Browsing by Author "Dhurandhar, Sanjeev"

Now showing 1 - 20 of 46

Adaptive filtering techniques for gravitational wave interferometric data : Removing long-term sinusoidal disturbances and oscillatory transients
(2000-02-12) Chassande-Mottin, E.; Dhurandhar, Sanjeev
We propose an adaptive denoising scheme for poorly modeled non-Gaussian features in the gravitational wave interferometric data. Preliminary tests on real data show encouraging results
Adaptive filtering techniques for gravitational wave interferometric data : Removing long-term sinusoidal disturbances and oscillatory transients
(2000-04-04) Chassande-Mottin, E.; Dhurandhar, Sanjeev
It is known by the experience gained from the gravitational wave detector proto-types that the interferometric output sig- nal will be corrupted by a signiﬁcant amount of non-Gaussian noise, large part of it being essentially composed of long-term sinusoids with slowly varying envelope (such as violin res- onances in the suspensions, or main power harmonics) and short-term ringdown noise (which may emanate from servo control systems, electronics in a non-linear state, etc.). Since non-Gaussian noise components make the detection and esti- mation of the gravitational wave signature more diﬃcult, a de- noising algorithm based on adaptive ﬁltering techniques (LMS methods) is proposed to separate and extract them from the stationary and Gaussian background noise. The strength of the method is that it does not require any precise model on the observed data : the signals are distinguished on the basis of their autocorrelation time. We believe that the robustness and simplicity of this method make it useful for data prepa- ration and for the understanding of the ﬁrst interferometric data. We present the detailed structure of the algorithm and its application to both simulated data and real data from the LIGO 40meter proto-type.
AIGO: a southern hemisphere detector for the worldwide array of ground based interferometric gravitational wave detectors
(2009-10-01) Dhurandhar, Sanjeev; Souradeep, Tarun; Coward, D
This paper describes the proposed AlGO detector for the worldwide array of interferometric gravitational wave detectors. The first part of the paper summarises the benefits that AlGO provides to the worldwide array of detectors. The second part gives a technical description of the detector, which will follow closely the Advanced LIGO design. Possible technical variations in the design are discussed.
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.
Astrophysical motivation for directed searches for a stochastic gravitational wave background
(IUCAA, 2015-02) Mazumder, Nairwita; Mitra, Sanjit; Dhurandhar, Sanjeev
Black holes as detectors of tachyons
(General Relativity and Gravation, 1978-01-17) Narlikar, J. V.; Dhurandhar, Sanjeev
Coherent versus coincidence detection of gravitational wave signals from compact inspiraling binaries
(2010-03-30) Dhurandhar, Sanjeev; Mukhopadhyay, Himan; Tagoshi, H.; et al.
We compare two multi-detector detection strategies, namely, the coincidence and the coherent, for the detection of spinless inspiraling compact binary gravitational wave (GW) signals. The coincident strategy treats the detectors as if they are isolated - com- pares individual detector statistics with their respective thresholds while the coherent strategy combines the detector network data phase coherently to obtain a single detection statistic which is then compared with a single threshold. In the case of geographically separated detectors, we also consider an enhanced coincidence strategy because the usual (naive) coincidence strategy yields poor results for misaligned detectors. For simplicity, we consider detector pairs having the same power spectral density of noise, as that of initial LIGO and also assume the noise to be stationary and Gaussian. We compare the performances of the methods by plotting the receiver operating characteristic (ROC) for the two strategies. A single astrophysical source as well as a distribution of sources is considered. We ﬁnd that the coherent strategy performs better than the two coincident strategies under the assumptions of stationary Gaussian detector noise.
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
Cross-correlation search for a hot spot of gravitational waves
(2011-05-31) Dhurandhar, Sanjeev; Tagoshi, H.; Okada, Yuta; et al.
