Browsing by Author "Sengupta, Anand"

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CMB power spectrum estimation using non-circular beam
(2011-07-06) Mitra, Sanjit; Sengupta, Anand; Souradeep, Tarun
The measurements of the angular power spectrum of the Cosmic Microwave Background (CMB) anisotropy has proved crucial to the emergence of cosmology as a precision science in recent years. In this remarkable data rich period, the limitations to precision now arise from the the inability to account for ﬁner systematic eﬀects in data analysis. The non-circularity of the experimental beam has become progressively important as CMB experiments strive to attain higher angular resolution and sensitivity. We present an analytic framework for studying the leading order eﬀects of a non- circular beam on the CMB power spectrum estimation. We consider a non-circular beam of ﬁxed shape but variable orientation. We compute the bias in the pseudo-Cl power spectrum estimator and then construct an unbiased estimator using the bias matrix. The covariance matrix of the unbiased estimator is computed for smooth, non-circular beams. Quantitative results are shown for CMB maps made by a hypothetical experiment with a non-circular beam comparable to our ﬁts to the WMAP beam maps described in the appendix and uses a toy scan strategy. We ﬁnd that signiﬁcant eﬀects on CMB power spectrum can arise due to non-circular beam on multipoles comparable to, and beyond, the inverse average beam-width where the pseudo-Cl approach may be the method of choice due to computational limitations of analyzing the large datasets from current and near future CMB experiments.
CMB power spectrum estimation with non-circular beam and incomplete sky coverage
(2007-02-05) Mitra, Sanjit; Sengupta, Anand; Souradeep, Tarun; et al.
Over the last decade, measurements of the CMB anisotropy has spearheaded the remarkable transition of cosmology into a precision science. However, addressing the systematic eﬀects in the increasingly sensitive, high resolution, ‘full’ sky measurements from diﬀerent CMB experiments pose a stiﬀ challenge. The analysis techniques must not only be computationally fast to contend with the huge size of the data, but, the higher sensitivity also limits the simplifying assumptions which can then be invoked to achieve the desired speed without compromising the ﬁnal precision goals. While maximum likelihood is desirable, the enormous computational cost makes the suboptimal method of power spectrum estimation using Pseudo-Cl unavoidable for high resolution data. The debiasing of the Pseudo-Cl needs account for non-circular beams, together with non-uniform sky coverage. We provide an analytic framework for correcting the power spectrum for the eﬀect of beam noncircularity and non-uniform sky coverage (including incomplete/masked sky maps). The approach is perturbative in the distortion of the beam from non-circularity allowing for rapid computations when the beam is mildly non-circular. When non-circular beam eﬀect is important, we advocate that it is computationally advantageous to employ ‘soft’ azimuthally apodized masks whose spherical harmonic transform die down fast with m.
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.
Non-circular beam correction to the CMB power spectrum
(2006-08-24) Souradeep, Tarun; Mitra, Sanjit; Sengupta, Anand; et al.
In the era of high precision CMB measurements, systematic eﬀects are beginning to limit the ability to extract subtler cosmological information. The non-circularity of the experimental beam has become progressively important as CMB experiments strive to attain higher angular resolution and sensitivity. The eﬀect of non-circular beam on the power spectrum is important at multipoles larger than the beam-width. For recent experiments with high angular resolution, optimal methods of power spectrum estimation are computationally prohibitive and sub-optimal approaches, such as the Pseudo-Cl method, are used. We provide an analytic framework for correcting the power spectrum for the eﬀect of beam non-circularity and non-uniform sky coverage (including incomplete/masked sky maps). The approach is perturbative in the distortion of the beam from non-circularity allowing for rapid computations when the beam is mildly non-circular. When non-circular beam eﬀect is important, we advocate that it is computationally advantageous to employ ‘soft’ azimuthally apodized masks whose spherical harmonic transform die down fast with m.
Relativistic anisotropic charged fluid spheres with varying cosmological constant
(2011-07-05) Ray, Saibal; Bhadra, Sumana; Sengupta, Anand
Static spherically symmetric anisotropic source has been studied for the Einstein- Maxwell ﬁeld equations assuming the erstwhile cosmological constant Λ to be a space-variable scalar, viz., Λ = Λ(r). Two cases are examined out of which one reduces to isotropic sphere. The solutions thus obtained are shown to be electromagnetic in origin as a particular case. It is also shown that the generally used pure charge condition, viz., ρ+pr = 0 is not always required for constructing electromagnetic mass models.