Event Rates of Gravitational Waves from merging Intermediate mass Black Holes: based on a Runaway Path to a SMBH

Based on a dynamical formation model of a supermassive black hole (SMBH), we estimate the expected observational profile of gravitational wave at ground-based detectors, such as KAGRA or advanced LIGO/VIRGO. Noting that the second generation of detectors have enough sensitivity from 10 Hz and up, we are able to detect the ring-down gravitational wave of a BH with the mass M < 2 × 103M⊙. This enables us to check the sequence of BH mergers to SMBHs via intermediate-mass BHs. We estimate the number density of galaxies from the halo formation model and estimate the number of BH mergers from the giant molecular cloud model assuming hierarchical growth of merged cores. At the designed KAGRA (and/or advanced LIGO/VIRGO), we find that the BH merger of its total mass M ∼ 60M⊙ is at the peak of the expected mass distribution. With its signal-to-noise ratio ρ = 10(30), we estimate the event rate R ∼ 200(20) per year in the most optimistic case, and we also find that BH mergers in the range M < 150M⊙ are R > 1 per year for ρ = 10. Thus, if we observe a BH with more than 100M⊙ in future gravitational-wave observations, our model naturally explains its source.

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Geometric Approach to Analytic Marginalisation of the Likelihood Ratio for Continuous Gravitational Wave Searches

Universe ◽

10.3390/universe7060174 ◽

2021 ◽

Vol 7 (6) ◽

pp. 174

Author(s):

Karl Wette

Keyword(s):

Gravitational Wave ◽

Likelihood Ratio ◽

Signal To Noise Ratio ◽

Geometric Approach ◽

The Other ◽

Efficient Computation ◽

Likelihood Ratios ◽

Signal To Noise ◽

Noise Ratio ◽

Optimal Signal

The likelihood ratio for a continuous gravitational wave signal is viewed geometrically as a function of the orientation of two vectors; one representing the optimal signal-to-noise ratio, and the other representing the maximised likelihood ratio or F-statistic. Analytic marginalisation over the angle between the vectors yields a marginalised likelihood ratio, which is a function of the F-statistic. Further analytic marginalisation over the optimal signal-to-noise ratio is explored using different choices of prior. Monte-Carlo simulations show that the marginalised likelihood ratios had identical detection power to the F-statistic. This approach demonstrates a route to viewing the F-statistic in a Bayesian context, while retaining the advantages of its efficient computation.

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Image-Guided Rendering with an Evolutionary Algorithm Based on Cloud Model

Computational Intelligence and Neuroscience ◽

10.1155/2018/4518265 ◽

2018 ◽

Vol 2018 ◽

pp. 1-19 ◽

Cited By ~ 1

Author(s):

Tao Wu

Keyword(s):

Evolutionary Algorithm ◽

Cloud Model ◽

Signal To Noise Ratio ◽

Structural Similarity ◽

Input Image ◽

Average Score ◽

Signal To Noise ◽

Feature Similarity ◽

Contrast Factor ◽

Noise Ratio

The process of creating nonphotorealistic rendering images and animations can be enjoyable if a useful method is involved. We use an evolutionary algorithm to generate painterly styles of images. Given an input image as the reference target, a cloud model-based evolutionary algorithm that will rerender the target image with nonphotorealistic effects is evolved. The resulting animations have an interesting characteristic in which the target slowly emerges from a set of strokes. A number of experiments are performed, as well as visual comparisons, quantitative comparisons, and user studies. The average scores in normalized feature similarity of standard pixel-wise peak signal-to-noise ratio, mean structural similarity, feature similarity, and gradient similarity based metric are 0.486, 0.628, 0.579, and 0.640, respectively. The average scores in normalized aesthetic measures of Benford’s law, fractal dimension, global contrast factor, and Shannon’s entropy are 0.630, 0.397, 0.418, and 0.708, respectively. Compared with those of similar method, the average score of the proposed method, except peak signal-to-noise ratio, is higher by approximately 10%. The results suggest that the proposed method can generate appealing images and animations with different styles by choosing different strokes, and it would inspire graphic designers who may be interested in computer-based evolutionary art.

