1. SEARCH FOR INSPIRALING BINARIES S. V. Dhurandhar IUCAA Pune, India

2. Inspiraling compact binaries GW

3. The inspiraling compact binary Two compact objects: Neutron stars /Blackholes spiraling in together Waveform cleanly modeled

6. Parameter Space for 1 – 30 solar masses

7. The matched filter Optimal filter in Gaussian noise: Detection probability is maximised for a given false alarm rate Stationary noise:

8. Matched filtering the inspiraling binary signal

9. Detection Strategy: Maximum Likelihood Parameters: Amplitude, t a,  a, m 1, m 2 Amplitude: Use normalised templates Scanning over t a : FFT Initial phase  a : Two templates for 0 and  and add in quadrature masses chirp times:     bank required Signal depends on many parameters

10. Detection Data: x (t) Templates: h 0 (t;     ) and h  (t;     ) Padding: about 4 times the longest signal Fix     Outputs: Use FFT to compute c 0 (  and c  (   is the time-lag: scan over t a Statistic: c 2 (  c 0 2 (  + c    (  Maximised over initial phase Conventionally we use its square root c(  Compare c(  with the threshold 

13. FLAT SEARCH

14. Parameter space for the mass range 1 – 30 solar masses Parameter Space

15. Hexagonal tiling of the parameter space Minimal match: 0.97 Density of templates: ~ 1300/sec 2 LIGO I psd

16. Cost of the flat search Longest chirp: 95 secs for lower cut-off of 30 Hz Sampling rate: 2048 Hz Length of data train (> x 4): 512 secs Number of points in the data train: N = 2 20 Length of padding of zeros: 512 – 95 = 417 secs This is also the processed length of data Number of templates: n t = 11050 Online speed reqd. = n t x 6 N log 2 N / 417 ~ 3.3 GFlop

17. Hierarchical Search

20. Comparison of contours (H = 0.8) with 256 Hz and 1024 Hz cut-off

21. Only hierarchy in masses: gain factor 25-30 Boundary effects not included Hierarchy on masses only

22. 92% power at f c = 256 Hz

24. Choice of the first stage threshold High enough to reduce false alarm rate -- reduce cost in the second stage -- For 2 18 points in a data train    or so Low enough to make the 1 st stage bank as coarse as possible and hence reduce the cost in the 1 st stage    S min )  S ~ 6

26. The first stage templates

28. Templates flowing out of the deemed parameter space are not wasted Zoomed view near low mass end

29. Need 535 templates

30. Cost of the EHS Longest chirp ~ 95 secs T data = 512 secs T pad = 417 secs f 1 samp = 512 Hz f 2 samp = 2048 Hz N 1 = 2 18 N 2 = 2 20   =.92 S min  S   = 8.2 ~ 6.05 n 1 = 535 templates n 2 = 11050 templates S min ~ 9.2  S 1 ~ 6 n 1 N 1 log 2 N 1 / T pad ~ 36 Mflops S 2 ~ n cross  6 N 2 log 2 N 2 / T pad ~ 13 Mflops S ~ 49 Mflops S flat ~ 3.3 GFlops n cross ~.82   Gain ~ 68

31. Optimised EHS

32. Performance of the code on real data S2 - L1 playground data was used – 256 seconds chunks, segwizard – data quality flags 18 hardware injections - recovered impulse time and SNR – matched filtering part of code was validated Monte-Carlo chirp injections with constant SNR - 679 chunks EHS pipeline ran successfully The coarse bank level generates many triggers which pass the  and   thresholds Clustering algorithm

33. The EHS pipeline Can run in standalone mode (local Beowulf) or in LDAS

34. Data conditioning Preliminary data conditioning: LDAS datacondAPI Downsamples the data at 1024 and 4096 Hz Welch psd estimate Reference calibration is provided Code data conditioning: Calculate response function, psd, h(f) Inject a signal

35. Template banks and matched filtering LAL routines generate fine and the coarse bank Compute   for templates with initial phases of 0 and  Hundreds of events are generated and hence a clustering algorithm is needed

36. The Clustering Algorithm Step 1: DBScan algorithm is used to identify clusters/islands Step 2: The cluster is condensed into an event which is followed up by a local fine bank search

37. DBScan (Ester et al 1996) 1. For every point p in C there is a q in C such that p is in the  -nbhd of q This breaks up the set of triggers into components 2.A cluster must have at least N min number of points – otherwise its an outlier

38. Condensing a cluster Figure of merit: l(x) is the Lagrange interpolation polynomial

39. Conclusions Galaxy based Monte Carlo simulation is required to figure out the efficiency of detection. This will incorporate current understanding of BNS distribution in masses and in space Hierarchical search frees up CPU for additional parameters

41. CONCLUSION * Results shown for Gaussian noise - Now looking at real data – S1, S2 - Performance in non-Gaussian noise - Event multiplicity needs to be condensed into a single event * Reducing computational cost with hierarchical approach frees up CPU power for additional parameters