GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence

Abstract

We report the observation of a gravitational-wave signal produced by the coalescence of two stellar-mass black holes. The signal, GW151226, was observed by the twin detectors of the Laser Interferometer Gravitational-Wave Observatory (LIGO) on December 26, 2015 at 03:38:53 UTC. The signal was initially identified within 70 s by an online matched-filter search targeting binary coalescences. Subsequent off-line analyses recovered GW151226 with a network signal-to-noise ratio of 13 and a significance greater than 5 $σ$. The signal persisted in the LIGO frequency band for approximately 1 s, increasing in frequency and amplitude over about 55 cycles from 35 to 450 Hz, and reached a peak gravitational strain of $3.4_{-0.9}^{+0.7} \times 10^{-22}$. The inferred source-frame initial black hole masses are $14.2_{-3.7}^{+8.3} M_{\odot}$ and $7.5_{-2.3}^{+2.3} M_{\odot}$ and the final black hole mass is $20.8_{-1.7}^{+6.1} M_{\odot}$. We find that at least one of the component black holes has spin greater than 0.2. This source is located at a luminosity distance of $440_{-190}^{+180}$ Mpc corresponding to a redshift $0.09_{-0.04}^{+0.03}$. All uncertainties define a 90 % credible interval. This second gravitational-wave observation provides improved constraints on stellar populations and on deviations from general relativity.

Figures (5)

• Figure 1: GW151226 observed by the LIGO Hanford (left column) and Livingston (right column) detectors, where times are relative to December 26, 2015 at 03:38:53.648 UTC. First row: Strain data from the two detectors, where the data are filtered with a$30-600-\mathrm{Hz}$ bandpass filter to suppress large fluctuations outside this range and band-reject filters to remove strong instrumental spectral lines [46]. Also shown (black) is the best-match template from a nonprecessing spin waveform model reconstructed using a Bayesian analysis [21] with the same filtering applied. As a result, modulations in the waveform are present due to this conditioning and not due to precession effects. The thickness of the line indicates the $90 \%$ credible region. See Fig. 5 for a reconstruction of the best-match template with no filtering applied. Second row: The accumulated peak signal-to-noise ratio $\left(\mathrm{SNR}_{\mathrm{p}}\right)$ as a function of time when integrating from the start of the best-match template, corresponding to a gravitational-wave frequency of 30 Hz , up to its merger time. The total accumulated $\mathrm{SNR}_{\mathrm{p}}$ corresponds to the peak in the next row. Third row: Signal-to-noise ratio (SNR) time series produced by time shifting the best-match template waveform and computing the integrated SNR at each point in time. The peak of the SNR time series gives the merger time of the best-match template for which the highest overlap with the data is achieved. The single-detector SNRs in LIGO Hanford and Livingston are 10.5 and 7.9, respectively, primarily because of the detectors' differing sensitivities. Fourth row: Time-frequency representation [47] of the strain data around the time of GW151226. In contrast to GW150914 [4], the signal is not easily visible.
• Figure 2: Search results from the two binary coalescence searches using their respective detection statistics$\hat{\rho}_{c}$ (a combined matched filtering signal-to-noise ratio, defined precisely in [14]; left) and $\ln \mathcal{L}$ (the log of a likelihood ratio, defined precisely in [17]; right). The event GW150914 is removed in all cases since it had already been confirmed as a real gravitational-wave signal. Both plots show the number of candidate events (search results) as a function of detection statistic with orange square markers. The mean number of background events as a function of the detection statistic is estimated using independent methods [18]. The background estimates are found using two methods: excluding all candidate events which are shown as orange square markers (purple lines) or including all candidate events except GW150914 (black lines). The scales along the top give the significance of an event in Gaussian standard deviations based on the corresponding noise background. The raised tail in the black-line background (left) is due to random coincidences of GW151226 in one detector with noise in the other detector and (right) due to the inclusion of GW151226 in the distribution of noise events in each detector. GW151226 is found with high significance in both searches. LVT151012 [5,18], visible in the search results at $\lesssim 2.0 \sigma$, is the third most significant binary black hole candidate event in the observing period.
• Figure 3: Posterior density function for the source-frame masses$m_{1}^{\text{source }}$ (primary) and $m_{2}^{\text{source }}$ (secondary). The one-dimensional marginalized distributions include the posterior density functions for the precessing (blue) and nonprecessing (red) spin waveform models where average (black) represents the mean of the two models. The dashed lines mark the $90 \%$ credible interval for the average posterior density function. The two-dimensional plot shows the contours of the $50 \%$ and $90 \%$ credible regions plotted over a color-coded posterior density function.
• Figure 4: Left: Posterior density function for the$\chi_{p}$ and $\chi_{\text{eff }}$ spin parameters (measured at 20 Hz ) compared to their prior distributions. The one-dimensional plot shows probability contours of the prior (green) and marginalized posterior density function (black) [58,59]. The two-dimensional plot shows the contours of the $50 \%$ and $90 \%$ credible regions plotted over a color-coded posterior density function. The dashed lines mark the $90 \%$ credible interval. Right: Posterior density function for the dimensionless component spins, $c \mathbf{S}_{1} /\left(G m_{1}^{2}\right)$ and $c \mathbf{S}_{2} /\left(G m_{2}^{2}\right)$, relative to the normal of the orbital plane $\hat{\mathbf{L}} . \mathbf{S}_{i}$ and $m_{i}$ are the spin angular momenta and masses of the primary ( $i=1$ ) and secondary ( $i=2$ ) black holes, $c$ is the speed of light and $G$ is the gravitational constant. The posterior density functions are marginalized over the azimuthal angles. The bins are designed to have equal prior probability; they are constructed linearly in spin magnitudes and the cosine of the tilt angles $\cos ^{-1}\left(\hat{\mathbf{S}}_{i} \cdot \hat{\mathbf{L}}\right)$.
• Figure 5: Estimated gravitational-wave strain from GW151226 projected onto the LIGO Livingston detector with times relative to December 26, 2015 at 03:38:53.648 UTC. This shows the full bandwidth, without the filtering used for Fig. 1. Top: The$90 \%$ credible region (as in [57]) for a nonprecessing spin waveform-model reconstruction (gray) and a direct, nonprecessing numerical solution of Einstein's equations (red) with parameters consistent with the $90 \%$ credible region. Bottom: The gravitational-wave frequency $f$ (left axis) computed from the numerical-relativity waveform. The cross denotes the location of the maximum of the waveform amplitude, approximately coincident with the merger of the two black holes. During the inspiral, $f$ can be related to an effective relative velocity (right axis) given by the post-Newtonian parameter $v / c=\left(G M \pi f / c^{3}\right)^{1 / 3}$, where $M$ is the total mass.