We investigate the recovery chances of highly spinning waveforms immersed in
LIGO S5-like noise by performing a matched filtering with 10^6 randomly chosen
spinning waveforms generated with the LAL package. While the masses of the
compact binary are reasonably well recovered (slightly overestimated), the same
does not hold true for the spins. We show the best fit matches both in the
time-domain and the frequency-domain. These encompass some of the spinning
characteristics of the signal, but far less than what would be required to
identify the astrophysical parameters of the system. An improvement of the
matching method is necessary, though may be difficult due to the noisy signal.Comment: 5 pages, 1 figure + 4 figure panels; Proceedings of the Eight Edoardo
  Amaldi Conference on Gravitational Waves (Amaldi8), New York, 2009; to be
  published in J. Phys.: Conf. Series (JPCS

László Veréb

László Á Gergely

Péter Raffai

Raymond V

Szabolcs Mészáros

van der Sluys M

Zoltán Keresztes

Journal of Physics : Conference Series

English

arXiv

Crossref

Journal of Physics Conference Series

Recovering a spinning inspiralling compact binary waveform immersed in LIGO-like noise with spinning templates

We investigate the recovery chances of highly spinning waveforms 
immersed in LIGO S5-like noise by performing a matched filtering 
with 106 randomly chosen spinning waveforms generated with the 
LAL package. While the masses of the compact binary are 
reasonably well recovered (slightly overestimated), the same 
does not hold true for the spins. We show the best fit matches 
both in the time-domain and the frequency-domain. These 
encompass some of the spinning characteristics of the signal, 
but far less than what would be required to identify the 
astrophysical parameters of the system. An improvement of the 
matching method is necessary, though may be difficult due to the 
noisy signal. © 2010 IOP Publishing Ltd

L, Veréb

Z, Keresztes

P, Raffai

Sz, Mészáros

LÁ, Gergely

ELTE Digital Institutional Repository (EDIT)

