Bounds on the speed of sound in dense matter, and neutron star structure

Abstract

The accurate determination of the maximum mass of the neutron stars is one of the most important tasks in astrophysics. It is directly related to the identification of the black holes in the universe, the production of neutron stars from the supernovae explosion, and the equation of state (EoS) of dense matter. However, not only the EoS is directly connected with neutron star masses, but also the speed of sound in dense matter is a crucial quantity which characterizes the stiffness of the EoS. The upper bound of the speed of sound imposes strong constraints on the maximum mass of neutron stars. However, this upper bound remains still an open issue. Recent observations, of binary neutron star systems, offer the possibility of measuring with high accuracy both the mass and the tidal polarizability of the stars. We study possible effects of the upper bound of the speed of sound on the upper bound of the mass and the tidal polarizability. We conclude that these kinds of measurements, combined with recent observations of neutron stars with masses close to $2 M_{\odot}$, will provide robust constraints on the equation of state of hadronic matter at high densities.Comment: 17 pages, 11 figure

Sound velocity and tidal deformability in compact stars

“…This "no-go" argument has been given support by several other works, notably in Refs. [5][6][7]. Furthermore exceeding from the conformal velocity in certain standard nuclear model results has been suggested to be associated with a generic feature of scalar extensions of general relativity [8].…”

Constraints on neutron stars equation of state using the tidal deformability derived from BNS mergers

“…During the late phase of the inspiral, the tidal interaction between the two compact bodies has a significant role to their gravitational field and orbital motion. The induced tidal field (; affects the quadrupole moment (; , and it's described by [5]:…”

“…The tidal parameter " , known as tidal love number, depends on the structure of the neutron star, i.e. its mass and equation of state, given by [5,6]:…”

Questions Related to the Equation of State of High-Density Matter

“…In sum, it is reasonable to take into account the well-established M > ∼ 2 M neutron stars when constraining equations of state. There are, for example, several papers that argue that these masses demonstrate that the conformal limit on the speed of sound, c s < c/ √ 3, is violated inside neutron stars (e.g., [25][26][27][28]). There are also long-standing nuclear arguments that M max < 2.9-3.2 M [29,30].…”