How would GW150914 look with future GW detector networks?

The first detected gravitational wave signal, GW150914, was produced by the coalescence of a stellar-mass binary black hole. Along with the subsequent detection of GW151226, GW170104 and the candidate event LVT151012, this gives us evidence for a population of black hole binaries with component masses in the tens of solar masses. As detector sensitivity improves, this type of source is expected to make a large contribution to the overall number of detections, but has received little attention compared to binary neutron star systems in studies of projected network performance. We simulate the observation of a system like GW150914 with different proposed network configurations, and study the precision of parameter estimates, particularly source location, orientation and masses. We find that the improvements to low frequency sensitivity that are expected with continued commissioning will improve the precision of chirp mass estimates by an order of magnitude, whereas the improvements in sky location and orientation are driven by the expanded network configuration. This demonstrates that both sensitivity and number of detectors will be important factors in the scientific potential of second generation detector networks.Comment: 18 pages, 5 figures, 2 table

Fixed Investment in the American Business Cycle, 1919-83

Contributions are made by this paper in three areas, methodological, data creation, and empirical. The methodological section finds that, while structural model building exercises may be useful in suggesting lists of variables that may play an explanatory role in investment equations, they generally achieve identification of structural parameters only by imposing arbitrary and unbelievable simplifying assumptions and exclusion restrictions.The paper advocates a hybrid methodology combining guidance from traditional structural models on the choice and form of explanatory variables to be included, with estimation in a reduced-form format that introduces all explanatory variables and the lagged dependent variable with the same number of unconstrained lag coefficients. The second contribution is the use of a new set of quarterly data for major expenditure categories of GNP extending back to 1919. The data file also contains quarterly data back to 1919 for other variables, including the capital stock, interest rates, the cost of capital including tax incentive effects, a proxy for Tobin's "Q", and the real money supply.The empirical results support the view that there are two basic impulses in the business cycle, real and financial.The real impulse appears in our statistical evidence as an autonomous innovation to investment in structures. We interpret these structures innovations as due in turn to changes in the rate of population growth, episodes of speculation and overbuilding, and Schumpeterian waves of innovation.The financial impulse works through the effect on investment of changes in the money supply, as well as the real interest rate (in the case of postwar investment in durable equipment).There is a strong role for the money supply as a determinant of investment behavior, relative to such other factors as the user cost of capital or Tobin's "Q". The role of the money supply is interpreted as primarily reflecting the banking contraction of 1929-33 and the episodes of credit crunches and disintermediation in the postwar years. Another feature of the empirical work is the attention paid to aggregation. Coefficient estimates are more stable when four types of investment expenditures are aggregated along the structures-equipment dimension than along the household-business dimension. Historical decompositions highlight the role of autonomous innovations in structures investment and in the money supply, and an inspection of residuals suggests that the main autonomous downward shift in spending in 1929-30 was in fixed investment, not nondurable consumption.

Digging the population of compact binary mergers out of the noise

Coalescing compact binaries emitting gravitational wave (GW) signals, as recently detected by the Advanced LIGO-Virgo network, constitute a population over the multi-dimensional space of component masses and spins, redshift, and other parameters. Characterizing this population is a major goal of GWobservations and may be approached via parametric models.We demonstrate hierarchical inference for such models with a method that accounts for uncertainties in each binary merger’s individual parameters, for mass-dependent selection effects, and also for the presence of a second population of candidate events caused by detector noise. Thus, the method is robust to potential biases from a contaminated sample and allows us to extract information from events that have a relatively small probability of astrophysical origin

Associating host galaxy candidates to massive black hole binaries resolved by pulsar timing arrays

We propose a novel methodology to select host galaxy candidates of future pulsar timing array (PTA) detections of resolved gravitational waves (GWs) from massive black hole binaries (MBHBs). The method exploits the physical dependence of the GW amplitude on the MBHB chirp mass and distance to the observer, together with empirical MBH mass–host galaxy correlations, to rank potential host galaxies in the mass–redshift plane. This is coupled to a null-stream based likelihood evaluation of the GW amplitude and sky position in a Bayesian framework that assigns to each galaxy a probability of hosting the MBHB generating the GW signal. We test our algorithm on a set of realistic simulations coupling the likely properties of the first PTA resolved GW signal to synthetic all-sky galaxy maps. For a foreseeable PTA sky-localization precision of 100 deg2, we find that the GW source is hosted with 50%(90%) probability within a restricted number of ≲ 50( ≲ 500) potential hosts. These figures are orders of magnitude smaller than the total number of galaxies within the PTA sky error-box, enabling extensive electromagnetic follow-up campaigns on a limited number of targets

