[Paper Review] Radius and equation of state constraints from massive neutron stars and GW190814

Yeunhwan Lim, Anirban Bhattacharya+2 more|arXiv (Cornell University)|Jul 13, 2020

Pulsars and Gravitational Waves ResearchPhysics and Astronomy85 references31 citations

TL;DR

This study constrains the neutron star equation of state using Bayesian inference, combining chiral effective field theory at low densities with a maximally stiff equation of state at high densities. It finds that a transition density of $ n_t \sim (2.39 - 2.95)n_0 $ is required to support 2.5–2.7 M$_\odot$ neutron stars, implying significant softening beyond 2.64$ n_0 $, and shows that heavy neutron star radii are strongly correlated with maximum mass, motivating future NICER observations of PSR J1614-2230 and PSR J0740+6620.

ABSTRACT

Motivated by the unknown nature of the $2.50-2.67\,M_\odot$ compact object in the binary merger event GW190814, we study the maximum neutron star mass based on constraints from low-energy nuclear physics, neutron star tidal deformabilities from GW170817, and simultaneous mass-radius measurements of PSR J0030+045 from NICER. Our prior distribution is based on a combination of nuclear modeling valid in the vicinity of normal nuclear densities together with the assumption of a maximally stiff equation of state at high densities, a choice that enables us to probe the connection between observed heavy neutron stars and the transition density at which conventional nuclear physics models must break down. We demonstrate that a modification of the highly uncertain supra-saturation density equation of state beyond 2.64 times normal nuclear density is required in order for chiral effective field theory models to be consistent with current neutron star observations and the existence of $2.6\,M_\odot$ neutron stars. We also show that the existence of very massive neutron stars strongly impacts the radii of $\sim 2.0\,M_\odot$ neutron stars (but not necessarily the radii of $1.4\,M_\odot$ neutron stars), which further motivates future NICER radius measurements of PSR J1614-2230 and PSR J0740+6620.

Motivation & Objective

• To determine the minimum transition density required for chiral EFT-based equations of state to support 2.5–2.7 M$_\odot$ neutron stars.
• To assess how the existence of massive neutron stars impacts the radii of typical 2.0 M$_\odot$ stars.
• To constrain the high-density behavior of the nuclear equation of state under the assumption that the GW190814 secondary is a neutron star.
• To identify the critical density at which conventional nuclear physics models break down.

Proposed method

• A Bayesian prior is constructed using chiral effective field theory for low densities and a maximally stiff equation of state (speed of sound = c) at high densities.
• The transition density $ n_t $ is assigned a uniform prior between 2$ n_0 $ and 4$ n_0 $, with $ n_0 = 0.16$ fm$^{-3} $.
• Posterior distributions are computed using likelihoods from NICER mass-radius measurements of PSR J0030+045 and tidal deformability constraints from GW170817.
• The equation of state is parameterized via a Taylor expansion in Fermi momentum, with potential energy densities expanded in powers of $ n^{(2+i/3)} $.
• A second-order phase transition model is used to describe the transition from nuclear matter to the stiff phase, with $ \Delta E = E_1/10 $.
• The joint likelihood combines NICER and LIGO/Virgo data using a product form, assuming statistical independence.

Experimental results

Research questions

• RQ1 What is the minimum transition density $ n_t $ required for chiral EFT-based equations of state to support 2.5–2.7 M$_\odot$ neutron stars?
• RQ2 How does the existence of massive neutron stars constrain the radii of 2.0 M$_\odot$ neutron stars?
• RQ3 Which equations of state are excluded by the observation of 2.6 M$_\odot$ neutron stars?
• RQ4 What is the critical density at which conventional nuclear physics models must break down to support such massive stars?
• RQ5 How do future NICER measurements of PSR J1614-2230 and PSR J0740+6620 inform the high-density equation of state?

Key findings

• A transition density of $ n_t \sim (2.39 - 2.95)n_0 $ is required to support 2.5–2.7 M$_\odot$ neutron stars, indicating that the equation of state must stiffen significantly beyond 2.64$ n_0 $.
• The existence of 2.6 M$_\odot$ neutron stars excludes only the softest equations of state with small radii and low tidal deformabilities.
• The radii of $ \sim $2.0 M$_\odot$ neutron stars are positively correlated with the maximum neutron star mass, suggesting they offer unique insights into ultra-dense matter.
• The central density of 1.4 M$_\odot$ neutron stars lies below the transition density, implying that their properties are less sensitive to high-density extrapolations.
• Future NICER radius measurements of PSR J1614-2230 and PSR J0740+6620 are strongly motivated, as they could further constrain the high-density equation of state.
• The study demonstrates that chiral EFT models require modification beyond 2.64$ n_0 $ to be consistent with current neutron star observations and the existence of 2.6 M$_\odot$ stars.