Temporal Analysis of High-Energy Transient Sources: An Adaptive Binning Approach in Time-Domain Astronomy

Context and motivation. In the era of multi–messenger astrophysics, the landmark joint detection GRB170817A/GW170817 established the first, and so far only, confirmed association between a short Gamma Ray Burst and a binary neutron star merger. This event demonstrated that precise, near, simultaneous localization of electromagnetic and gravitational wave signals is essential for unambiguous source identification. Maximizing the scientific return of future joint detections requires continuous high-energy monitoring and rapid, accurate localization capabilities, naturally enabled by distributed, constellation-style missions that triangulate events through inter-satellite time-of-arrival delay measurements. Nanosatellites and the low–count challenge. Nanosatellites drastically reduce barriers to space science through small mass, rideshare compatibility, and COTS–based integration. However, their modest effective areas (typically ≲ 100 cm2) constrain time-domain analyses to a low-count Poisson-limited regime. In such conditions, fixed–bin light curves may either smooth out fast variability (if bins are too coarse) or become dominated by shot noise (if too fine), biasing traditional timing estimators. Methods: Estimation of delays. This thesis develops a timing toolkit designed for such constraints. First, light curves are constructed using an adaptive binning approach that stabilizes the per-bin count statistics without sacrificing temporal resolution, enabling the recovery of variability across a wide range of timescales. Second, I introduce a simulation-free cross-correlation estimator that operates directly on photon time-of-arrival lists. By minimizing the Poisson imprint intrinsic to flux randomization techniques, which repeatedly simulate from noisy templates, this method yields stable, unbiased lag estimates with near nominal coverage. Across photon count regimes, the Modified Double Pool method improves both accuracy and computational efficiency, with only the expected √2 precision penalty due to halving-reshuffle process. Constellations for localization: performance and FoV. Localization accuracy is quantified for realistic three-satellite constellations, exploring platform sizes (3U–27U) and baselines ranging from low–Earth separations to Earth–L1 distances. Using non–imaging, wide field detectors, such configurations achieve quasi–hemispherical instantaneous coverage, a major advantage over the ∼ 1.4 sr field of view and Earth occultation of low Earth orbit instruments such as Swift/BAT. A triplet with 𝐴eff ∼ 360 cm2 per node and baselines of ∼ 2.5 × 106 km can reach Swift/BAT class localizations, while smaller nodes still achieve arcminute accuracy under favorable geometry and count rate. These results should enable rapid, targeted follow-up by partner facilities with minimal tiling, reducing the risk of missing the earliest and most informative transient phases. SpIRIT in–orbit operations. This thesis also encompasses the in–orbit activities of the 6U SpIRIT satellite, focusing on the onboard HERMES payload. These include commissioning and first-light operations, execution of the observing program, and an end-to-end data reduction pipeline producing time-tagged event lists, light curves, and preliminary spectra. Operational effects affecting background, calibration, timing, pointing, and data continuity are identified and mitigated through dedicated procedures. Bright X–ray targets are analyzed, including a tentative HERMES detection of the Sco X–1 spectrum, with detailed interval selection, background modeling, response application, and consistency checks. On–orbit validation of microsecond timing. High precision timing is demonstrated using the 6U SpIRIT CubeSat equipped with a HERMES detector. During a single 730 s on–axis observation of the Crab pulsar, the canonical double-peaked profile was resolved at > 5𝜎, showcasing microsecond-level performance previously associated only with flagship observatories. Fundamental physics: limits on Lorentz invariance violation. The timing framework is further applied to tests of Lorentz Invariance Violation (LIV) through energy-dependent photon propagation in GRBs. By measuring inter-band lags between MeV–GeV light curves and a keV reference band, and statistically disentangling intrinsic source delays from propagation-induced terms, I obtain, at 95% C.L., first-order lower limits of 𝐸QG > 1.25 × 1016 GeV (subluminal) and 𝐸QG > 2.49 × 1016 GeV (superluminal). Faint source timing: ULX hard lags. Beyond Gamma Ray Bursts, the toolkit proves effective for extremely faint sources such as Ultraluminous X–ray sources (ULXs). Statistically significant hard lags are detected both over full XMM–Newton exposures and within windows of ∼10 ks, supporting a scenario of inward propagation of accretion rate fluctuations in super Eddington, geometrically thick flows. The measured lags, of order 1 ks, correspond to characteristic distances of ∼ 0.001 AU from the compact object, where the soft X-Ray emission mechanisms remain under investigation.