Studying stellar binary systems with the Laser Interferometer Space Antenna using Delayed Rejection Markov chain Monte Carlo methods

Bayesian analysis of LISA data sets based on Markov chain Monte Carlo methods has been shown to be a challenging problem, in part due to the complicated structure of the likelihood function consisting of several isolated local maxima that dramatically reduces the efficiency of the sampling techniques. Here we introduce a new fully Markovian algorithm, a Delayed Rejection Metropolis-Hastings Markov chain Monte Carlo method, to efficiently explore these kind of structures and we demonstrate its performance on selected LISA data sets containing a known number of stellar-mass binary signals embedded in Gaussian stationary noise.Comment: 12 pages, 4 figures, accepted in CQG (GWDAW-13 proceedings

The First Two Years of Electromagnetic Follow-Up with Advanced LIGO and Virgo

We anticipate the first direct detections of gravitational waves (GWs) with Advanced LIGO and Virgo later this decade. Though this groundbreaking technical achievement will be its own reward, a still greater prize could be observations of compact binary mergers in both gravitational and electromagnetic channels simultaneously. During Advanced LIGO and Virgo's first two years of operation, 2015 through 2016, we expect the global GW detector array to improve in sensitivity and livetime and expand from two to three detectors. We model the detection rate and the sky localization accuracy for binary neutron star (BNS) mergers across this transition. We have analyzed a large, astrophysically motivated source population using real-time detection and sky localization codes and higher-latency parameter estimation codes that have been expressly built for operation in the Advanced LIGO/Virgo era. We show that for most BNS events the rapid sky localization, available about a minute after a detection, is as accurate as the full parameter estimation. We demonstrate that Advanced Virgo will play an important role in sky localization, even though it is anticipated to come online with only one-third as much sensitivity as the Advanced LIGO detectors. We find that the median 90% confidence region shrinks from ~500 square degrees in 2015 to ~200 square degrees in 2016. A few distinct scenarios for the first LIGO/Virgo detections emerge from our simulations.Comment: 17 pages, 11 figures, 5 tables. For accompanying data, see http://www.ligo.org/scientists/first2year

Parameter estimation on gravitational waves from neutron-star binaries with spinning components

Inspiraling binary neutron stars are expected to be one of the most significant sources of gravitational-wave signals for the new generation of advanced ground-based detectors. We investigate how well we could hope to measure properties of these binaries using the Advanced LIGO detectors, which began operation in September 2015. We study an astrophysically motivated population of sources (binary components with masses $1.2~\mathrm{M}_\odot$--$1.6~\mathrm{M}_\odot$ and spins of less than $0.05$) using the full LIGO analysis pipeline. While this simulated population covers the observed range of potential binary neutron-star sources, we do not exclude the possibility of sources with parameters outside these ranges; given the existing uncertainty in distributions of mass and spin, it is critical that analyses account for the full range of possible mass and spin configurations. We find that conservative prior assumptions on neutron-star mass and spin lead to average fractional uncertainties in component masses of $\sim 16\%$, with little constraint on spins (the median $90\%$ upper limit on the spin of the more massive component is $\sim 0.7$). Stronger prior constraints on neutron-star spins can further constrain mass estimates, but only marginally. However, we find that the sky position and luminosity distance for these sources are not influenced by the inclusion of spin; therefore, if LIGO detects a low-spin population of BNS sources, less computationally expensive results calculated neglecting spin will be sufficient for guiding electromagnetic follow-up.Comment: 10 pages, 9 figure

The Mock LISA Data Challenges: from Challenge 3 to Challenge 4

The Mock LISA Data Challenges are a program to demonstrate LISA data-analysis capabilities and to encourage their development. Each round of challenges consists of one or more datasets containing simulated instrument noise and gravitational waves from sources of undisclosed parameters. Participants analyze the datasets and report best-fit solutions for the source parameters. Here we present the results of the third challenge, issued in Apr 2008, which demonstrated the positive recovery of signals from chirping Galactic binaries, from spinning supermassive--black-hole binaries (with optimal SNRs between ~ 10 and 2000), from simultaneous extreme-mass-ratio inspirals (SNRs of 10-50), from cosmic-string-cusp bursts (SNRs of 10-100), and from a relatively loud isotropic background with Omega_gw(f) ~ 10^-11, slightly below the LISA instrument noise.Comment: 12 pages, 2 figures, proceedings of the 8th Edoardo Amaldi Conference on Gravitational Waves, New York, June 21-26, 200