New Tricks for Old Stars: Studying Compact Objects Through Novel Methodologies in Timing, Energy and Imaging

To understand astronomical objects and their environments, it is essential to study their behavior across time, energy and space. For compact objects, these analyses provide a unique window into physics in extreme environments, probing transient behavior, accretion processes, and tests of spacetime and gravity in the high field regime. In this thesis, I present novel approaches to revolutionize timing and spectral analysis and imaging with polarimetry in astronomy. I first present two novel methodologies for astronomical timing analysis: 1) Wiener Deconvolution to resolve the response function generating time lags across different energy bands and 2) Mutual Information as a powerful tool to identify time lags without assuming underlying linearity. I establish methodological framework and demonstrate efficacy of methodologies through toy models for generalized utilization of astronomical timing and lag analysis. I then present the results of novel methodologies applied to radio data from the black hole binary MAXI J1820+070. These approaches not only help in identifying time lags with much higher accuracy and precision, but also reveal numerous previously undetected lags, offering new insights into how the compact jet in MAXI J1820+070 behaves across different energies. I then extend the astronomical application of Wiener Deconvolution to 2D, enabling estimates of the first ever high resolution X-ray polarimetry images, and present preliminary results for the Supernova Remnant Cas A. Finally, I explore magnetar spectral line analysis and modeling, and show how we can learn about the behaviour of magnetic fields at their most intense through spectral lines detected from magnetars with current and future detectors.