Optical Testing of Retroreflectors for Cryogenic Applications

A laser tracker (LT) is an important coordinate metrology tool that uses laser interferometry to determine precise distances to objects, points, or surfaces defined by an optical reference, such as a retroreflector. A retroreflector is a precision optic consisting of three orthogonal faces that returns an incident laser beam nearly exactly parallel to the incident beam. Commercial retroreflectors are designed for operation at room temperature and are specified by the divergence, or beam deviation, of the returning laser beam, usually a few arcseconds or less. When a retroreflector goes to extreme cold (.35 K), however, it could be anticipated that the precision alignment between the three faces and the surface figure of each face would be compromised, resulting in wavefront errors and beam divergence, degrading the accuracy of the LT position determination. Controlled tests must be done beforehand to determine survivability and these LT coordinate errors. Since conventional interferometer systems and laser trackers do not operate in vacuum or at cold temperatures, measurements must be done through a vacuum window, and care must be taken to ensure window-induced errors are negligible, or can be subtracted out. Retroreflector holders must be carefully designed to minimize thermally induced stresses. Changes in the path length and refractive index of the retroreflector have to be considered. Cryogenic vacuum testing was done on commercial solid glass retroreflectors for use on cryogenic metrology tasks. The capabilities to measure wavefront errors, measure beam deviations, and acquire laser tracker coordinate data were demonstrated. Measurable but relatively small increases in beam deviation were shown, and further tests are planned to make an accurate determination of coordinate errors

Alignment Cube with One Diffractive Face

An enhanced alignment cube has been invented for use in a confined setting (e.g., a cryogenic chamber) in which optical access may be limited to a single line of sight. Whereas traditional alignment-cube practice entails the use of two theodolites aimed along two lines of sight, the enhanced alignment cube yields complete alignment information through use of a single theodolite aimed along a single line of sight. Typically, an alignment cube is placed in contact with a datum surface or other reference feature on a scientific instrument during assembly or testing of the instrument. The alignment cube is then used in measuring a small angular deviation of the feature from a precise required orientation. Commonly, the deviation is expressed in terms of rotations (Rx,Ry,Rz) of the cube about the corresponding Cartesian axes (x,y,z). In traditional practice, in order to measure all three rotations, it is necessary to use two theodolites aimed at two orthogonal faces of the alignment cube, as shown in the upper part of the figure. To be able to perform such a measurement, one needs optical access to these two faces. In the case of an alignment cube inside a cryogenic chamber or other enclosed space, the optical-access requirement translates to a requirement for two windows located along the corresponding two orthogonal lines of sight into the chamber. In a typical application, it is difficult or impossible to provide two windows. The present enhanced version of the alignment cube makes it possible to measure all three rotations by use of a single line of sight, thereby obviating a second window

Spectral and Wavefront Error Performance of WFIRST-AFTA Bandpass Filter Coating Prototypes

The Cycle 5 design baseline for the Wide-Field Infrared Survey Telescope Astrophysics Focused Telescope Assets (WFIRST/AFTA) instrument includes a single wide-field channel (WFC) instrument for both imaging and slit-less spectroscopy. The only routinely moving part during scientific observations for this wide-field channel is the element wheel (EW) assembly. This filter-wheel assembly will have 8 positions that will be populated with 6 bandpass filters, a blank position, and a Grism that will consist of a three-element assembly to disperse the full field with an undeviated central wavelength for galaxy redshift surveys. All filter elements in the EW assembly will be made out of fused silica substrates (110 mm diameter) that will have the appropriate bandpass coatings according to the filter designations (Z087, Y106, J129, H158, F184, W149 and Grism). This paper presents and discusses the performance (including spectral transmission and reflected/transmitted wavefront error measurements) of a subset of bandpass filter coating prototypes that are based on the WFC instrument filter compliment. The bandpass coating prototypes that are tested in this effort correspond to the Z087, W149, and Grism filter elements. These filter coatings have been procured from three different vendors to assess the most challenging aspects in terms of the in-band throughput, out of band rejection (including the cut-on and cutoff slopes), and the impact the wavefront error distortions of these filter coatings will have on the imaging performance of the wide-field channel in the WFIRST/AFTA observatory

