We obtain an empirical relation for the neutron star maximum mass arising from a particular combination of the saturation density ($n_0$), the effective mass ($m^{*}$), and (when present) the vector meson self-coupling constant ($\zeta$) within the relativistic mean-field model framework. Observations of massive neutron stars heavier than $\approx 2M_{\odot }$ have eliminated the softest equation of state from consideration and impose strong constraints on nuclear interactions used to model dense nuclear matter. To date, numerous efforts have been made to refine relativistic mean-field models through the inclusion of additional mesons, such as the $\delta$ meson, as well as through the introduction of additional couplings. We show that current relativistic mean field models, including our own constructions, exhibit a maximum neutron star mass that is primarily determined by the combination of the saturation density, the effective mass at saturation, and the vector meson self-coupling constant. When constraining the pure neutron matter equation of state using chiral effective field theory (ChEFT) at low densities, 250 parameter sets were generated to derive an empirical formula for the maximum mass of neutron stars and apply the formula with the present relativistic mean field models.

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• Nuclear astrophysics
• Nuclear matter in neutron stars