Status of the Search for Gravitational Wave Ringdowns from Perturbed BlackHoles Sarah Caudill for the LIGO Scientific Collaboration and the Virgo Collaboration The Ringdown Waveform S5 Ringdown Horizon Distance h 0 •! •! time We review recent changes made to the ringdown analysis pipeline to increase sensitivity and efficiency. We review the pipeline’s efficiency at recovering full inspiral-merger-ringdown waveforms in the mass range 25-100 M !.
Coherent compact binary coalescence searches for external triggers with large sky-position errors Shaon Ghosh 1 , Sukanta Bose 1 1 Washington State University, Pullman, WA Short hard gamma-ray bursts (SGRBs) are conjectured to have compact binary coalescences (CBCs) as progenitors. Therefore, SGRBs provide external triggers for searching signals from CBCs in gravitational-wave (GW) detectors. Whereas for many SGRBs the sky-position is determined by the electromagnetic detections with high accuracy, for some others it can be off by several degrees. Here we develop a method for coherently searching a patch of the sky, several degrees wide, for CBC signals in multiple baselines of GW detectors. We compare its performance in Gaussian noise with that of an all-sky (or “blind”) search and a targeted search and show where it can perform better than the latter two. · Short duration gamma ray bursts A gamma ray burst (GRB) is one of the most violent events in the Universe. These events are classified broadly into two categories. The events that are longer than a duration of two seconds are called long duration GRBs and those that are shorter are termed as short duration GRBs or SGRBs. The latter type is conjectured to have compact binary coalescences (CBCs), involving at least one neutron star, as progenitors. However, the sky position for some of them may not be known accurately enough through electromagnetic observations. Formulating robust strategies for searching GW signals from those sources is the main objective here. · External trigger pipeline The algorithm used for searching GW signals from SGRBs is called the External Trigger pipeline . Prior information about the sky position and the time of arrival of the signal is assumed to be known to some accuracy. This means that instead of doing a ’blind search’ in time and sky position, one can concentrate on a small time window and on a particular sky position (“known sky”) or a set of skypositions (i.e., on a “sky patch”). The external trigger pipeline focuses on a time window of six seconds around the external trigger time that one obtains from a GRB alert. The background is calculated by analysing the off-source times, away from the six-second time-window that includes the GRB trigger time. Figure 1 shows a schematic diagram of the hierarchical coherent stage of the external trigger pipeline. The coincident stage of the pipeline for M-interferometers supplies the GW triggers for the coherent stage to run on. • The known-sky search Since in an externally triggered search the sky position of the target is available beforehand, one can perform a coherent search for that sky position alone. This is what is done currently. But as we show below, this strategy can suffer in some cases. – Pros 1. This is computationally very cheap. 2. The false-alarm rate is expected to be smaller than the all-sky search. 3. since we are looking at the very spot of the sky for which we were alerted we are not having to worry about constructing a sky grid and hence we are not concerned at all about looking at a point slightly away from the point of interest. – Cons 1. In a hierarchical search pipeline, due to the mass-pair template variances across detectors, as described above, a skyposition measurement different from the true one can yield a higher signal-to-noise ratio (SNR). Thus, a known-sky search can hurt detection efficiency. 2. A significant error in a GRB’s sky position measurement in EM can hurt the SNR recovered by a known-sky search. • The sky-patch search The pros and cons of the two methods discussed above can guide us to develop an optimized way of searching the sky that benefits from the advantages of those methods, while mitigating the effect of their pitfalls. This new method uses the information from the GRB alert about the sky position and constructs a mini sky-grid around that point, andincluding it as one of the grid points. This ensures that: * We have the alerted sky position not falling in the “holes” of our grid spacing. * Parameter covariance error will not cause too much damage since we are not searching at a single sky position. An adjacent sky position in the grid may well yield the largest SNR. The detection efficiency will be helped. * The false-alarm rate will be smaller than the all-sky search. * If a GRB satellite provides large sky position errors, the sky-patch of the apporpiate size insures against a false GW dismissal. * The computational cost, though larger than that of the known-sky search, nevertheless can be significantly smaller than the all-sky one if we optimize the grid size and the grid spacing for efficiency and speed. The time taken to run the search increases as we increase