Ultracompact hybrid stars consistent with multimessenger astrophysics

In this work, we consider the consequences of phase transition in dense QCD on the properties of compact stars and implications for the observational program in gravitational wave and x-ray astrophysics. The key underlying assumption of our modeling is a strong first-order phase transition past the point where the hadronic branch of compact stars reaches the two-solar mass limit. Our analysis predicts ultracompact stars with very small radii—in the range of 6–9 km—living on compact star sequences that are entirely consistent with the current multimessenger data. We show that sequences featuring two-solar mass hadronic stars consistent with radio-pulsar observations are also consistent with the inferences of large radii for massive neutron stars by NICER x-ray observations of neutron stars and the small radii predicted by gravitational waves analysis of the binary neutron star inspiral event GW170817 for our models that feature a strong first-order QCD phase transition.

Figure 1

$M-R$ relation for hybrid EOS models with a phase transition at high density for stiff-stiff nucleonic EOSs with $L_{\mathrm{sym}}=105$, $Q_{\mathrm{sat}}=900\mathrm{MeV}$, and soft-soft one with $L_{\mathrm{sym}}=45$, $Q_{\mathrm{sat}}=300\mathrm{MeV}$. The sequences of stars are constructed from a nucleonic model by fixing $M_{\max }^{\mathrm{H}}/M_{\odot }=2.0$ on the nucleonic branch, while varying the $M_{\max }^{\mathrm{Q}}/M_{\odot }$ in the range 1.0–2.0 and the speed of sound squared $s$. For comparison, we also show the sequences in the case of low-maximum hadronic mass $M_{\max }^{\mathrm{H}}/M_{\odot }=1.3$, studied previously in Refs. [21, 24], for the same speeds of sound. Note that GW170817 ellipses assume a hadronic EOS and constrain only the hadronic branches of the stellar sequences.

Figure 2

$M-R$ relation for hybrid EOS models featuring high density phase transition with two examples of nucleonic EOSs, specifically the soft-stiff one with $L_{\mathrm{sym}}=45$, $Q_{\mathrm{sat}}=900\mathrm{MeV}$ and stiff-soft one $L_{\mathrm{sym}}=105$, $Q_{\mathrm{sat}}=300\mathrm{MeV}$. The value of sound speed squared is fixed at $s=1.0$.

Figure 3

Radial profiles of energy density and pressure (on a logarithmic scale) for twin stars with masses $M=M_{\max }^Q=1.40M_{\odot }$. The results for purely nucleonic stars are shown by dotted, and those for hybrid stars are shown by solid lines. Two nucleonic EOSs have been used: a soft-stiff one with $L_{\mathrm{sym}}=45$, $Q_{\mathrm{sat}}=900\mathrm{MeV}$ and a stiff-soft one with $L_{\mathrm{sym}}=105$, $Q_{\mathrm{sat}}=300\mathrm{MeV}$. The quark core and crust regions are shaded for clarity.

Figure 4

Dimensionless TD of compact objects for a fixed value of binary chirp mass $\mathcal{M}/M_{\odot }=1.186$. The shaded regions correspond to the 50% and 90% CIs taken from the analysis of the GW170817 event. The EOS models with strong first-order phase transition are fixed by the values $M_{\max }^{\mathrm{H}}/M_{\odot }=2.0$ and $M_{\max }^{\mathrm{Q}}/M_{\odot }=1.2$ (red curves), 1.4 (blue curves), 1.6 (dark blue curves), and $s=1.0$. The type of binary components (Q/H) with mass $M_1-M_2$ are indicated in the plot. Panel (a): soft-soft and stiff-soft hadronic EOS results are shown by solid and dashed lines; panel (b): soft-stiff and stiff-stiff hadronic EOSs are shown by solid and dashed lines. The upper left inset shows a schematic $M-R$ diagram for the cases $M_{\max }^{\mathrm{Q}}/M_{\odot }=1.4$, 1.6, where the binary is of the Q-H type and the hybrid branch lies above the average value $M/M_{\odot }=1.362$. The right inset shows the same for $M_{\max }^{\mathrm{Q}}/M_{\odot }=1.2$, in which case the binary is of the H-Q type with the hybrid branch lying below the average value $M/M_{\odot }=1.362$. These two cases are marked in the plots and insets by Latin numerals I and II, respectively.

Figure 5

Dimensionless TD for the case of EOSs with the hybrid branch covering a range of masses around the average value $M/M_{\odot }=1.362$ as illustrated in the upper inset showing the $M-R$ relation. The remaining parameters are chosen as in Fig. 4. There are four types of binaries composed of hadronic (H) and/or hybrid (Q) stars. Panel (a): soft-soft and stiff-soft hadronic EOS results are shown with solid and dashed lines; (b): soft-stiff and stiff-stiff hadronic EOSs are shown by solid and dashed lines.