Hierarchical analysis of gravitational-wave measurements of binary black hole spin-orbit misalignments

Binary black holes may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. The formation channel leaves an imprint on the alignment between the black hole spins and the orbital angular momentum. Gravitational waves from these systems directly encode information about the spin--orbit misalignment angles, allowing them to be (weakly) constrained. Identifying sub-populations of spinning binary black holes will inform us about compact binary formation and evolution. We simulate a mixed population of binary black holes with spin--orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock gravitational-wave observations of these populations. Assuming a population with dimensionless spin magnitudes of $\chi = 0.7$, we show that tens of observations will make it possible to distinguish the presence of subpopulations of coalescing binary black holes based on their spin orientations. With $100$ observations it will be possible to infer the relative fraction of coalescing binary black holes with isotropic spin directions (corresponding to dynamical formation in our models) with a fractional uncertainty of $\sim 40\%$. Meanwhile, only $\sim 5$ observations are sufficient to distinguish between extreme models---all binary black holes either having exactly aligned spins or isotropic spin directions.Comment: 12 pages, 9 figures. Updated to match version published in MNRAS as 10.1093/mnras/stx176

Parameter estimation on compact binary coalescences with abruptly terminating gravitational waveforms

Gravitational-wave astronomy seeks to extract information about astrophysical systems from the gravitational-wave signals they emit. For coalescing compact-binary sources this requires accurate model templates for the inspiral and, potentially, the subsequent merger and ringdown. Models with frequency-domain waveforms that terminate abruptly in the sensitive band of the detector are often used for parameter-estimation studies. We show that the abrupt waveform termination contains significant information that affects parameter-estimation accuracy. If the sharp cutoff is not physically motivated, this extra information can lead to misleadingly good accuracy claims. We also show that using waveforms with a cutoff as templates to recover complete signals can lead to biases in parameter estimates. We evaluate when the information content in the cutoff is likely to be important in both cases. We also point out that the standard Fisher matrix formalism, frequently employed for approximately predicting parameter-estimation accuracy, cannot properly incorporate an abrupt cutoff that is present in both signals and templates; this observation explains some previously unexpected results found in the literature. These effects emphasize the importance of using complete waveforms with accurate merger and ringdown phases for parameter estimation.Comment: Very minor changes to match published versio

Inference on gravitational waves from coalescences of stellar-mass compact objects and intermediate-mass black holes

Gravitational waves from coalescences of neutron stars or stellar-mass black holes into intermediate-mass black holes (IMBHs) of $\gtrsim 100$ solar masses represent one of the exciting possible sources for advanced gravitational-wave detectors. These sources can provide definitive evidence for the existence of IMBHs, probe globular-cluster dynamics, and potentially serve as tests of general relativity. We analyse the accuracy with which we can measure the masses and spins of the IMBH and its companion in intermediate-mass ratio coalescences. We find that we can identify an IMBH with a mass above $100 ~ M_\odot$ with $95\%$ confidence provided the massive body exceeds $130 ~ M_\odot$. For source masses above $\sim200 ~ M_\odot$, the best measured parameter is the frequency of the quasi-normal ringdown. Consequently, the total mass is measured better than the chirp mass for massive binaries, but the total mass is still partly degenerate with spin, which cannot be accurately measured. Low-frequency detector sensitivity is particularly important for massive sources, since sensitivity to the inspiral phase is critical for measuring the mass of the stellar-mass companion. We show that we can accurately infer source parameters for cosmologically redshifted signals by applying appropriate corrections. We investigate the impact of uncertainty in the model gravitational waveforms and conclude that our main results are likely robust to systematics.Comment: 9 pages, 11 figure

Double Compact Objects II: Cosmological Merger Rates

The development of advanced gravitational wave (GW) observatories, such as Advanced LIGO and Advanced Virgo, provides impetus to refine theoretical predictions for what these instruments might detect. In particular, with the range increasing by an order of magnitude, the search for GW sources is extending beyond the "local" Universe and out to cosmological distances. Double compact objects (neutron star-neutron star (NS-NS), black hole-neutron star (BH-NS) and black hole-black hole (BH-BH) systems) are considered to be the most promising gravitational wave sources. In addition, NS-NS and/or BH-NS systems are thought to be the progenitors of gamma ray bursts (GRBs), and may also be associated with kilonovae. In this paper we present the merger event rates of these objects as a function of cosmological redshift. We provide the results for four cases, each one investigating a different important evolution parameter of binary stars. Each case is also presented for two metallicity evolution scenarios. We find that (i) in most cases NS-NS systems dominate the merger rates in the local Universe, while BH-BH mergers dominate at high redshift; (ii) BH-NS mergers are less frequent than other sources per unit volume, for all time; and (iii) natal kicks may alter the observable properties of populations in a significant way, allowing the underlying models of binary evolution and compact object formation to be easily distinguished. This is the second paper in a series of three. The third paper will focus on calculating the detection rates of mergers by gravitational wave telescopes.Comment: 8 pages, 10 figures, second in series, accepted for Ap

