A DISSERTATION SUBMITTED TO THE DEPARTMENT OF PHYSICS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

Abel Lawrence Peirson V

March 2023

Measuring X-ray polarization has been a major goal in astrophysics for the last 40 years. With the launch of NASA's Imaging X-ray Polarimetry Explorer (IXPE) in December 2021, soft X-ray polarimetry (1-10 keV) is now possible. In this thesis, I introduce an optimal signal extraction method for X-ray polarimeters based on gas pixel detectors. Using IXPE's thus improved sensitivity, I make progress towards identifying the high-energy emission processes and magnetic field geometries responsible for radiation in blazar jets. First, I develop a simulation-based inference framework for measuring X-ray polarization as a function of time, energy, and position in gas pixel detectors, proving that for a fixed model budget the framework is optimal. Second, I propose a simple geometrical jet model to study the polarization properties of leptonic blazar jets, including their observed EVPA rotations and their detection prospects with IXPE. Finally, I interpret IXPE's measurements of BL Lacertae across the synchro-Compton transition region to suggest leptonic-dominated emission processes in blazars, and of Mrk 421 to provide evidence for helical magnetic fields as the source of EVPA rotations.