Search for gravitational waves from binary inspirals in S3 and S4 LIGO data

We report on a search for gravitational waves from the coalescence of compact binaries during the third and fourth LIGO science runs. The search focused on gravitational waves generated during the inspiral phase of the binary evolution. In our analysis, we considered three categories of compact binary systems, ordered by mass: (i) primordial black hole binaries with masses in the range $0.35M_{\odot }<m_1$, $m_2<1.0M_{\odot }$, (ii) binary neutron stars with masses in the range $1.0M_{\odot }<m_1$, $m_2<3.0M_{\odot }$, and (iii) binary black holes with masses in the range $3.0M_{\odot }<m_1$, $m_2<m_{\max }$ with the additional constraint $m_1+m_2<m_{\max }$, where $m_{\max }$ was set to $40.0M_{\odot }$ and $80.0M_{\odot }$ in the third and fourth science runs, respectively. Although the detectors could probe to distances as far as tens of Mpc, no gravitational-wave signals were identified in the 1364 hours of data we analyzed. Assuming a binary population with a Gaussian distribution around $0.75-0.75M_{\odot }$, $1.4-1.4M_{\odot }$, and $5.0-5.0M_{\odot }$, we derived 90%-confidence upper limit rates of $4.9{\mathrm{yr}}^{-1}{L}_{10}^{-1}$ for primordial black hole binaries, $1.2{\mathrm{yr}}^{-1}{L}_{10}^{-1}$ for binary neutron stars, and $0.5{\mathrm{yr}}^{-1}{L}_{10}^{-1}$ for stellar mass binary black holes, where $L_{10}$ is ${10}^{10}$ times the blue-light luminosity of the Sun.

Figure 1

Blue-light luminosities and horizon distances for LIGO’s observatories. In the left panel, the horizontal bars represent the noncumulative intrinsic blue-light luminosity of the galaxies or clusters within each bin of physical distance, as obtained from a standard astronomy catalog [4]. Some bins are identified by the dominant contributor galaxy or cluster. The merger rate of binaries within a galaxy or cluster is assumed to scale with its blue-light luminosity. The detectability of a binary depends on the effective distance between the source and detector, which is dependent on both the physical distance separating them and their relative orientation [see Eq. (2)]. The solid line shows the cumulative blue-light luminosity as a function of effective distance (hereafter, the effective cumulative blue-light luminosity), of the binary sources which would be observed by the LIGO detectors if they had perfect detection efficiency (i.e., all binaries are detectable). Explicitly, a binary in M31 (at a physical distance of 0.7 Mpc) with an effective distance of 5 Mpc will contribute to the intrinsic luminosity at 0.7 Mpc and will contribute to the effective cumulative luminosity at a distance of 5 Mpc. Although a binary will have slightly different orientation with respect to each LIGO observatory and therefore slightly different effective distances, the difference in the effective cumulative luminosity shown on this plot would not be distinguishable. The effective cumulative luminosity starts at $1.7L_{10}$ (Milky Way contribution), and begins increasing at a distance of $\sim 1\mathrm{Mpc}$, with the contribution of nearby galaxies M31 and M33. The cumulative luminosity observable by our search (not shown), as expressed in Eq. (8), depends also on the detection efficiency of our search (see Fig. 5) and will be less than the effective cumulative luminosity. In the right panel, the curves represent the horizon distance in each LIGO detector as a function of total mass of the binary system, during S3 (dashed lines) and S4 (solid lines). We also plot the horizon distance of L1 during S2. The sharp drop of horizon distance around a total mass of $2M_{\odot }$ is related to a different lower cut-off frequency, $f_L$, used in the PBH binary search and the BNS/BBH searches. The $f_L$ values are summarized in Table 2. The high cutoff frequency occurs at the last stable orbit. The horizon distance for non equal mass systems scales by a factor $\sqrt{4m_1{m}_2}/(m_1+m_2)$.

Figure 2

Accidental events and detected simulated injections. This plot shows the distribution of effective SNR, ${\rho }_{\mathrm{eff}}$, as defined in Eq. (3), for time-shifted coincident triggers and detected simulated injections (typical S4 BNS result). Some of the injections are detected in all three detectors but no background triggers are found in triple-coincidence in any of the 100 time shifts performed. The H1-L1 and H1-H2 time-shifted coincidence triggers have low effective SNR (left-bottom corner).

Figure 3

Cumulative histograms of the combined SNR, ${\rho }_c$, for in-time coincident candidates events (triangles) and estimated background from accidental coincidences (crosses and 1 standard-deviation ranges), for the S4 PBH binary (left), S4 BNS (middle), and S4 BBH (right) searches. In each search, the loudest candidate (found in nonplayground time) corresponds to an accidental coincidence rate of about 1 during the entire S4 run.

Figure 4

Time offset between the H1 and H2 SNR time series, using the same template. Around the loudest candidate found in the S3 BBH search (left panel), the maximum of the H2 SNR time series is offset by 38 ms with respect to the maximum of the H1 SNR time series, which is placed at zero time in this plot. In contrast, simulated injections of equivalent gravitational wave waveforms with the same SNR and masses give a time-offset distribution centered around zero with a standard deviation about 6.5 ms (right panel).

Figure 5

Detection efficiency versus effective distance for the different searches (S4 run). The BBH and BNS efficiencies are similar, mainly because the loudest candidate in the BBH search is twice as loud as in the BNS search (See Table 4).

Figure 6

Upper limits on the binary inspiral coalescence rate per year and per $L_{10}$ as a function of total mass of the binary, for PBH binaries (left), BNS (middle), and BBH (right) searches. The darker area shows the excluded region after accounting for marginalization over estimated systematic errors. The lighter area shows the additional excluded region if systematic errors are ignored. In the PBH binary and BNS searches, upper limits decrease with increasing total mass, because more-distant sources can be detected. In the BBH search, upper limits decrease down to about 30 solar mass and then grow where signals become shorter; this feature can be seen in the expected horizon distance as well (See Fig. 1).