Reexamining constraints on neutron star properties from perturbative QCD

The implications of perturbative QCD (pQCD) calculations on neutron stars are carefully examined. While pQCD calculations above baryon chemical potentials ${\ensuremath{\mu}}_{B}\ensuremath{\approx}2.4$ GeV demonstrate the potential of ruling out a wide range of neutron star equations of state (EOSs), such constraints only affect the most massive neutron stars in the vicinity of the Tolman-Oppenheimer-Volkoff limit, resulting in constraints that are orthogonal to current or expected astrophysical bounds. In the most constraining scenario, pQCD considerations favor low values of the squared speed sound ${C}_{s}$ at high ${\ensuremath{\mu}}_{B}$ relevant for the most massive neutron stars, but leave predictions of the radii and tidal deformabilities almost unchanged. Such considerations become irrelevant if the maximum speed of sound squared inside neutron stars does not exceed about ${C}_{s,\mathrm{max}}\ensuremath{\approx}0.5$, or if pQCD breaks down below ${\ensuremath{\mu}}_{B}\ensuremath{\approx}2.9$ GeV. Furthermore, the large pQCD uncertainties preclude any meaningful bounds on the neutron star EOS at the moment. Interestingly, if pQCD predictions for the pressure at around ${\ensuremath{\mu}}_{B}\ensuremath{\approx}2.5$ GeV are refined and found to be low ($\ensuremath{\lesssim}1.5$ GeV/${\mathrm{fm}}^{3}$), evidence for a soft neutron star inner core EOS in combination with the existence of two-solar-mass pulsars would indicate the presence of color superconductivity beyond neutron star densities. I point out that two-solar-mass pulsars place robust upper bounds on this nonperturbative effect and require the pairing gap to be less than ${\mathrm{\ensuremath{\Delta}}}_{\mathrm{CFL}}\ensuremath{\le}500\phantom{\rule{3.33333pt}{0ex}}\text{MeV}$ at ${\ensuremath{\mu}}_{B}\ensuremath{\approx}2.5\phantom{\rule{3.33333pt}{0ex}}\text{GeV}$.