Browsing by Author "Pai, A."

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Computational cost for detecting inspiraling binaries using a network of laser interferometric detectors
(2001-08-15) Pai, A.; Bose, Sukanta; Dhurandhar, Sanjeev
We extend a coherent network data-analysis strategy developed earlier for detecting Newtonian waveforms to the case of post-Newtonian (PN) waveforms. Since the PN waveform depends on the individual masses of the inspiraling binary, the parameter-space dimension increases by 1 from that of the Newtonian case. We obtain the number of templates and estimate the computational costs for PN waveforms: For a lower mass limit of 1M⊙, for LIGO-I noise, and with 3% maximum mismatch, the online computational speed requirement for single detector is a few Gﬂops; for a two-detector network it is hundreds of Gﬂops and for a three-detector network it is tens of Tﬂops. Apart from idealistic networks, we obtain results for realistic networks comprising of LIGO and VIRGO. Finally, we compare costs incurred in a coincidence detection strategy with those incurred in the coherent strategy detailed above
Data-analysis strategy for detecting gravitational-wave signals from inspiraling compact binaries with a network of laser-interferometric detectors
(2000-04-24) Pai, A.; Dhurandhar, Sanjeev; Bose, Sukanta
A data-analysis strategy based on the maximum-likelihood method (MLM) is presented for the detection of gravitational waves from inspiraling compact binaries with a network of laser- nterferometric detectors having arbitrary orientations and arbitrary locations around the globe. For simplicity, we restrict ourselves to the Newtonian inspiral waveform. However, the formalism we develop here is also applicable to a waveform with post-Newtonian (PN) corrections. The Newtonian waveform depends on eight parameters: the distance r to the binary, the phase δc of the waveform at the time of ﬁnal coalescence, the polarization-ellipse angle ψ, the angle of inclination ǫ of the binary orbit to the line of sight, the source-direction angles {θ, φ}, the time of ﬁnal coalescence tc at the ﬁducial detector, and the chirp time ξ. All these parameters are relevant for a chirp search with multiple detectors, unlike the case of a single detector. The primary construct on which the MLM s based is the network likelihood ratio (LR). We obtain this ratio here. For the Newtonian inspiral waveform, the LR is a function of the eight signal-parameters. In the MLM-based detection strategy, the LR must be maximized over all of these parameters. Here, we show that it is possible to maxi- mize it analytically with respect to four of the eight parameters, namely, {r, δc, ψ, ǫ}. Maximization over the time of arrival is handled most eﬃciently by using the Fast-Fourier-Transform algorithm, as in the case of a single detector. This not only allows us to scan the parameter space continu- ously over these ﬁve parameters but also cuts down substantially on the computational costs. The analytical maximization over the four parameters yields the optimal statistic on which the decision must be based. The value of the statistic also depends on the nature of the noises in the detectors. Here, we model these noises to be mainly Gaussian, stationary, and uncorrelated for every pair of detectors. Instances of non-Gaussianity, as are present in detector outputs, can be accommodated n our formalism by implementing vetoing techniques similar to those applied for single detectors. Our formalism not only allows us to express the likelihood ratio for the network in a very simple and compact form, but also is at the basis of giving an elegant geometric interpretation to the de- tection problem. Maximization of the LR over the remaining three parameters is handled as follows. Owing to the arbitrary locations of the detectors in a network, the time of arrival of a signal at any detector will, in general, be diﬀerent from those at the others and, consequently, will result in signal time-delays. For a given network, these time delays are determined by the source-direction angles {θ, φ}. Therefore, to maximize the LR over the parameters {θ, φ} one needs to scan over the possible time-delays allowed by a network. We opt for obtaining a bank of templates for the chirp time and the time-delays. This means that we construct a bank of templates over ξ, θ, and φ. We ﬁrst discuss “idealized” networks with all the detectors having a common noise curve for simplicity. Such an exercise nevertheless yields useful estimates about computational costs, and also tests the formalism developed here. We then consider realistic cases of networks comprising of the LIGO and VIRGO detectors: These include two-detector networks, which pair up the two LIGOs or VIRGO with one of the LIGOs, and the three-detector network that includes VIRGO and both the LIGOs. For these networks we present the computational speed requirements, network sensitivities, and source-direction resolutions.
Detection of gravitational waves from inspiraling compact binaries using a network of interferometric detectors
(2000-06-28) Bose, Sukanta; Pai, A.; Dhurandhar, Sanjeev
We formulate the data analysis problem for the detection of the New- tonian waveform from an inspiraling compact-binary by a network of arbi- trarily oriented and arbitrarily distributed laser interferometric gravitational wave detectors. We obtain for the ﬁrst time the relation between the opti- mal statistic and the magnitude of the network correlation vector, which is constructed from the matched network-ﬁlter. This generalizes the calculation reported in an earlier work (gr-qc/9906064), where the detectors are taken to be coincident.
