The null result (i.e., the absence of the detection of GWs) was concluded from a search for GWs specif- ically from systems with total mass between 25 and 100 M, using the search pipeline as described in
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting non-spinning EOBNRv2 injected waveforms Various total mass bins
All H1L1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(a)
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting non-spinning EOBNRv2 injected waveforms Various total mass bins
All H1V1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(b)
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting non-spinning EOBNRv2 injected waveforms Various total mass bins
All L1V1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(c)
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting non-spinning EOBNRv2 injected waveforms Various total mass bins
All H1L1V1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(d)
Figure 8.1: The efficiency at recovering EOBNRv2 injections with a FAR less than that of the loudest fore- ground event. The colors indicate bins of total mass. 40 distance bins were used. The error bars reflect binomial counting errors. Any bumps at distances greater than 500 Mpc are due to noise triggers in two or more detectors that happen to be coincident with each other and with the injected signal. S6-VSR2/3 data at Category 4.
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting non-spinning IMRPhenomB injected waveforms Various total mass bins
All H1L1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(a)
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting non-spinning IMRPhenomB injected waveforms Various total mass bins
All H1V1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(b)
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting non-spinning IMRPhenomB injected waveforms Various total mass bins
All L1V1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(c)
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting non-spinning IMRPhenomB injected waveforms Various total mass bins
All H1L1V1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(d)
Figure 8.2: The efficiency at recovering non-spinning IMRPhenomB injections with a FAR less than that of the loudest foreground event. The colors indicate bins of total mass. 40 distance bins were used. The error bars reflect binomial counting errors. Any bumps at distances greater than 500 Mpc are due to noise triggers in two or more detectors that happen to be coincident with each other and with the injected signal.
S6-VSR2/3 data at Category 4.
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting spinning IMRPhenomB injected waveforms Various total mass bins
All H1L1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(a)
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting spinning IMRPhenomB injected waveforms Various total mass bins
All H1V1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(b)
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting spinning IMRPhenomB injected waveforms Various total mass bins
All L1V1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(c)
0 200 400 600 800 1000
0.00.20.40.60.81.0
Efficiency at detecting spinning IMRPhenomB injected waveforms Various total mass bins
All H1L1V1 time in S6-VSR2/3
Distance
Fraction recovered
25.0-37.5 37.5-50.0 50.0-62.5 62.5-75.0 75.0-87.5 87.5-100.0
(d)
Figure 8.3: The efficiency at recovering spinning IMRPhenomB injections with a FAR less than that of the loudest foreground event. The colors indicate bins of total mass. 40 distance bins were used. The error bars reflect binomial counting errors. Any bumps at distances greater than 500 Mpc are due to noise triggers in two or more detectors that happen to be coincident with each other and with the injected signal. S6-VSR2/3 data at Category 4.
Chapter 7. The ranking statistic for coincident events produced by the pipeline was the combinedρhigh, given by Equation (7.18). In order to compare events from different analysis periods and observation times, this ranking statistic was turned into an inverse false alarm rate (IFAR). The IFAR, our detection statistic, was calculated in the following manner. First, for each analysis period, each observation time is considered separately (remember, the number of analysis periods multiplied by the number of observation times is the number of analysis times: 24). For each analysis time, the candidate GW events from the zerolag, timeslides, and injection runs are split into two groups: those with a minimum template duration (among the templates matched in each detector) less than 0.2 s, and those with a minimum template duration greater than 0.2 s.
In the case of H1L1V1 observation time, these groups are further split by the combination of detectors that produced the event — i.e., H1L1, H1V1, L1V1, and H1L1V1. The FAR for each event is equal to the number of timeslide events (in the same analysis time/template duration/detector combination group) with a ranking statistic greater than the event being considered. See Figure 8.4 for a cumulative histogram of the IFARs at this stage. Then, the FARs are combined across the template duration groups and coincident detectors for a single analysis period. This combining process necessitates re-normalizing the FARs. Because some of the groups have lower minimum IFAR values (the vertical lines in Figure 8.4) than others, we normalize by the number of groups with IFARs lower than the old IFAR. See Figure 8.5 for a cumulative histogram of the combined IFARs for a single analysis period.