Offshoring and the State of American Manufacturing

The rapid growth of offshoring has sparked a contentious debate over its impact on the U.S. manufacturing sector, which has recorded steep employment declines yet strong output growth—a fact reconciled by the notable gains in manufacturing productivity. We maintain, however, that the dramatic acceleration of imports from developing countries has imparted a significant bias to the official statistics. In particular, the price declines associated with the shift to low-cost foreign suppliers generally are not captured in input cost and import price indexes. To assess the implications of offshoring bias for manufacturing productivity and value added, we implement the bias correction developed by Diewert and Nakamura (2009) to the input price index in a growth accounting framework, using a variety of assumptions about the magnitude of the discounts from offshoring. We find that from 1997 to 2007 average annual multifactor productivity growth in manufacturing was overstated by 0.1 to 0.2 percentage point and real value added growth by 0.2 to 0.5 percentage point. Furthermore, although the bias from offshoring represents a relatively small share of real value added growth in the computer and electronic products industry, it may have accounted for a fifth to a half of the growth in real value added in the rest of manufacturing

Validation of a Food Frequency Questionnaire for Hispanics

INTRODUCTION: The Hispanic population will grow to comprise one fourth of the U.S. population by 2050. Compared with non-Hispanic whites, Hispanics have disproportionately higher rates of obesity, diabetes, and other diet-related conditions. Valid methods for studying the dietary intake of this group are needed. METHODS: From June through September 2000, we conducted a study of low-income Hispanic men and women (n = 89) who were recruited for a validation study of the Spanish-language food frequency questionnaire used in the Study of Women's Health Across the Nation. The mean age of the participants was 36.8 years, 42% were male, and 92% had been born in Mexico. Three 24-hour dietary recalls provided the reference data. The food frequency questionnaire was administered by interview, with a portion-size graphic to aid in quantitation. The questionnaire asked about diet in the previous 12 months. Mean nutrient values, correlation coefficients, and the sensitivity and specificity for identifying people with intakes of less than the recommended levels were calculated. RESULTS: Mean energy and macronutrient intake estimates were significantly higher by the food frequency questionnaire than by the 24-hour dietary recalls. Cholesterol, saturated fat, dietary fiber, iron, vitamin A, and percentage of energy from fat were not significantly different by the two methods. The median of unadjusted correlations was 0.52 and of deattenuated correlations was 0.61. The median sensitivity was 0.62, and the median specificity was 0.76. CONCLUSION: The Study of Women's Health Across the Nation Spanish food frequency questionnaire appears to be reasonably valid in assessing the dietary intakes of Hispanics. Correlations tended to be higher than those found in other validation studies in Hispanic populations. Interviewer administration of questionnaires may be necessary in this population

Accuracy of inference on the physics of binary evolution from gravitational-wave observations

The properties of the population of merging binary black holes encode some of the uncertain physics of the evolution of massive stars in binaries. The binary black hole merger rate and chirp mass distribution are being measured by ground-based gravitational-wave detectors. We consider isolated binary evolution and explore how accurately the physical model can be constrained with such observations by applying the Fisher information matrix to the merging black hole population simulated with the rapid binary population synthesis code COMPAS. We investigate variations in four COMPAS parameters: common envelope efficiency, kick velocity dispersion, and mass loss rates during the luminous blue variable and Wolf--Rayet stellar evolutionary phases. We find that 1000 observations would constrain these model parameters to a fractional accuracy of a few percent. Given the empirically determined binary black hole merger rate, we can expect gravitational-wave observations alone to place strong constraints on the physics of stellar and binary evolution within a few years.Comment: 12 pages, 9 figures; version accepted by Monthly Notices of the Royal Astronomical Societ

Deeper, Wider, Sharper: Next-Generation Ground-Based Gravitational-Wave Observations of Binary Black Holes

Next-generation observations will revolutionize our understanding of binary black holes and will detect new sources, such as intermediate-mass black holes. Primary science goals include: Discover binary black holes throughout the observable Universe; Reveal the fundamental properties of black holes; Uncover the seeds of supermassive black holes.Comment: 14 pages, 3 figures, White Paper Submitted to Astro2020 (2020 Astronomy and Astrophysics Decadal Survey) by GWIC 3G Science Case Team (GWIC: Gravitational Wave International Committee

Criteria for Continuous-Variable Quantum Teleportation

We derive an experimentally testable criterion for the teleportation of quantum states of continuous variables. This criterion is especially relevant to the recent experiment of Furusawa et al. [Science 282, 706-709 (1998)] where an input-output fidelity of $0.58 \pm 0.02$ was achieved for optical coherent states. Our derivation demonstrates that fidelities greater than 1/2 could not have been achieved through the use of a classical channel alone; quantum entanglement was a crucial ingredient in the experiment.Comment: 12 pages, to appear in Journal of Modern Optic