Search of S3 LIGO data for gravitational wave signals from spinning black hole and neutron star binary inspirals

We report on the methods and results of the first dedicated search for gravitational waves emitted during the inspiral of compact binaries with spinning component bodies. We analyze 788 hours of data collected during the third science run (S3) of the LIGO detectors. We searched for binary systems using a detection template family specially designed to capture the effects of the spin-induced precession of the orbital plane. We present details of the techniques developed to enable this search for spin-modulated gravitational waves, highlighting the differences between this and other recent searches for binaries with nonspinning components. The template bank we employed was found to yield high matches with our spin-modulated target waveform for binaries with masses in the asymmetric range $1.0M_{\odot }<m_1<3.0M_{\odot }$ and $12.0M_{\odot }<m_2<20.0M_{\odot }$ which is where we would expect the spin of the binary’s components to have a significant effect. We find that our search of S3 LIGO data has good sensitivity to binaries in the Milky Way and to a small fraction of binaries in M31 and M33 with masses in the range $1.0M_{\odot }<m_1$, $m_2<20.0M_{\odot }$. No gravitational wave signals were identified during this search. Assuming a binary population with spinning components and Gaussian distribution of masses representing a prototypical neutron star–black hole system with $m_1\simeq 1.35M_{\odot }$ and $m_2\simeq 5M_{\odot }$, we calculate the 90%-confidence upper limit on the rate of coalescence of these systems to be $15.9{\mathrm{yr}}^{-1}{\mathrm{L}}_{10}^{-1}$, where ${\mathrm{L}}_{10}$ is ${10}^{10}$ times the blue light luminosity of the Sun.

Figure 1

The gravitational waveforms predicted from the late inspiral phase of two different neutron star–black hole systems, one consisting of nonspinning bodies (upper plot) and the other consisting of maximally spinning bodies (lower plot). Both systems are identical apart from the spin of their component bodies. Spin-induced precession of the binary’s orbital plane causes modulation of the gravitational wave signal and can be clearly seen in the lower plot.

Figure 2

Moment functions $C_7(\beta )$ (solid line) and $S_7(\beta )$ (dashed line) for the initial LIGO design noise power spectral density. For values of $\beta \gtrsim 200{\mathrm{Hz}}^{2/3}$ we see that these moments become small and can be neglected—this is what we call the strong modulation approximation.

Figure 3

A template bank generated with minimal match $=0.95$ using 2048 seconds of H1 data taken during S3. The crosses show the positions of individual templates in the $({\psi }_0,{\psi }_3,\beta )$ parameter space. For each template a value for the cutoff frequency $f_{\mathrm{cut}}$ is estimated using Eq. (8). This bank requires a three-dimensional template placement scheme in order to place templates in the $({\psi }_0,{\psi }_3,\beta )$ parameter space. Previous searches for nonspinning systems have used two-dimensional placement schemes.

Figure 4

Plots showing the best match achieved by filtering a series of simulated signals through the template bank described in this section. The values on the x and y axes correspond to the component masses of the binary source to which the simulated signal corresponds. The shade of gray in the plots shows the best match achieved for a given simulated signal; lighter shades of gray indicate that a higher match was achieved. The four subplots correspond to four different spin configurations of the binary source. The top-left subplot shows results for a nonspinning binary system. The top-right subplot shows results for a system consisting of one nonspinning object and one maximally spinning object with its spin slightly misaligned with the orbital angular momentum. We would expect this system to precess. The bottom two subplots show results for two generic precessing systems consisting of two maximally spinning bodies with spins and orbital angular momentum all misaligned with each other. We see that the region of the mass plane for which we obtain matches $>0.9$ is largest for the nonspinning system and tends to be concentrated in the asymmetric mass region loosely bounded by $1.0M_{\odot }<m_1<3.0M_{\odot }$ and $12.0M_{\odot }<m_2<20.0M_{\odot }$.

Figure 5

Distance to which an optimally oriented nonspinning $(2,16)M_{\odot }$ binary can be detected with $\mathrm{SNR}=8$ throughout S3. For systems with spinning components, the horizon distance would be equal to or less than what is shown in this figure since any spin-induced precession would cause the system to become less than optimally oriented and therefore reduce the measured amplitude of its emission. We see a large improvement in the sensitivity of H1 during this science run.

Figure 6

Cumulative histogram of the combined SNR, ${\rho }_c$, for in-time coincident triggers (triangles) and our background (crosses with one-sigma deviation shown) for all H1-H2 and H1-H2-L1 times within S3. We see a small excess in the number of in-time coincident triggers with combined SNR $\sim 45$. This excess was investigated and was caused by an excess of H1-H2 coincident triggers. Since H1 and H2 are colocated, both detectors are affected by the same local disturbances (e.g., seismic activity) which contributes to the number of in-time coincidences but which is under-represented in time-shift estimates of the background.

Figure 7

Scatter plot of SNR for coincident triggers in H1-H2 times. The black circles represent in-time coincident triggers, and the light-colored (red) pluses represent time-shift coincident triggers that we use to estimate the background. Note that due to our signal-based veto on $\mathrm{H}1/\mathrm{H}2$ SNR, we see no coincident triggers with ${\rho }_{\mathrm{H}1}<{\rho }_{\mathrm{H}2}$.

Figure 8

Upper limits on the spinning binary coalescence rate per ${\mathrm{L}}_{10}$ as a function of the total mass of the binary. For this calculation, we have evaluated the efficiency of the search using a population of binary systems with $m_1=1.35M_{\odot }$ and $m_2$ uniformly distributed between $2M_{\odot }$ and $20M_{\odot }$. The darker area on the plot shows the region excluded after marginalization over the estimated systematic errors, whereas the lighter region shows the region excluded if these systematic errors are ignored. The effect of marginalization is typically small ($<1\%$). The initial decrease in the upper limit corresponds to the increasing amplitude of the signals as total mass increases. The subsequent increase in the upper limit is due to the countereffect that as the total mass increases the signals become shorter and have fewer cycles in LIGO’s frequency band of good sensitivity.