IUCAA Preprints
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Item Effect of sine-Gaussian glitches on searches for binary coalescence(IUCAA, 2015-02) Canton, T. D.; Bhagwat, S.; Dhurandhar, SanjeevItem Time-Delay Interferometry(IUCAA, 2015-02) Tinto, Massimo; Dhurandhar, SanjeevItem Astrophysical motivation for directed searches for a stochastic gravitational wave background(IUCAA, 2015-02) Mazumder, Nairwita; Mitra, Sanjit; Dhurandhar, SanjeevItem Extended hierarchical search (EHS) algorithm for detection of gravitational waves from inspiraling compact binaries(2001-04-01) Sengupta, Anand; Dhurandhar, Sanjeev; Lazzarini, Albert; et al.Pattern matching techniques like matched filtering will be used for online extraction of gravitational wave signals buried inside detector noise. This involves cross correlating the detector output with hundreds of thousands of templates spanning a multi-dimensional parameter space, which is very expensive computationally. A faster implementation algorithm was devised by Mohanty and Dhurandhar [1996] using a hierarchy of templates over the mass parameters, which speeded up the procedure by about 25 to 30 times. We show that a further reduction in computational cost is possible if we extend the hierarchy paradigm to an extra parameter, namely, the time of arrival of the signal. In the first stage, the chirp waveform is cut-off at a relatively low frequency allowing the data to be coarsely sampled leading to cost saving in performing the FFTs. This is possible because most of the signal power is at low frequencies, and therefore the advantage due to hierarchy over masses is not compromised. Results are obtained for spin-less templates up to the second post-Newtonian (2PN) order for a single detector with LIGO I noise power spectral density. We estimate that the gain in computational cost over a flat search is about 100.Item Computational cost for detecting inspiraling binaries using a network of laser interferometric detectors(2001-08-15) Pai, A.; Bose, Sukanta; Dhurandhar, SanjeevWe 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 aboveItem Algebraic approach to time-delay data analysis for LISA(2001-12-20) Dhurandhar, Sanjeev; Nayak, K. R.; Vinet, J-Y.Cancellation of laser frequency noise in interferometers is crucial for attaining the requisite sensitivity of the triangular 3-spacecraft LISA configuration. 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. Since it is impossible to maintain equal distances between spacecrafts, laser noise cancellation must be achieved by appropriately combining the six beams with appropriate time-delays. It has been shown in several recent papers that such combinations are possible. In this paper, we present a rigorous and systematic formalism based on algebraic geometrical methods involving computational commutative algebra, which generates in principle all the data combinations cancelling the laser frequency noise. The relevant data combinations form the first module of syzygies, as it is called in the literature of algebraic geometry. The module is over a polynomial ring in three variables, the three variables corresponding to the three time-delays around the LISA triangle. Specifically, we list several sets of generators for the module whose linear combinations with polynomial coefficients generate the entire module. We find that this formalism can also be extended in a straight forward way to cancel Doppler shifts due to optical bench motions. The two modules are infact isomorphic. We use our formalism to obtain the transfer functions for the six beams and for the generators. We specifically investigate monochromatic gravitational wave sources in the LISA band and carry out the maximisiation over linear combinations of the generators of the signal-to-noise ratios with the frequency and source direction angles as parameters.Item Searching for gravitational waves from rotating neutron stars(2000-01-15) Dhurandhar, SanjeevRotating neutron stars are one of the important sources of gravitational waves (GW) for the ground based as well as space based detectors. Since the waves are emitted continuously, the source is termed as a continuous gravitational wave (CGW) source. The expected weakness of the signal requires long integration times ( year). The data analysis problem involves tracking the phase coherently over such large integration times, which makes it the most computationally intensive problem among all GW sources envisaged. In this article, the general problem of data analysis is discussed, and more so, in the context of searching for CGW sources orbiting another companion object. The problem is important because there are several pulsars, which could be deemed to be CGW sources orbiting another companion star. Differential geometric techniques for data analysis are described and used to obtain computational costs. These results are applied to known systems to assess whether such systems are detectable with current (or near future) computing resources.Item Searching for continuous gravitational wave sources in binary systems(2000-12-14) Dhurandhar, Sanjeev; Vecchio, AlbertoItem Detection of gravitational waves from inspiraling compact binaries using a network of interferometric detectors(2000-06-28) Bose, Sukanta; Pai, A.; Dhurandhar, SanjeevWe 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.Item 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, SukantaA 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.