4.6 Search results
4.6.1 Low mass
The low mass search used non-spinning post-Newtonian inspiral templates computed to 0PN in amplitude and 3.5PN in phase to search for compact binary coalescence in the range 2M ≤Mtotal≤
Table 4.3: Rate upper limits of BNS, BBH, and NSBH coalescence. We give the computed rate upper limits for our three canonical sources, assuming Gaussian mass distributions around the central values mNS = 1.35±0.04MandmBH= 5.0±1.0M. The effective mean sensitive distance is given byDavg = (3V /4π)1/3; the horizon distance isDhoriz= 2.26Davg (see Sec. 4.1). For the spinning upper limits, we assume a black hole spin distribution that is uniform in magnitude between zero and the maximal value ofGm2/cand spin angles that are uniformly distributed on the sphere. We neglect neutron star spin.
System BNS NSBH BBH
Component masses (M)
1.35 / 1.35 1.35 / 5.0 5.0 / 5.0
Dhorizon (Mpc) 40 80 90
Non-spinning upper limit (Mpc−3yr−1)
1.3×10−4 3.1×10−5 6.4×10−6 Spinning upper limit
(Mpc−3yr−1) · · · 3.6×10−5 7.4×10−6
25M. Single detector triggers in the search were ranked according to the statistic
ˆ ρ=
ρ
[(1+χ6red)/2]1/6 ifχ2red>1 ρ ifχ2red≤1,
(4.28)
where ρis the usual signal-to-noise ratio and χ2red is the traditionalχ2 per degree of freedom (see Sec. 3.3.3). The (effective) signal-to-noise for a coincident event is given by
ρc=s X
detectorsi
ˆ
ρ2i. (4.29)
The background is a strong function of mass. Therefore, background triggers were split into three chirp mass bins, and the significance of each event in the actual search was computed relative the background in that event’s chirp mass bin. In a later step, the triggers from different mass bins are combined into one set to account for the trials factor associated with having three separate mass bins. The most significant event was an L1V1 coincidence in L1V1 time with a combined false alarm rate of 1.2 yr−1. The second and third most significant events had combined false alarm rates of 2.2 yr−1 and 5.6 yr−1 respectively. All of these events were consistent with background. Having analyzed approximately half a year of data, we expect the loudest event to have a false alarm rate of∼2 yr−1.
In the absence of any plausible gravitational wave signal, we place upper limits on the event rate using the loudest event statistic just described. We considered several different source populations for computing the upper limits. In Tbl. 4.3 we present the marginalized upper limits at the 90%
confidence level, assuming canonical mass distributions for BNS (m1=m2= 1.35±0.04M), BBH
96
Figure 4.6: Upper limits on the binary coalescence rate as a function of mass. We show the upper limits on coalescence rate derived from the measured search depth for the two CBC searches as a function ofMtotal. The vertical line indicates the boundary between the low and high mass searches. For the low mass search, the injections were distributed uniformlyMtotal and in m1 for a given Mtotal. For the high mass search, we used injections distributed uniformly overm1-m2; the total mass bins above correspond the equal mass bins in Tbl. 4.4. The dark bars indicate upper limits from previous searches. The light bars indicate the combined upper limits, including the results of this search.
(m1 = m2 = 5±1M), and NSBH (m1 = 1.35±0.04M, m2 = 5±1M) systems. In our simulations, the non-spinning BNS injections were computed in the post-Newtonian approximation;
all other systems were modeled with the EOBNR waveform family. Spinning injections were all per- formed using theSpinTaylorT4model4. We considered (i) a population of non-spinning compact binaries and (ii) a population of binaries in which the black hole spin is uniformly distributed in magnitude between 0 and the maximal spin Gm2/c and spin angles uniformly distributed on the sphere. We neglect neutron star spin, as we do not expect neutron stars to have large spins. From the table, we see that the search was less sensitive to the population with spin compared to the population without spin.
We also compute upper limits, shown in Fig. 4.6, as a function of Mtotal, using an injection population distributed uniformly overM and uniformly overm1 for a givenM. For NSBH systems we present the upper limit as a function of black hole mass, keeping the neutron star mass fixed in
4Note that the use of different waveform models for the spinning and non-spinning injections was accidental, but conservatively we can estimate the waveform differences to be about 10% in amplitude (introducing a 30% error in volume).
3.0 8.0 13.0 18.0 23.0 Component Mass (M)
10−5 10−4
Rate(Mpc−3yr−1)
(a)
BNS NSBH BBH
10−10 10−9 10−8 10−7 10−6 10−5 10−4 10−3
RateEstimatesMpc−3yr−1
(b)
Figure 4.7: Coalescence rate upper limit rates for BNS, NSBH, and BBH systems. In the left figure, we show the upper limits for NSBH as a function of the black hole mass, with the neutron star mass restricted to the range 1−3M. To the right, we compare the upper limits for BNS, NSBH, and BBH given in Tbl. 4.3 to the predicted rates given in Ref. [31]. The light gray regions display the upper limits obtained in the S5/VSR1 analysis; dark gray regions show the upper limits obtained in this analysis, using the S5/VSR1 limits as priors. The new limits are up to a factor of 1.4 improvement over the previous results. The lower (blue) regions show the spread in the astrophysically predicted rates, with the dashed-black lines showing the “realistic” estimates. Note: In Ref. [31], NSBH and BBH rates were quoted using a black-hole mass of 10M. We have therefore rescaled the S5 and S6 NSBH and BBH upper limits in this plot by a factor of (M5/M10)5/2, whereM10is the chirp mass of a binary in which the black hole mass is 10M, andM5 is the chirp mass of a binary in which the black hole mass is 5M.
the range 1−3M(Fig. 4.7a). In these calculations, the injected signals were non-spinning inspiral- merger-ringdown signals computed in the EOBNR approximation. Fig. 4.7b compares the upper limits obtained in this analysis (dark gray regions) to limits obtained in our previous searches up to S5/VSR1 [47] (light gray region) and to predicted rates (blue regions) for BNS, NSBH, and BBH systems. The improvement over the previous limits is up to a factor of 1.4, depending on binary mass; this reflects the additional observation time and improved sensitivity of the S6/VSR2-3 data with respect to all previous observations.
While the rates presented here represent an improvement over the previously published results from earlier LIGO and Virgo science runs, they are still above the astrophysically predicted rates of binary coalescence. There are numerous uncertainties involved in estimating astrophysical rates, including limited numbers of observations and unknown model parameters; consequently the rate estimates are rather uncertain. For BNS systems the estimated rates vary between 1×10−8 and 1×10−5Mpc−3yr−1, with a “realistic” estimate of 1×10−6Mpc−3yr−1. For BBH and NSBH, realistic estimates of the rate are 5×10−9Mpc−3yr−1and 3×10−8Mpc−3yr−1with at least an order of magnitude uncertainty in either direction [31]. In all cases, the upper limits derived here are two
98
8 9 10 11 12 13
Combined SNRρc, long duration events 10−2
10−1 100 101 102 103 104 105
Eventspersearchtime
Background Coincident events
(a) Long duration events
8 9 10 11 12 13
Combined SNRρc, short duration events 10−2
10−1 100 101 102 103
Eventspersearchtime
Background Coincident events
(b) Short duration events
Figure 4.8: Loudest events in the high mass search. We show the cumulative distributions of coincident events in the long (left) and short (right) duration categories for all of the S6/VSR2-3 high mass search.
Grey shaded bands indicate 1σ–5σconsistency with the estimated background distribution.
to three orders of magnitude above the “realistic” estimated rates, and about a factor of ten above the most optimistic predictions.