Improving the sensitivity of LISA
(2002-10-04) Nayak, K. R.; Pai, A.; Dhurandhar, Sanjeev
It has been shown in several recent papers that the six Doppler data streams obtained from a triangular LISA conﬁguration can be combined by appropriately delaying the data streams for cancelling the laser frequency noise. Raw laser noise is several orders of magnitude above the other noises and thus it is essential to bring it down to the level of other noises such as shot, acceleration, etc. A rigorous and systematic formalism using the powerful techniques of computational commutative algebra was developed which generates in principle all the data combinations cancelling the laser frequency noise. The relevant data combinations form a ﬁrst module of syzygies. In this paper we use this formalism to advantage for optimising the sensitivity of LISA by analysing the noise and signal covariance matrices. The signal covariance matrix is calculated for binaries whose frequency changes at most adiabatically and the signal is averaged over polarisations and directions. We then present the extremal SNR curves for all the data combinations in the module. They correspond to the eigenvectors of the noise and signal covariance matrices. A LISA ‘network’ SNR is also computed by combining the outputs of the eigenvectors. We show that substantial gains in sensitivity can be obtained by employing these strategies. The maximum SNR curve can yield an improvement upto 70 % over the Michelson, mainly at high frequencies, while the improvement using the network SNR ranges from 40 % to over 100 %. Finally, we describe a simple toy model, in which LISA rotates in a plane. In this analysis, we estimate the improvement in the LISA sensitivity, if one switches from one data combination to another as it rotates. Here the improvement in sensitivity, if one switches optimally over three cyclic data combinations of the eigenvector is about 55 % on an average over the LISA band-width. The corresponding SNR improvement increases to 60 %, if one maximises over the module
Optimising the directional sensitivity of LISA
(2011-07-05) Nayak, K. R.; Dhurandhar, Sanjeev; Pai, A.
It was shown in a previous work that the data combinations canceling laser frequency noise constitute a module - the module of syzygies. The cancellation of laser frequency noise is crucial for obtaining the requisite sensitivity for LISA. In this work we show how the sensitivity of LISA can be optimised for a monochromatic source - a compact binary - whose direction is known, by using appropriate data combinations in the module. A stationary source in the barycentric frame appears to move in the LISA frame and our strategy consists of coherently tracking the source by appropriately switching the data combinations so that they remain optimal at all times. Assuming that the polarisation of the source is not known, we average the signal over the polarisations. We ﬁnd that the best statistic is the ‘network’ statistic, in which case LISA can be construed of as two independent detectors. We compare our results with the Michelson combination, which has been used for obtaining the standard sensitivity curve for LISA, and with the observable obtained by optimally switching the three Michelson combinations. We ﬁnd that for sources lying in the ecliptic plane the improvement in SNR increases from 34% at low frequencies to nearly 90% at around 20 mHz. Finally we present the signal-to-noise ratios for some known binaries in our galaxy. We also show that, if at low frequencies SNRs of both polarisations can be measured, the in
Radiation pressure induced instabilities in laser interferometric detectors of gravitational waves
(2015-03-13) Pai, A.; Dhurandhar, S.V.; Hello, P.; Vinet, J.Y.
The large scale interferometric gravitational wave detectors consist of Fabry-Perot cavities operating at very high powers ranging from tens of kW to MW. The high powers may result in several nonlinear effects which would affect the performance of the detector. In this paper, we investigate the effects of radiation pressure, which tend to displace the mirrors from their resonant position resulting in the detuning of the cavity. We observe a remarkable effect, namely, that the freely hanging mirrors gain energy continuously and swing with increasing amplitude. It is found that the 'time delay', that is, the time taken for the field to adjust to its instantaneous equilibrium value, when the mirrors are in motion, is responsible for this effect. This effect is likely to be important in the optimal functioning of the full-scale interferometers such as the VIRGO and LIGO.
Time delay interferometry and LISA optimal sensitivity
(2011-07-05) Pai, A.; Nayak, K. R.; Dhurandhar, Sanjeev; et al.
The sensitivity of LISA depends on the suppression of several noise sources; dominant one is laser frequency noise. It has been shown that the six Doppler data streams obtained from three space-crafts can be appropriately time delayed and optimally combined to cancel this laser frequency noise. We show that the optimal data combinations when operated in a network mode improves the sensitivity over Michelson ranging from 40% to 100%. In this article, we summarize these results. We further show that the residual laser noise in the optimal data combination due to typical arm-length inaccuracy of 200 m is much below the level of optical path and the proof mass noises.