Abstract: Neutron stars (NSs) allow us to probe fundamental interactions at densities otherwise inaccessible in the lab, up to as much as ~6 times nuclear saturation density. By using multi-messenger astrophysical observations of NSs, we can constrain the Equation of State (EoS) of dense matter and better determine how astrophysical objects may behave in a variety of environments. I will review the basic principles behind recent observations of coalescing compact binaries containing NSs with Gravitational Waves as well as both radio and X-ray observations of pulsars. Using these observations, I’ll show how we can learn about both the microphysical properties of nuclear interactions and correlations with their macroscopic properties at the same time. In particular, I will show tantalizing hints at the possibility of phase transitions within NS cores, our ability to determine when nuclear theoretic calculations break down, and implications for the radii and masses NSs may achieve. Throughout, I’ll highlight how modeling assumptions can (strongly) affect our conclusions and advocate for transparency within such analyses, including which data is selected for analysis.
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