36th Annual Report (2023-24)

23 to go below this lower limit. However, there are interesting astrophysical sources emitting GWat low frequencies. The solution is to go into space. The Laser Interferometer Space Antenna (LISA) is a space-based gravitational wave detector that is sensitive in the low-frequency band from 10^-5 Hz - 10^-1 Hz. However, LISA is plagued by laser frequency noise about 6 or 7 orders above the other ambient noises. Time-delay interferometry (TDI) is a technique in which the data streams are combined with appropriate time delays so that the laser frequency noise is cancelled or suppressed. Sanjeev Dhurandhar and his collaborators have used algebraic-geometric methods to find TDI combinations of data streams - an exact solution - the null space, namely, the module of syzygies (terminology by David Hilbert) is obtained for the static case. Since the arm-lengths are mildly time-varying, they Taylor-expanded the time-delay operators and obtained approximate solutions at the required order. Matrix methods have also been found to be useful. [M. Tinto and S. Dhurandhar, Living Reviews in Relativity (Springer), Vol. 24, article 1, (2021); M. Tinto, S. Dhurandhar and P. Joshi, Phys. Rev. D 104, 044033 (2021); S. Dhurandhar, P. Joshi and M. Tinto, Phys. Rev. D 105, 084063 (2022); M. Tinto, S. Dhurandhar and D. Malakar, Phys. Rev. D 107, 082001 (2023); M. Tinto and S. Dhurandhar, Phys. Rev. D 108, 082003 (2023)] Parameter estimation of gravitational-wave signals is a computationally expensive process which increases with longer signal durations. Relative binning is a promising solution to accelerate the likelihood evaluations, which uses the smooth variation (in frequency) of the ratio of neighbouring waveforms in the parameter space. This approximation reduces the number of frequency points at which the waveform needs to be evaluatedwhile sampling, thus reducing ParameterEstimation(PE) ¬ Relative BInning in Bilby: the computation time. Apratim Ganguly, along with his collaborators, has implemented his method in Bilby, an open-source Bayesian inference package. [arXiv: 2312.06009] interactions of black holes: Sajal Mukherjee, Sanjit Mitra and Sourav Chatterjee (TIFR) showed that the hyperbolic encounters of black holes may be detected by the next generation GW detectors. Even multiple present generation detectors observing for several years have non-negligible chances for detection of these events. Since GWs only from coalescing binaries have so far been detected, discovery of new types of events will be highly exciting. Moreover, these events can complement the CBC detections (which probe blackholes in binaries) in obtainingmore precise estimates of the population of Black Holes in the universe. [MNRAS 508, 5064–5073 (2021)] Probing the formation channels of CBCs with their centre-of-mass acceleration: Avinash Tiwari and Shasvath J. Kapadia, in collaboration with Aditya Vijaykumar (CITA), Sourav Chatterjee (TIFR) and Giacomo Fragione (Northwestern University) are exploring the possibility of constraining line-of- sight acceleration (LOSA) of the centre of mass of CBCs. Detectors sensitive at low frequencies, such as proposed space-based detectors LISA and DECIGO, are best suited to observe this acceleration, although sufficiently large accelerations may also be detectable in future ground-based detectors such as Cosmi c Exp l o r e r and E i ns t e i n Telescope. Avinash et al are also investigating how LOSA and its higher time derivatives can be used to probe the gravitational potential of the CBC's environment, thus determining their formation channel on a single-event basis. Avinash, Aditya and Shasvath will be contributing to the LVK Collaboration with analyses related to this work. Rates&Populations (R&P) ¬ ¬ D e t e c t a b i l i t y o f h y p e r b o l i c [MNRAS, 527, 3, (2024), Astrophys. J., 954, 105 (2023)] on merger rate density models: Anupreeta More computed the fraction of the GWevents that are expected to be strongly lensed for different types of lenses where the deflector is either an individual galaxy or a cluster of galaxy. The unlensed to lensed rates are - Galaxy ~ 1 : O(1000) Galaxy-clusters ~ 1: O(1000) but rarer than galaxy-scale lenses by a factor of 2 The binary black hole merger rate density model determines the strong lensing rates. Thus, (non-)detection of strong lenses in the GW data can constrain the underlying family of merger rate density models. [Lensing LVK collaboration: Abbott et al. ApJ, Vol 923, Issue 1, id.14, 24 pp. 2021, Abbott et al. 2023 - arXiv:2304.08393] Microlensing by isolated point-mass lens: Isolated point-mass Microlensing introduces frequency dependent modulations in the GW signals. Anuj Mishra, Anupreeta More, Sukanta Bose and collaborators showed that if Gravitational Lensing ¬ ¬ Strong lensing rates and constraints ¬ ¬ F i g : M i c r o l e n s i n g p a r ame t e r s o f GW200208_130117 overlap with low to high confidence regions of detectable microlensed signalswhich needs further investigation.