Properties of the Binary Black Hole Merger GW150914

On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a gravitational-wave transient (GW150914); we characterize the properties of the source and its parameters. The data around the time of the event were analyzed coherently across the LIGO network using a suite of accurate waveform models that describe gravitational waves from a compact binary system in general relativity. GW150914 was produced by a nearly equal mass binary black hole of masses $36_{-4}^{+5}{M}_{\odot }$ and $29_{-4}^{+4}{M}_{\odot }$; for each parameter we report the median value and the range of the 90% credible interval. The dimensionless spin magnitude of the more massive black hole is bound to be $<0.7$ (at 90% probability). The luminosity distance to the source is $410_{-180}^{+160}\mathrm{Mpc}$, corresponding to a redshift $0.09_{-0.04}^{+0.03}$ assuming standard cosmology. The source location is constrained to an annulus section of $610{\mathrm{deg}}^2$, primarily in the southern hemisphere. The binary merges into a black hole of mass $62_{-4}^{+4}{M}_{\odot }$ and spin $0.67_{-0.07}^{+0.05}$. This black hole is significantly more massive than any other inferred from electromagnetic observations in the stellar-mass regime.

Figure 1

Posterior PDFs for the source-frame component masses $m_1^{\text{source}}$ and $m_2^{\text{source}}$. We use the convention that $m_2^{\text{source}}\le m_1^{\text{source}}$, which produces the sharp cut in the two-dimensional distribution. In the one-dimensional marginalized distributions we show the Overall (solid black), IMRPhenom (blue), and EOBNR (red) PDFs; the dashed vertical lines mark the 90% credible interval for the Overall PDF. The two-dimensional plot shows the contours of the 50% and 90% credible regions plotted over a color-coded PDF.

Figure 2

Posterior PDFs for the source luminosity distance $D_L$ and the binary inclination ${\theta }_{JN}$. In the one-dimensional marginalized distributions we show the Overall (solid black), IMRPhenom (blue), and EOBNR (red) PDFs; the dashed vertical lines mark the 90% credible interval for the Overall PDF. The two-dimensional plot shows the contours of the 50% and 90% credible regions plotted over a color-coded PDF.

Figure 3

PDFs for the source-frame mass and spin of the remnant BH produced by the coalescence of the binary. In the one-dimensional marginalized distributions we show the Overall (solid black), IMRPhenom (blue), and EOBNR (red) PDFs; the dashed vertical lines mark the 90% credible interval for the Overall PDF. The two-dimensional plot shows the contours of the 50% and 90% credible regions plotted over a color-coded PDF.

Figure 4

An orthographic projection of the PDF for the sky location of GW150914 given in terms of right ascension $\alpha$ (measured in hours and labeled around the edge of the figure) and declination $\delta$ (measured in degrees and labeled inside the figure). The contours of the 50% and 90% credible regions are plotted over a color-coded PDF. The sky localization forms part of an annulus, set by the time delay of $6.9_{-0.4}^{+0.5}\mathrm{ms}$ between the Livingston and Hanford detectors.

Figure 5

Left: PDFs (solid black line) for the ${\chi }_p$ and ${\chi }_{\mathrm{eff}}$ spin parameters compared to their prior distribution (green line). The dashed vertical lines mark the 90% credible interval. The one-dimensional plots show probability contours of the prior (green) and marginalized PDF (black). The two-dimensional plot shows the contours of the 50% and 90% credible regions plotted over a color-coded PDF. Right: PDFs for the dimensionless component spins $c{\mathit{S}}_1/(G{m}_1^2)$ and $c{\mathit{S}}_2/(G{m}_2^2)$ relative to the normal to the orbital plane $\mathit{L}$, marginalized over uncertainties in the azimuthal angles. The bins are constructed linearly in spin magnitude and the cosine of the tilt angles, $\cos {\theta }_{L{S}_i}={\mathit{S}}_i·\mathit{L}/(|{\mathit{S}}_i||\mathit{L}|)$, where $i=\{1,2\}$, and therefore have equal prior probability.

Figure 6

Time-domain data (sampled at 2048 Hz) and reconstructed waveforms of GW150914, whitened by the noise power spectral density (in Fig. 1 of Ref. [1] the data are band passed and notched filtered), for the H1 (top) and L1 (bottom) detectors. Times are shown relative to September 14, 2015 at 09:50:45 UTC. The ordinate axes on the right are in units of noise standard deviations from zero—i.e., the peak alone is an $\sim 4\text{−}\sigma$ excursion relative to the instrument noise at that time—and on the left are normalized in order to preserve the strain amplitude at 200 Hz. The waveforms are plotted as bands representing the uncertainty in the reconstruction. Shaded regions correspond to the 90% credible regions for the reconstructed waveforms. The broadest (dark blue) shaded region is obtained with the model that does not assume a particular waveform morphology, but instead uses a linear combination of sine-Gaussian wavelets. The lighter, narrower shaded region (cyan) is the result from the modeled analyses using IMRPhenom and EOBNR template waveforms. The thin grey lines are the data. The agreement between the reconstructed waveforms using the two models is found to be $94_{-3}^{+2}\%$.