New constraints on radii and tidal deformabilities of neutron stars from GW170817 (1803.00549v2)

Abstract: We explore in a parameterized manner a very large range of physically plausible equations of state (EOSs) for compact stars for matter that is either purely hadronic or that exhibits a phase transition. In particular, we produce two classes of EOSs with and without phase transitions, each containing one million EOSs. We then impose constraints on the maximum mass, ($M < 2.16 M_{\odot}$), and on the dimensionless tidal deformability ($\tilde{\Lambda} <800$) deduced from GW170817, together with recent suggestions of lower limits on $\tilde{\Lambda}$. Exploiting more than $10^9$ equilibrium models for each class of EOSs, we produce distribution functions of all the stellar properties and determine, among other quantities, the radius that is statistically most probable for any value of the stellar mass. In this way, we deduce that the radius of a purely hadronic neutron star with a representative mass of $1.4\,M_{\odot}$ is constrained to be $12.00!<!R_{1.4}/{\rm km}!<!13.45$ at a $2$-$\sigma$ confidence level, with a most likely value of $\bar{R}{1.4}=12.39\,{\rm km}$; similarly, the smallest dimensionless tidal deformability is $\tilde{\Lambda}{1.4}!>!375$, again at a $2$-$\sigma$ level. On the other hand, because EOSs with a phase transition allow for very compact stars on the so-called `twin-star' branch, small radii are possible with such EOSs although not probable, i.e. $8.53!<!R_{1.4}/{\rm km}!<!13.74$ and $\bar{R}{1.4}=13.06\,{\rm km}$ at a $2$-$\sigma$ level, with $\tilde{\Lambda}{1.4}!>!35.5$ at a $3$-$\sigma$ level. Finally, since these EOSs exhibit upper limits on $\tilde{\Lambda}$, the detection of a binary with total mass of $3.4\,M_{\odot}$ and $\tilde{\Lambda}_{1.7}!>!461$ can rule out twin-star solutions.

• The paper constrains a 1.4 M☉ neutron star’s radius to 12.00–13.45 km and establishes a tidal deformability lower bound of 375 using GW170817 observations.
• The paper employs over a billion equation-of-state models, covering both hadronic and phase-transition scenarios to challenge extreme compact-star models.
• The paper shows that while phase-transition models allow for compact twin-star configurations, such outcomes appear statistically unlikely under current observational constraints.

Analyzing Neutron Star Properties from Gravitational-wave Observations

The advent of gravitational-wave astronomy has allowed for profound advancements in our understanding of neutron stars. The paper under discussion focuses on deriving constraints on the radii and tidal deformabilities of neutron stars using observations from event GW170817. This neutron star binary merger, observed by LIGO and Virgo detectors, provides pivotal data for evaluating the properties of such compact stars. Specifically, the paper investigates a broad range of equations of state (EOSs), utilizing more than a billion equilibrium models to ascertain the most probable stellar properties.

EOS Exploration and Constraints

The authors generate two classes of EOSs—hadronic and those with phase transitions—each with one million variations. The EOSs adhere to constraints on maximum mass and tidal deformability as deduced from GW170817. The paper utilizes these constraints, including a maximum neutron star mass of less than 2.16 $M_{\odot}$ and a dimensionless tidal deformability $\tilde{\Lambda}<800$, coupled with recent empirical suggestions proposing lower limits on $\tilde{\Lambda}$.

In the exploration of these EOSs, the authors deduce that for purely hadronic models, the radius of a neutron star with a mass of 1.4 $M_{\odot}$ is constrained to 12.00-13.45 km at a 2-$\sigma$ confidence level, with a most likely radius of 12.39 km. Moreover, a lower bound of $\tilde{\Lambda}_{1.4}>375$ is established within this confidence level. These constraints are significant as they rule out several extreme EOSs, which posit unreasonably small radii or tidal deformabilities inconsistent with observed data.

Implications of Phase Transitions

The inclusion of EOSs permitting phase transitions allows for the possibility of extremely compact configurations on the so-called "twin-star" branch. Although these configurations support smaller radii, namely 8.53-13.74 km, their statistical probability remains low, suggesting they represent a less probable outcome under current observational constraints. Notably, EOSs with phase transitions allow for very low tidal deformabilities ($\tilde{\Lambda}>35.5$) at a 3-$\sigma$ level, providing crucial tests for ruling out these configurations through future gravitational-wave detections.

Practical and Theoretical Implications

This research has significant implications for both theory and observation. The EOSs with realistic constraints narrow the possibilities for the internal structure of neutron stars, hinting at the physical processes that must occur at the extreme conditions within these objects. Practically, they aid in interpreting future gravitational-wave data, particularly with respect to better constraining or ruling out theoretical models that predict either exotic states of matter or alternate forms of compact objects, such as hybrid quark-hadron stars.

Future Perspective

As gravitational-wave astronomy continues to mature, the paper indicates that a more refined description of neutron matter—especially in the transition region from nuclear saturation densities to higher baryon densities—is crucial. Future observations, especially those from high-mass mergers, can further illuminate the phase structure of dense matter, potentially confirming or rejecting the presence of phase transitions suggested by "twin-star" configurations.

In conclusion, this paper represents a comprehensive and expert evaluation of neutron-star properties derived from gravitational-wave observations. It underscores the strength of combining multimessenger data with numerical simulations to probe the dense matter equation of state, paving the way for more refined models and potentially transformative insights into the properties of matter under extreme conditions.