Strong model-agnostic constraints for twin-star solutions

Abstract

We perform a model-agnostic Bayesian analysis of the neutron-star-matter equation of state (EoS), using known ab-initio constraints and astrophysical observations to limit its behavior at intermediate densities. Permitting explicit first-order phase transitions allows us to systematically search for twin-star solutions, i.e. the existence of stars degenerate in mass but differing in radius. We find that current observational constraints exclude all but two classes of twin stars. The first is characterized by a first-order transition occurring at a very low density, where the material properties of the system either stay largely intact or move away from the conformal limit. In the second, more interesting class, the discontinuity in the mass-radius curve emerges after a rapid crossover transition at a significantly higher density, with the speed of sound exhibiting two sharp peaks at distinct densities. Since neither class shows clear conformalization upon entering the second branch, the standard twin-star scenario linking the mass-radius discontinuity to deconfinement can be firmly ruled out, while even the remaining solutions -- disfavored by per-mille Bayes factors and in tension with theoretical bounds -- are likely to be excluded in the future.

Figures (3)

• Figure 1: Progressive impact of astrophysical constraints (from left to right) on the mass-radius relation (top), the EoS (middle), and the correlation between the parameters $n_1$ and $\delta n$ (bottom) for twin-star solutions. Shading from light to dark blue indicates increasing normalized likelihood (calibrated separately for each column), with values smaller than $10^{-2}$ shown in gray, while the FOPT- and non-FOPT-induced twin-star solutions are distinguished by circular and cross markers on the third row. Green lines and bands in the EoS panels show the median and $68\%$ credible interval of the central density in maximally massive stars. At high densities, the dark and light red regions represent the pQCD constraints imposed on the pressure and sound speed, respectively, while at low densities, the dark and light red bands correspond to CEFT pressure constraints up to $1.1\,n_s$ (imposed on our results) and $2\,n_s$ (shown here for illustrative purposes), respectively. For the latter results, the narrow non-transparent bands correspond to 1-$\sigma$ and the wider transparent ones to 2-$\sigma$ estimates.
• Figure 2: Ten highest-likelihood twin-star EoSs from twin categories 1 (upper row) and 2 (lower row). From left to right we show the squared sound speed ($c_{\rm s}^2$), conformal anomaly ($\Delta$) and conformal distance ($d_{\rm c}$). Green lines and bands show the median and $68\%$ credible interval of the central density of maximally massive stars, while the N2LO CEFT error bands are shown as in Fig. \ref{['fig:constraints']}Drischler:2020fvz. Finally, we note that the blue line segments correspond to stable twin-star branches, solid gray lines to unstable parts, and dotted lines to the phase transition region.
• Figure 3: Examples of the two viable twin-star classes 1 (upper row) and 2 (bottom row), including both the EoSs (left column) and corresponding mass–radius curves (right column). Stable stellar branches are shown in blue, unstable ones in gray, and the transition region in the EoS plot in dashed gray. Black dots and stars mark the end of the first and the start of the second stable branch, respectively.