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تسجيل مستخدم جديدSupplement: The Rate of Binary Black Hole Mergers Inferred from Advanced LIGO Observations Surrounding GW150914
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Supplemental information for a Letter reporting the rate of binary black hole (BBH) coalescences inferred from 16 days of coincident Advanced LIGO observations surrounding the transient gravitational wave signal GW150914. In that work we reported various rate estimates whose 90% credible intervals fell in the range $2$--$600 , mathrm{Gpc}^{-3} mathrm{yr}^{-1}$. Here we give details of our method and computations, including information about our search pipelines, a derivation of our likelihood function for the analysis, a description of the astrophysical search trigger distribution expected from merging BBHs, details on our computational methods, a description of the effects and our model for calibration uncertainty, and an analytic method of estimating our detector sensitivity that is calibrated to our measurements.
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A transient gravitational-wave signal, GW150914, was identified in the twin Advanced LIGO detectors on September 14, 2015 at 09:50:45 UTC. To assess the implications of this discovery, the detectors remained in operation with unchanged configurations
over a period of 39 d around the time of the signal. At the detection statistic threshold corresponding to that observed for GW150914, our search of the 16 days of simultaneous two-detector observational data is estimated to have a false alarm rate (FAR) of $< 4.9 times 10^{-6} , mathrm{yr}^{-1}$, yielding a $p$-value for GW150914 of $< 2 times 10^{-7}$. Parameter estimation followup on this trigger identifies its source as a binary black hole (BBH) merger with component masses $(m_1, m_2) = left(36^{+5}_{-4},29^{+4}_{-4}right) , M_odot$ at redshift $z = 0.09^{+0.03}_{-0.04}$ (median and 90% credible range). Here we report on the constraints these observations place on the rate of BBH coalescences. Considering only GW150914, assuming that all BBHs in the Universe have the same masses and spins as this event, imposing a search FAR threshold of 1 per 100 years, and assuming that the BBH merger rate is constant in the comoving frame, we infer a 90% credible range of merger rates between $2$--$53 , mathrm{Gpc}^{-3} mathrm{yr}^{-1}$ (comoving frame). Incorporating all search triggers that pass a much lower threshold while accounting for the uncertainty in the astrophysical origin of each trigger, we estimate a higher rate, ranging from $13$--$600 , mathrm{Gpc}^{-3} mathrm{yr}^{-1}$ depending on assumptions about the BBH mass distribution. All together, our various rate estimates fall in the conservative range $2$--$600 , mathrm{Gpc}^{-3} mathrm{yr}^{-1}$.
In Advanced LIGO, detection and astrophysical source parameter estimation of the binary black hole merger GW150914 requires a calibrated estimate of the gravitational-wave strain sensed by the detectors. Producing an estimate from each detectors diff
erential arm length control loop readout signals requires applying time domain filters, which are designed from a frequency domain model of the detectors gravitational-wave response. The gravitational-wave response model is determined by the detectors opto-mechanical response and the properties of its feedback control system. The measurements used to validate the model and characterize its uncertainty are derived primarily from a dedicated photon radiation pressure actuator, with cross-checks provided by optical and radio frequency references. We describe how the gravitational-wave readout signal is calibrated into equivalent gravitational-wave-induced strain and how the statistical uncertainties and systematic errors are assessed. Detector data collected over 38 calendar days, from September 12 to October 20, 2015, contain the event GW150914 and approximately 16 of coincident data used to estimate the event false alarm probability. The calibration uncertainty is less than 10% in magnitude and 10 degrees in phase across the relevant frequency band 20 Hz to 1 kHz.
We present results on the mass, spin, and redshift distributions with phenomenological population models using the ten binary black hole mergers detected in the first and second observing runs completed by Advanced LIGO and Advanced Virgo. We constra
in properties of the binary black hole (BBH) mass spectrum using models with a range of parameterizations of the BBH mass and spin distributions. We find that the mass distribution of the more massive black hole in such binaries is well approximated by models with no more than 1% of black holes more massive than $45,M_odot$, and a power law index of $alpha = {1.3}^{+1.4}_{-1.7}$ (90% credibility). We also show that BBHs are unlikely to be composed of black holes with large spins aligned to the orbital angular momentum. Modelling the evolution of the BBH merger rate with redshift, we show that it is at or increasing with redshift with 93% probability. Marginalizing over uncertainties in the BBH population, we find robust estimates of the BBH merger rate density of $R = {53.2}^{+55.8}_{-28.2}$ Gpc$^{-3}$ yr$^{-1}$ (90% credibility). As the BBH catalog grows in future observing runs, we expect that uncertainties in the population model parameters will shrink, potentially providing insights into the formation of black holes via supernovae, binary interactions of massive stars, stellar cluster dynamics, and the formation history of black holes across cosmic time.
On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-wave Observatory (LIGO) simultaneously observed the binary black hole merger GW150914. We report the results of a matched-filter search using relativist
ic models of compact-object binaries that recovered GW150914 as the most significant event during the coincident observations between the two LIGO detectors from September 12 to October 20, 2015. GW150914 was observed with a matched filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203 000 years, equivalent to a significance greater than 5.1 {sigma}.
The first observational run of the Advanced LIGO detectors, from September 12, 2015 to January 19, 2016, saw the first detections of gravitational waves from binary black hole mergers. In this paper we present full results from a search for binary bl
ack hole merger signals with total masses up to $100 M_odot$ and detailed implications from our observations of these systems. Our search, based on general-relativistic models of gravitational wave signals from binary black hole systems, unambiguously identified two signals, GW150914 and GW151226, with a significance of greater than $5sigma$ over the observing period. It also identified a third possible signal, LVT151012, with substantially lower significance, and with an 87% probability of being of astrophysical origin. We provide detailed estimates of the parameters of the observed systems. Both GW150914 and GW151226 provide an unprecedented opportunity to study the two-body motion of a compact-object binary in the large velocity, highly nonlinear regime. We do not observe any deviations from general relativity, and place improved empirical bounds on several high-order post-Newtonian coefficients. From our observations we infer stellar-mass binary black hole merger rates lying in the range $9-240 mathrm{Gpc}^{-3} mathrm{yr}^{-1}$. These observations are beginning to inform astrophysical predictions of binary black hole formation rates, and indicate that future observing runs of the Advanced detector network will yield many more gravitational wave detections.
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