The cross-correlation search has been previously applied to map the gravitational wave (GW) stochastic background in the sky and also to target GW from rotating neutron stars/pulsars. Here we investigate how the cross-correlation method can be used to target a small region in the sky spanning at most a few pixels, where a pixel in the sky is determined by the diﬀraction limit which depends on the (i) baseline joining a pair of detectors and (ii) detector bandwidth. Here as one of the promising targets, we consider the Virgo cluster - a ”hot spot” spanning few pixels - which could contain, as estimates suggest ~ 10¹¹ neutron stars, of which a small fraction would continuously emit GW in the bandwidth of the detectors. For the detector baselines, we consider advanced detector pairs among LCGT, LIGO, Virgo, ET etc. Our results show that suﬃcient signal to noise can be accumulated with integration times of the order of a year. The results improve for the multibaseline search. This analysis could as well be applied to other likely hot spots in the sky and other possible pairs of detectors.
Cross-correlation search for periodic gravitational waves
(2007-12-10) Dhurandhar, Sanjeev; Mukhopadhyay, Himan; Badri, Krishnan; et al.
In this paper we study the use of cross-correlations between multiple gravitational wave (GW) data streams for detecting long-lived periodic signals. Cross orrelation searches between data from multiple detectors have traditionally been used to search for stochastic GW signals, but recently they have also been used in directed searches for periodic GWs. Here we further adapt the cross-correlation statistic for periodic GW searches by taking into account both the non-stationarity and the long term-phase coherence of the signal. We study the statistical properties and sensitivity of this search, its relation to existing periodic wave searches, and describe the precise way in which the cross- correlation statistic interpolates between semi-coherent and fully-coherent methods. Depending on the maximum duration over we wish to preserve phase coherence, the cross-correlation statistic can be tuned to go from a standard cross-correlation statistic using data from distinct detectors, to the semi-coherent time-frequency methods with increasing coherent time baselines, and all the way to a full coherent search. This leads to a uni ed framework for studying periodic wave searches and can be used to make informed trade-o s between computational cost, sensitivity, and robustness against signal uncertainties.
Data analysis techniques for gravitational wave observations
(2011-07-06) Dhurandhar, Sanjeev
Astrophysical sources of gravitational waves fall broadly into three categories: (i) transient and bursts, (ii) periodic or continuous wave and (iii) stochastic. Each type of source requires a di®erent type of data analysis strategy. In this talk various data analysis strategies will be reviewed. Optimal ¯ltering is used for extracting binary inspirals; Fourier transforms over Doppler shifted time intervals are computed for long duration periodic sources; optimally weighted cross-correlations for stochastic background. Some recent schemes which e±ciently search for inspirals will be described. The performance of some of these techniques on real data obtained will be discussed. Finally, some results on cancellation of systematic noises in laser interferometric space antenna (LISA) will be presented and future directions indicated.
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.
Detecting gravitational waves from inspiraling binaries with a network of geographically separated detectors: coherent versus coincident strategies
(2009-10-01) Mukhopadhyay, Himan; Tagoshi, H.; Dhurandhar, Sanjeev; et al.
We compare two strategies of multi-detector detection of compact binary inspiral signals, namely, the coincidence and the coherent for the realistic case of geographically separated detectors. The naive coincident strategy treats the detectors as if they are isolated - compares individual detector statistics with their respective thresholds while the coherent strategy combines the detector network data coherently to obtain a single detection statistic which is then compared with a single threshold. We also consider an enhanced coincidence strategy which is intermediate in the sense that though the individual statistics are added in quadrature and the sum compared with a single threshold, the estimated parameters are also checked for consistency. For simplicity, we consider detector pairs having the same power spectral density of noise, as that of initial LIGO and also assume the noise to be stationary and Gaussian. Further, since we consider the detectors to be widely separated on Earth, we take the instrumental noises to be uncorrelated; the wide separation implicitly means that since the detector arms must lie parallel to the Earth’s surface, the detectors necessarily have diﬀerent orientations. We compare the performances of the methods by plotting the receiver operating characteristics (ROC) for the strategies. Several results are derived analytically in order to gain insight. Simulations are performed in order to plot the ROC curves. A single astrophysical source as well as a distribution of sources is considered. We assume one year data train and a mass range of 1 − 40M⊙ for the case of astrophysically distributed sources. We ﬁnd that the coherent strategy is superior to the two coincident strategies that we consider. Remarkably, the detection probability of the coherent strategy is 50% better than the naive coincident strategy. One the other hand, diﬀerence in performance between the coherent strategy and enhanced coincident strategy is not very large. Even in this situation, it is not diﬃcult to perform the real data analysis with the coherent strategy. The bottom line is that the coherent strategy is a good detection strategy.
