Mapping Cluster Mass Distributions via Gravitational Lensing of Background Galaxies

We present a new method for measuring the projected mass distributions of galaxy clusters. The gravitational amplification is measured by comparing the joint distribution in redshift and magnitude of galaxies behind the cluster with that of field galaxies. We show that the total amplification is directly related to the surface mass density in the weak field limit, and so it is possible to map the mass distribution of the cluster. The method is shown to be limited by discreteness noise and galaxy clustering behind the lens. Galaxy clustering sets a lower limit to the error along the redshift direction, but a clustering independent lensing signature may be obtained from the magnitude distribution at fixed redshift. Statistical techniques are developed for estimating the surface mass density of the cluster. We extend these methods to account for any obscuration by cluster halo dust, which may be mapped independently of the dark matter. We apply the method to a series of numerical simulations and show the feasibility of the approach. We consider approximate redshift information, and show how the mass estimates are degraded.Comment: ApJ in press. 23 pages of LaTeX plus figs. Text & figs available by anonymous ftp from resun03.roe.ac.uk in directory /pub/jap/lens (you need btp.tex and apj.sty

Transcendental numbers and the topology of three-loop bubbles

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.Comment: 4 pages in REVTeX, 1 PostScript figure included, submitted to Phys. Rev. Let

Non-parametric mass reconstruction of A1689 from strong lensing data with SLAP

We present the mass distribution in the central area of the cluster A1689 by fitting over 100 multiply lensed images with the non-parametric Strong Lensing Analysis Package (SLAP, Diego et al. 2004). The surface mass distribution is obtained in a robust way finding a total mass of 0.25E15 M_sun/h within a 70'' circle radius from the central peak. Our reconstructed density profile fits well an NFW profile with small perturbations due to substructure and is compatible with the more model dependent analysis of Broadhurst et al. (2004a) based on the same data. Our estimated mass does not rely on any prior information about the distribution of dark matter in the cluster. The peak of the mass distribution falls very close to the central cD and there is substructure near the center suggesting that the cluster is not fully relaxed. We also examine the effect on the recovered mass when we include the uncertainties in the redshift of the sources and in the original shape of the sources. Using simulations designed to mimic the data, we identify some biases in our reconstructed mass distribution. We find that the recovered mass is biased toward lower masses beyond 1 arcmin (150 kpc) from the central cD and that in the very center we may be affected by degeneracy problems. On the other hand, we confirm that the reconstructed mass between 25'' and 70'' is a robust, unbiased estimate of the true mass distribution and is compatible with an NFW profile.Comment: 11 pages, 12 figures. MNRAS submitted. A full resolution of the paper can be found in http://darwin.physics.upenn.edu/SLAP

Connections between Deep-Inelastic and Annihilation Processes at Next-to-Next-to-Leading Order and Beyond

We have discovered 7 intimate connections between the published results for the radiative corrections, \Ck, to the Gross--Llewellyn Smith (GLS) sum rule, in deep-inelastic lepton scattering, and the radiative corrections, \Cr, to the Adler function of the flavour-singlet vector current, in \ee annihilation. These include a surprising relation between the scheme-independent single-electron-loop contributions to the 4-loop QED $\beta$\/-function and the zero-fermion-loop abelian terms in the 3-loop GLS sum rule. The combined effect of all 7 relations is to give the factorization of the 2-loop $\beta$\/-function in \Ds\equiv\Ck\Cr-1=\frac{\Be}{\Aq}\left\{S_1\Cf\Aq+\left[S_2\Tf\Nf +\Sa\Ca+\Sf\Cf\right]\Cf\Aq^2\right\}+O(\Aq^4)\,, where \Aq=\al(\mu^2=Q^2)/4\pi is the \MS coupling of an arbitrary colour gauge theory, and S_1=-\Df{21}{2}+12\Ze3\,;\quad S_2=\Df{326}{3}-\Df{304}{3}\Ze3\,;\quad \Sa=-\Df{629}{2}+\Df{884}{3}\Ze3\,;\quad \Sf=\Df{397}{6}+136\Ze3-240\Ze5 specify the sole content of \Ck that is not already encoded in \Cr and \Be=Q^2\rd\Aq/\rd Q^2 at O(\Aq^3). The same result is obtained by combining the radiative corrections to Bjorken's polarized sum rule with those for the Adler function of the non-singlet axial current. We suggest possible origins of $\beta$ in the `Crewther discrepancy', \Ds, and determine \Ds/(\Be/\Aq), to all orders in \Nf\Aq, in the large-\Nf limit, obtaining the {\em entire\/} series of coefficients of which $S_1$ and $S_2$ are merely the first two members.Comment: 11 pages, LATEX, preprint INR-820/93, OUT-4102-45; In memoriam Sergei Grogorievich Corishny, 1958-198