Cumulative histograms of the IFAR are used as a visual means to identify potential gravitational wave events. Any zerolag event that lies to the right of the grey lines that trace each of the 100 timeslide experiments has a lower FAR than we expect for a background event, given our analysis (i.e., a false alarm probability (FAP)<1%). Sometimes, however, there is a dearth of timeslide events for a particular detector combination.
This will falsely elevate a given zerolag event in the same category. Prior to opening the box, we decided that we will combine the background from an adjacent analysis period if this is the case.
We can see from Figure 8.5 that no foreground (zerolag) events lie to the right of the timeslide distri- butions; all foreground events are consistent with expected background. The same can be said for the other analysis periods. Thus, no candidate GW events were found with FAP<1% in this search.
The calculated combined FARs are then used to calculate the sensitivity of the search and the astrophysical upper limits on the rate of high-mass CBCs, as described in Section 7.8 and Section 7.8.1. The search sensitivities are calculated separately for the EOBNRv2 injections, the spinning IMRPhenomB injections, and the non-spinning IMRPhenomB injections. This is done because each set of waveforms is trusted over a different set of mass ranges. As the EOBNRv2 injections have been checked against numerical relativity for the largest spread of total masses and mass ratios, these are the only injections used for evaluating the upper limit. The upper limit calculation used the S5 results as a prior. Table 8.2 summarizes the sensitivity (in terms of distance) and upper limit results from Reference [17]. Figure 8.6 visualizes the upper limits (left panel) and sensitive distances (right panel) in component-mass space. The sensitive distances in Table 8.2 and the right panel of Figure 8.6 are in good semi-quantitative agreement with the expectations (see Section 2.2.2), which
Figure 8.4: A cumulative histogram of the uncombined IFARs for the H1L1V1 observation time of a single analysis period (965174343-3369744). The 100 grey lines trace the cumulative IFARs for each timeslide experiment. The colored dots indicate coincident events for each detector combination involved in the zerolag candidate GW event. The expected background dashed line traces the length of the observation divided by the value on the x-axis (the expected number of events with IFAR greater than or equal to a given IFAR is equal to the length of the observation time divided by the IFAR).
assume Gaussian noise and an SNR threshold of 8. Note that the horizon distances shown in Figure 2.19 are a factor of 2.26 larger than the sensitive distances, since the horizon distance calculation assumes optimally oriented CBCs. IMRPhenomB waveforms can be used to calculate our sensitive distance for CBCs whose component objects are spinning (remember, we restrict ourselves to the cases where the spin vectors of each component object are parallel to each other). The sensitive distance calculated with the IMRPhenomB waveforms is visualized in Figure 8.7 for different total mass and combined spin ranges.
Figure 8.5: A cumulative histogram of the combined (across each group in Figure 8.4) IFARs for the H1L1V1 observation time of a single analysis period (965174343-3369744). The 100 grey lines trace the cumulative IFARs for each timeslide experiment. The colored dots indicate coincident events for all detector combinations involved in the zerolag candidate GW event. The expected background dashed line traces the length of the observation divided by the value on the x-axis (the expected number of events with IFAR greater than or equal to a given IFAR is equal to the length of the observation time divided by the IFAR).
