Browsing by Author "Mitra, Sanjit"

Now showing 1 - 9 of 9

Astrophysical motivation for directed searches for a stochastic gravitational wave background
(IUCAA, 2015-02) Mazumder, Nairwita; Mitra, Sanjit; Dhurandhar, Sanjeev
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.
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.
Gravitational Waves
(2013-07-23) Mitra, Sanjit
Improving the efficiency of the detection of gravitational wave signals from inspiraling compact binaries: Chebyshev interpolation
(2005-07-01) Mitra, Sanjit; Dhurandhar, Sanjeev; Finn, L. S.
Inspiraling compact binaries are promising sources of gravitational waves for ground and spacebased laser interferometric detectors. The time-dependent signature of these sources in the detectors is a well-characterized function of a relatively small number of parameters; thus, the favored analysis technique makes use of matched ﬁltering and maximum likelihood methods. As the parameters that characterize the source model are varied so do the templates against which the detector data are compared in the matched ﬁlter. For small variations in the parameters, the output of the matched ﬁlter for the diﬀerent templates are closely correlated. Current analysis methodology samples the matched ﬁlter output at parameter values chosen so that the correlation between successive samples is 97%. Correspondingly, with the additional information available with each successive template evaluation is, in a real sense, only 3% of that already provided by the nearby templates. The reason for such a dense coverage of parameter space is to minimize the chance that a real signal, near the detection threshold, will be missed by the parameter space sampling. Here we describe a straightforward and practical way of using interpolation to take advantage of the correlation between the matched ﬁlter output associated with nearby points in the parameter space to signiﬁcantly reduce the number of matched ﬁlter evaluations without sacriﬁcing the eﬃciency with which real signals are recognized. Because the computational cost of the analysis is driven almost exclusively the matched ﬁlter evaluations, a reduction in the number of templates evaluations translates directly into an increase in computational eﬃciency. Because the computational cost of the analysis is large, the increased eﬃciency translates also into an increase in the size of the parameter space that can be analyzed and, thus, the science that can be accomplished with the data. As a demonstration we compare the present “dense sampling” analysis methodology with our proposed “interpolation” methodology, restricted to one dimension of the multi-dimensional analysis problem. We ﬁnd that the interpolated search reduces by 25% the number of ﬁlter evaluations required by the dense search with 97% correlation to achieve the same eﬃciency of detection for an expected false alarm probability. Generalized to the two dimensional space used in the computationally-limited current analyses this suggests a factor of two increase in computational eﬃciency; generalized to the full seven dimensional parameter space that characterizes the signal associated with an eccentric binary system of spinning neutron stars or black holes it suggests an order of magnitude increase in computational eﬃciency.
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.
Revealing Non-circular beam effect in WMAP-7 CMB maps with BipoSH measures of Statistical Isotropy
(IUCAA, 2015-02) Joshi, Nidhi; Das, Santanu; Mitra, Sanjit
Statistical isotropy violation in WMAP CMB maps due to non-circular beams
(IUCAA, 2015-02) Das, Santanu; Mitra, Sanjit; Rotti, Aditya