Mass-radius relation, moment of inertia, and tidal love numbers of anisotropic neutron stars in f (R,T) gravity

TL;DR

The paper studies anisotropic neutron stars in $f(R,T)$ gravity with the simple $f(R,T)=R+2\beta T$ form and Horvat anisotropy, constrained by GW170817 and GW190814. It derives modified field and TOV equations, computes the slow-rotation moment of inertia, and evaluates polar and axial tidal Love numbers and tidal deformability for two EoS across a grid of $\alpha$ and $β$. The results show $\alpha$ has the dominant effect on mass, radius, and TLNs, while $β$ provides a smaller, systematic modulation; in particular, BPS$+β$ NSs can satisfy GW170817 constraints for certain $α,β$, whereas QHD NSs tend to yield smaller $\Lambda$ and can align with GW190814 under specific anisotropy. Overall, the study identifies NSs within this MG framework that could correspond to the GW170817 binary components and the GW190814 secondary, underscoring the role of anisotropy and $f(R,T)$ coupling in heavy NS phenomenology.

Abstract

The mass-radius relation, moment of inertia, and tidal love numbers of anisotropic neutron stars (NSs) have been investigated in $f(R,T)$ gravity by imposing two equations of state (EoS). We use the simplest form $f(R,T)=R+2βT$ model and adopt the anisotropy approach called Horvat model. To examine the viability of our calculations, we utilize the constraints from GW170817 and GW190814 observations. Moreover, we consider three values of $β$, i.e. $β=0$, $β=-0.01$, $β=-0.02$ and four anisotropy parameters $α$, i.e. $α=-0.12$, $α=-0.06$, $α=0.06$, $α=0.12$. Our findings suggest that all physical quantities depend on both parameters $α$ and $β$. Nevertheless, the impact of $α$ is much more significant than $β$. The calculation of masses satisfy each used constraints for specific values of $α$ and $β$. In the case of the moment of inertia, the results are compatible with the constraint obtained from radio observation of heavy pulsar. On the other hand, the tidal deformability of the NSs composed of one EoS satisfy the GW170817 constraint while the NSs composed of the other one EoS are too small. These small numbers can be interpreted as the property of secondary object observed in GW190814. As a result, our theoretical investigation of NSs constructed with two EoS can be NSs candidates for GW170817 and GW190814, respectively.

Figures (7)

• Figure 1: Mass of Neutron stars vs radius for two different EoS plotted based on variations of $\beta$ and $\alpha$, where (a)$\beta=0\space\mathrm{(GR)}$, (b) $\beta=-0.01$, and (c) $\beta=-0.02$. The vertical and horizontal cyan+red regions in the $M$ vs $r$ curve are the additional constraints from $\mathrm{GW170817}$ showing areas that cannot be occupied by neutron stars (excluded regions). The horizontal cyan+red regions indicate maximum masses that are too small for neutron stars. Meanwhile, the vertical cyan+red regions indicate that stars within these regions have radii that are too small.bauswein2017neutronThe two horizontal black lines are the allowed radii for neutron stars according to $\mathrm{GW170817}$. The allowed radii of NSs with masses of $1.4\space M_{\odot}$ and $2.0\space M_{\odot}$ are $R_{1.4}=12.42_{-0.99}^{+0.52}\space\mathrm{km}$ and $R_{2.0}=12.12_{-1.23}^{+1.11}\space\mathrm{km}$.altiparmak2022sound.
• Figure 2: Moment of inertia vs radius for two different EoS plotted based on variations of $\beta$ and $\alpha$, where (a)$\beta=0\space\mathrm{(GR)}$, (b) $\beta=-0.01$, and (c) $\beta=-0.02$.
• Figure 3: Polar TLNs vs compactness for QHD EoS plotted based on variations of $\beta$ and $\alpha$, where (a)$\beta=0\space\mathrm{(GR)}$, (b) $\beta=-0.01$, and (c) $\beta=-0.02$.
• Figure 4: Polar TLNs vs compactness for BPS EoS plotted based on variations of $\beta$ and $\alpha$, where (a)$\beta=0\space\mathrm{(GR)}$, (b) $\beta=-0.01$, and (c) $\beta=-0.02$.
• Figure 5: Axial TLNs vs compactness for two different EoS plotted based on variations of $\beta$ and $\alpha$, where (a)$\beta=0\space\mathrm{(GR)}$, (b) $\beta=-0.01$, and (c) $\beta=-0.02$.