Mass along the Line of Sight to the Gravitational Lens B1608+656: Galaxy Groups and Implications for H_0

We report the discovery of four groups of galaxies along the line of sight to the B1608+656 gravitational lens system. One group is at the redshift of the primary lensing galaxy (z = 0.631) and appears to have a low mass, with eight spectroscopically confirmed members and an estimated velocity dispersion of 150 ± 60 km s^(-1). The three other groups are in the foreground of the lens. These groups contain ~10 confirmed members each and are located at redshifts of 0.265, 0.426, and 0.52. Two of the three additional groups are centered roughly on the lens system, while the third is centered ~1' south of the lens. We investigate the effect of each of the four groups on the gravitational lensing potential of the B1608+656 system, with a particular focus on the implications for the value of H_0 derived from this system. We find that each group provides an external convergence of ~0.005-0.060, depending on the assumptions made in the calculation. For the B1608+656 system, the stellar velocity dispersion of the lensing galaxy has been measured, thus breaking the mass sheet degeneracy due to the group that is physically associated with the lens. The effect of the other groups along the line of sight can be folded into the overall uncertainties due to large-scale structure (LSS) along the line of sight. Because B1608+656 appears to lie along an overdense line of sight, the LSS will cause the measurement of H_0 to be biased high for this system. This effect could be 5% or greater

Keck spectroscopy of CLASS gravitational lenses

We present the optical spectra of four newly discovered gravitational lenses from the Cosmic Lens All-Sky Survey (CLASS). These observations were carried out using the Low Resolution Imaging Spectrograph on the W. M. Keck-I Telescope as part of a program to study galaxy-scale gravitational lenses. From our spectra we found the redshift of the background source in CLASS B0128+437 (z_s=3.1240+-0.0042) and the lensing galaxy redshifts in CLASS B0445+123 (z_l=0.5583+-0.0003) and CLASS B0850+054 (z_l=0.5883+-0.0006). Intriguingly, we also discovered that CLASS B0631+519 may have two lensing galaxies (z_l,1=0.0896+-0.0001, z_l,2=0.6196+-0.0004). We also found a single unidentified emission line from the lensing galaxy in CLASS B0128+437 and the lensed source in CLASS B0850+054. We find the lensing galaxies in CLASS B0445+123 and CLASS B0631+519 (l,2) to be early-type galaxies with Einstein Radii of 2.8-3.0 h^{-1} kpc. The deflector in CLASS B0850+054 is a late-type galaxy with an Einstein Radius of 1.6 h^{-1} kpc.Comment: 9 pages, 5 figures, accepted for publication in MNRA

Simulation of a semiflexible polymer in a narrow cylindrical pore

The probability that a randomly accelerated particle in two dimensions has not yet left a simply connected domain ${\cal A}$ after a time $t$ decays as $e^{-E_0t}$ for long times. The same quantity $E_0$ also determines the confinement free energy per unit length $\Delta f=k_BT\thinspace E_0$ of a semiflexible polymer in a narrow cylindrical pore with cross section ${\cal A}$. From simulations of a randomly accelerated particle we estimate the universal amplitude of $\Delta f$ for both circular and rectangular cross sections.Comment: 10 pages, 2 eps figure

Upon the existence of short-time approximations of any polynomial order for the computation of density matrices by path integral methods

In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and bounded from below potentials. While for Theorem 2, which is ``experimental'', I only provide a ``physicist's'' proof, I believe the present development is mathematically sound. As a verification, I explicitly construct two short-time approximations to the density matrix having convergence orders 3 and 4, respectively. Furthermore, in the Appendix, I derive the convergence constant for the trapezoidal Trotter path integral technique. The convergence orders and constants are then verified by numerical simulations. While the two short-time approximations constructed are of sure interest to physicists and chemists involved in Monte Carlo path integral simulations, the present article is also aimed at the mathematical community, who might find the results interesting and worth exploring. I conclude the paper by discussing the implications of the present findings with respect to the solvability of the dynamical sign problem appearing in real-time Feynman path integral simulations.Comment: 19 pages, 4 figures; the discrete short-time approximations are now treated as independent from their continuous version; new examples of discrete short-time approximations of order three and four are given; a new appendix containing a short review on Brownian motion has been added; also, some additional explanations are provided here and there; this is the last version; to appear in Phys. Rev.

