Constraint on the maximum mass of neutron stars using GW170817 event

Masaru Shibata, Enping Zhou, Kenta Kiuchi, and Sho Fujibayashi

Phys. Rev. D 100, 023015 – Published 26 July 2019

Abstract

We revisit the constraint on the maximum mass of cold spherical neutron stars coming from the observational results of GW170817. We develop a new framework for the analysis by employing both energy and angular momentum conservation laws as well as solid results of latest numerical-relativity simulations and of neutron stars in equilibrium. The new analysis shows that the maximum mass of cold spherical neutron stars can be only weakly constrained as $M_{\max} ≲ 2.3 M_{⊙}$ . Our present result illustrates that the merger remnant neutron star at the onset of collapse to a black hole is not necessarily rapidly rotating and shows that we have to take into account the angular momentum conservation law to impose the constraint on the maximum mass of neutron stars.

Received 9 May 2019

DOI:https://doi.org/10.1103/PhysRevD.100.023015

Physics Subject Headings (PhySH)

Gravitational wave sources

Neutron stars & pulsars

Numerical relativity

Gravitation, Cosmology & Astrophysics

Authors & Affiliations

Masaru Shibata^1,2, Enping Zhou ¹, Kenta Kiuchi^1,2, and Sho Fujibayashi¹

¹Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Muhlenberg 1, Potsdam-Golm 14476, Germany
²Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, 606-8502, Japan

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Issue

Vol. 100, Iss. 2 — 15 July 2019

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Images

Figure 1
Several important curves for rigidly rotating neutron stars in the plane of the gravitational mass ( $M$ ) as a function of the central density ( $ρ_{c}$ ). In this example, we employ EOS-6 (see Sec. 3) as the neutron-star equation of state. The lower and upper solid curves show the sequences of nonrotating neutron stars (labeled by $J = 0$ ) and rigidly rotating neutron stars at mass shedding limits. The dashed curve shows the sequence of neutron stars that are marginally stable to gravitational collapse (the sequence of the turning points); the neutron stars in the lower-density side of this dashed curve are stable, otherwise they are unstable. The filled circles denote the predicted points at the onset of collapse for GW170817 in this model equation of state with $M_{out} + M_{eje} = 0.048$ , 0.096, and $0.150 M_{⊙}$ (from higher to lower mass: see Sec. 3).
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Figure 2
Gravitational mass, $M$ , ratio of $M$ to $M_{\max}$ ( $f_{r}$ ), ratio of baryon rest mass to the gravitational mass, $f_{MS}$ , and rotational kinetic energy $T = J Ω / 2$ as functions of $J$ for rigidly rotating neutron stars along the marginally stable sequence (i.e., along the turning point sequence) with selected equations of state (see Table 1). Note that $M$ at $J = 0$ is $M_{\max}$ .
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Figure 3
Relation between $f_{0} / f_{MS}$ and $M_{\max}$ for marginally stable rigidly rotating neutron stars with several equations of state listed in Table 1. The lower and upper ends of each uncertainty range correspond to $J = 0$ and $J = J_{\max}$ , respectively. The numbers attached in each data denote the model equations of state. The tilted lines show the relation of Eq. (2.17) for $f_{r} = 1.20, 1.18, 1.16, \dots, 1.04, 1.02$ , and 1.00 (from left to right) with $(M_{out} + M_{eje}) / f_{MS} = 0.04 M_{⊙}$ (left panel) and $0.08 M_{⊙}$ (right panel) and with $M = 2.74 M_{⊙}$ . The thick lines are for $f_{r} = 1.20$ , 1.10, and 1.00.
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Figure 4
Top-left, top-right, and bottom-left panels display $E_{GW, p}$ and $E_{ν}$ as functions of $M_{out} + M_{eje}$ for EOS-3, 6, and 9, respectively, and for the $1.35 - 1.40 M_{⊙}$ case. Associated with the uncertainties in $J_{0}$ and $E_{GW, i}$ , an uncertainty exists in $E_{GW, p}$ and $E_{ν}$ . The three curves for each plot in the top-left, top-right, and bottom-left panels denote the upper and lower bounds (thick curves) as well as the central value (thin curve) for $E_{GW, p}$ and $E_{ν}$ . The horizontal dot-dot line shows $E_{GW, p} = 0.125 M_{⊙} c^{2}$ (plausible upper limit of $E_{GW, p}$ [22]). Bottom-right panel shows $f_{r}$ as a function of $M_{out} + M_{eje}$ for EOS-1, 3, 6, 9, and 11. For EOS-1, the solution for $f_{r}$ does not exist for small value of $M_{out} + M_{eje}$ . For EOS-11, $E_{ν}$ becomes negative for $M_{out} + M_{eje} \leq 0.02 M_{⊙}$ and $\geq 0.127 M_{⊙}$ , and, thus, we do not plot the solution for these ranges.
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Figure 5
Left panel: $f_{0}$ for the case of $1.20 - 1.55 M_{⊙}$ and $1.35 - 1.40 M_{⊙}$ binary neutron stars and $f_{MS}$ for spherical maximum-mass stars as a function of the maximum mass for a variety of equations of state. Right panel: The same as the left panel but for $f_{0} / f_{MS}$ . We plot the data with equations of state by which $2 M_{⊙}$ neutron stars are reproduced and dimensionless tidal deformability of $1.35 M_{⊙}$ star, $Λ_{1.35}$ , is smaller than 1000.
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