Model-Free Multi-Probe Lensing Reconstruction of Cluster Mass Profiles

Lens magnification by galaxy clusters induces characteristic spatial variations in the number counts of background sources, amplifying their observed fluxes and expanding the area of sky, the net effect of which, known as magnification bias, depends on the intrinsic faint-end slope of the source luminosity function. The bias is strongly negative for red galaxies, dominated by the geometric area distortion, whereas it is mildly positive for blue galaxies, enhancing the blue counts toward the cluster center. We generalize the Bayesian approach of Umetsu et al. for reconstructing projected cluster mass profiles, by incorporating multiple populations of background sources for magnification bias measurements and combining them with complementary lens distortion measurements, effectively breaking the mass-sheet degeneracy and improving the statistical precision of cluster mass measurements. The approach can be further extended to include strong-lensing projected mass estimates, thus allowing for non-parametric absolute mass determinations in both the weak and strong regimes. We apply this method to our recent CLASH lensing measurements of MACS J1206.2-0847, and demonstrate how combining multi-probe lensing constraints can improve the reconstruction of cluster mass profiles. This method will also be useful for a stacked lensing analysis, combining all lensing-related effects in the cluster regime, for a definitive determination of the averaged mass profile.Comment: 13 pages, 2 figures; Typo corrections (Appendix A.2.) to match the published version in Ap

Subaru Weak Lensing Study of Seven Merging Clusters: Distributions of Mass and Baryons

We present and compare projected distributions of mass, galaxies, and the intracluster medium (ICM) for a sample of merging clusters of galaxies based on the joint weak-lensing, optical photometric, and X-ray analysis. Our sample comprises seven nearby Abell clusters, for which we have conducted systematic, deep imaging observations with Suprime-Cam on Subaru telescope. Our seven target clusters, representing various merging stages and conditions, allow us to investigate in details the physical interplay between dark matter, ICM, and galaxies associated with cluster formation and evolution. A1750 and A1758 are binary systems consisting of two cluster-sized components, A520, A754, A1758N, A1758S, and A1914 are on-going cluster mergers, and A2034 and A2142 are cold-front clusters. In the binary clusters, the projected mass, optical light, and X-ray distributions are overall similar and regular without significant substructures. On-going and cold-front merging clusters, on the other hand, reveal highly irregular mass distributions. Overall the mass distribution appears to be similar to the galaxy luminosity distribution, whereas their distributions are quite different from the ICM distribution in a various ways. We also measured for individual targets the global cluster parameters such as the cluster mass,the mass-to-light ratio, and the ICM temperature. A comparison of the ICM and virial temperatures of merging clusters from X-ray and weak-lensing analyses, respectively, shows that the ICM temperature of on-going and cold-front clusters is significantly higher than the cluster virial temperature by a factor of $\sim 2$. This temperature excess in the ICM could be explained by the effects of merger boosts.Comment: "High-resolution pictures available at http://www.astr.tohoku.ac.jp/~okabe/files/7merger_color.pdf". The published version is available on-line free of charge by the end of 2008 at http://pasj.asj.or.jp/v60/n2/600223/600223.pd

Clear evasion of the uncertainty relation with very small probability

We entertain the idea that the uncertainty relation is not a principle, but rather it is a consequence of quantum mechanics. The uncertainty relation is then a probabilistic statement and can be clearly evaded in processes which occur with a very small probability in a tiny sector of the phase space. This clear evasion is typically realized when one utilizes indirect measurements, and some examples of the clear evasion appear in the system with entanglement though the entanglement by itself is not essential for the evasion. The standard Kennard's relation and its interpretation remain intact in our analysis. As an explicit example, we show that the clear evasion of the uncertainty relation for coordinate and momentum in the diffraction process discussed by Ballentine is realized in a tiny sector of the phase space with a very small probability. We also examine the uncertainty relation for a two-spin system with the EPR entanglement and show that no clear evasion takes place in this system with the finite discrete degrees of freedom.Comment: 21 pages and 1 figure. The title has been changed. The presentation of the entire manuscript has been modified and expanded. This revised version is to appear in the November issue of Progress of Theoretical Physic

Uncertainty relation and probability: Numerical illustration

The uncertainty relation and the probability interpretation of quantum mechanics are intrinsically connected, as is evidenced by the evaluation of standard deviations. It is thus natural to ask if one can associate a very small uncertainty product of suitably sampled events with a very small probability. We have shown elsewhere that some examples of the evasion of the uncertainty relation noted in the past are in fact understood in this way. We here numerically illustrate that a very small uncertainty product is realized if one performs a suitable sampling of measured data which occur with a very small probability. It is also shown that our analysis is consistent with the Landau-Pollak type uncertainty relation. It is suggested that the present analysis may help reconcile the contradicting views about the "standard quantum limit" in the detection of gravitational waves.Comment: 27 pages, 4 figures. To appear in Progress of Theoretical Physics (kyoto

A Precise Cluster Mass Profile Averaged from the Highest-Quality Lensing Data

We outline our methods for obtaining high precision mass profiles, combining independent weak-lensing distortion, magnification, and strong-lensing measurements. For massive clusters the strong and weak lensing regimes contribute equal logarithmic coverage of the radial profile. The utility of high-quality data is limited by the cosmic noise from large scale structure along the line of sight. This noise is overcome when stacking clusters, as too are the effects of cluster asphericity and substructure, permitting a stringent test of theoretical models. We derive a mean radial mass profile of four similar mass clusters of high-quality HST and Subaru images, in the range R=40kpc/h to 2800kpc/h, where the inner radial boundary is sufficiently large to avoid smoothing from miscentering effects. The stacked mass profile is detected at 58-sigma significance over the entire radial range, with the contribution from the cosmic noise included. We show that the projected mass profile has a continuously steepening gradient out to beyond the virial radius, in remarkably good agreement with the standard Navarro-Frenk-White form predicted for the family of CDM-dominated halos in gravitational equilibrium. The central slope is constrained to lie in the range, -dln{\rho}/dln{r}=0.89^{+0.27}_{-0.39}. The mean concentration is c_{vir}=7.68^{+0.42}_{-0.40} (at a mean virial mass 1.54^{+0.11}_{-0.10}\times 10^{15} M_{sun}/h), which is high for relaxed, high-mass clusters, but consistent with LCDM when a sizable projection bias estimated from N-body simulations is considered. This possible tension will be more definitively explored with new cluster surveys, such as CLASH, LoCuSS, Subaru HSC, and XXM-XXL, to construct the c-M relation over a wider mass range.Comment: Accepted by ApJ, minor text changes (10 pages, 3 figures