0 20 40 60 80 100
m1(M)
0 20 40 60 80 100
m2(M)
8.7 5.9 4.2 4.1 4.3
3.3 2.4 2.2 1.7 1.5 1.8 3.8 1.7 1.4 1.0 1.0 1.3
0.9 0.7 0.8 0.7
5.9 4.2 4.1 4.3
2.4 2.2 1.7 1.5 1.8 3.8
1.4 1.0 1.0 1.3
0.7 0.8
Merger rate limit (10−7Mpc−3yr−1)
(a)
0 20 40 60 80 100
m1(M)
0 20 40 60 80 100
m2(M)
75 72 77 75 61 61 52 49 32
102 116 140 139 131 130 121 116 94
152 172 181 187 189 177 156
194 210 224 223 201
230 253 224
257
75 72 77 75 61 61 52 49 32 116 140 139 131130 121 116 94
172 181 187189 177 156 210 224223 201
253224
Sensitive distance (Mpc)
(b)
Figure 8.6:Left—Upper limits (90% confidence) on BBH coalescence rates in units of10−7Mpc−3yr−1as a function of binary component masses, evaluated using EOBNRv2 waveforms. Right—Average sensitive distance for this search to binary systems described by EOBNRv2 signal waveforms, in Mpc [17].
Table 8.2: The search’s sensitive distances and coalescence rate upper limits, quoted over 9M-wide component-mass bins labelled by their central values. We also quote the chirp mass Mat the center of each bin. The sensitive distance in Mpc (averaged over the observation time and over source sky location and orientation) is given for EOBNR waveforms in S5 data rescaled for consistency with NR results [23], and for EOBNRv2, IMRPhenomB non-spinning (“PhenomB nonspin”) and IMRPhenomB spinning (“PhenomB spin”) waveforms in the S6-VSR2/3 data. The last two columns report 90%-confidence rate upper limits in units of10−7Mpc−3yr−1, for bins with component mass ratios1 ≤m1/m2 ≤ 4, for S5 data (revised relative to [23]) and the cumulative upper limits over S5 and S6-VSR2/3 data, as presented in this work.
Waveforms EOBNR EOBNR PhenomB nonspin PhenomB spin EOBNR EOBNR
Search data S5 S6-VSR2/3 S6-VSR2/3 S6-VSR2/3 S5 S5+S6-VSR2/3
m1 m2 M Distance Distance Distance Distance UL UL
(M) (M) (M) (Mpc) (Mpc) (Mpc) (Mpc)
10−7 Mpc3yr
10−7 Mpc3yr
14 14 13 81 102 105 106 18 8.7
23 14 16 95 116 126 126 12 5.9
32 14 18 102 140 132 135 8.8 4.2
41 14 21 107 139 141 145 7.8 4.1
50 14 22 107 131 137 149 8.2 4.3
23 23 20 116 152 148 149 7.4 3.3
32 23 24 133 172 172 179 4.9 2.4
41 23 27 143 181 178 183 4.3 2.2
50 23 29 145 187 188 198 3.4 1.7
59 23 32 143 189 188 192 3.2 1.5
68 23 34 140 177 180 191 3.7 1.8
77 23 36 119 156 176 170 5.6 3.8
32 32 28 148 194 190 197 3.4 1.7
41 32 32 164 210 219 220 2.5 1.4
50 32 35 177 224 221 214 1.9 1.0
59 32 38 174 223 221 214 2.0 1.0
68 32 40 162 201 199 210 2.4 1.3
41 41 36 183 230 222 224 1.6 0.9
50 41 39 191 253 253 258 1.4 0.7
59 41 43 194 224 239 236 1.4 0.8
50 50 44 192 257 218 217 1.4 0.7
25.0 37.5 50.0 62.5 75.0 87.5 100.0 Total mass (M)
100 150 200 250
Sensitivedistance(Mpc)
χ <0 χ= 0 χ >0
Figure 8.7: Dependence on aligned spin and total mass of the averaged sensitive distance of our search to phenomenological inspiral-merger-ringdown waveforms. For each of 6 bins in total massM, we show the sensitivity for IMRPhenomB signals with negative aligned spin parameterχ(left), non-spinning signals (centre) and signals with positive aligned spin parameter (right). The simulated signal parameters were restricted to mass ratios between 1 and 4 and aligned spins between -0.85 and 0.85 [17].