Improved analysis of GW190412 with a precessing numerical relativity surrogate waveform model

The recent observation of GW190412, the first high-mass ratio binary black hole merger, by the LIGO-Virgo Collaboration (LVC) provides a unique opportunity to probe the impact of subdominant harmonics and precession effects encoded in a gravitational wave signal. We present refined estimates of source parameters for GW190412 using nrsur7dq4, a recently developed numerical relativity waveform surrogate model that includes all $\ell \le 4$ spin-weighted spherical harmonic modes as well as the full physical effects of precession. We compare our results with two different variants of phenomenological precessing binary black hole waveform models, imrphenompv3hm and imrphenomxphm, as well as to the LVC results. Our results are broadly in agreement with imrphenomxphm results and the reported LVC analysis compiled with the seobnrv4phm waveform model, but in tension with imrphenompv3hm. Using the nrsur7dq4 model, we provide a tighter constraint on the mass ratio (${0.26}_{-0.06}^{+0.08}$) as compared to the LVC estimate of ${0.28}_{-0.07}^{+0.13}$ (both reported as median values with 90% credible intervals). We also constrain the binary to be more face on, and find a broader posterior for the spin precession parameter. We further find that even though $\ell =4$ harmonic modes have negligible signal-to-noise ratio, omission of these modes will influence the estimated posterior distribution of several source parameters including chirp mass, effective inspiral spin, luminosity distance, and inclination. We also find that commonly used model approximations, such as neglecting the asymmetric modes (which are generically excited during precession), have negligible impact on parameter recovery for moderate signal-to-noise ratio events similar to GW190412.

Figure 1

Estimated parameters for GW190412 using three different waveform models: nrsur7dq4, imrphenomxphm, and imrphenompv3hm. While the nrsur7dq4 analysis is done with lower frequency cutoff $f_{\mathrm{low}}=40\mathrm{Hz}$, imrphenomxphm parameter estimation has been carried out with two different values of minimum frequency: $f_{\mathrm{low}}=\{20,40\}\mathrm{Hz}$. In panel (a), we show the estimated two-dimensional contours for 90% confidence interval and one-dimensional kernel density estimates (KDEs) using Gaussian kernel for the source-frame chirp mass ${\mathcal{M}}^{\text{source}}(M_{\odot }$) and mass ratio $q$. Panels (b), (c), and (d) report the corresponding contours and histograms for (effective inspiral spin ${\chi }_{\mathrm{eff}}$, spin precession ${\chi }_p$), (luminosity distance $D_L$, orbital inclination angle ${\theta }_{JN}$), and (declination $\delta$, right ascension $\alpha$), respectively. Posteriors for nrsur7dq4 and imrphenompv3hm are shown in black and blue, receptively. For imrphenomxphm, we plot the posteriors in red and green for analysis starting from 20 and 40 Hz, respectively. Dashed lines in the one-dimensional panels represent 90% credible intervals.

Figure 2

Estimated parameters for GW190412 using the nrsur7dq4 waveform model varying the spherical harmonic $(l,m)$ mode content. For all analyses, we use a lower frequency cutoff $f_{\mathrm{low}}=40\mathrm{Hz}$. In panel (a), we show the estimated two-dimensional contours for 90% confidence interval and one-dimensional KDEs using Gaussian kernel for the source-frame chirp mass ${\mathcal{M}}^{\text{source}}(M_{\odot }$) and mass ratio $q$. Panels (b), (c), and (d) report the corresponding contours and histograms for (effective inspiral spin ${\chi }_{\mathrm{eff}}$, spin precession ${\chi }_p$), (luminosity distance $D_L$, inclination angle ${\theta }_{JN}$), and (declination $\delta$, right ascension $\alpha$), respectively. Posteriors for nrsur7dq4 analysis with all modes ${\ell }_{\max }=2$, ${\ell }_{\max }=3$, and ${\ell }_{\max }=4$ are plotted in orange, green, and black lines, respectively. Dashed lines in the one-dimensional posterior plots demarcate the 90% credible regions.

Figure 3

Estimated effective inspiral spin ${\chi }_{\mathrm{eff}}$ and spin precession ${\chi }_p$ for GW190412 event using nrsur7dq4 waveform. We show the two-dimensional contours and one-dimensional KDEs using Gaussian kernel of ${\chi }_{\mathrm{eff}}$ and ${\chi }_p$ obtained using the nrsur7dq4 waveform model in black. We then show the posteriors using nrsur7dq4 after imposing two different modelling approximations that are often assumed for building phenomenological and EOB models. The posteriors recovered (i) after the omission of asymmetric modes is shown in light blue (“Approximation I”) and (ii) assuming the model reduces to an aligned-spin model in the coprecessing frame is shown in deep blue (“Approximation II”). (Details in text; see Sec. 3c). We find no noticeable difference between posteriors obtained from default nrsur7dq4 model and these approximations.

Figure 4

Parameter recovery for the synthetic injections with the nrsur7dq4 waveform model for two different values of mass ratio: $q_{\mathrm{inj}}=0.33$ and $q_{\mathrm{inj}}=0.25$. In (a), we show the estimated two-dimensional contours for 90% confidence interval and one-dimensional KDEs for the source-frame chirp mass ${\mathcal{M}}^{\text{source}}(M_{\odot }$) and mass ratio $q$. Panels (b), (c), and (d) report the corresponding contours and KDEs using Gaussian kernel for (effective inspiral spin ${\chi }_{\mathrm{eff}}$, spin precession ${\chi }_p$), (luminosity distance $D_L$, inclination angle ${\theta }_{JN}$), and (declination $\delta$, right ascension $\alpha$), respectively. Posteriors for $q_{\mathrm{inj}}=0.25$ are shown in violet while $q_{\mathrm{inj}}=0.33$ posteriors are plotted in orange. In both two-dimensional and one-dimensional panels, dashed dotted lines indicate the true injection values. Dashed lines in the one-dimensional panels represent 90% credible regions.