2007 (IPP)
Permanent URI for this collectionhttp://localhost:4000/handle/11007/334
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Item Physical and algebraical models of LISA(2007-11-27) Dhurandhar, SanjeevItem Gravitational wave radiometry: Mapping a stochastic gravitational wave background(2007-08-20) Mitra, Sanjit; Dhurandhar, Sanjeev; Souradeep, Tarun; et al.The problem of the detection and mapping of a stochastic gravitational wave background (SGWB), either cosmological or astrophysical, bears a strong semblance to the analysis of the cosmic microwave background (CMB) anisotropy and polarization, which too is a stochastic eld, statistically described in terms of its correlation properties. An astrophysical gravitational wave background (AGWB) will likely arise from an incoherent superposition of unmodelled and/or unresolved sources and cosmological gravitational wave backgrounds (CGWB) are also predicted in certain scenarios. The basic statistic we use is the cross-correlation between the data from a pair of detectors. In order to `point' the pair of detectors at di erent locations one must suitably delay the signal by the amount it takes for the gravitational waves (GW) to travel to both detectors corresponding to a source direction. Then the raw (observed) sky map of the SGWB is the signal convolved with a beam response function that varies with location in the sky. We rst present a thorough analytic understanding of the structure of the beam response function using an analytic approach employing the stationary phase approximation. The true sky map is obtained by numerically deconvolving the beam function in the integral (convolution) equation. We adopt the maximum likelihood framework to estimate the true sky map using the conjugate gradient method that has been successfully used in the broadly similar, well-studied CMB map making problem. We numerically implement and demonstrate the method on signal generated by simulated (unpolarized) SGWB for the GW radiometer consisting of the LIGO pair of detectors at Hanford and Livingston. We include `realistic' additive Gaussian noise in each data stream based on the LIGO-I noise power spectral density. The extension of the method to multiple baselines and polarized GWB is outlined. In the near future the network of GW detectors, including the Advanced LIGO and Virgo detectors that will be sensitive to sources within a thousand times larger spatial volume, could provide promising data sets for GW radiometry.Item 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.Item 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.