Supersymmetry of Noncompact MQCD-like Membrane Instantons and Heat Kernel Asymptotics

We perform a heat kernel asymptotics analysis of the nonperturbative superpotential obtained from wrapping of an M2-brane around a supersymmetric noncompact three-fold embedded in a (noncompact) G_2-manifold as obtained in [1], the three-fold being the one relevant to domain walls in Witten's MQCD [2], in the limit of small "zeta", a complex constant that appears in the Riemann surfaces relevant to defining the boundary conditions for the domain wall in MQCD. The MQCD-like configuration is interpretable, for small but non-zero zeta as a noncompact/"large" open membrane instanton, and for vanishing zeta, as the type IIA D0-brane (for vanishing M-theory cicle radius). We find that the eta-function Seeley de-Witt coefficients vanish, and we get a perfect match between the zeta-function Seeley de-Witt coefficients (up to terms quadratic in zeta) between the Dirac-type operator and one of the two Laplace-type operators figuring in the superpotential. This is an extremely strong signature of residual supersymmetry for the nonperturbative configurations in M-theory considered in this work.Comment: 21 pages, LaTeX; v3: several clarifying remarks added, to appear in JHE

Gauge Fixing and BFV Quantization

Nonsingularity conditions are established for the BFV gauge-fixing fermion which are sufficient for it to lead to the correct path integral for a theory with constraints canonically quantized in the BFV approach. The conditions ensure that anticommutator of this fermion with the BRST charge regularises the path integral by regularising the trace over non-physical states in each ghost sector. The results are applied to the quantization of a system which has a Gribov problem, using a non-standard form of the gauge-fixing fermion.Comment: 14 page

PS J1721+8842: A gravitationally lensed dual AGN system at redshift 2.37 with two radio components

Dual-Active Galactic Nuclei (AGN) are a natural consequence of the hierarchical structure formation scenario, and can provide an important test of various models for black hole growth. However, due to their rarity and difficulty to find at high redshift, very few confirmed dual-AGN are known at the epoch where galaxy formation peaks. Here we report the discovery of a gravitationally lensed dual-AGN system at redshift 2.37 comprising two optical/IR quasars separated by 6.5 ± 0.6 kpc, and a third compact (Reff = 0.45 ± 0.02 kpc) red galaxy that is offset from one of the quasars by 1.7 ± 0.1 kpc. From Very Large Array imaging at 3 GHz, we detect 600 and 340 pc-scale radio emission that is associated with both quasars. The 1.4 GHz luminosity densities of the radio sources are about 1024.35 W Hz−1, which is consistent with weak jets. However, the low brightness temperature of the emission is also consistent with star-formation at the level of 850 to 1150 M⊙ yr−1. Although this supports the scenario where the AGN and/or star-formation is being triggered through an ongoing triple-merger, a post-merger scenario where two black holes are recoiling is also possible, given that neither has a detected host galaxy

A dynamically cold disk galaxy in the early Universe

The extreme astrophysical processes and conditions that characterize the early Universe are expected to result in young galaxies that are dynamically different from those observed today. This is because the strong effects associated with galaxy mergers and supernova explosions would lead to most young star-forming galaxies being dynamically hot, chaotic and strongly unstable. Here we report the presence of a dynamically cold, but highly star-forming, rotating disk in a galaxy at redshift ($z$) 4.2, when the Universe was just 1.4 billion years old. Galaxy SPT-S J041839-4751.9 is strongly gravitationally lensed by a foreground galaxy at $z = 0.263$, and it is a typical dusty starburst, with global star-forming and dust properties that are in agreement with current numerical simulations and observations of its galaxy population. Interferometric imaging at a spatial resolution of about 60 pc reveals a ratio of rotational-to-random motions of $V/\sigma = 9.7\pm 0.4$, which is at least four times larger than expected from any galaxy evolution model at this epoch, but similar to the ratios of spiral galaxies in the local Universe. We derive a rotation curve with the typical shape of nearby massive spiral galaxies, which demonstrates that at least some young galaxies are dynamically akin to those observed in the local Universe, and only weakly affected by extreme physical processes.Comment: Published in Nature on 12 August 2020. The published version is available at http://www.nature.com/articles/s41586-020-2572-

Geodesic Flow on the Diffeomorphism Group of the circle

We show that certain right-invariant metrics endow the infinite-dimensional Lie group of all smooth orientation-preserving diffeomorphisms of the circle with a Riemannian structure. The study of the Riemannian exponential map allows us to prove infinite-dimensional counterparts of results from classical Riemannian geometry: the Riemannian exponential map is a smooth local diffeomorphism and the length-minimizing property of the geodesics holds.Comment: 15 page

Dynamical percolation on general trees

H\"aggstr\"om, Peres, and Steif (1997) have introduced a dynamical version of percolation on a graph $G$. When $G$ is a tree they derived a necessary and sufficient condition for percolation to exist at some time $t$. In the case that $G$ is a spherically symmetric tree, H\"aggstr\"om, Peres, and Steif (1997) derived a necessary and sufficient condition for percolation to exist at some time $t$ in a given target set $D$. The main result of the present paper is a necessary and sufficient condition for the existence of percolation, at some time $t\in D$, in the case that the underlying tree is not necessary spherically symmetric. This answers a question of Yuval Peres (personal communication). We present also a formula for the Hausdorff dimension of the set of exceptional times of percolation.Comment: 24 pages; to appear in Probability Theory and Related Field