Optimisation des recherches de coalescences binaires

1. Optimisation des recherches de coalescences binaires Benoît Mours LAPP - Annecy Réunion LISA-France 20 Janvier 2005

2. Recherche de Binaires Que peut-on apprendre avec Virgo pour LISA? • Forme d’onde bien connue  • filtrage adapté • Espace des paramètres grand  • méthodes de pavage? • Méthodes d’analyse efficaces  • méthodes hiérarchiques • analyse multi-bandes • Problèmes pratiques  • clustering des événements; • extraction des paramètres des évènements; • vetos • … Réunion LISA-France

3. Template Placement Matchmin = 0.9 PN 2.5 • Some problems just for 2 parameters… • Optimality of paving difficult to obtain • For high minimal match (close to 1),iso-match contours = ellipses • Problem partially solved, at low PN order • For low minimal match ( <0.95) iso-matchcontour shapes can be anything(well, almost…) • How to optimally pave a spacewith any shapes • One point (match) calculation = 0.1 s - 1 s computing time… • Calculation of an image 100*100 : 15min - 3 h ! • Difficult to do placement… but you need to (hierarchical searches) Example of the difference between a calculated iso-match contour and the biggest possible ellipse inscribed inside it (same center point) Réunion LISA-France

4. Reconstruction of "exact" contours • Build a "skeleton" of the contour by following the line of minimal steepness: • Algorithm : • search for the max match on a line perpendicular to the previous progression direction • on this line, search for the two points corresponding to searched min match Each point is found with a very simple (fast) binary method Reconstruction time : a few tens of seconds to a few tens of minutes (fmin = 30 Hz, fmax = LSO, sampling = 1 kHz) Réunion LISA-France

5. Place next line Place two lines Start from a three-contour cell Build the next set of two lines independently, starting from a point on the border of the first set Build the rest of the set of two lines Keep only external line (in light gray) Cover space line by line Placement for the whole space Réunion LISA-France

6. t1.5 The low match points Match distribution of test points t0 Test coverage of parameter space Matchmin = 0.9 Masses : 1-30 Msol fmin = 30 Hz, fmax = LSO t1.5 t0 Réunion LISA-France

7. CB search cost issue • Optimal search requires large computing resources • especially for low mass / low minimal frequency • The critical factors are: • the number of templates needed • chirp length dominated by low frequency evolution • the size of the FFT involved in the matched filtering • chirp length / sampling frequency • Cheaper analysis can be done by splitting the frequency band • Suitable for hierarchical searches Réunion LISA-France

8. duration sampling Multi Band Analysis: Basic • CB templates : • Have long duration because of low frequency part • Need high sampling because of high frequency part • Are more numerous in grid for larger frequency band • Split the analysis in a few frequency bands: • Expected gain up to factors 100 for CPU and 500 for storage • for 3 bands, low minimal mass, low minimal frequency Réunion LISA-France

9. M2 M2 M2 M2 Split analysis in a few frequency bands… • 1st step of multi band analysis • Different Grid of templates for each frequency band: REAL templates • Short templates in high frequency grid • Less templates (especially in high frequency grid) • Down-sampled data & templates in low frequency grid(s) • Less & Shorter FFTs • REAL Templates grids are all applied to data independently • 2 outputs for each filter (P & Q) M1 M1 M1 Réunion LISA-France M1

10. … And Recombine Full Band Templates REAL REAL • 2d step of multi band analysis • One grid for full frequency band: VIRTUAL templates • Associated with a real template in each band (Best < VT,RT > match in each band) • Computed and used for initialization only • VT Hierarchical step: • Check if any associated real template triggers (SNR Thresholds defined for each bands) • Coherent sum of bands outputs: • Lower frequency band(s) interpolation • Time delay & phase shift (from < VT,RT > match) • Standard SNR search on recombined output • Clustering REAL VIRTUAL Réunion LISA-France

11. Check 2 bands vs 1 band • Systematic comparisons • same efficiency • same purity • good SNR correlation • Increased computing efficiency • limited due to narrow-band spectrum used in MDCs so far Réunion LISA-France

12. LIGO/Virgo Analysis, 3/2 Bands • 3 bands analysis • 40 Hz -> 108 Hz • 108 Hz ->158 Hz • 158 Hz -> 2048 Hz • Equivalent results • Slight difference due to different window lengths Réunion LISA-France

13. Clustering temporel des Micro-évènements • But: 1 évènement dans les données -> 1 seul candidat • Critère de regroupement: temps de fin d’évènement (date + durée du signal théorique) • + Logique pour tourner en ligne: prise en compte du délai variable entre la date du micro-évènement et son apparition dans les donnes sorties de MBTA • Permet de choisir une coupure et générer directement une liste d’évènements Réunion LISA-France

14. + + + + + Clustering in Parameter space Grid Response To Events (SNR) Réunion LISA-France

15. Remarques • L’analyse des données de LISA semble plus compliquée que pour Virgo • De multiples problèmes se présentent lors de la mise en oeuvre d’une analyse • L’analyse de Virgo nous prépare à celle de LISA Réunion LISA-France