Testing the Detection Statistic

In this section we will look at the new detection statistic, to see how well it performs in a GRB analysis. We will start by looking at the SNR time series for the two GRBs analysed. Figure 5.1 shows the coherent SNR (top panel) and the reweighted SNR (bottom panel) time series for GRB 170817A. The plots show the triggers for every template in the template bank,11clustered such that only the most significant trigger in each 0.1 second window is kept. In the top panel we can see the coherent SNR time series looks clean, and GW 170817 is clearly visible at the correct time with a coherent SNR of 29.22, which is comparable to the coherent SNR of 31.26 PyGRB obtained in O2.12 The bottom panel shows the reweighted SNR time series. We can see that some of the noise transients that peak the coherent SNR have been downweighted to have a comparable significance to background noise, but the GW is still clearly visible. In figure 5.2 we plot the coherent (top panel) and reweighted (bottom panel) SNR time series for GRB 170112A. From the coherent SNR time series we can see that there are several significant glitches. The reweighted SNR time series shows that these glitches were downweighted to be no more significant than background noise.

From the time series plots, it seems that the reweighted SNR is behaving as expected. In figure 5.3 we have plotted the null SNR against the coherent SNR (left) and reweighted SNR (right) for GRB 170817A13, in order ensure that triggers are being correctly reweighted by the null SNR. The null SNR shows no significant deviations from the background level, with a peak of just 5.22. Only a few points are above the 4.25 threshold required to reweight a trigger by the null SNR, see equation (4.75), but the triggers that exceed this threshold are being appropriately downweighted.

Similarly, in figures 5.4 and 5.5, we plot the coherent SNR (left) and reweighted SNR (right) against the network χ2 for GRB 170817A and GRB 170112A respec- tively. Figure 5.4 shows that the triggers with higher network χ2 are downweighted more. The GW, visible as the rightmost point in each plot, is downweighted but still far more significant than any background event. In figure 5.5, we see that the glitches in the data around GRB 170112A have a high coherent SNR and a high

10

GRB 170112A was not a single sky point analysis when analysed by PyGRB in O2, but did have a small sky error. The O2 PyGRB analysis searched over three sky points.

11

There are about 190000 templates in the template bank.

12_{Some differences in SNR are to be expected as the search is using different PSD options to the}

O2 PyGRB search.

13

As GRB 170112A was a two detector analysis, there was no null SNR. Hence this plot is only made for GRB 170817A.

Figure 5.1: Coherent and Reweighted SNR Time Series for GRB 170817A. The top panel shows the coherent SNR vs time for GRB 170817A. The GW is clearly visible, as are some smaller peaks that are due to noise. The bottom panel shows the reweighted SNR time series. The background noise has been downweighted but the GW is still very prominent. It is noteworthy that the peaks in coherent SNR that were due to noise have mostly been downweighted to be less significant than the median background trigger.

Chapter 5. The Future of PyGRB

Figure 5.2: Coherent and Reweighted SNR Time Series for GRB 170112A. The top panel shows the coherent SNR vs time for GRB 170112A. There is no GW, but several glitches are clearly visible. The bottom panel shows the reweighted SNR. We can see that the gltiches have been downweighted to be less significant than the median background trigger.

network χ2, but are appropriately downweighted so that these loud glitches are no more significant than background events.

We also plotted the peak coherent and reweighted SNR in each 6-second off- source trial, as well as the on-source. The results for GRB 170817A can be seen in figure 5.6. As we do not have timeslides, there are not many off-source trials (892 in total), but we can clearly see that the on-source trial, marked by the blue and red stars, are substantially louder than the background for both the coherent and reweighted SNR. Note that the coherent SNR has a small tail of higher significance events at around a coherent SNR of 7-9, which does not appear in the reweighted SNR. In figure 5.7 we make the analogous plot for GRB 170112A. As the data contained several glitches, this plot shows a long tail of events with a very high coherent SNR, which the reweighted SNR does not have. We can also see that the coherent SNR and reweighted SNR in the on-source window, indicated by the red and blue stars respectively, are consistent with background. The new code finds a p-value for the loudest event in the on-source data is 0.14.14 This plot shows the importance of the reweighting. Suppose there had been a GW in the on-source of GRB 170112A that had a coherent SNR of ∼ 30 and a reweighted SNR of ∼ 23, as GW 170817 did. In this case, the GW would not have had a higher coherent SNR

Figure 5.3: Null SNR vs Reweighted SNR for GRB 170817A. Here we plot the null SNR against the coherent SNR (left) and the reweighted SNR (right) for GRB 170817A. Only triggers with a null SNR above 4.25 are reweighted by the null SNR (with the other triggers being reweighted only by their χ2 values). We can see that these triggers have been downweighted more than the triggers with a low null SNR. The GW is clearly visible on the right of both plots.

Chapter 5. The Future of PyGRB

Figure 5.4: Network χ2 vs Coherent and Reweighted SNR for GRB 170817A. Here we plots the network χ2 _{against the coherent SNR (left) and}

reweighted SNR (right) for GRB 170817A. We can see that the higher the net- work χ2 of a trigger, the more it is downweighted. The GW is clearly visible on the right of both plots.

than all of the off-source trials, making a detection claim based on the coherent SNR impossible. Using the reweighted SNR, the GW would have been far more significant than anything in the background. With more off-source trials, this could allow us to claim a detection.

We also injected BNS waveforms with an opening angle of up to 30◦ into the off-source data of GRB 170817A in order to measure the search sensitivity. In figure 5.8 we have plotted the injection distance against time. From this we can see that the BNS waveforms are detectable up to about 200 Mpc. In figure 5.9, we show an analogous plot from the O2 PyGRB analysis of GRB 170817A. We can see that the old code could also detect these waveforms up to a distance of about 200 Mpc.15