Hough search for continuous gravitational waves using LIGO S4 data

Transcription

1 Hough search for coiuous graviaioal waves usig LIGO S4 daa A.M. Sies for he LIGO Scieific Collaboraio Uiversia de les Illes Balears, Spai Alber Eisei Isiu, Germay MG11, GW4- GW daa Aalysis Berli - July 23-29, 2006 LIGO-G Z

2 Coe Iroducio The Hough rasform Overview of S2 aalysis Improvemes for S4 Prelimiary S4 resuls Fuure work

3 Sources of Coiuous Graviaioal Waves This alk shows resuls for isolaed sources oly. Search ca deeced ay periodic source. Upper limis are se o graviaioal-wave ampliude, h 0, of roaig riaxial ellipsoid. A B Credis: A. image by Jolie Creigho; LIGO Lab Docume G Z. B. image by M. Kramer; Press Release PR0003, Uiversiy of Macheser - Jodrell Bak Observaory, 2 Augus C. image by Daa Berry/NASA; NASA News Release posed July 2, 2003 o Spacefligh Now. D. image from a simulaio by Chad Haa ad Bejami Owe; B. J. Owe's research page, Pe Sae Uiversiy. Mouai o euro sar C Accreig euro sar LIGO-G W Precessig euro sar D Oscillaig euro sar

4 The expeced waveform Expeced waveform from a isolaed spiig NS is siusoidal wih small spi-dow: si cos,, A h A h h F h F h Φ Φ ψ ψ Φ ! 2 f π φ d f I c G h h A h A r zz cos cos ε π ι ι Doppler frequecy modulaio due o moio of Earh ad ampliude modulaio due o deecor aea paer. For seig upper limis oly, we assume he emissio mechaism is due o deviaios of he pulsar s shape from perfec axial symmery, f GW 2f r

5 Icohere power-sum mehods Frequecy Three mehods have bee developed o search for cumulaive excess power from a hypoheical periodic graviaioal wave sigal by examiig successive specral esimaes: SackSlide PowerFlux Time Hough They are all based o breakig up he daa io segmes, FFT each, producig Shor 30 mi Fourier Trasforms SFTs from h, as a cohere sep alhough oher cohere iegraios ca be used if oe icreasig he legh of he segmes, ad he rack he frequecy drifs due o Doppler modulaios ad df/d as he icohere sep. Oher fully cohere mehods: Frequecy domai mach filerig/maximum likelihood esimaio Time domai Bayesia parameer esimaio

6 Differeces amog he icohere mehods Wha is exacly summed? SackSlide Normalized power power divided by esimaed oise Averagig gives expecaio of 1.0 i absece of sigal Hough Weighed biary cous 0/1 ormalized power below/above SNR, wih weighig based o aea paer ad deecor oise PowerFlux Average srai power wih weighig based o aea paer ad deecor oise Sigal esimaor is direc excess srai oise circular polarizaio ad 4 liear polarizaio projecios

7 The Hough rasform The Hough rasform is a geeral mehod for paer recogiio ha was developed ad paeed may years ago. We use he Hough rasform o fid a paer produced by he Doppler modulaio & spi-dow of a GW sigal i he ime-frequecy plae of our daa. For isolaed NS he expeced paer depeds o: {α,δ, f 0, f } ˆ ˆ ˆ 0 0 f f f c f f f & v δ α

8 Review of S2 Hough aalysis Sar wih 1800s SFTs for each deecor Selec frequecy bis by seig a hreshold o ormalized power gives ime-frequecy collecio of 0s ad 1s For N SFTs, he fial umber cou for a give parameer space poi is N i where 0 i i 1 1 Usig 0s ad 1s leads o gai i compuaioal efficiecy ad i is more robus agais large rasie power arifacs

9 S2 aalysis covered Hz, over he whole sky, ad 11 values of he firs spidow f Hz, f Hz s 1 Templaes: Number of sky poi emplaes scales like frequecy sky 300 Hz Hz Hz Three IFOs aalyzed separaely No sigal deeced Upper limis obaied for each 1 Hz bad by sigal ijecios: Populaio-based frequeis limis o h 0 averagig over sky locaio ad pulsar orieaio Hough S2: UL Summary Feb.14-Apr.14,2003 Deecor L1 H1 H2 Frequecy Hz h 0 95% 4.43x x x10-23

10 Frequeis upper limi Perform he Hough rasform for a se of pois i parameer space λ{α,δ,f 0,f i } S, give he daa: HT: S N λ λ Deermie he maximum umber cou * * max λ: λ S Deermie he probabiliy disribuio p h 0 for a rage of h 0 The 95% frequeis upper limi h 0 95% is he value such ha for repeaed rials wih a sigal h 0 h 0 95%, we would obai * more ha 95% of he ime 0.95 N * p h 0 95% Compue p h 0 via Moe Carlo sigal ijecios

