Searching for the full symphony of black hole binary mergers

Current searches for the gravitational-wave signature of compact binary mergers rely on matched-filtering data from interferometric observatories with sets of modeled gravitational waveforms. These searches currently use model waveforms that do not include the higher-order mode content of the gravitational-wave signal. Higher-order modes are important for many compact binary mergers and their omission reduces the sensitivity to such sources. In this work we explore the sensitivity loss incurred from omitting higher-order modes. We present a new method for searching for compact binary mergers using waveforms that include higher-order mode effects, and evaluate the sensitivity increase that using our new method would allow. We find that, when evaluating sensitivity at a constant rate-of-false alarm, and when including the fact that signal-consistency tests can reject some signals that include higher-order mode content, we observe a sensitivity increase of up to a factor of 2 in volume for high mass ratio, high total-mass systems. For systems with equal mass, or with total mass $\sim 50M_{\odot }$, we see more modest sensitivity increases, $<10\%$, which indicates that the existing search is already performing well. Our new search method is also directly applicable in searches for generic compact binaries.

Figure 1

The imaginary component of the complex overlap between ${\widehat{h}}_{+}$ and ${\widehat{h}}_{\times }$ for the representative early Advanced LIGO noise curve (top), and for the predicted design sensitivity curve of Advanced LIGO (bottom). The overlap is numerically minimized over inclination and reference orbital phase within each of the pixels shown on these plots.

Figure 2

The left panel shows the distribution of templates, as a function of the total mass and mass ratio, for the template bank created for the early Advanced LIGO noise curve. The black crosses indicate the templates that are needed to cover the parameter space if higher-order modes are omitted, the red circles indicate the additional templates that are required if higher-order modes are included in the search parameter space. The right panel shows the distribution of the inclination angle of the higher-order mode waveforms in the template bank created for the Advanced LIGO design noise curve.

Figure 3

The signal recovery fraction plotted as a function of the total mass and mass ratio. The top panels show results using a representative early Advanced LIGO sensitivity curve, while the bottom panels use the design Advanced LIGO sensitivity. The left panels are generated using appropriate template banks that do not include higher-order mode waveforms, the right panels are generated with template banks that include higher-order mode waveforms.

Figure 4

Left: Cumulative distribution of fitting factors for the 500 000 higher-order mode signal waveforms we describe in Sec. 5b. The black curves show results for the Advanced LIGO design sensitivity curve and the red curves show results for the representative early Advanced LIGO sensitivity curve. Dotted lines indicate results when using template banks that do not include higher-order modes, solid lines show results using template banks including higher-order mode waveforms. Right: Distribution of fitting factors as a function of the source orientation $(\iota ,\phi )$ for 500 signal waveforms with total mass of $95M_{\odot }$ and mass ratio of 8.

Figure 5

The sensitivity ratio between a search using higher-order mode waveforms as templates and a search using non-higher-order-mode waveforms as templates, evaluating sensitivity using only signal-to-noise ratio to rank potential events. Plotted for the early Advanced LIGO sensitivity curve (left) and the Advanced LIGO design sensitivity curve (right). The plots on the top row consider the full injection set, while plots on the bottom row consider only injections where the inclination ($\iota$) is between 60 and 120 degrees. The sensitivity is evaluated at a false-alarm rate of 1 per 1000 years, which includes the larger background that is present when using higher-order mode waveforms as templates, as more template waveforms are needed. Values greater than one indicate an increase in sensitivity, values less than one indicate a decrease in sensitivity.

Figure 6

Impact of higher-modes on the ${\chi }^2$ signal consistency test. We plot ${\chi }^2$ against signal-to-noise ratio for a randomly chosen subset of the simulated signals discussed in Sec. 6. The inclination angle of the simulated signals are shown on the color bar, here we restrict the inclination angle to values between 0 and $\pi /2$ by taking $\pi /2-|\pi /2-\iota |$. The dashed lines denote contours of equal ${\rho }_{\text{reweighted}}$. The left panel shows the results when searching with a template bank that does not include higher-order mode waveforms, the right panel shows the results when searching with higher-order mode templates. Both panels are generated using the design Advanced LIGO sensitivity curves.

Figure 7

The relative sensitivity between a search using higher-order mode waveforms as templates and a search using nonhigher-order-mode waveforms as templates when evaluating sensitivity using ${\rho }_{\text{reweighted}}$ at a constant rate of false alarm. Plotted for the representative early Advanced LIGO sensitivity curve (left) and the design Advanced LIGO sensitivity curve (right). The plots on the top row consider the full injection set, while plots on the bottom row consider only injections where the inclination ($\iota$) is between 60 and 120 degrees. The sensitivity is evaluated at a false-alarm rate of 1 per 1000 years, which includes the larger background that is present when using higher-order mode waveforms as templates. Values greater than one indicate an increase in sensitivity, values less than one indicate a decrease in sensitivity. Here the color bars are capped at a value of 2 to aid distinguishability of values between 1 and 2. However some values are larger than this, especially in the lower right panel, where the points with highest mass and highest mass ratio have a relative sensitive volume of $\sim 4$.