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

20 janvier 2005Réunion LISA-France2 Recherche de Binaires Que peut-on apprendre avec Virgo pour LISA? Forme donde bien connue filtrage adapté Espace des paramètres grand méthodes de pavage? Méthodes danalyse efficaces méthodes hiérarchiques analyse multi-bandes Problèmes pratiques clustering des événements; extraction des paramètres des évènements; vetos …

20 janvier 2005Réunion LISA-France3 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-match contour shapes can be anything (well, almost…) How to optimally pave a space with 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) Template Placement Example of the difference between a calculated iso-match contour and the biggest possible ellipse inscribed inside it (same center point) Match min = 0.9 PN 2.5

20 janvier 2005Réunion LISA-France4 Build a "skeleton" of the contour by following the line of minimal steepness: Reconstruction of "exact" contours 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) 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

20 janvier 2005Réunion LISA-France5 Placement for the whole space Place two lines Start from a three-contour cell Build the rest of the set of two lines Place next line Build the next set of two lines independently, starting from a point on the border of the first set Keep only external line (in light gray) Cover space line by line

20 janvier 2005Réunion LISA-France6 Test coverage of parameter space Match min = 0.9 Masses : 1-30 M sol f min = 30 Hz, fmax = LSO Match distribution of test points The low match points

20 janvier 2005Réunion LISA-France7 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

20 janvier 2005Réunion LISA-France8 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 sampling duration

20 janvier 2005Réunion LISA-France9 Split analysis in a few frequency bands… 1 st 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 M2 M1

20 janvier 2005Réunion LISA-France10 … And Recombine Full Band Templates 2 d step of multi band analysis One grid for full frequency band: VIRTUAL templates Associated with a real template in each band (Best 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 match) Standard SNR search on recombined output Clustering REAL VIRTUAL

20 janvier 2005Réunion LISA-France11 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

20 janvier 2005Réunion LISA-France12 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

20 janvier 2005Réunion LISA-France13 But: 1 évènement dans les données -> 1 seul candidat Critère de regroupement: temps de fin dévènement (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 dévènements Clustering temporel des Micro-évènements

20 janvier 2005Réunion LISA-France14 Clustering in Parameter space Grid Response To Events (SNR) + +

20 janvier 2005Réunion LISA-France15 Remarques Lanalyse des données de LISA semble plus compliquée que pour Virgo De multiples problèmes se présentent lors de la mise en oeuvre dune analyse Lanalyse de Virgo nous prépare à celle de LISA