arXiv subjects

Sanjeev V. Dhurandhar

Publications and source records attributed to Sanjeev V. Dhurandhar.

6 recordsLinked to original sources

arXiv2026

A product template bank to search for compact binary coalescences microlensed by isolated point mass lenses

Gravitational waves (GW) from stellar mass compact binary coalescences (CBCs) that encounter a lens whose Schwarzschild radius is comparable to the GW wavelength, will be microlensed, leading to frequency-dependent modulations in the observed signal. Neglecting such wave-optics effects in standard templated searches for CBCs can result in signal-to-noise ratio (SNR) losses as large as 30%. Here, we present a prescription for constructing a template bank targeted at microlensed GWs. We consider CBCs microlensed by isolated point mass lenses, whose frequency-dependent amplification factor is known to have a closed-form analytical expression. However, to construct the template bank, it suffices to use the geometric optics approximation, effectively modeling the microlensed signal as overlapping signals. Moreover, given that matched filtering is mostly sensitive to the phase of the GW signal, we use the phase of the amplification factor to compute the metric elements. The usual CBC parameter space is appended by two extra parameters: (i) the time-delay ($t_d$) between images and (ii) the relative-magnification ($μ_r$). By identifying the region of the lensing parameter space where the fitting factor (FF) falls below 97% due to wave-optics effects, we construct a template bank consisting of ~4000 templates covering the selected lensing region, independent of the values of the unlensed CBCs' parameters. We show that the bank targeting microlensed CBCs is, to a very good approximation, a Cartesian product of the unlensed CBC bank and the bank spanning the lensing parameters. We demonstrate the effectiveness of our method by evaluating fitting factors using both the unlensed CBC bank and the product template bank, finding a reduction of up to a factor of ~10 in the mismatch, as well as consistency with the prescribed minimal match criterion of 0.97 used in the construction of the banks.

gr-qc↗

arXiv2005

Time-Delay Interferometry

Equal-arm interferometric detectors of gravitational radiation allow phase measurements many orders of magnitude below the intrinsic phase stability of the laser injecting light into their arms. This is because the noise in the laser light is common to both arms, experiencing exactly the same delay, and thus cancels when it is differenced at the photo detector. In this situation, much lower level secondary noises then set overall performance. If, however, the two arms have different lengths (as will necessarily be the case with space-borne interferometers), the laser noise experiences different delays in the two arms and will hence not directly cancel at the detector. In order to solve this problem, a technique involving heterodyne interferometry with unequal arm lengths and independent phase-difference readouts has been proposed. It relies on properly time-shifting and linearly combining independent Doppler measurements, and for this reason it has been called Time-Delay Interferometry (or TDI). This article provides an overview of the theory and mathematical foundations of TDI as it will be implemented by the forthcoming space-based interferometers such as the Laser Interferometer Space Antenna (LISA) mission. We have purposely left out from this first version of our ``Living Review'' article on TDI all the results of more practical and experimental nature, as well as all the aspects of TDI that the data analysts will need to account for when analyzing the LISA TDI data combinations. Our forthcoming ``second edition'' of this review paper will include these topics.

gr-qc↗

arXiv2001

Extended hierarchical search (EHS) algorithm for detection of gravitational waves from inspiraling compact binaries

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.

gr-qc↗

arXiv2000

A study of the gravitational wave form from pulsars

We present analytical and numerical studies of the Fourier transform (FT) of the gravitational wave (GW) signal from a pulsar,taking into account the rotation of the Earth for a one day observation period.

astro-ph↗

arXiv2000

Searching for continuous gravitational wave sources in binary systems

We consider the problem of searching for continuous gravitational wave sources orbiting a companion object. This issue is of particular interest because the LMXB's, and among them Sco X-1, might be marginally detectable with 2 years coherent observation time by the Earth-based laser interferometers expected to come on line by 2002, and clearly observable by the second generation of detectors. Moreover, several radio pulsars, which could be deemed to be CW sources, are found to orbit a companion star or planet, and the LIGO/VIRGO/GEO network plans to continuously monitor such systems. We estimate the computational costs for a search launched over the additional five parameters describing generic elliptical orbits using match filtering techniques. These techniques provide the optimal signal-to-noise ratio and also a very clear and transparent theoretical framework. We provide ready-to-use analytical expressions for the number of templates required to carry out the searches in the astrophysically relevant regions of the parameter space, and how the computational cost scales with the ranges of the parameters. We also determine the critical accuracy to which a particular parameter must be known, so that no search is needed for it. In order to disentangle the computational burden involved in the orbital motion of the CW source, from the other source parameters (position in the sky and spin-down), and reduce the complexity of the analysis, we assume that the source is monochromatic and its location in the sky is exactly known. The orbital elements, on the other hand, are either assumed to be completely unknown or only partly known. We apply our theoretical analysis to Sco X-1 and the neutron stars with binary companions which are listed in the radio pulsar catalogue.

gr-qc↗

arXiv1999

Detection of gravitational waves using a network of detectors

We formulate the data analysis problem for the detection of the Newtonian coalescing-binary signal by a network of laser interferometric gravitational wave detectors that have arbitrary orientations, but are located at the same site. We use the maximum likelihood method for optimizing the detection problem. We show that for networks comprising of up to three detectors, the optimal statistic is essentially the magnitude of the network correlation vector constructed from the matched network-filter. Alternatively, it is simply a linear combination of the signal-to-noise ratios of the individual detectors. This statistic, therefore, can be interpreted as the signal-to-noise ratio of the network. The overall sensitivity of the network is shown to increase roughly as the square-root of the number of detectors in the network. We further show that these results continue to hold even for the restricted post-Newtonian filters. Finally, our formalism is general enough to be extended to address the problem of detection of such waves from other sources by some other types of detectors, e.g., bars or spheres, or even by networks of spatially well-separated detectors.

gr-qc↗