Improved Analysis of GW150914 Using a Fully Spin-Precessing Waveform Model

This paper presents updated estimates of source parameters for GW150914, a binary black-hole coalescence event detected by the Laser Interferometer Gravitational-wave Observatory (LIGO) in 2015 [Abbott et al. Phys. Rev. Lett. 116, 061102 (2016).]. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] presented parameter estimation of the source using a 13-dimensional, phenomenological precessing-spin model (precessing IMRPhenom) and an 11-dimensional nonprecessing effective-one-body (EOB) model calibrated to numerical-relativity simulations, which forces spin alignment (nonprecessing EOBNR). Here, we present new results that include a 15-dimensional precessing-spin waveform model (precessing EOBNR) developed within the EOB formalism. We find good agreement with the parameters estimated previously [Abbott et al. Phys. Rev. Lett. 116, 241102 (2016).], and we quote updated component masses of ${35}_{-3}^{+5}$ ${\mathrm{M}}_{\odot }$ and $30_{-4}^{+3}$ ${\mathrm{M}}_{\odot }$ (where errors correspond to 90% symmetric credible intervals). We also present slightly tighter constraints on the dimensionless spin magnitudes of the two black holes, with a primary spin estimate $<0.65$ and a secondary spin estimate $<0.75$ at 90% probability. Abbott et al. [Phys. Rev. Lett. 116, 241102 (2016).] estimated the systematic parameter-extraction errors due to waveform-model uncertainty by combining the posterior probability densities of precessing IMRPhenom and nonprecessing EOBNR. Here, we find that the two precessing-spin models are in closer agreement, suggesting that these systematic errors are smaller than previously quoted.

Popular Summary

On September 14, 2015, the Laser Interferometer Gravitational-Wave Observatory (LIGO) detected a binary black hole coalescence event, GW150914.

Spin is known to be intrinsic to stellar-mass black holes, and previous work presented parameter estimation of the source using a 13-dimensional, phenomenological model with precessing spin (i.e., the spins of the individual black holes are not assumed to be aligned with the orbital angular momentum of the binary; “precessing IMRPhenom”) and an 11-dimensional nonprecessing effective-one-body model calibrated to numerical-relativity simulations, which forces spin alignment (“nonprecessing EOBNR”). Here, we share new results that include a 15-dimensional precessing-spin waveform model developed within the effective one-body formalism. This model takes into account the 6 degrees of freedom associated with black hole spin.

We recover good agreement with the parameters estimated previously, and we quote updated black hole component masses of roughly 35 and 30 times the mass of the Sun. We also present slightly tighter constraints on the dimensionless spin magnitudes of the two black holes: a primary spin estimate of 0.65 and a secondary spin estimate of 0.75, where a value of 0.0 indicates no spin rotation and a value of 1.0 indicates maximal rotation. Previous work estimated the systematic parameter-extraction errors due to waveform-model uncertainty by combining the posterior probability densities of precessing IMRPhenom and nonprecessing EOBNR. Here, we find that the two precessing-spin models are in closer agreement, suggesting that these systematic errors are smaller than previously quoted.

We expect that our findings will pave the way for more precise estimates of black hole parameters recovered during Advanced LIGO’s second observing run, which is slated to commence in 2016. In particular, our results will be most applicable to black hole pairs with a larger mass asymmetry than the GW150914 system discovered in 2015.

Figure 1

Comparing nonprecessing EOBNR (light yellow, top), precessing IMRPhenom (light blue, middle), and precessing EOBNR (light red, bottom) 90% credible intervals for select GW150914 source parameters. The darker intervals represent error estimates for (from left to right) the 5%, 50%, and 95% quantiles, estimated by Bayesian bootstrapping.

Figure 2

Posterior probability densities for the source-frame component masses $m_1^{\text{source}}$ and $m_2^{\text{source}}$, where $m_2^{\text{source}}\le m_1^{\text{source}}$. We show one-dimensional histograms for precessing EOBNR (red) and precessing IMRPhenom (blue); the dashed vertical lines mark the 90% credible intervals. The two-dimensional density plot shows 50% and 90% credible regions plotted over a color-coded posterior density function.

Figure 3

Posterior probability densities for the dimensionless spin magnitudes. (See Fig. 2 for details.)

Figure 4

Posterior probability density of BH spin directions, plotted as in Fig. 5 of Ref. [2].

Figure 5

Posterior probability densities of the effective spin and perpendicular effective spin. (See Fig. 2 for details.)

Figure 6

Posterior probability densities of the opening angle between the two spins, ${\theta }_{12}$, and the angle between the in-plane projections of the spins, ${\varphi }_{12}$. (See Fig. 2 for details.)

Figure 7

A visual comparison of the precessing EOBNR model with NR GW polarizations computed by the SXS Collaboration at (approximately) the GW150914 MaP parameters. The intrinsic parameters of the NR waveform are $q=0.81$, $a_1=0.34$, $a_2=0.67$. The inclination is $\iota =2.856\mathrm{rad}$. The alignment of the precessing EOBNR waveform is obtained from the sky- and polarization-averaged overlap with the NR waveform. For more details on the alignment procedure, see Ref. [18].

Figure 8

Posterior probability densities for the source-frame component masses $m_1^{\text{source}}$ and $m_2^{\text{source}}$, where $m_2^{\text{source}}\le m_1^{\text{source}}$ (left panel) and effective aligned ${\chi }_{\mathrm{eff}}$ and effective precessing spins ${\chi }_{\mathrm{p}}$ (right panel) for an eventlike NR mock signal close to MaP parameters. In the one-dimensional marginalized distributions, we show the precessing EOBNR (red) and precessing IMRPhenom (blue) probability densities with dashed vertical lines marking 90% credible intervals. The two-dimensional plot shows the contours of the 50% and 90% credible regions of the precessing EOBNR over a color-coded posterior density function. The true parameter values are indicated by a red asterisk or black dot-dashed line.

Figure 9

Comparison of parameter estimates obtained by combining the nonprecessing-EOBNR and precessing-IMRPhenom models (as in Ref. [2]; light purple bars at the top) and by combining the precessing-EOBNR and precessing-IMRPhenom models (light green bars at the bottom). We show 90% credible intervals for selected GW150914 source parameters. The darker intervals represent uncertainty estimates for the 5%, 50%, and 95% quantiles (from left to right), as estimated by the Bayesian bootstrap.