Unveiling the Physics of Core-Collapse Supernovae with the Line Emission Mapper: Observing Cassiopeia A

(Abridged) Core-collapse supernova remnants (SNRs) display complex morphologies and asymmetries, reflecting anisotropies from the explosion and early interactions with the circumstellar medium (CSM). Spectral analysis of these remnants can provide critical insights into supernova (SN) engine dynamics, the nature of progenitor stars, and the final stages of stellar evolution, including mass-loss mechanisms in the millennia leading up to the SN. This white paper evaluates the potential of the Line Emission Mapper (LEM), an advanced X-ray probe concept proposed in response to NASA 2023 APEX call, to deliver high-resolution spectra of SNRs. Such capabilities would allow detailed analysis of parent SNe and progenitor stars, currently beyond our possibilities. We employed a hydrodynamic model that simulates the evolution of a neutrino-driven SN from core-collapse to a 2000-year-old mature remnant. This model successfully replicates the large-scale properties of Cassiopeia A at an age of about 350 years. Using this model, we synthesized mock LEM spectra from different regions of the SNR, considering factors like line shifts and broadening due to plasma bulk motion and thermal ion motion, deviations from ionization and temperature equilibrium, and interstellar medium absorption. Analyzing these mock spectra with standard tools revealed LEM impressive capabilities. We demonstrated that fitting these spectra with plasma models accurately recovers the line-of-sight velocity of the ejecta, enabling 3D structure exploration of shocked ejecta, similar to optical methods. LEM also distinguishes between Doppler and thermal broadening of ion lines and measures ion temperatures near the limb of SNRs, providing insights into ion heating at shock fronts and cooling in post-shock flows. This study highlights LEM potential to advance our understanding of core-collapse SN dynamics and related processes.