Scalarized neutron stars with a highly relativistic core in scalar-tensor gravity

TL;DR

The paper investigates scalar-tensor gravity in the regime of highly relativistic neutron stars, where cores can harbor regions with $\tilde{T}>0$ that trigger scalarization. It demonstrates the emergence of multiple scalarized branches at fixed central density due to oscillatory scalar-field profiles inside the star, a phenomenon present for both negative and positive $\beta$ and explained via differences between DEF and MO coupling functions. By solving the modified TOV equations in the Einstein frame and applying slow-rotation and tidal perturbations, the authors compute the moment of inertia and tidal deformability for massless and massive scalar fields, revealing that scalarized NSs generally have smaller $M$, $R$, $I$, and $\lambda$ than GR for the same ADM mass, with the scalar mass suppressing these effects. The results provide concrete, observable predictions for pulsar-timing and gravitational-wave experiments and highlight how the boundedness of the effective coupling differentiates DEF from MO dynamics in highly compact stars.

Abstract

Compact stars in scalar-tensor (ST) gravity have been extensively investigated, but relatively few studies have focused on highly relativistic neutron stars (NSs) with an extremely dense core region where the trace of the energy-momentum tensor reverses its sign. In this regime, we identify the origin of the phenomenon where {\it multiple} scalarized solutions exist for a {\it fixed} central density, arising from the oscillatory profile of the scalar field inside the star. This origin further indicates that the multi-branch structure emerges for both negative and positive $β$, the quadratic-term coefficient in the effective coupling function between the scalar field and conventional matter in the Einstein frame. By comparing the Damour--Esposito-Farèse and Mendes-Ortiz models of the ST gravity, we demonstrate that their distinct scalarization behaviors stem from whether the effective coupling function is bounded. We also compute for scalarized NSs with a highly relativistic dense core in ST theories the moment of inertia and tidal deformability that are relevant to pulsar-timing and gravitational-wave experiments.

Figures (10)

• Figure 1: Illustration of scalarization in the massless DEF theory for various negative $\beta$ values. The top, middle, and bottom panels display the baryonic mass $M_{\rm b}$ as a function of (rescaled) central density $\tilde{\varepsilon}_c$, the mass-radius relation, and the moment of inertia $I$ of the NS, respectively.
• Figure 2: Illustration of scalarization in massive DEF theory for various negative $\beta$ values. The scalar mass corresponds to a Compton wavelength of $2\pi\cdot10\,\mathrm{km}$. The top, middle, and bottom panels display the mass-radius relation, the moment of inertia, and the tidal deformability of NSs, respectively. The $\beta=-6$ case is not sufficient to trigger scalarization in this case.
• Figure 3: The figure illustrates properties for different EOSs of NSs. In the top panel, the critical radius is plotted as a function of the central mass density normalized by the nuclear saturation density, with unstable configurations indicated by dashed lines. The bottom panel displays a conventional mass-radius diagram for NSs, where the critical radius is represented by the colorbar. The red line and shaded region correspond to the constraint value and uncertainty, $\mathscr{C}=0.262^{+0.011}_{-0.017}$, from Ref. Podkowka:2018gib, indicating the minimum compactness that NSs should have in order to possess a region where $\tilde{T}>0$.
• Figure 4: The asymptotic scalar field value $\varphi_0$ versus the central scalar field value $\varphi_c$ for various central pressure of NSs in the massless DEF theory (upper panel) and massless MO theory (bottom panel) with $\beta=100$. The EOS is taken to be the polytropic AP4 model.
• Figure 5: The scalar field profiles of five scalarized NS solutions are shown, corresponding to the five smallest central values of the scalar field (from top to bottom, $\varphi_c$ increases successively) in the massless DEF theory with $\beta = 100$, $\tilde{\varepsilon}_c = 2 \times 10^{15}\,\mathrm{g\cdot cm^{-3}}$, and the AP4 EOS. Red dots denote the zero points of the scalar field profiles. The yellow dots labeled with '0' mark the designated boundary condition $\varphi(\rho\to\infty)=0$, while each positive integer indicates the number of nodes in the corresponding solution. Each subsequent scalarized solution possesses one more node than the previous one.