Searches for long-transient gravitational waves from newborn magnetars triggered by electromagnetic counterparts with current and next-generation detectors

Long-transient gravitational waves, lasting from hours to days, form an intermediate class of signals between short-duration compact binary coalescences and persistent continuous waves. A promising source of such signals is the newborn magnetar: a rapidly rotating, highly magnetised neutron star formed in a core-collapse supernova or binary neutron star merger. Strong internal magnetic fields can induce non-axisymmetric deformations in the stellar structure, driving gravitational-wave emission at twice the rotation frequency while causing the star to spin down on timescales of hours to days. In this thesis, we use a signal model for long-transient gravitational waves from newborn magnetars in the regime where spin-down is dominated by gravitational-wave emission. The waveform is characterised by a continuously decreasing frequency and strain amplitude, governed by the initial spin frequency and ellipticity of the source. We implement this model within an improved version of the Generalized Frequency Hough search pipeline, GFH-v2, which is designed to efficiently track such signals over large parameter spaces. We validate the GFH-v2 pipeline through an extensive injection study using LIGO O4a data, characterising its sensitivity as a function of source parameters and establishing the detection threshold and follow-up procedure. We then apply the pipeline in a directed search for gravitational-wave emission from the possible magnetar remnant of SN 2023ixf, one of the nearest core-collapse supernovae of the last decade in the M101 galaxy, using data from LIGO Engineering Run 15 (ER15). In parallel, we develop a multi-messenger framework connecting magnetar spin-down to shock-breakout emission observable in the near-ultraviolet, with particular application to the upcoming ULTRASAT satellite mission. We compute the expected UV light curves, detection horizons, and event rates for magnetar-driven supernovae, demonstrating that ULTRASAT will be able to identify magnetar-forming events and provide electromagnetic triggers for directed gravitational-wave searches. No evidence for gravitational-wave emission associated with SN 2023ixf is found in the analysed data. We thus place upper limits on the maximum detectable distance as a function of initial frequency and ellipticity. While these limits fall below the distance to SN 2023ixf, they represent a sensitive directed search of these signals applied to ER15 data and demonstrate the operational readiness of the GFH-v2 framework for future searches. The methods and results presented here provide a foundation for long-transient searches targeting nearby core-collapse supernovae in forthcoming LIGO-Virgo-KAGRA observing runs.