Using a three-flavor Nambu–Jona-Lasinio model to describe the charge-parity violating effects through axion field, we investigate the axion effects on quark matter and quark-matter cores in massive hybrid stars. Within the range from 0 to $\pi$, the axion field $a/f_a$ decreases the baryon chemical potential of the first-order phase transition, leading to an increase in normalized pressure and stiffening of the quark matter equation of state. The effect of axions on hybrid star matter that includes the hadron-quark phase transition is contrary to expectations. The axion field shifts the onset of the hadron-quark mixed phase to lower densities but slightly softens the equation of state of the mixed phase matter, which also results in a slight decrease in the maximum mass and corresponding radius of the hybrid stars. However, we also find that the lowering of the onset of the mixed phase significantly increases the radius and mass of the quark-matter core in the hybrid star. Therefore, our results indicate that with axion effects, a sizable quark-matter core can appear in $2M_{\odot }$ massive neutron stars.

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• Nuclear matter in neutron stars
• QCD phase transitions
• Quark matter