldovich (SZ) effect. Using a pilot sample that comprises ten MaDCoWS galaxy clusters, accessible to ACA and representative of the median sample richness, we infer the masses of the selected galaxy clusters and respective detection significance by means of a Bayesian analysis of the interferometric data. Our test of the "Verification with the ACA - Localization and Cluster Analysis" (VACA LoCA) program demonstrates that the ACA can robustly confirm the presence of the virialized intracluster medium in galaxy clusters previously identified in full-sky surveys. In particular, we obtain a significant detection of the SZ effect for seven out of the ten VACA LoCA clusters. We note that this result is independent of the assumed pressure profile. However, the limited angular dynamic range of the ACA in Band 3 alone, short observational integration times, and possible contamination from unresolved sources limit the detailed characterization of the cluster properties and the inference of the cluster masses within scales appropriate for the robust calibration of mass-richness scaling relations.Comment: 19 pages (including appendices), 14 figures, and 4 tables; accepted for publication in A&

Galaxy Cluster Scaling Relations between Bolocam Sunyaev-Zel'dovich Effect and Chandra X-ray Measurements

We present scaling relations between the integrated Sunyaev-Zel'dovich Effect (SZE) signal, $Y_{\rm SZ}$, its X-ray analogue, $Y_{\rm X}\equiv M_{\rm gas}T_{\rm X}$, and total mass, $M_{\rm tot}$, for the 45 galaxy clusters in the Bolocam X-ray-SZ (BOXSZ) sample. All parameters are integrated within $r_{2500}$. $Y_{2500}$ values are measured using SZE data collected with Bolocam, operating at 140 GHz at the Caltech Submillimeter Observatory (CSO). The temperature, $T_{\rm X}$, and mass, $M_{\rm gas,2500}$, of the intracluster medium are determined using X-ray data collected with Chandra, and $M_{\rm tot}$ is derived from $M_{\rm gas}$ assuming a constant gas mass fraction. Our analysis accounts for several potential sources of bias, including: selection effects, contamination from radio point sources, and the loss of SZE signal due to noise filtering and beam-smoothing effects. We measure the $Y_{2500}$--$Y_{\rm X}$ scaling to have a power-law index of $0.84\pm0.07$, and a fractional intrinsic scatter in $Y_{2500}$ of $(21\pm7)\%$ at fixed $Y_{\rm X}$, both of which are consistent with previous analyses. We also measure the scaling between $Y_{2500}$ and $M_{2500}$, finding a power-law index of $1.06\pm0.12$ and a fractional intrinsic scatter in $Y_{2500}$ at fixed mass of $(25\pm9)\%$. While recent SZE scaling relations using X-ray mass proxies have found power-law indices consistent with the self-similar prediction of 5/3, our measurement stands apart by differing from the self-similar prediction by approximately 5$\sigma$. Given the good agreement between the measured $Y_{2500}$--$Y_{\rm X}$ scalings, much of this discrepancy appears to be caused by differences in the calibration of the X-ray mass proxies adopted for each particular analysis.Comment: 31 pages, 15 figures, accepted by ApJ 04/11/2015. This version is appreciably different from the original submission: it includes an entirely new appendix, extended discussion, and much of the material has been reorganize

Pancreatic remnant fate

There is eternal discussion on the best surgical method of pancreatoduodenectomy and reconstruction method. Several different methods of pancreatic stump anastomosis exist. The most popular argument taken into account in the discussion is the frequency of early postoperative complications. Relatively fewer papers analyse the late functional outcome of pancreatic surgery and the method of anastomosis employed. Authors presented short series of 12 patients after pancreatic surgery with analysis of pancreatic remnant morphology and function. Pancreatic remnant volume, pancreatic duct distension and stool elastase-1 test were analysed. There was no correlation of pancreatic exo- or endocrine insufficiency with the volume of pancreatic remnant or the kind of surgery or anastomosis performed