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Register a new userComparing compact binary parameter distributions I: Methods
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Richard O'Shaughnessy
Publication date
2012
fields
Physics
and research's language is
English
Authors
R. OShaughnessy
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Being able to measure each mergers sky location, distance, component masses, and conceivably spins, ground-based gravitational-wave detectors will provide a extensive and detailed sample of coalescing compact binaries (CCBs) in the local and, with third-generation detectors, distant universe. These measurements will distinguish between competing progenitor formation models. In this paper we develop practical tools to characterize the amount of experimentally accessible information available, to distinguish between two a priori progenitor models. Using a simple time-independent model, we demonstrate the information content scales strongly with the number of observations. The exact scaling depends on how significantly mass distributions change between similar models. We develop phenomenological diagnostics to estimate how many models can be distinguished, using first-generation and future instruments. Finally, we emphasize that multi-observable distributions can be fully exploited only with very precisely calibrated detectors, search pipelines, parameter estimation, and Bayesian model inference.
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We estimate binary compact object merger detection rates for LIGO, including the binaries formed in ellipticals long ago. Specifically, we convolve hundreds of model realizations of elliptical- and spiral-galaxy population syntheses with a model for elliptical- and spiral-galaxy star formation history as a function of redshift. Our results favor local merger rate densities of 4times 10^{-3} {Mpc}^{-3}{Myr}^{-1} for binary black holes (BH), 3times 10^{-2} {Mpc}^{-3}{Myr}^{-1} for binary neutron stars (NS), and 10^{-2} {Mpc}^{-3}{Myr}^{-1} for BH-NS binaries. Mergers in elliptical galaxies are a significant fraction of our total estimate for BH-BH and BH-NS detection rates; NS-NS detection rates are dominated by the contribution from spiral galaxies. Using only models that reproduce current observations of Galactic NS-NS binaries, we find slightly higher rates for NS-NS and largely similar ranges for BH-NS and BH-BH binaries. Assuming a detection signal-to-noise ratio threshold of 8 for a single detector (as part of a network), corresponding to radii Cv of the effective volume inside of which a single LIGO detector could observe the inspiral of two 1.4 M_sun neutron stars of 14 Mpc and 197 Mpc, for initial and advanced LIGO, we find event rates of any merger type of 2.9* 10^{-2} -- 0.46 and 25-400 per year (at 90% confidence level), respectively. We also find that the probability P_{detect} of detecting one or more mergers with this single detector can be approximated by (i) P_{detect}simeq 0.4+0.5log (T/0.01{yr}), assuming Cv=197 {Mpc} and it operates for T years, for T between 2 days and 0.1 {yr}); or by (ii) P_{detect}simeq 0.5 + 1.5 log Cv/32{Mpc}, for one year of operation and for $Cv$ between 20 and 70 Mpc. [ABRIDGED]
We model the gravitational-wave background created by double compact objects from isolated binary evolution across cosmic time using the textbf{textit{StarTrack}} binary population code. We include population I/II stars as well as metal-free population III stars. Merging and non-merging double compact object binaries are taken into account. In order to model the low frequency signal in the band of the space antenna LISA, we account for the evolution of the redshift and the eccentricity. We find an energy density of $Omega_{GW} sim 1.0 times 10^{-9}$ at the reference frequency of 25 Hz for population I/II only, making the background detectable at 3 $sigma$ after about 7 years of observation with the current generation of ground based detectors, such as LIGO, Virgo and Kagra, operating at design sensitivity. The contribution from population III is one order of magnitude below the population I/II for the total background, but dominates the residual background, after detected sources have been removed, in 3G detectors. It modifies the shape of the spectrum which starts deviating from the usual power law $Omega_{GW}(f) sim f^{2/3}$ after $sim 10$ Hz. The contribution from the population of non merging binaries, on the other hand, is negligible, being orders of magnitude below. Finally, we observe that the eccentricity has no impact in the frequency band of LISA or ground based detectors.
