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

Lupus I Observations from the 2010 Flight of the Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry

The Balloon-borne Large Aperture Submillimeter Telescope for Polarimetry (BLASTPol) was created by adding polarimetric capability to the BLAST experiment that was flown in 2003, 2005, and 2006. BLASTPol inherited BLAST's 1.8 m primary and its Herschel/SPIRE heritage focal plane that allows simultaneous observation at 250, 350, and 500 μm. We flew BLASTPol in 2010 and again in 2012. Both were long duration Antarctic flights. Here we present polarimetry of the nearby filamentary dark cloud Lupus I obtained during the 2010 flight. Despite limitations imposed by the effects of a damaged optical component, we were able to clearly detect submillimeter polarization on degree scales. We compare the resulting BLASTPol magnetic field map with a similar map made via optical polarimetry. (The optical data were published in 1998 by J. Rizzo and collaborators.) The two maps partially overlap and are reasonably consistent with one another. We compare these magnetic field maps to the orientations of filaments in Lupus I, and we find that the dominant filament in the cloud is approximately perpendicular to the large-scale field, while secondary filaments appear to run parallel to the magnetic fields in their vicinities. This is similar to what is observed in Serpens South via near-IR polarimetry, and consistent with what is seen in MHD simulations by F. Nakamura and Z. Li

A Titanium Nitride Absorber for Controlling Optical Crosstalk in Horn-Coupled Aluminum LEKID Arrays for Millimeter Wavelengths

We discuss the design and measured performance of a titanium nitride (TiN) mesh absorber we are developing for controlling optical crosstalk in horn-coupled lumped-element kinetic inductance detector arrays for millimeter-wavelengths. This absorber was added to the fused silica anti-reflection coating attached to previously-characterized, 20-element prototype arrays of LEKIDs fabricated from thin-film aluminum on silicon substrates. To test the TiN crosstalk absorber, we compared the measured response and noise properties of LEKID arrays with and without the TiN mesh. For this test, the LEKIDs were illuminated with an adjustable, incoherent electronic millimeter-wave source. Our measurements show that the optical crosstalk in the LEKID array with the TiN absorber is reduced by 66\% on average, so the approach is effective and a viable candidate for future kilo-pixel arrays.Comment: 7 pages, 5 figures, accepted for publication in the Journal of Low Temperature Physic

Horn-Coupled, Commercially-Fabricated Aluminum Lumped-Element Kinetic Inductance Detectors for Millimeter Wavelengths

We discuss the design, fabrication, and testing of prototype horn-coupled, lumped-element kinetic inductance detectors (LEKIDs) designed for cosmic microwave background (CMB) studies. The LEKIDs are made from a thin aluminum film deposited on a silicon wafer and patterned using standard photolithographic techniques at STAR Cryoelectronics, a commercial device foundry. We fabricated twenty-element arrays, optimized for a spectral band centered on 150 GHz, to test the sensitivity and yield of the devices as well as the multiplexing scheme. We characterized the detectors in two configurations. First, the detectors were tested in a dark environment with the horn apertures covered, and second, the horn apertures were pointed towards a beam-filling cryogenic blackbody load. These tests show that the multiplexing scheme is robust and scalable, the yield across multiple LEKID arrays is 91%, and the noise-equivalent temperatures (NET) for a 4 K optical load are in the range 26\thinspace\pm6 \thinspace \mu \mbox{K} \sqrt{\mbox{s}}

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

The Effect of Helium Sedimentation on Galaxy Cluster Masses and Scaling Relations

Recent theoretical studies predict that the inner regions of galaxy clusters may have an enhanced helium abundance due to sedimentation over the cluster lifetime. If sedimentation is not suppressed (e.g., by tangled magnetic fields), this may significantly affect the cluster mass estimates. We use Chandra X-ray observations of eight relaxed galaxy clusters to investigate the upper limits to the effect of helium sedimentation on the measurement of cluster masses and the best-fit slopes of the Y_X - M_500 and Y_X - M_2500 scaling relations. We calculated gas mass and total mass in two limiting cases: a uniform, un-enhanced abundance distribution and a radial distribution from numerical simulations of helium sedimentation on a timescale of 11 Gyrs. The assumed helium sedimentation model, on average, produces a negligible increase in the gas mass inferred within large radii (r < r500) (1.3 +/- 1.2 per cent) and a (10.2 +/- 5.5) per cent mean decrease in the total mass inferred within r < r500. Significantly stronger effects in the gas mass (10.5 +/- 0.8 per cent) and total mass (25.1 +/- 1.1 per cent) are seen at small radii owing to a larger variance in helium abundance in the inner region, r < 0.1 r500. We find that the slope of the Y_X -M_500 scaling relation is not significantly affected by helium sedimentation.Comment: 11 pages, accepted for publication in Astronomy and Astrophysic