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The Eccentric and Accelerating Stellar Binary Black Hole Mergers in Galactic Nuclei: Observing in Ground and Space Gravitational-wave Observatories

The Astrophysical Journal ◽

10.3847/1538-4357/ac2c07 ◽

2021 ◽

Vol 923 (2) ◽

pp. 139

Author(s):

Fupeng Zhang ◽

Xian Chen ◽

Lijing Shao ◽

Kohei Inayoshi

Keyword(s):

Black Hole ◽

Gravitational Wave ◽

Signal To Noise Ratio ◽

Galactic Nuclei ◽

Signal To Noise ◽

High Eccentricity ◽

Massive Black Hole ◽

Binary Black Holes ◽

Binary Black Hole ◽

Space Observatories

Abstract We study the stellar binary black holes (BBHs) inspiraling/merging in galactic nuclei based on our numerical method GNC. We find that 3%–40% of all newborn BBHs will finally merge due to various dynamical effects. In a five-year mission, up to 104, 105, and ∼100 of BBHs inspiraling/merging in galactic nuclei can be detected with signal-to-noise ration >8 in Advanced LIGO (aLIGO), Einstein/DECIGO, and TianQin/LISA/TaiJi, respectively. Roughly tens are detectable in both LISA/TaiJi/TianQin and aLIGO. These BBHs have two unique characteristics. (1) Significant eccentricities: 1%–3%, 2%–7%, or 30%–90% of them have e i > 0.1 when they enter into aLIGO, Einstein, or space observatories, respectively. Such high eccentricities provide a possible explanation for that of GW190521. Most highly eccentric BBHs are not detectable in LISA/Tianqin/TaiJi before entering into aLIGO/Einstein, as their strain becomes significant only at f GW ≳ 0.1 Hz. DECIGO becomes an ideal observatory to detect those events, as it can fully cover the rising phase. (2) Up to 2% of BBHs can inspiral/merge at distances ≲103 r SW from the massive black hole, with significant accelerations, such that the Doppler phase drift of ∼10–105 of them can be detected with signal-to-noise ratio >8 in space observatories. The energy density of the gravitational-wave backgrounds (GWBs) contributed by these BBHs deviates from the power-law slope of 2/3 at f GW ≲ 1 mHz. The high eccentricity, significant accelerations, and the different profile of the GWB of these sources make them distinguishable, and thus interesting for future gravitational-wave detections and tests of relativities.

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Signal to noise ratio in a satellite gravitational wave experiment

Acta Astronautica ◽

10.1016/0094-5765(75)90066-1 ◽

1975 ◽

Vol 2 (5-6) ◽

pp. 535-537 ◽

Cited By ~ 2

Author(s):

V.B. Braginsky

Keyword(s):

Gravitational Wave ◽

Signal To Noise Ratio ◽

Signal To Noise ◽

Wave Experiment ◽

Noise Ratio

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COALESCENCE RATE OF SUPERMASSIVE BLACK HOLE BINARIES DERIVED FROM COSMOLOGICAL SIMULATIONS: DETECTION RATES FOR LISA AND ET

International Journal of Modern Physics D ◽

10.1142/s0218271811020433 ◽

2011 ◽

Vol 20 (12) ◽

pp. 2399-2417 ◽

Cited By ~ 5

Author(s):

CH. FILLOUX ◽

J. A. DE FREITAS PACHECO ◽

F. DURIER ◽

J. C. N. DE ARAUJO

Keyword(s):

Black Holes ◽

Gravitational Wave ◽

Detection Rate ◽

Signal To Noise Ratio ◽

Supermassive Black Holes ◽

Frequency Interval ◽

Signal To Noise ◽

Cosmological Simulations ◽

Coalescence Rate ◽

Noise Ratio

The coalescence history of massive black holes has been derived from cosmological simulations, in which the evolution of those objects and that of the host galaxies are followed in a consistent way. The present study indicates that supermassive black holes having masses greater than ~ 109 M⊙ underwent up to 500 merger events along their history. The derived coalescence rate per comoving volume and per mass interval permitted to obtain an estimate of the expected detection rate distribution of gravitational wave signals ("ring-down") along frequencies accessible by the planned interferometers either in space (LISA) or in the ground (Einstein). For LISA, in its original configuration, a total detection rate of about 15 yr-1 is predicted for events having a signal-to-noise ratio equal to 10, expected to occur mainly in the frequency range 4–9 mHz. For the Einstein gravitational wave telescope, one event each 14 months down to one event each four years is expected with a signal-to-noise ratio of 5, occurring mainly in the frequency interval 10–20 Hz. The detection of these gravitational signals and their distribution in frequency would be in the future an important tool able to discriminate among different scenarios explaining the origin of supermassive black holes.

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The NANOGrav 12.5-year Data Set: Search for Non-Einsteinian Polarization Modes in the Gravitational-wave Background

The Astrophysical Journal ◽

10.3847/2041-8213/ac401c ◽

2021 ◽

Vol 923 (2) ◽

pp. L22

Author(s):

Zaven Arzoumanian ◽

Paul T. Baker ◽

Harsha Blumer ◽

Bence Bécsy ◽

Adam Brazier ◽

...