Detecting gravitional waves from inspiraling binaries with a network of detectors: coherent strategies by correlated detectors
(2007-02-03) Tagoshi, H.; Mukhopadhyay, Himan; Dhurandhar, Sanjeev; et al.
We discuss the coherent search strategy to detect gravitational waves from inspiraling compact binaries by a network of correlated laser interferometric detectors. From the maximum likelihood ratio statistic, we obtain a coherent statistic which is slightly diﬀerent from and generally better than what we obtained in our previous work. In the special case when the cross spectrum of two detectors normalized by the power spectrum density is constant, the new statistic agrees with the old one. The quantitative diﬀerence of the detection probability for a given false alarm rate is also evaluated in a simple case.
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.
Effect of sine-Gaussian glitches on searches for binary coalescence
(IUCAA, 2015-02) Canton, T. D.; Bhagwat, S.; Dhurandhar, Sanjeev
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.
A faster implementation of the hierarchical search algorithm for detection of gravitational waves from inspiraling compact binaries
(2011-06-05) Sengupta, Anand; Dhurandhar, Sanjeev; Lazzarini, Albert
The ﬁrst scientiﬁc runs of kilometer scale laser interferometric detectors like LIGO are underway. Data from these detectors will be used to look for signatures of gravitational waves (GW) from astrophysical objects like inspiraling neutron star/blackhole binaries using matched ﬁltering. The computational resources required for online ﬂat-search implementation of the matched ﬁltering are large if searches are carried out for small total mass. Flat search is implemented by constructing a single discrete grid of densely populated template waveforms spanning the dynamical parameters - masses, spins - which are correlated with the interferometer data. The correlations over the kinematical parameters can be maximized apriori without constructing a template bank over them. Mohanty and Dhurandhar (1996) showed that a signiﬁcant reduction in computational resources can be accomplished by using a hierarchy of such template banks where candidate events triggered by a sparsely populated grid is followed up by the regular, dense ﬂat search grid. The estimated speed up in this method was a factor ∼ 25 over the ﬂat search. In this paper we report an improved implementation of the hierarchical search, wherein we extend the domain of hierarchy to an extra dimension - namely the time of arrival of the signal in the bandwidth of the interferometer. This is accomplished by lowering the Nyquist sampling rate of the signal in the trigger stage. We show that this leads to further improvement in the eﬃciency of data analysis and speeds up the online computation by a factor of ∼ 65 − 70 over the ﬂat search. We also take into account and discuss issues related to template placement, trigger thresholds and other peculiar problems that do not arise in earlier implementation schemes of the hierarchical search. We present simulation results for 2PN waveforms embedded in the noise expected for initial LIGO detectors.
Fundamentals of the LISA Stable Flight Formation
(2011-07-06) Dhurandhar, Sanjeev; Nayak, K. R.; Koshti, S.
General relativistic treatment of LISA optical links
(2008-05) Dhurandhar, Sanjeev; Vinet, J-Y.; Nayak, K. R.
LISA is a joint spae mission of the NASA and the ESA for deteting low frequeny gravitational waves in the band 10−5 − 1 Hz. In order to attain the requisite sensitivity for LISA, the laser frequeny noise must be suppressed below the other seondary noises suh as the optial path noise, a eleration noise et. This is ahieved by ombining time-delayed data for whih preise knowledge of time-delays is required. The gravitational eld, mainly that of the Sun and the motion of LISA a e t the time-delays and the opti al links. Further, the e e t of the gravitational eld of the Earth on the orbits of spaeraft is inluded. This leads to additional exing over and above that of the Sun. We have written anumerial ode whih omputes the optial links, that is, the time-delays with great auray∼ 10−2 metres - more than what is required for time delay interferometry (TDI) - for most of the orbit and with su ient auray within ∼ 10 metres for an integrated time window of about six days, when one of the arms tends to be tangent to the orbit. Our analysis of the optial links is fully general relativisti and the numerial ode takes into aount e ets suh as the Sagna, Shapiro delay, et. We show that with the deemed parameters in the design of LISA, there are symmetries inherent in the on guration of LISA and in the physi s, whih may be used e etively to suppress the residual laser noise in the modi ed rst generation TDI. We demonstrate our results for some important TDI variables.