the grid size. This is maximum for an all sky search and minimum for the know sky mode. In Fig. 2 we show the time taken to run one instance of the coherent code with different sky patch sizes. FIG. 3: Efficiency plots for coincident stage, and the coherent stage in known-sky, all-sky and skypatch modes of different sizes. The left plot shows low-mass bin, the middle one the medium-mass bin, and the right one the high-mass bin. We also studied how the sky-patch efficiencies vary with changing step-size. We choose three different step sizes for the sky-patch grids, namely 1 degree (default), 0.5 degree (fine), and 2 degrees (coarse). The result shown in Fig. 4 reveals no significant change in efficiency, indicating that the choice of the step size is not going to cost us in efficiency at least up to a step-size of 2 degrees. Hence, we can improve in computational cost by choosing a coarse grid. FIG. 4: Efficiency plots for coherent-stage sky-patch search with varying step size. Left panel shows low-mass bin, middle panel shows medium-mass binand right panel the high-mass bin. We also studied the performance of the known-sky mode for a different sky position than that of the location of GRB090709B. Somewhat arbitrarily, we chose this location to be (0, 0) and did a comparative study of the detection efficiencies in Fig. 5. FIG. 1: The coherent stage of the hierarchical external trigger search pipeline · An optimal strategy for searching in the sky • The all-sky search The standard CBC coherent pipeline [1,3] does a blind search over a discrete grid covering the whole sky. We call this the “all sky” search. Here we maximize the coherent statistic over all the sky positions in a sky grid and store its search parameters if its value exceeds a preset threshold. – Pros 1. Most importantly, the mass-pair templates that yield a coincident trigger among different interfeormeters are generally different because the interferometers have different noise PSDs and, consequently, different template banks. This (typically small) inconsistency is concomitant with slightly inaccurate arrival times in those interferometers, and can yield a measured sky-position that is at variance with that of a GRB alert. Therefore, an all sky search has a greater chance of recovering triggers. 2. GRB observations in the electromanetic (EM) window can have large sky position errors. For example, Fermi can have a sky position resolution as bad as 20 degrees for some of the GRBs it detects. – Cons 1. By constructing a discrete grid we create the possibility of the trigger position to be in the gap between 4 grid points. This will cause in recovering of a much weaker secondary trigger or worse, loss of the trigger altogether. 2. All sky search is computationally expensive. 3. Searching over the entire sky increases the false-alarm rate. FIG. 2: Timing plots for the coherent code for different sky-patch sizes. The x-axis represents the size of the sky patch, where a value of n implies a sky-patch with (n × n) points. The timing values in the y-axis are given in seconds and are averaged over 100 trial runs. · Comparison of the different sky mode searches Here we compare the different sky mode (all sky, known sky, sky patch) searches in Gaussian noise for the sky position of one of the LIGO Science Run 6 (S6) GRBs, namely, GRB090709B. We compare the detection efficiency of signals injected. We define detection efficiency as the ratio of the number of triggers recovered with a coherent SNR larger than the largest background SNR for a given distance bin to the total number of injected triggers in the respective bins. We do these for three mass bins, namely, the lowmass (0.00, 3.48]M ⊙, medium-mass (3.48, 6.00]M ⊙ and high-mass (6.00, 20.0]M ⊙ bins. For comparison we also plot the coincident stage efficiencies of the recovered triggers, where the efficiency is calculated for the coincident effective SNR. FIG. 5: Efficiency plots for a coherent known-sky search for GRBs with two different sky positions occuring at the same time. Left panel shows low-mass bin, middle panel shows for medium-mass binand right panel for the high-mass bin. What we observe here is that the performance varies as a function of the sky position of the GRB. This is expected since the network sensitivity itself varies with the sky position. Accordingly, sky-patches with step-size and sky-coverage adapted to a network’s varying sensitivity (in sky position) are more optimal than those that have these parameters fixed for all sky positions. We plan to present that study in the future. Acknowledgements We thank Alex Dietz, Nick Fotopoulos, Ian Harry, Gregory Mendell and Fred Raab for helpful discussions. This work was supported in part by NSF grant PHY-0855679. References 1. A. Pai, S. Dhurandhar, and S. Bose, Phys. Rev. D 64, 042004 (2001), gr-qc/0009078. 2. J. A Badie et al The Astrophysical Journal, 715:14531461 (2010). 3. S. Bose, T. Dayanga, S. Ghosh, D. Talukder, “A blind hierarchical coherent search for gravitational-wave signals from coalescing compact binaries in a network of interferometric detectors,” LIGO document number LIGO-P1000183-v1 (2010).