GW150914: First results from the search for binary black hole coalescence with Advanced LIGO

Abstract

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 relativistic 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 203000 years, equivalent to a significance greater than 5.1 σ.

FIG. 1.

The four-dimensional search parameter space covered by the template bank shown projected into the component-mass plane, using the convention m₁ > m₂. The lines bound mass regions with different limits on the dimensionless aligned-spin parameters χ₁ and χ₂. Each point indicates the position of a template in the bank. The circle highlights the template that best matches GW150914. This does not coincide with the best-fit parameters due to the discrete nature of the template bank.

FIG. 2.

Cumulative distribution of fitting factors obtained with the template bank for a population of simulated aligned-spin binary black hole signals. Less than 1% of the signals have an matched-filter SNR loss greater than 3%, demonstrating that the template bank has good coverage of the target search space.

FIG. 3.

The effective fitting factor between simulated precessing binary black hole signals and the template bank used for the search as a function of detector-frame total mass and mass ratio, averaged over each rectangular tile. The effective fitting factor gives the volume-averaged reduction in the sensitive distance of the search at fixed matched-filter SNR due to mismatch between the template bank and signals. The cross shows the location of GW150914. The high effective fitting factor near GW150914 demonstrates that the aligned-spin template bank used in this search can effectively recover systems with misaligned spins and similar masses to GW150914.

FIG. 4.

Distributions of noise triggers over re-weighted SNR , for Advanced LIGO engineering run data taken between September 2 and September 9, 2015. Each line shows triggers from templates within a given range of gravitational-wave frequency at maximum strain amplitude, f_peak. Left: Triggers obtained from H1, L1 data respectively, using a fixed number of p = 16 frequency bands for the χ² test. Right: Triggers obtained with the number of frequency bands determined by the function p = ⌊0.4(f_peak/Hz)^2/3⌋. Note that while noise distributions are suppressed over the whole template bank with the optimized choice of p, the suppression is strongest for templates with lower f_peak values. Templates that have a f_peak < 220Hz produce a large tail of noise triggers with high re-weighted SNR even with the improved χ²-squared test tuning, thus we separate these templates from the rest of the bank when calculating the noise background.

FIG. 5.

The distribution of the differences in the number of events between consecutive time shifts, where C_i denotes the number of events in the ith time shift. The green line shows the predicted distribution for independent Poisson processes with means equal to the average event rate per time shift. The blue histogram shows the distribution obtained from time-shifted analyses. The variance of the time-shifted background distribution is 1.996, consistent with the predicted variance of 2. The distribution of background event counts in adjacent time shifts is well modeled by independent Poisson processes.

FIG. 6.

Two projections of parameters in the multi-dimensional likelihood ratio ranking for GstLAL (Left: H1, Right: L1). The relative positions of GW150914 (red cross) and LVT151012 (blue plus) are indicated in the ξ²/ρ² vs matched-filter SNR plane. The yellow–black colormap shows the natural logarithm of the probability density function calculated using only coincident triggers that are not coincident between the detectors. This is the background model used in the likelihood ratio calculation. The red–blue colormap shows the natural logarithm of the probability density function calculated from both coincident events and triggers that are not coincident between the detectors. The distribution showing both candidate events and non-coincident triggers has been masked to only show regions which are not consistent with the background model. Rather than showing the θ_i bins in which GW150914 and LVT151012 were found, θ_i has been marginalized over to demonstrate that no background triggers from any bin had the parameters of GW150914.

FIG. 7.

Left: Search results from the PyCBC analysis. The histogram shows the number of candidate events (orange) and the number of background events due to noise in the search class where GW150914 was found (black) as a function of the search detection-statistic and with a bin width of $\Delta {\widehat{\rho }}_c=0.2$. The significance of GW150914 is greater than 5.1 σ. The scales immediately above the histogram give the significance of an event measured against the noise backgrounds in units of Gaussian standard deviations as a function of the detection-statistic. The black background histogram shows the result of the time-shift method to estimate the noise background in the observation period. The tail in the black-line background of the binary coalescence search is due to random coincidences of GW150914 in one detector with noise in the other detector. The significance of GW150914 is measured against the upper gray scale. The purple background histogram is the background excluding coincidences involving GW150914 and it is the background to be used to assess the significance of the second loudest event; the significance of this event is measured against the upper purple scale. Right: Search results from the GstLAL analysis. The histogram shows the observed candidate events (orange) as a function of the detection statistic $\mathcal{L}$. The black line indicates the expected background from noise where candidate events have been included in the noise background probability density function. The purple line indicates the expected background from noise where candidate events have not been included in the noise background probability density function. The independently-implemented search methods and different background estimation method confirm the discovery of GW150914.

FIG. 8.

Left: PyCBC matched-filter SNR (blue), re-weighted SNR (purple) and χ² (green) versus time of the best-matching template at the time of GW150914. The top plot shows the Hanford detector; bottom, Livingston. Right: Observed matched-filter SNR (blue) and expected matched-filter SNR (purple) versus time for the best-matching template at the time of GW150914, as reported by the GstLAL analysis. The expected matched-filter SNR is based on the autocorrelation of the best-matching template. The dashed black lines indicate 1σ deviations expected in Gaussian noise.

FIG. 9.

Variation in $\widehat{\rho }$ when the time-dependent parameter $\Im {\kappa }_T$ is adjusted. The solid blue curve represents $\widehat{\rho }$ averaged over 16 software injections, with waveform parameters identical to the best-fit template for GW150914. $\widehat{\rho }$ decreases as $\Im {\kappa }_T$ deviates from its nominal value. The green dashed curve is a quadratic fit, and represents the approximate behavior of $\langle \widehat{\rho }\rangle$ if we had used a much larger number of software injections. The grey histogram represents the measured values of $\Im {\kappa }_T$ for times used in the analysis on September 14 and 15.

FIG. 10.

PyCBC ${\chi }_r^2$ (top row) and GstLAL ξ² (bottom row) versus SNR in each detector. Triggers associated with a set of simulated binary black hole signals that are added in software are shown, colored by the false alarm rate that they were recovered with (crosses). Also shown are triggers associated with simulated signals that were added to the detectors. We see a clear separation between these simulated signals and background noise triggers (black dots; for plotting purposes, a threshold was applied to the background, indicated by the gray region). Lines of constant re-weighted SNR (gray dashed lines) are shown in the PyCBC plot; plotted are $\widehat{\rho }=\left\{8,10,14,20\right\}$.