Causality and perturbative-QCD constraints on first-order phase transitions in neutron stars

Abstract

Causality bounds the compactness and maximum mass of neutron stars. We generalise this bound to equations of state (EOSs) with a first-order phase transition between maximally stiff phases. In units of the transition energy density, the problem depends only on $q=\ptr/\etr$ and $j=Δ\ve/\etr$. The maximum compactness equals the smooth value $\mathcal{C}=0.354$ for $q\to 0$ or $j\to 0$, is unaffected for $q\gtrsim 0.67$, and is otherwise reduced by typically $\lesssim 0.04$ when the maximum-mass star is a hybrid star and by up to $0.13$ when it is the last hadronic star. Matching to a Baym--Pethick--Sutherland crust and a chiral-EFT polytrope at $n_m=1.1n_0$ and inverting the bound, no causal EOS supports $2.01\,\Msun$ if the energy-density jump exceeds $\simeq 460$--$495\mathrm{MeV}\mathrm{f}{\mathrm{m}}^{-3}$. Additionally, imposing radius constraint of $R\ge 11.6$~km it shrinks to $\simeq 235$--$395\mathrm{MeV}\mathrm{f}{\mathrm{m}}^{-3}$. These limits hold whatever the matter above the transition, for onsets within $\simeq 0.2n_0$ of $n_m$. Relaxing maximal stiffness, we build EOSs with a transition at ${\mu }_{\mathrm{tr}}=1000$--$1300$~MeV, matched to perturbative QCD (pQCD) at $2.6$~GeV. pQCD limits the jump; EOSs compatible with PSR J0740+6620, J1614$-$2230, J0437$-$4715, J0614$-$3329, GW170817, and XTE J1814-338 appear only at ${\mu }_{\mathrm{tr}}=1200$ and $1250$~MeV; and inside the causal window, the largest jump agrees with the bound within the grid resolution. Finally, inserting a transition at $2.01\,\Msun$ into hadronic EOSs that satisfy five pulsar observations, the EOS with the lowest break density gives a narrow stable hybrid window ($ΔM\simeq0.005\,\Msun$), compatible with XTE J1814-338 for jumps of $6$--$8n_0$ and with pQCD; three EOSs with higher break densities give none.

arXiv comment15 pages, 9 figures