Revisiting the Rhoades-Ruffini bound

Abstract

We revisit the derivation of the Rhoades-Ruffini bound on the upper limit for the maximum mass of neutron stars and find that the assumption made there for the onset of an ultimately stiff phase of high-density matter is not stringent. Relaxing this assumption and allowing for an onset of stiff non-nucleonic matter under neutron star constraints at the saturation density or below boost the upper limit of the theoretically possible maximum mass to $4~M_\odot$ or higher, in the mass-gap region between neutron stars and stellar-mass black holes. We provide a fit formula for the dependence of this upper limit on the speed of sound and the onset density of the deconfinement transition.

Figures (7)

• Figure S1: Pressure vs. chemical potential for the hadronic baseline EoS DD2npY (dash-dotted line) and CSS quark matter with different values of the constant sound speed squared (different colored solid lines). The deconfinement onset density $n_{\mathrm{onset}}=n_0=0.15$ fm$^{-3}$ while the density jump at the transition vanishes, $\Delta n=0$.
• Figure S2: Mass-Radius relations for hybrid stars with onset density $n_{\rm onset}=0.15$ fm$^{-3}$ (solid lines) for different values of the constant squared speed of sound. The maximum mass configurations lie on the dotted line described by the linear fit formula \ref{['eq:Mmax-R']}. For comparison, the sequence of purely hadronic neutron stars described by the DD2npY-T EoS is shown by a dashed black line.
• Figure S3: Radius $R=R_{\rm max}$ of the maximum mass configuration as a function of the squared sound speed $c_s^2$, when the onset of deconfinement is at $n_{\rm onset}=n_0=0.15$ fm$^{-3}$ and the transition degenerates to a crossover with vanishing density jump $\Delta n=0$.
• Figure S4: Maximum mass of the hybrid neutron stars as a function of the onset density $n_{\rm onset}$ for selected values of the constant squared speed of sound of the high-density phase $c_s^2$= 0.30 (violet), 0.33 (magenta), 0.40 (pink), 0.50 (blue), 0.60 (cyan), 0.70 (green), 0.80 (brown), 0.90 (orange) and 1.00 (red). Stable hybrid stars are obtained for onset densities below $n_{\rm onset,max}=0.93$ fm$^{-3}$.
• Figure S5: The dependence of the four fit parameters $M_1$, $M_2$, $\alpha$, and $\beta$ of the maximum mass formula \ref{['eq:Mmax']} in the text on the squared speed of sound $c_s^2$.