This paper is the first in a set that analyses the covariance matrices of clustering statistics obtained from several approximate methods for gravitational structure formation. We focus here on the covariance matrices of anisotropic two-point correlation function measurements. Our comparison includes seven approximate methods, which can be divided into three categories: predictive methods that follow the evolution of the linear density field deterministically (ICE-COLA, Peak Patch, and Pinocchio), methods that require a calibration with N-body simulations (Patchy and Halogen), and simpler recipes based on assumptions regarding the shape of the probability distribution function (PDF) of density fluctuations (log-normal and Gaussian density fields). We analyse the impact of using covariance estimates obtained from these approximate methods on cosmological analyses of galaxy clustering measurements, using as a reference the covariances inferred from a set of full N-body simulations. We find that all approximate methods can accurately recover the mean parameter values inferred using the N-body covariances. The obtained parameter uncertainties typically agree with the corresponding N-body results within 5% for our lower mass threshold, and 10% for our higher mass threshold. Furthermore, we find that the constraints for some methods can differ by up to 20% depending on whether the halo samples used to define the covariance matrices are defined by matching the mass, number density, or clustering amplitude of the parent N-body samples. The results of our configuration-space analysis indicate that most approximate methods provide similar results, with no single method clearly outperforming the others.
Significant human and observational resources have been dedicated to electromagnetic followup of gravitational-wave events detected by Advanced LIGO and Virgo. As the sensitivity of LIGO and Virgo improves, the rate of sources detected will increase. Margalit & Metzger (2019; arXiv:1904.11995) have suggested that it may be necessary to prioritize observations of future events. Optimal prioritization requires a rapid measurement of a gravitational-wave events masses and spins, as these can determine the nature of any electromagnetic emission. We extend the relative binning method of Zackay et al. (2018; arXiv:1806.08792) to a coherent detector-network statistic. We show that the method can be seeded from the output of a matched-filter search and used in a Bayesian parameter measurement framework to produce marginalized posterior probability densities for the sources parameters within 20 minutes of detection on 32 CPU cores. We demonstrate that this algorithm produces unbiased estimates of the parameters with the same accuracy as running parameter estimation using the standard gravitational-wave likelihood. We encourage the adoption of this method in future LIGO-Virgo observing runs to allow fast dissemination of the parameters of detected events so that the observing community can make best use of its resources.
We use the Fisher information matrix to investigate the angular resolution and luminosity distance uncertainty for coalescing binary neutron stars (BNSs) and neutron star-black hole binaries (NSBHs) detected by the third-generation (3G) gravitational-wave (GW) detectors. Our study focuses on an individual 3G detector and a network of up to four 3G detectors at different locations including the US, Europe, China and Australia for the proposed Einstein Telescope (ET) and Cosmic Explorer (CE) detectors. We in particular examine the effect of the Earths rotation, as GW signals from BNS and low mass NSBH systems could be hours long for 3G detectors. We find that, a time-dependent antenna beam-pattern function can help better localize BNS and NSBH sources, especially those edge-on ones. The medium angular resolution for one ET-D detector is around 150 deg$^2$ for BNSs at a redshift of $z=0.1$. The medium angular resolution for a network of two CE detectors in the US and Europe respectively is around 20 deg$^2$ at $z=0.2$ for the simulated BNS and NSBH samples. While for a network of two ET-D detectors, the similar angular resolution can be achieved at a much higher redshift of $z=0.5$. The angular resolution of a network of three detectors is mainly determined by the baselines between detectors regardless of the CE or ET detector type. We discuss the implications of our results to constrain the Hubble constant $H_0$, the deceleration parameter $q_0$ and the equation-of-state (EoS) of dark energy. We find that in general, if 10 BNSs or NSBHs at $z=0.1$ with known redshifts are detected, $H_0$ can be measured with an accuracy of $0.9%$. If 1000 face-on BNSs at $z<2$ are detected with known redshifts, we are able to achieve $Delta q_0=0.002$, or $Delta w_0=0.03$ and $Delta w_a=0.2$ for dark energy.(Abridged version).
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