The NANOGrav 15-year Data Set: Search for Anisotropy in the Gravitational-Wave Background

The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has reported evidence for the presence of an isotropic nanohertz gravitational wave background (GWB) in its 15 yr dataset. However, if the GWB is produced by a population of inspiraling supermassive black hole binary (SMBHB) systems, then the background is predicted to be anisotropic, depending on the distribution of these systems in the local Universe and the statistical properties of the SMBHB population. In this work, we search for anisotropy in the GWB using multiple methods and bases to describe the distribution of the GWB power on the sky. We do not find significant evidence of anisotropy, and place a Bayesian $95\%$ upper limit on the level of broadband anisotropy such that $(C_{l>0} / C_{l=0}) < 20\%$. We also derive conservative estimates on the anisotropy expected from a random distribution of SMBHB systems using astrophysical simulations conditioned on the isotropic GWB inferred in the 15-yr dataset, and show that this dataset has sufficient sensitivity to probe a large fraction of the predicted level of anisotropy. We end by highlighting the opportunities and challenges in searching for anisotropy in pulsar timing array data.Comment: 19 pages, 11 figures; submitted to Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email [email protected]

The NANOGrav 15-year Data Set: Bayesian Limits on Gravitational Waves from Individual Supermassive Black Hole Binaries

Evidence for a low-frequency stochastic gravitational wave background has recently been reported based on analyses of pulsar timing array data. The most likely source of such a background is a population of supermassive black hole binaries, the loudest of which may be individually detected in these datasets. Here we present the search for individual supermassive black hole binaries in the NANOGrav 15-year dataset. We introduce several new techniques, which enhance the efficiency and modeling accuracy of the analysis. The search uncovered weak evidence for two candidate signals, one with a gravitational-wave frequency of $\sim$4 nHz, and another at $\sim$170 nHz. The significance of the low-frequency candidate was greatly diminished when Hellings-Downs correlations were included in the background model. The high-frequency candidate was discounted due to the lack of a plausible host galaxy, the unlikely astrophysical prior odds of finding such a source, and since most of its support comes from a single pulsar with a commensurate binary period. Finding no compelling evidence for signals from individual binary systems, we place upper limits on the strain amplitude of gravitational waves emitted by such systems.Comment: 23 pages, 13 figures, 2 tables. Accepted for publication in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email [email protected]

The NANOGrav 15-Year Data Set: Detector Characterization and Noise Budget

Pulsar timing arrays (PTAs) are galactic-scale gravitational wave detectors. Each individual arm, composed of a millisecond pulsar, a radio telescope, and a kiloparsecs-long path, differs in its properties but, in aggregate, can be used to extract low-frequency gravitational wave (GW) signals. We present a noise and sensitivity analysis to accompany the NANOGrav 15-year data release and associated papers, along with an in-depth introduction to PTA noise models. As a first step in our analysis, we characterize each individual pulsar data set with three types of white noise parameters and two red noise parameters. These parameters, along with the timing model and, particularly, a piecewise-constant model for the time-variable dispersion measure, determine the sensitivity curve over the low-frequency GW band we are searching. We tabulate information for all of the pulsars in this data release and present some representative sensitivity curves. We then combine the individual pulsar sensitivities using a signal-to-noise-ratio statistic to calculate the global sensitivity of the PTA to a stochastic background of GWs, obtaining a minimum noise characteristic strain of $7\times 10^{-15}$ at 5 nHz. A power law-integrated analysis shows rough agreement with the amplitudes recovered in NANOGrav's 15-year GW background analysis. While our phenomenological noise model does not model all known physical effects explicitly, it provides an accurate characterization of the noise in the data while preserving sensitivity to multiple classes of GW signals.Comment: 67 pages, 73 figures, 3 tables; published in Astrophysical Journal Letters as part of Focus on NANOGrav's 15-year Data Set and the Gravitational Wave Background. For questions or comments, please email [email protected]

The NANOGrav 15-year data set: Search for Transverse Polarization Modes in the Gravitational-Wave Background