"Sixth root of unity" and Feynman diagrams: hypergeometric function approach point of view

We briefly discuss the transcendental constants generated through the epsilon-expansion of generalized hypergeometric functions and their interrelation with the "sixth root of unity."Comment: 6 pages, presented at "Loops and Legs in Quantum Field Theory 2010", Woerlitz, Germany, April 2010; v2: Eq.(2) is improve

Using the Hopf Algebra Structure of QFT in Calculations

We employ the recently discovered Hopf algebra structure underlying perturbative Quantum Field Theory to derive iterated integral representations for Feynman diagrams. We give two applications: to massless Yukawa theory and quantum electrodynamics in four dimensions.Comment: 28 p, Revtex, epsf for figures, minor changes, to appear in Phys.Rev.

Three-dimensional multi-probe analysis of the galaxy cluster A1689

arXiv:1503.01482v2.-- et al.We perform a three-dimensional multi-probe analysis of the rich galaxy cluster A1689, one of the most powerful known lenses on the sky, by combining improved weak-lensing data from new wide-field ${{BVR}}_{{\rm C}}i\prime z\prime$ 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 two-dimensional 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 an axis ratio of ~0.7 in projection, aligned well with the distributions of cluster galaxies and intracluster gas. When assuming a spherical halo, our full weak-lensing analysis yields a projected halo concentration of ${c}_{200{\rm c}}^{2{\rm D}}=8.9\pm 1.1$ (${c}_{\mathrm{vir}}^{2{\rm D}}\sim 11$), consistent with and improved from earlier weak-lensing work. We find excellent consistency between independent 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°). We obtain a halo mass ${M}_{200{\rm c}}=(1.2\pm 0.2)\times {10}^{15}\;{M}_{\odot }\;{h}^{-1}$ and a halo concentration ${c}_{200{\rm c}}=8.4\pm 1.3$, which overlaps with the $\gtrsim 1\sigma$ 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 0.9 Mpc is ${10}_{-2}^{+3}\%$, a typical value for high-mass clusters. 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 MPlanck/MGL = 0.70 ± 0.15 and 0.58 ± 0.10 with and without corrections for lensing projection effects, respectively.The work is partially supported by the Ministry of Science and Technology of Taiwan under the grant MOST 103-2112-M-001-030-MY3. M. S. acknowledges financial contributions from contracts ASI/INAF I/023/12/0, by the PRIN MIUR 2010–2011 “The dark universe and the cosmic evolution of baryons: from current surveys to Euclid” and by the PRIN INAF 2012 “The universe in the box: multiscale simulations of cosmic structure.” M. N. acknowledges financial support from PRIN INAF 2014. J. M. D. acknowledges support of the consolider project CSD2010-00064 and AYA2012-39475-C02-01 funded by the Ministerio de Economia y Competitividad. N. O. is supported by a Grant-in-Aid from the Ministry of Education, Culture, Sports, Science, and Technology of Japan (26800097). This work was partially supported by “World Premier International Research Center Initiative (WPI Initiative)” and the Funds for the Development of Human Resources in Science and Technology under MEXT, Japan.Peer Reviewe

Free Form Lensing Implications for the Collision of Dark Matter and Gas in the Frontier Fields Cluster MACSJ0416.1-2403

We present a free form mass reconstruction of the massive lensing cluster MACSJ0416.1-2403 using the latest Hubble Frontier Fields data. Our model independent method finds that the extended lensing pattern is generated by two elongated, closely projected clusters of similar mass. Our lens model identifies new lensed images with which we improve the accuracy of the dark matter distribution. We find that the bimodal mass distribution is nearly coincident with the bimodal X-ray emission, but with the two dark matter peaks lying closer together than the centroids of the X-ray emisison. We show this can be achieved if the collision has occurred close to the plane and such that the cores are deflected around each other. The projected mass profiles of both clusters are well constrained because of the many interior lensed images, leading to surprisingly flat mass profiles of both components in the region 15-100 kpc. We discuss the extent to which this may be generated by tidal forces in our dynamical model which are large during an encounter of this type as the cores "graze" each other. The relative velocity between the two cores is estimated to be about 1200 km/s and mostly along the line of sight so that our model is consistent with the relative redshift difference between the two cD galaxies (dz = 0.04).Comment: 22 pages, 18 figures, 2 table

The nature of power corrections in large β0\beta_0 approximation

We investigate the nature of power corrections and infrared renormalon singularities in large $\beta_0$ approximation. We argue that the power correction associated with a renormalon pole singularity should appear at O(1), in contrast to the renormalon ambiguity appearing at $O(1/\beta_0)$, and give an explanation why the leading order renormalon singularities are generically poles.Comment: 6 page