arXiv:0911.0473v3  [gr-qc]  12 May 2010Recovering a spinning inspiralling compact binarywaveform immersed in LIGO-like noise with spinningtemplatesLászló Veréb1,2, Zoltán Keresztes1,2⋆, Péter Raffai3†, SzabolcsMészáros4, László Á. Gergely1,2,5‡1 Department of Theoretical Physics, University of Szeged, Tisza Lajos krt 84-86, Szeged6720, Hungary2 Department of Experimental Physics, University of Szeged, Dóm tér 9, Szeged 6720, Hungary3 Institute of Physics, Loránd Eötvös University, Pázmany Péter s 1/A, Budapest 1117,Hungary4 Department of Optics and Quantum Electronics, University of Szeged, Dóm tér 9, Szeged6720, Hungary5 Institute for Advanced Study, Collegium Budapest, Szentháromság u 2, Budapest 1014,HungaryE-mail: ∗zkeresztes@titan.physx.u-szeged.hu †praffai@bolyai.elte.hu‡gergely@physx.u-szeged.huAbstract. We investigate the recovery chances of highly spinning waveforms immersed inLIGO S5-like noise by performing a matched filtering with 106 randomly chosen spinningwaveforms generated with the LAL package. While the masses of the compact binary arereasonably well recovered (slightly overestimated), the same does not hold true for the spins. Weshow the best fit matches both in the time-domain and the frequency-domain. These encompasssome of the spinning characteristics of the signal, but far less than what would be required toidentify the astrophysical parameters of the system. An improvement of the matching methodis necessary, though may be difficult due to the noisy signal.We report on an attempt to recover a gravitational wave signal hinjection immersed in LIGOS5-like noise by a matched filtering with 106 randomly chosen templates generated with spinningwaveforms [1]. We applied the following process to generate a LIGO S5-like noise sample of Nelements: (i) cut out a stretch of 2N elements from an arbitrary sample of real LIGO S5 noise,(ii) cut the stretch into half, resulting in two stretches of N elements, (iii) Fourier-transfom bothstretches with an FFT method, resulting in two samples of N complex elements, (iv) combine themagnitude values of the first spectrum with the phase values of the second spectrum, resultingin a complex spectrum of N elements, (v) apply an inverse FFT on the combined spectrum, anduse the real part of the resulting array as our LIGO S5-like noise sample. This method has theadvantage of preserving the basic spectral and statistical properties of the original LIGO data,while discarding any real gravitational wave signatures that might be present within the originaldata stretch.The matched filtering follows the method described in Ref. [2]. Namely, we calculate the-4e-20-3e-20-2e-20-1e-20 0 1e-20 2e-20 3e-20 4e-20 0  0.5  1  1.5  2  2.5  3  3.5htspinning-injection-4e-20-3e-20-2e-20-1e-20 0 1e-20 2e-20 3e-20 4e-20 0  0.5  1  1.5  2  2.5  3  3.5htnon-spinning versionFigure 1. The injected signal (red) and its spinn-less counterpart (blue).overlap between the noisy injection hn,i and the spinning templates htemplate asO [hn,i, htemplate] =〈hn,i|htemplate〉√〈hn,i|hn,i〉 〈htemplate|htemplate〉, (1)where〈h1|h2〉 = 4Re∫ fmaxfminh̃1 (f) h̃∗2(f)Sn (f)df , (2)with h̃i (f) the Fourier transform of hi (t) and Sn (f) the power spectral density of the noise. Wechoose fmin = 50Hz and fmax = 600Hz, which lies in the best sensitivity of the LIGO detectors,also the post-Newtonian prediction for the waveform can be considered reasonably accurate.The most lengthy templates in this domain were found to last for approximately 3 sec.10210−2810−2710−2610−2510−2410−2310−2210−2110−20f [Hz]SSD [1/sqrt(Hz)]  noisenoise+signalsignalFigure 2. The strain spectral density of the signal (red), noise (grey) and injected signal +noise (magenta).On theoretical grounds, an infinitely long data series would be required for exactdetermination of the power spectrum. In order to achieve a stability of the power spectrumof the order of 1%, we would like to have at least 100 periods of all frequencies to be included inthe power spectrum, therefore a minimal length of the templates of 100× (1/50Hz) = 2 sec wasimposed. As we know where the injection commences in the noise time sequence, we simplifyTable 1. The parameters of the injection and 5 best fit templates.name m1(M⊙) m2(M⊙) χ1 χ2 cos β1 ϕ1 cos β2 ϕ2injection 3.553 3.358 0.983 0.902 0.984 1.109 0.978 0.957560884.wave 4.805 3.336 0.230 0.293 −0.599 1.327 −0.621 0.006467403.wave 4.092 3.405 0.868 0.891 −0.520 1.275 0.363 3.925313940.wave 3.569 3.540 0.753 0.413 0.306 1.458 −0.092 2.67993938.wave 5.012 3.152 0.280 0.424 0.947 2.593 0.888 2.34080521.wave 4.278 4.360 0.736 0.475 −0.620 5.959 0.945 3.290our analysis by comparing with templates beginning at the same instant t0. Further, we alsoassume identical antenna functions of√2/2 both for the injection and templates. Moreover, allparameters of the injection and templates other then the masses mi and spins (given by theirdimensionless magnitude χi, polar and azimuthal angles βi, ϕi, taken in the inertial system withthe line of sight on the z-axis) were kept fixed. These parameters were the distance of the binaryd = 1Mpc, and the polar angle of the orbital angular momentum Θ = 1.4299. The initial phaseΦS = 0.We picked up the injection signal as one of the longests available (see Fig 1). The presence ofa high spin induces a strong amplitude modulation, but also a less visible frequency modulation.For comparison, we