Keyword(s):

Gravitational Wave ◽

Signal To Noise Ratio ◽

Simulated Data ◽

Reference Frequency ◽

Spatial Correlations ◽

Signal To Noise ◽

Data Set ◽

Upper Limits ◽

Theories Of Gravity ◽

Gravitational Wave Background

Abstract We search NANOGrav’s 12.5 yr data set for evidence of a gravitational-wave background (GWB) with all the spatial correlations allowed by general metric theories of gravity. We find no substantial evidence in favor of the existence of such correlations in our data. We find that scalar-transverse (ST) correlations yield signal-to-noise ratios and Bayes factors that are higher than quadrupolar (tensor-transverse, TT) correlations. Specifically, we find ST correlations with a signal-to-noise ratio of 2.8 that are preferred over TT correlations (Hellings and Downs correlations) with Bayesian odds of about 20:1. However, the significance of ST correlations is reduced dramatically when we include modeling of the solar system ephemeris systematics and/or remove pulsar J0030+0451 entirely from consideration. Even taking the nominal signal-to-noise ratios at face value, analyses of simulated data sets show that such values are not extremely unlikely to be observed in cases where only the usual TT modes are present in the GWB. In the absence of a detection of any polarization mode of gravity, we place upper limits on their amplitudes for a spectral index of γ = 5 and a reference frequency of f yr = 1 yr−1. Among the upper limits for eight general families of metric theories of gravity, we find the values of A TT 95 % = ( 9.7 ± 0.4 ) × 10 − 16 and A ST 95 % = ( 1.4 ± 0.03 ) × 10 − 15 for the family of metric spacetime theories that contain both TT and ST modes.

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Are stellar-mass black-hole binaries too quiet for LISA?

Monthly Notices of the Royal Astronomical Society Letters ◽

10.1093/mnrasl/slz104 ◽

2019 ◽

Vol 488 (1) ◽

pp. L94-L98 ◽

Cited By ~ 18

Author(s):

Christopher J Moore ◽

Davide Gerosa ◽

Antoine Klein

Keyword(s):

Black Hole ◽

Event Rate ◽

Signal To Noise Ratio ◽

High Mass ◽

Signal To Noise ◽

Expected Number ◽

Detector Performance ◽

High Frequencies ◽

Black Hole Binaries ◽

Long Duration

ABSTRACT The progenitors of the high-mass black-hole mergers observed by LIGO and Virgo are potential LISA sources and promising candidates for multiband GW observations. In this letter, we consider the minimum signal-to-noise ratio these sources must have to be detected by LISA bearing in mind the long duration and complexity of the signals. Our revised threshold of ρthr ∼ 15 is higher than previous estimates, which significantly reduces the expected number of events. We also point out the importance of the detector performance at high frequencies and the duration of the LISA mission, which both influence the event rate substantially.

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Inferring the lensing rate of LIGO–Virgo sources from the stochastic gravitational wave background

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa3813 ◽

2020 ◽

Vol 501 (2) ◽

pp. 2451-2466

Author(s):

Suvodip Mukherjee ◽

Tom Broadhurst ◽

Jose M Diego ◽

Joseph Silk ◽

George F Smoot

Keyword(s):

Gravitational Wave ◽

Upper Bound ◽

Laser Interferometer ◽

Event Rate ◽

High Redshift ◽

Design Sensitivity ◽

Stochastic Background ◽

Strong Lensing ◽

Event Rates ◽

Gravitational Wave Background

ABSTRACT Strong lensing of gravitational waves (GWs) is more likely for distant sources but predicted event rates are highly uncertain with many astrophysical origins proposed. Here, we open a new avenue to estimate the event rate of strongly lensed systems by exploring the amplitude of the stochastic gravitational wave background (SGWB). This method can provide a direct upper bound on the high-redshift binary coalescing rates, which can be translated into an upper bound on the expected rate of strongly lensed systems. We show that from the ongoing analysis of the Laser Interferometer Gravitational-wave Observatory (LIGO)-Virgo and in the future from the LIGO–Virgo design sensitivity stringent bounds on the lensing event rate can be imposed using the SGWB signal. Combining measurements of loud GW events with an unresolved stochastic background detection will improve estimates of the numbers of lensed events at high redshift. The proposed method is going to play a crucial in understanding the population of lensed and unlensed systems from GW observations.

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Mining the data

Gravitational-Wave Astronomy ◽

10.1093/oso/9780198568032.003.0008 ◽

2019 ◽

pp. 150-174

Author(s):

Nils Andersson

Keyword(s):

Data Analysis ◽

Bayesian Inference ◽

Gravitational Wave ◽

Signal To Noise Ratio ◽

Bayesian Inference Analysis ◽

Matched Filtering ◽

Signal To Noise ◽

Wave Data ◽

Key Concepts ◽

Noise Ratio

This chapter introduces the ideas used in gravitational-wave data analysis, starting from matched filtering and building up to Bayesian inference analysis. Key concepts like the signal-to-noise ratio are defined and their use in actual searches is demonstrated by examples.

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