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Register a new userNew Coordinates for the Amplitude Parameter Space of Continuous Gravitational Waves
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The parameter space for continuous gravitational waves (GWs) can be divided into amplitude parameters (signal amplitude, inclination and polarization angles describing the orientation of the source, and an initial phase) and phase-evolution parameters. The division is useful in part because the Jaranowski-Krolak-Schutz (JKS) coordinates on the four-dimensional amplitude parameter space allow the GW signal to be written as a linear combination of four template waveforms with the JKS coordinates as coefficients. We define a new set of coordinates on the amplitude parameter space, with the same properties, which is more closely connected to the physical amplitude parameters. These naturally divide into two pairs of Cartesian-like coordinates on two-dimensional subspaces, one corresponding to left- and the other to right-circular polarization. We thus refer to these as CPF (circular polarization factored) coordinates. The corresponding two sets of polar coordinates (known as CPF-polar) can be related in a simple way to the physical parameters. We illustrate some simplifying applications for these various coordinate systems, such as: a calculation of Jacobians between various coordinate systems; an illustration of the signal coordinate singularities associated with left- and right-circular polarization, which correspond to the origins of the two two-dimensional subspaces; and an elucidation of the form of the log-likelihood ratio between hypotheses of Gaussian noise with and without a continuous GW signal. These are used to illustrate some of the prospects for approximate evaluation of a Bayesian detection statistic defined by marginalization over the physical parameter space. Additionally, in the presence of simplifying assumptions about the observing geometry, we are able to explicitly evaluate the integral for the Bayesian detection statistic, and compare it to the approximate results.
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Gravitational wave astronomy opened dramatically in September 2015 with the LIGO discovery of a distant and massive binary black hole coalescence. The more recent discovery of a binary neutron star merger, followed by a gamma ray burst and a kilonova, reinforces the excitement of this new era, in which we may soon see other sources of gravitational waves, including continuous, nearly monochromatic signals. Potential continuous wave (CW) sources include rapidly spinning galactic neutron stars and more exotic possibilities, such as emission from axion Bose Einstein clouds surrounding black holes. Recent searches in Advanced LIGO data are presented, and prospects for more sensitive future searches discussed.
We calculate the amplitude of the de Broglie gravitational waves using the standard Einstein General Relativity. We find that these waves disappear in the limit $hbar to 0$ and when their source has a large mass and volume. From the experimental point of view, the knowledge of the amplitude allows to estimate the magnitude of the effect of the wave on a sphere of test particles. We propose also to measure a very special shift angle that does not change with time.
Wide parameter space searches for long lived continuous gravitational wave signals are computationally limited. It is therefore critically important that available computational resources are used rationally. In this paper we consider directed searches, i.e. targets for which the sky position is known accurately but the frequency and spindown parameters are completely unknown. Given a list of such potential astrophysical targets, we therefore need to prioritize. On which target(s) should we spend scarce computing resources? What parameter space region in frequency and spindown should we search? Finally, what is the optimal search set-up that we should use? In this paper we present a general framework that allows to solve all three of these problems. This framework is based on maximizing the probability of making a detection subject to a constraint on the maximum available computational cost. We illustrate the method for a simplified problem.
We present a first proof-of-principle study for using deep neural networks (DNNs) as a novel search method for continuous gravitational waves (CWs) from unknown spinning neutron stars. The sensitivity of current wide-parameter-space CW searches is limited by the available computing power, which makes neural networks an interesting alternative to investigate, as they are extremely fast once trained and have recently been shown to rival the sensitivity of matched filtering for black-hole merger signals. We train a convolutional neural network with residual (short-cut) connections and compare its detection power to that of a fully-coherent matched-filtering search using the WEAVE pipeline. As test benchmarks we consider two types of all-sky searches over the frequency range from $20,mathrm{Hz}$ to $1000,mathrm{Hz}$: an `easy search using $T=10^5,mathrm{s}$ of data, and a `harder search using $T=10^6,mathrm{s}$. Detection probability $p_mathrm{det}$ is measured on a signal population for which matched filtering achieves $p_mathrm{det}=90%$ in Gaussian noise. In the easiest test case ($T=10^5,mathrm{s}$ at $20,mathrm{Hz}$) the DNN achieves $p_mathrm{det}sim88%$, corresponding to a loss in sensitivity depth of $sim5%$ versus coherent matched filtering. However, at higher-frequencies and longer observation time the DNN detection power decreases, until $p_mathrm{det}sim13%$ and a loss of $sim 66%$ in sensitivity depth in the hardest case ($T=10^6,mathrm{s}$ at $1000,mathrm{Hz}$). We study the DNN generalization ability by testing on signals of different frequencies, spindowns and signal strengths than they were trained on. We observe excellent generalization: only five networks, each trained at a different frequency, would be able to cover the whole frequency range of the search.
We transform the metric of an isolated matter source in the multipolar post-Minkowskian approximation from harmonic (de Donder) coordinates to radiative Newman-Unti (NU) coordinates. To linearized order, we obtain the NU metric as a functional of the mass and current multipole moments of the source, valid all-over the exterior region of the source. Imposing appropriate boundary conditions we recover the generalized Bondi-van der Burg-Metzner-Sachs residual symmetry group. To quadratic order, in the case of the mass-quadrupole interaction, we determine the contributions of gravitational-wave tails in the NU metric, and prove that the expansion of the metric in terms of the radius is regular to all orders. The mass and angular momentum aspects, as well as the Bondi shear, are read off from the metric. They are given by the radiative quadrupole moment including the tail terms.
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