Constraining scalar-tensor theories of gravity from the most massive neutron stars

Scalar-tensor (ST) theories of gravity are natural phenomenological extensions to general relativity. Although these theories are severely constrained both by solar system experiments and by binary pulsar observations, a large set of ST families remain consistent with these observations. Recent work has suggested probing the unconstrained region of the parameter space of ST theories based on the stability properties of highly compact neutron stars. Here, the dynamical evolution of very compact stars in a fully nonlinear code demonstrates that the stars do become unstable and that the instability, in some cases, drives the stars to collapse. We discuss the implications of these results in light of recent observations of the most massive neutron star yet observed. In particular, such observations suggest that such a star would be subject to the instability for a certain regime; its existence therefore supports a bound on the ST parameter space.

Figure 1

Characterization of initial stellar models. Top: Mass versus compactness of spherical, non-rotating neutron star equilibrium configurations for different polytropic exponent (e.g. stiffness) in the polytropic EoS $p=K{\rho }^{\mathrm{\Gamma }}$. The transition between models with $T$ everywhere negative to models with $T$ positive in a central region is marked (solid circles) for each value of $\mathrm{\Gamma }$. The stable branch lies on the left of the maximum of the curve. Solutions for three microphysical EoS are also included, showing that their structure lies between that of the polytropes with $\mathrm{\Gamma }=2.5$ and $\mathrm{\Gamma }=3$. Bottom: Mass versus compactness for rigidly rotating neutron stars with fixed $\mathrm{\Gamma }=3$ but different rotational frequencies. Notice that the transition in $T$ lies at roughly the same compactness as for the nonrotating models.

Figure 2

Dynamics of a highly compact ($C=0.29$), non-rotating star. Top: Central value of the rest-mass density, ${\rho }_c$, as a function of time. Bottom: Central value of the scalar field, ${\phi }_c$. Note that the $\beta =0$ solution is stable whereas the scalar field grows initially for nonvanishing $\beta$. However, only for $\beta >{\beta }_{\mathrm{crit}}$ does the central density grow apparently without bound, collapsing to a black hole. For $\beta <{\beta }_{\mathrm{crit}}$, the scalar field oscillates, sometimes transitioning to negative values. The solutions with $\beta =109$ and 115 eventually collapse. Here ${\beta }_{\mathrm{crit}}\approx 90\pm 10$ with the uncertainty arising due to late time instability.

Figure 3

Evolution of the scalar field for a highly compact ($C=0.29$), nonrotating star with $\beta =80$. The scalar field as a function of radius at different times during the evolution is shown. Also shown is the equilibrium configuration (solid black) within ST with the same central density as the initial data. At late times the solution relaxes to the equilibrium configuration with a slowly damped, oscillating central region.

Figure 4

Stability region as a function of compactness for nonrotating solutions. The value of $\beta$ at which our numerical evolutions collapse to black hole are shown (blue dots) along with a rough estimate of its uncertainty. The results from the linearized analysis for the eng case of Ref. [4] (because of the similarity of that case with the $\mathrm{\Gamma }=3$ case) are also shown (red dotted curve) for comparison. In the region between the two curves, the instability is quickly suppressed by nonlinear effects and the star settles into a stable state. A vertical line (black solid line) indicates the compactness of the most massive star observed assuming a radius of 10.5 km [22]. The shaded region (green) around that vertical line indicates the uncertainty in radius (i.e., assuming half of the maximum error) leading to a range of 10–11 km.