Tidal deformability of neutron and hyperon stars within relativistic mean field equations of state

We systematically study the tidal deformability for neutron and hyperon stars using relativistic mean field equations of state (EOSs). The tidal effect plays an important role during the early part of the evolution of compact binaries. Although, the deformability associated with the EOSs has a small correction, it gives a clean gravitational wave signature in binary inspiral. These are characterized by various Love numbers $k_l\left(l=2,3,4\right)$, that depend on the EOS of a star for a given mass and radius. The tidal effect of star could be efficiently measured through an advanced LIGO detector from the final stages of an inspiraling binary neutron star merger.

Figure 1

The equations of state obtained for nuclear and hypernuclear matter under charge neutrality as well as the $\beta$-equilibrium condition for G2 [24], FSUGold2 [47], FSUGold [27], and NL3 [37] force parameters are compared with the empirical data [48] (shaded area in the graph) for $r_{ph}=R$ with the uncertainty of $2\sigma$. Here, $R$ and $r_{ph}$ are the neutron radius and the photospheric radius, respectively.

Figure 2

The mass-radius profile for the force parameters like G2 [24], FSUGold2 [47], FSUGold [27], and NL3 [37] used. The solid circles ($r_{ph}=R$) and triangles ($r\gg R$) represent the observational constraints [48], where $r_{ph}$ is the photospheric radius. The vertical shaded region corresponds to the recent observation [30, 31].

Figure 3

The tidal Love numbers $k_2,k_3,k_4$ as a function of the mass of the four selected EOSs of the neutron star.

Figure 4

Same as Fig. 3 but for hyperon star.

Figure 5

Surficial Love number $h_l$ as a function of compactness $C$ of a neutron star, for selected values of $l$.

Figure 6

The magnetic tidal Love number for selected EOSs.

Figure 7

The tidal deformability $\lambda$ as a function of the compactness $C$ for the four EOS with and without hyperon.

Figure 8

Tidal deformability $\lambda$ of a single neutron star as a function of the neutron-star mass for a range of EOSs. The estimate of uncertainties in measuring $\lambda$ for equal mass binaries at a distance of $D=100$ Mpc is shown for the advanced LIGO detector in shaded area. (b) Same as (a), but for hyperon star.

Figure 9

(a), (c) The mass cut-off frequency $f_c$ profile of normal and hyperon stars using four EOSs. (b) The tidal deformability with cut-off frequency plot of the neutron star. (d) Same as (b), but for hyperon star.