Introduction The data analysis challenge Current Solutions A New Solution Conclusions and future work A “fast” parameter space search for continuous gravitational waves from known binary systems C Messenger University of Glasgow December 19, 2006 GWDAW 11 C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge Current Solutions A New Solution Conclusions and future work Outline 1 Introduction Overview of the data analysis problem 2 The data analysis challenge The sources 3 Current Solutions The fully coherent approach The Stack-Slide approach The Radiometer approach 4 A New Solution A New Solution :The sideband search The proposed search Following up candidates 5 Conclusions and future work C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge Current Solutions Overview of the data analysis problem A New Solution Conclusions and future work Introduction Non-axisymmetric spinning neutron stars are thought to be candidates for continuous gravitational waves sources. “Targetted” searches for known isolated and binary pulsars have been/are being done at an unprecented sensitivity. “Parameter space” searches fall into 2 catagories “blind” searches eg. all sky search [Col06] “semi-targetted” searches where the parameter space is constrained by previous EM observations eg. Sco X-1 search [Col06] Parameter space searches for continuous gravitational waves sources are typically computationally limited. eg. Coherent S2 Sco X-1 search limited to observation time of ∼ 6 hours. New search strategies are required (proposed method adapted from [RCE03]). C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge Current Solutions The sources A New Solution Conclusions and future work LMXB’s LMXB’s consist of a neutron star (NS) (or black hole) in orbit with a lower mass companion star (either main sequence, white dwarf or evolved star). The lower mass companion has filled its Roche Lobe and material is being transferred into an accretion disk around the NS. accretion disk. These are not seen as pulsars so the frquency is unknown (although some exhibit type 1 X-Ray bursts). GW emission mechanism Asymmetries in the NS crust caused and sustained indirectly by infalling material [Wag84, UCB00]. C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge Current Solutions The sources A New Solution Conclusions and future work Millisecond accreting X-Ray pulsars An accreting binary system where pulses in the X-Ray emission are observed at the NS rotation frequency. The pulses are generated by infalling material being channelled onto “hotspots” on the NS surface. Small subset (7 currently known) have spin periods of order 10 − 3 sec and are known as millisecond (or recycled) pulsars. GW emission mechanism Asymmetries in the NS crust caused and sustained indirectly by infalling material [Wag84, UCB00, MP05]. C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge Current Solutions The sources A New Solution Conclusions and future work Binary Radio Pulsars Radio pulsars in binary systems typically have very well defined orbital and phase parameters but not all of them. The work by [PW] and consequent results [Col] leave ∼ 40 radio pulsars as unsuitable for the single filter time domain analysis. GW emission mechanism Long term asymmetries in the NS crust [Bil98, UCB00, Cut02] C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge The fully coherent approach Current Solutions The Stack-Slide approach A New Solution The Radiometer approach Conclusions and future work The fully coherent approach Using matched filtering, we perform a Accreting binary pulsar search over a bank of templates. 16 10 total templates A metric approach is used to optimally 10 14 12 10 place templates. Number of Templates frequency templates 10 10 10 8 The F -statistic is then computed for i c 6 e t r orbital templates 10 m e d e c t o r j n p − u e d 4 l a t 10 r r e c o c projected metric u n e t r i m each template [JKS98]. e d e c t o j 10 2 n p r u 10 0 This approach was used for the S2 −2 10 3 4 5 6 10 10 10 10 Observation Time Span, T span (sec) analysis [Col06]. Key Problem for LMXB’s This approach is computationally prohibitive T comp ∝ T 7 (for Sco X-1 T < 10 5 sec). C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge The fully coherent approach Current Solutions The Stack-Slide approach A New Solution The Radiometer approach Conclusions and future work The Stack-Slide approach This is an incoherent search. Stack-Slide example The data are split into M contiguous chunks. time time A coherent search is t performed on each chunk. frequency frequency normalised stacked power The search products are summed (stacked) as a time function of source frequency frequency frequency (slid) [BCCS98]. C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge The fully coherent approach Current Solutions The Stack-Slide approach A New Solution The Radiometer approach Conclusions and future work The Radiometer approach The radiometer approach has been developed initially for the analysis of Radiometer example the GW stochastic background [Bal06, Col04]. t It can be used to target a particular sky location. It cross corrolates data between 2 detectors and uses the signals (if present) as filters. C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge A New Solution :The sideband search Current Solutions The proposed search A New Solution Following up candidates Conclusions and future work A toy model example Let us define a toy model binary signal as � � � 2 π � �� h ( t ) = g ( t ) h 0 cos 2 π f 0 t + a sin P ( t − t 0 ) + φ 0 , where g ( t ) is the time domain window function. This can be decomposed in the frequency domain to give m g ( f ) ∗ h 0 ˜ � J n (2 π f 0 a ) e − i ( nt 0 + φ 0 ) δ ( f − f n ) h ( f ) = ˜ 2 n = − m where M = 2 m + 1 ≈ 4 π f 0 a . The power is then m g ( f ) | 2 ∗ h 2 h ( f ) | 2 ≈ | ˜ | ˜ 0 � J 2 n (2 π f 0 a ) δ 2 ( f − f n ) 4 n = − m C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge A New Solution :The sideband search Current Solutions The proposed search A New Solution Following up candidates Conclusions and future work The frequency domain signal h ( f ) | 2 is localised in M ≈ 4 π f 0 a For T � 3 P the signal power | ˜ “spikes”. Each “spike” is seperated Example signal profile by 1 / P Hz The relative amplitude of 3.5 x 10 4 each “spike” is defined by 3 2.5 the f 0 and a . t 2 |h(f)| 2 The power/ F -statistic is 1.5 independent of the orbital 1 phase parameter (usually 0.5 0 the time of periapse 0.04 0.06 0.08 0.1 0.12 0.14 0.16 frequency (Hz) passage t p ). C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge A New Solution :The sideband search Current Solutions The proposed search A New Solution Following up candidates Conclusions and future work Dealing with gaps In the (very likely) situation where the data contains large and frequent gaps in time we deal with this by computing the Fourier transform of the window function g ( t ). Example ˜ g ( f ) 5 20 x 10 Example g ( t ) 15 t 10 Re(g(f)) g(t) 5 0 T T + T time 0 0 s −5 −1 −0.5 0 0.5 1 frequency (Hz) −5 x 10 C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge A New Solution :The sideband search Current Solutions The proposed search A New Solution Following up candidates Conclusions and future work Orbital eccentricity We can use the Fourier series expansion of the sin and cos of the eccentric anomoly E ( t ) ( k ∈ −∞ , . . . , − 1 , 1 , . . . ∞ ) eg. � 1 cos E = − e 2 + k J k − 1 ( ke ) cos k M . Eccentric signal example Non-zero eccentricity acts to spread power amonst 8000 existing sidebands. t 6000 Results in change in 2F 4000 relative amplitude of 2000 spikes not location. 0 199.9996 200 200.0004 frequency (Hz) C Messenger A “fast” GW search for CW’s from binary systems
Introduction The data analysis challenge A New Solution :The sideband search Current Solutions The proposed search A New Solution Following up candidates Conclusions and future work Searching with a “comb” First compute F -statistic The comb demodulating for sky position only. SIGNAL 2F(f) Use a finite sized flat comb c ( f ) COMB t of unit amplitude teeth each f0 frequency spaced by 1 / P Hz as a template SIGNAL * COMB → SNR loss < 35% C(f) The comb will have M = 4 π f 0 a f0 frequency teeth. The detection statistic C ( f ) = c ( f ) ∗ 2 F ( f ) (1) C Messenger A “fast” GW search for CW’s from binary systems
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