Motivated by the unknown nature of the $2.50\text{–}2.67M_{\odot }$ compact object in the binary merger event GW190814, we study the maximum neutron star mass based on constraints from low-energy nuclear physics, neutron star tidal deformabilities from GW170817, and simultaneous mass-radius measurements of PSR J0030+045 from NICER. Our prior distribution is based on a combination of nuclear modeling valid in the vicinity of normal nuclear densities together with the assumption of a maximally stiff equation of state at high densities, a choice that enables us to probe the connection between observed heavy neutron stars and the transition density at which conventional nuclear physics models must break down. We demonstrate that a modification of the highly uncertain suprasaturation density equation of state beyond 2.64 times normal nuclear density is required in order for chiral effective field theory models to be consistent with current neutron star observations and the existence of $2.6M_{\odot }$ neutron stars. We also show that the existence of very massive neutron stars strongly impacts the radii of $\approx 2.0M_{\odot }$ neutron stars (but not necessarily the radii of $1.4M_{\odot }$ neutron stars), which further motivates future NICER radius measurements of PSR $\mathrm{J1614}-2230$ and PSR J0740+6620.

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• Equations of state of nuclear matter
• Gravitational wave sources
• Nuclear astrophysics
• Nuclear many-body theory
• Nuclear matter
• Nuclear matter in neutron stars
• Nuclear physics of explosive environments
• Nucleon-nucleon interactions
• Binary stars