have also represented on Fig 1 the corresponding non-spinning signal, withthe same masses, but the spins switched off.injectedσ<0.012160.01216<σ<0.060810.06081<σ<0.12163 3 7 11 15 19 23 27 3  7  11  15  19  23  27m2m1 0 0.2 0.4 0.6 0.8 1 0  0.2  0.4  0.6  0.8  1χ2χ1-1-0.5 0 0.5 1 0  1  2  3  4  5  6cosβ1ϕ1-1-0.5 0 0.5 1 0  1  2  3  4  5  6cosβ2ϕ2Figure 3. The injection and the best fit matches from 106 templates. The mass is roughlyrecovered, though sligtly overestimated, however the information contained in the spins is not.The spinning signal is injected in the middle of a finite stretch of LIGO-like data with doublethe length of the signal. The noise has the basic statistical characteristics (e.g. amplitudedistribution, spectral compatibility) of the LIGO 4 km detectors during the 5th science run.The segment to be analyzed is filtered with a zero-phase 50−600 Hz bandpass filter, and a zero-phase notch filter mitigating the effect of narrow insensitivity peaks of detector spectrum. Afterremoving one-fourth of the data segment from both ends due to filter transients, this leaves halfthe length of the initial noise sequence including the signal for further processing. The strainspectral density, defined as the square root of the periodogram, computed under MatLab [3], isrepresented on Fig 2 for the signal, noise and noisy signal.-4e-20-3e-20-2e-20-1e-20 0 1e-20 2e-20 3e-20 4e-20 0  0.5  1  1.5  2  2.5  3  3.5htspinning-injection-4e-20-3e-20-2e-20-1e-20 0 1e-20 2e-20 3e-20 4e-20 0  0.5  1  1.5  2  2.5  3  3.5ht560884.template σ=0.00283-4e-20-3e-20-2e-20-1e-20 0 1e-20 2e-20 3e-20 4e-20 0  0.5  1  1.5  2  2.5  3  3.5ht467403.template σ=0.00411-4e-20-3e-20-2e-20-1e-20 0 1e-20 2e-20 3e-20 4e-20 0  0.5  1  1.5  2  2.5  3  3.5ht313940.template σ=0.00916-4e-20-3e-20-2e-20-1e-20 0 1e-20 2e-20 3e-20 4e-20 0  0.5  1  1.5  2  2.5  3  3.5ht93938.template σ=0.01051-4e-20-3e-20-2e-20-1e-20 0 1e-20 2e-20 3e-20 4e-20 0  0.5  1  1.5  2  2.5  3  3.5ht80521.template σ=0.01216Figure 4. The injected signal and the five best matches. Their serial numbers from amongthe 106 randomly generated templates is also indicated.The overlap between the noisy injection and the injected signal itself was found to beO [hn,i, hinjection] = 0.83426. Therefore we define an auxiliary quantityσ =∣∣∣∣1− O [hn,i, htemplate]O [hn,i, hinjection]∣∣∣∣(3)for characterizing the closeness of the overlap of a template with the noisy injection toO [hn,i, hinjection]. The parameters of a number of > 20 templates with the lowest values of σare represented on Fig 3. While it is comforting to realize that (although slightly overestimated)the masses are reasonably well recovered, the spins are not. There is a considerable scatter inboth their magnitudes and orientations.10210−2810−2710−2610−2510−2410−2310−2210−21f [Hz]SSD [1/sqrt(Hz)]  non−spinningspinning10210−2810−2710−2610−2510−2410−2310−2210−21f [Hz]SSD [1/sqrt(Hz)]10210−2810−2710−2610−2510−2410−2310−2210−21f [Hz]SSD [1/sqrt(Hz)]10210−2810−2710−2610−2510−2410−2310−2210−21f [Hz]SSD [1/sqrt(Hz)]10210−2810−2710−2610−2510−2410−2310−2210−21f [Hz]SSD [1/sqrt(Hz)]10210−2810−2710−2610−2510−2410−2310−2210−21f [Hz]SSD [1/sqrt(Hz)]Figure 5. The strain spectral density of the injected signal (red) and its spin-less counterpart(blue) and the five best matches (green).We picked up the 5 best fits, showed their parameters in Table 1 and represented the respectivewaveforms on Fig 4; also their strain spectral density on Fig 5. For comparison, the injectedsignal is also shown.We conclude that even with all the simplifying assumptions adopted, (a) either the numberof 106 templates employed was still insufficient or (b) the 6 additional parameters introduced bythe spins cause severe degeneracies, which cannot be resolved by this method. In this contextwe note that the use of a Markov-chain Monte-Carlo technique [4], [5] may turn useful in therecovery of spinning signals. We also plan to investigate how the use of Advanced LIGO-likedata would change these conclusions.Acknowledgements: We acknowledge interactions with Gyula Szabó and István Szapudi in theearly stages of this work and discussions with Vivien Raymond on the suitable frequency range.This work was supported by the Polányi and Sun Programs of the Hungarian National Officefor Research and Technology (NKTH). ZK and LÁG were further supported by the HungarianScientific Research Fund (OTKA) grant no. 69036. LÁG is grateful to the organizers of theAmaldi8 meeting for support.References[1] https://www.lsc-group.phys.uwm.edu/daswg/projects/lal/nightly/docs/html/LALSTPNWaveformTest 8c-source.html[2] Vaishnav B, Hinder I, Herrmann F, Shoemaker D 2007 Phys. Rev. D 76 084020[3] http://www.mathworks.com/access/helpdesk/help/toolbox/signal/index.html?/access/helpdesk/help/toolbox/signal/periodogram.html[4] van der Sluys M, Raymond V, Mandel I, Roever C, Christensen N, Kalogera V, Meyer R, Vecchio A 2008Class.Quant.Grav. 25 184011[5] Raymond V, van der Sluys MV, Mandel I, Kalogera V, Roever C, Christensen N, 2009 Class.Quant.Grav. 26114007

Recovering a spinning inspiralling compact binary waveform immersed in
  LIGO-like noise with spinning templates

Recovering a spinning inspiralling compact binary waveform immersed in LIGO-like noise with spinning templates

Abstract

Similar works

Full text

Available Versions

Crossref

ELTE Digital Institutional Repository (EDIT)