11 Number cou disribuio for sigal ijecios i S2 daa L1: Hz, * 202, 1000 ijecios 0.1% 30.5% 87.0% 1 p h 0 ideally biomial for a arge search, bu: No saioariy i he oise Ampliude modulaio of he sigal for differe SFTs Differe sesiiviy for differe sky locaios ad pulsar orieaios Radom mismach bewee sigal & emplaes smear ou he biomial disribuios

12 Fourh Sciece Ru S4 Sesiiviy February 22, 2005 March 23, 2005 Srai Sesiiviy [1/SqrHz] S5 is currely ruig a desig sesiiviy! Frequecy Hz

13 Improvemes for S4 The S2 Hough search has bee modified o ake io accou ha he SFTs have differe oise floors ad he sigal ampliude chages i ime SNR chages across SFTs We use a weighed Hough o give more weigh o SFTs havig greaer SNR. Weighs are proporioal o he beam paer fucios ad iversely proporioal o he SFT oise floor. Weighig mehod applied o Hough was iiially suggesed by C.Palomba ad S.Frasca a GWDAW-2004 ad i is similar o he oe used by he PowerFlux mehod. Number cou is o a ieger aymore i 1 Usig he weighs does o lead o ay loss i compuaioal efficiecy or robusess i 1 I has also bee geeralized o he Muli-IFO case N w i i N w i N

14 Improvemes for S4 Nomial sesiiviy for give FA ad FD assumig a perfecly mached emplae averaged over sky, orieaios ad polarizaio agles: h 0 S S 5.34 N erfc 1 1/ 2 1/ 4 2α H S T coh erfc 1 2β H Improved Sesiiviy: Assumes emplae is perfecly mached o sigal, ad average over all pulsar orieaios ad polarizaio agles bu o over sky-posiios Opimal choice of weighs is: Opimally weighs should be calculaed a same sky-locaio as sigal 1/ 2 r h S X i S i r w r w X 1/ 2 i 2 i F F i S i 2 i F F w i i S 2 2 S T i coh

15 Improvemes for S4 Gai i sesiiviy is large if sadard deviaio of SFT oise floors is large or if sigal ampliude chages rapidly across SFTs Mea umber cou is uchaged due o ormalizaio of weighs: Nα N exp Sadard deviaio always icreases: r σ w α 1 α ρ h Number cou hreshold for a give false alarm: h r Nα 2 w 2 α1 α erfc 1 2α H

16 Improveme i deecio efficiecy Sigal ijecios i fake daa, Hz, radom sky-posiio ad polarizaio agles. Number cou hreshold se for α H Improveme i sesiiviy a 90% efficiecy is roughly 10% i sigal ampliude for a perfecly mached emplae ad saioary oise. The gai depeds o pulsar orieaio Will be somewha degraded whe searchig i a sky-pach because of a mismach ad also because we will use a sigle se of weighs for he whole sky-pach calculaed a he ceer, bu sesiiviy ca also improve i case of o-saioary oise.

17 The S4 Hough search As before, ipu daa is a se of N 1800s SFTs o demodulaios Weighs allow us o use SFTs from all hree IFOs ogeher: 1004 SFTS from H1, 1063 from H2 ad 899 from L1 Search frequecy bad Hz 1 spi-dow parameer. Spidow rage [-2.2,0] 10-9 Hz/s wih a resoluio of Hz/s All sky search Sky is broke up io 92 paches 0.4 rad 0.4 rad wide Lie cleaig used o remove kow arrow specral lies All-sky upper limis se i 0.25 Hz bads Muli-IFO ad sigle IFOs have bee aalyzed

18 Coribuio of differe IFOs Figure plos he relaive oise weighs from H1, H2 ad L1 IFO All w w i i

19 Hisogram of Hough umber cous for he H1 deecor Hisogram of he Hough umber cou compared o a Gaussia disribuio for he H1 deecor 1004 SFTs i he frequecy bad Hz. Number of emplaes aalyzed i each sky pach ~ <>202.7 σ12.94 obaied from he weighs <>202.7 σ14.96

20 Loudes eves for every 0.25 Hz Muli ierferomeer case Hz Prelimiary Sigificace defied as s max -<>/σ

21 Improvemes due o he weighs Compariso of he All-sky 95% upper limis obaied by Moe- Carlo ijecios for he muli- IFO case. The average improveme by usig weighs i his bad is 9.25% for he muli-ifo case, bu oly ~6% for he sigle IFO

22 Prelimiary Upper Limis Prelimiary Bes UL for L1: for H1: for Muli: I urs ou ha UL ca be fied by wih C11.0± 0.5 h 95% 0 N C 1 i i 1 S 2 1/ 4 S T 1/ 2 coh, S max sigificace erfc

23 Aalysis of Hardware Ijecios Prelimiary

24 Aalysis of Hardware Ijecios Prelimiary

25 Coclusios & Fuure work Resuls are ieresig, bu much beer resuls are o he way! Improvemes for S5: S5: ~2x beer sesiiviy, 12x or more daa Icrease he ime of he cohere sep Hough o F-saisic segmes from muliple IFOs Ogoig developme of Hierarchical pipelie ha combies cohere ad semi-cohere searches