Recently we found compelling evidence for a gravitational wave background with Hellings and Downs (HD) correlations in our 15-year data set. These correlations describe gravitational waves as predicted by general relativity, which has two transverse polarization modes. However, more general metric theories of gravity can have additional polarization modes which produce different interpulsar correlations. In this work we search the NANOGrav 15-year data set for evidence of a gravitational wave background with quadrupolar Hellings and Downs (HD) and Scalar Transverse (ST) correlations. We find that HD correlations are the best fit to the data, and no significant evidence in favor of ST correlations. While Bayes factors show strong evidence for a correlated signal, the data does not strongly prefer either correlation signature, with Bayes factors $\sim 2$ when comparing HD to ST correlations, and $\sim 1$ for HD plus ST correlations to HD correlations alone. However, when modeled alongside HD correlations, the amplitude and spectral index posteriors for ST correlations are uninformative, with the HD process accounting for the vast majority of the total signal. Using the optimal statistic, a frequentist technique that focuses on the pulsar-pair cross-correlations, we find median signal-to-noise-ratios of 5.0 for HD and 4.6 for ST correlations when fit for separately, and median signal-to-noise-ratios of 3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the signal-to-noise-ratios for each of the correlations are comparable, the estimated amplitude and spectral index for HD are a significantly better fit to the total signal, in agreement with our Bayesian analysis.Comment: 11 pages, 5 figure

How to Detect an Astrophysical Nanohertz Gravitational-Wave Background

Analysis of pulsar timing data have provided evidence for a stochastic gravitational wave background in the nHz frequency band. The most plausible source of such a background is the superposition of signals from millions of supermassive black hole binaries. The standard statistical techniques used to search for such a background and assess its significance make several simplifying assumptions, namely: i) Gaussianity; ii) isotropy; and most often iii) a power-law spectrum. However, a stochastic background from a finite collection of binaries does not exactly satisfy any of these assumptions. To understand the effect of these assumptions, we test standard analysis techniques on a large collection of realistic simulated datasets. The dataset length, observing schedule, and noise levels were chosen to emulate the NANOGrav 15-year dataset. Simulated signals from millions of binaries drawn from models based on the Illustris cosmological hydrodynamical simulation were added to the data. We find that the standard statistical methods perform remarkably well on these simulated datasets, despite their fundamental assumptions not being strictly met. They are able to achieve a confident detection of the background. However, even for a fixed set of astrophysical parameters, different realizations of the universe result in a large variance in the significance and recovered parameters of the background. We also find that the presence of loud individual binaries can bias the spectral recovery of the background if we do not account for them.Comment: 14 pages, 8 figure

The NANOGrav 15 yr Data Set: Search for Transverse Polarization Modes in the Gravitational-wave Background

Recently we found compelling evidence for a gravitational-wave background with Hellings and Downs (HD) correlations in our 15 yr data set. These correlations describe gravitational waves as predicted by general relativity, which has two transverse polarization modes. However, more general metric theories of gravity can have additional polarization modes, which produce different interpulsar correlations. In this work, we search the NANOGrav 15 yr data set for evidence of a gravitational-wave background with quadrupolar HD and scalar-transverse (ST) correlations. We find that HD correlations are the best fit to the data and no significant evidence in favor of ST correlations. While Bayes factors show strong evidence for a correlated signal, the data does not strongly prefer either correlation signature, with Bayes factors ∼2 when comparing HD to ST correlations, and ∼1 for HD plus ST correlations to HD correlations alone. However, when modeled alongside HD correlations, the amplitude and spectral index posteriors for ST correlations are uninformative, with the HD process accounting for the vast majority of the total signal. Using the optimal statistic, a frequentist technique that focuses on the pulsar-pair cross-correlations, we find median signal-to-noise ratios of 5.0 for HD and 4.6 for ST correlations when fit for separately, and median signal-to-noise ratios of 3.5 for HD and 3.0 for ST correlations when fit for simultaneously. While the signal-to-noise ratios for each of the correlations are comparable, the estimated amplitude and spectral index for HD are a significantly better fit to the total signal, in agreement with our Bayesian analysis