Numerical relativity injection analysis of signals from generically spinning intermediate mass black hole binaries in Advanced LIGO data

The advent of gravitational wave (GW) astronomy has provided us with observations of black holes more massive than those known from x-ray astronomy. However, the observation of an intermediate-mass black hole (IMBH) remains a big challenge. After their second observing run, the LIGO & Virgo Scientific collaborations (LVC) placed upper limits on the coalescence rate density of nonprecessing IMBH binaries (IMBHBs). In this Numerical Relativity Injection Analysis (NuRIA), we explore the sensitivity of two of the search pipelines used by the LVC to signals from 69 numerically simulated IMBHBs with total mass greater than $200M_{\odot }$ having generic spins, out of which 27 have a precessing orbital plane. In particular, we compare the matched-filter search PyCBC, and the coherent model-independent search technique cWB. We find that, in general, cWB is more sensitive to IMBHBs than PyCBC, with the difference in sensitivity depending on the masses and spins of the source. Consequently, we use cWB to place the first upper limits on the merger rate of generically spinning IMBH binaries using publicly available data from the first Advanced LIGO observing run.

Figure 1

Amplitude modulus of the gravitational-wave modes of different binary black hole systems with mass ratio $q=3$ and varying spins and a total mass of $M=210M_{\odot }$. The systems have edge-on orientation and are located at a distance of 100 Mpc. The source parameters are defined at a starting frequency of 16 Hz. We note that the amplitude of the (3,3) and (4,4) mode increases relative to (2,2) mode from no spin case to systems with spins. The spins also impact both the duration of the signal. The strains have been obtained from to the publicly available Georgia Tech catalogue. The corresponding simulations have ID GT0453, GT0596, GT0838, and GT0874. The oscillations in the (4,2) mode in the top left panel are due to numerical noise. We note, however, that the overlap with an equivalent waveform from the SXS code is around 0.94 and the mode itself is so weak that it does not have any significant impact.

Figure 2

cWB vs PyCBC: Comparison of the sensitive distance reach of cWB and PyCBC at $\mathrm{IFAR}=2.94\mathrm{yr}$. The results correspond to injections made in the first two chunks of data from the first Advanced LIGO observing run. The effect of higher modes and precession on the search causes the unmodeled algorithm to outperform the matched-filter search as indicated by the positive values.

Figure 3

cWB vs PyCBC: Comparison of sensitive distance reach of cWB and PyCBC, for $\mathrm{IFAR}=300\mathrm{yr}$, as a function of the source parameters. The effect of higher modes and precession causes the unmodeled algorithm to outperform (as indicated by positive values) the matched-filter search, which does not incorporate these two effects. We have checked that the apparent alteration of trends at high mass in panels (a) and (c) is consistent with statistical uncertainty.

Figure 4

cWB: The plot shows the sensitive distance reach for this set of injections for $\mathrm{IFAR}=2.94\mathrm{yr}$. As a general trend, the sensitivity drops with increasing total mass and mass ratio.

Figure 5

90% upper limit on merger rate density ($R_{90\%}$) for our target IMBHB sources, expressed ${\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$. We set our most stringent upper limit at $0.36{\mathrm{Gpc}}^{-3}{\mathrm{yr}}^{-1}$ for the symmetric mass system with total mass of $210M_{\odot }$ and ${\chi }_p=0.42$ and ${\chi }_{\mathrm{eff}}=0.5114$.

Figure 6

Sensitivity of cWB as a function of the binary spins. When ${\chi }_p=0$, an increase in ${\chi }_{\mathrm{eff}}$, causes an increment of the sensitive distance reach while a decrease in ${\chi }_{\mathrm{eff}}$ causes the sensitivity to drop.

Figure 7

Ratio of the sensitivity of cWB to signals including and omitting higher modes. Values of ${\mathrm{\Delta }}_D$ indicate that cWB is equally sensitive to both kinds of signals while large values indicate an increase in the sensitivity when higher modes are included. The higher modes provide extra signal power as the total mass and mass ratio increase, leading to an important increment of the sensitivity of the search.

Figure 8

Top: Amplitude of the Fourier transforms of the (2,2) and (3,3) modes of the GT0446 numerical simulation scaled to total mass of $500M_{\odot }$ at a distance of 100 Mpc. We have chosen an inclination $\iota =60°$ to make the (3,3) mode sufficiently prominent. Bottom: Frequency and amplitude of the (2,2) as a function of time.