Astrophysical assumptions and equation of state framework have larger impact on equation of state inference than individual neutron star observations

The wide range of nuclear densities achieved in neutron stars makes them probes of dense nuclear behavior in the form of the nuclear equation of state (EoS). Studying neutron stars both in isolation, with X-ray measurements and pulse profiling, and in dynamic events, such as neutron star mergers, have provided insight into these high nuclear densities. Though nominally congruent, here we highlight impact of implicit assumptions embedded in joint analysis of these messengers and their systematic impact on EoS inference. We show that astrophysical assumptions and EoS framework can have a larger effect on inferred EoS than individual contemporary neutron star observations. Performing a proof-of-concept demonstration using the chronologically first few observational constraints, after the application of 5 to 6 observational constraints, additional observations provided diminishing returns and modified the inferred EoS by shifting the radius of a 1.4 $\unit{M_\odot}$ NS by $\sim$ 0.1 km. By contrast, astrophysical priors, specifically the spin and mass ratio motivated by astrophysical source population uncertainties, and EoS framework tend to impact EoS inference much more substantially by shifting the 1.4 $\unit{M_\odot}$ NS radius by $\sim$ 0.5 km and by modifying shape of inferred mass-radius relationship. The inferred EoS depends strongly on the adopted choice of spectral parameterizations: when we employ a framework which explicitly enforces causality, we find a strong phase-transition-like feature at $\sim 10^{14.5}$ g cm$^{-3}$.