Less accurate but more efficient family of search templates for detection of gravitational waves from inspiraling compact binaries

Physical Review D

Volumn 64, Issue 4, 2001, Pages

  Chronopoulos, Andreas E ^a   Apostolatos, Theocharis A ^a  

^a UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

ACCELERATION; ACCURACY; ARTICLE; ASTRONOMY; CALCULATION; CORRELATION FUNCTION; GEOMETRY; GRAVITY; INTERFEROMETRY; PHYSICS; SIGNAL DETECTION; SIGNAL NOISE RATIO;

EID: 0035881734     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.64.042003     Document Type: Article

References (25)

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10. Due to irregular shape of the space of interest, the cells of the lattice of templates at the border of the space of interest lie partly outside of it. Thus, by dividing the volume of the space of interest by the volume of each cell we introduce an error in the estimated number of templates; see Eq. (2.9). Although this error may seem insignificant for cells with very small size, the space of interest has such a peculiar shape that for a large fraction of it its width is of the order of the cell's size. Therefore, Χ is a small but not negligible correction (of the order of 10%). Behind the non-negligible character of this spill-over effect lies the effective dimensionality of the parameter space: although a very large number of cells are required to cover the space of interest along one axis, a much smaller number is required for the other axis (see Ref. [17]).
11. The deformation of the lattice due to variations of the metric along the parameter space is equivalent to an overlap between neighboring hypercubes. However, if these variations are very small within a cell, as it happens with the case we have examined, the overlap is negligible.
12. The spill-over effect (see Ref. [10]) leads to higher number than the number of templates one computes through the integral of Eq. (2.9), while the concavity of the enclosing surfaces of Fig. 3 leads to a slight overestimation of the number of templates when prisms are used to approximately measure the total volume of Fig. 3. Although it is difficult to estimate accurately the significance of the two effects, we could omit them on the grounds that both are quite small and have opposite effects. In addition, whatever the outcome of these two effects is, the percentage drop of the required number of templates, when the assumed family of templates is used, is hardly affected.
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16. tψ(f) (see Ref. [14]), where M is the chirp mass of the binary, ψ(f) is the phase of the wave, D is the distance to the source, and Q is a geometric factor related to the orientation of the binary with respect to the arms of the detector (the strength of the two polarized waves depends on the direction of propagation, and the interferometric detector picks them up with relative efficiencies that depend on the relative direction of the polarization axes and its arms).
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18. n-Newtonian signals (with n ≥ 1) is unacceptably low, FF≈0.6.
19. The numerical discrepancy between our CPU formula [see Eq. (3.13)] and that of Owen and Sathyaprakash [Eq. (2.18) of Ref. [13]] is partly due to different notation used and partly due to different enumeration of the floating operations (see Ref. [17]). The numerical results, that we compare, are both computed through the same formula, Eq. (3.14), though.
20. See B. Schutz, in The Detection of Gravitational Waves, edited by D. G. Blair (Cambridge University Press, Cambridge, England, 1991), pp. 406-452.
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24. Although the sampling rate will be quite high (a few kHz) for technical reasons, there is no need to keep these high frequencies when analyzing the data, since cross correlation is highly suppressed at high frequencies due to photon shot noise in the detctor.
25. See B. Schutz, in The Detection of Gravitational Waves, edited by D. G. Blair (Cambridge University Press, Cambridge, England, 1991), pp. 424-425.