Effects of Nontrivial Topology on Neutron Star Rotation and its Potential Observational Implications

TL;DR

The paper investigates how nontrivial topology in neutron star cores, modeled as Nambu-Goto cosmic strings with tension $\mu$, can couple to stellar rotation and generate pulsar glitches along with characteristic gravitational-wave signals. By formulating a rotating NS spacetime with a deficit parameter $\alpha = 1 - 4\mu$ and solving the rotational equation across hadronic and hybrid EOS, the study reveals a semi-universal relation between the fractional spin change $\Delta\Omega/\Omega$ and the string tension via $G\mu$, enabling inference of string strength from observations. It also derives the energy budget including dipole and defect-induced gravitational-wave losses, reproduces glitch-like spin-up events via a phenomenological fit, and predicts a combined GW signature consisting of continuous emission plus bursts scaling as $(G\mu)^{5/3}$ that could be detectable by current or near-future detectors. Overall, the work links topological defects to observable NS phenomenology, offering a potential route to test for CSs in dense matter through pulsar timing and gravitational-wave observations.

Abstract

Rotational irregularities are one of the prominent observational features that most pulsars exhibit. These glitches, which are sudden increases in spin angular velocity, remains an open problem. In this study, we have investigated the potential role of nontrivial topological defects, specifically in the form of Nambu-goto-type CSs, and its connection to spin irregularities. Such CSs which are one-dimensional topological defects may be formed during various symmetry-breaking and phase transition scenarios and can interact with the neutron stars. In this work, we see that the appearance of such topological defects trapped within the core can lead to the coupling of the string tension with the angular velocity, leading to the abrupt rotational changes observed as pulsar glitches. We have further studied how these coupling may generate detectable gravitational waves as a mixture of continuous and burst signals. The evolution of cusps of CSs trapped within neutron stars and the neutron star's mass quadruple moment change due to rotation could produce distinctive gravitational wave signatures, well within the noise cutoff of advLIGO. Our study highlights a potential connection between topological defects, pulsar glitches, and gravitational wave emissions, offering a possible avenue for observationally testing the presence of CSs and their astrophysical effects.

Figures (4)

• Figure 1: The curves represent different theoretical models of the (EOS) of NS matter. These models include both hadronic (Had) and hybrid (Hyb) EOS. The shaded region at the top around 2.35 solar masses corresponds to the mass measurement of PSR J0952-0607, which is currently considered one of the heaviest known NSs. This region serves as an upper constraint on the NS mass. The blue vertical band around 12 km corresponds to the radius constraint derived from observations of PSR J0030+0451, based on NICER measurements. This provides a constraint on the NS radius. Almost all curves fall within the observed mass-radius limits suggests that these models remain viable under current observations.
• Figure 2: (left panel) The plot represents a model of rotational frame dragging for a compact star normalized with the central angular velocity, with varying values of $G\mu$ (order of $10^{-7}$) corresponding to different levels of gravitational tension or the energy density of the string. As the radial distance from the center increases, the frame dragging velocity slightly exceeds the central angular velocity, and this effect becomes more pronounced as $G\mu$ increases implying that in systems with stronger gravitational interactions (or higher energy density), rotational effects are more pronounced, particularly in the outer regions. (right panel) The plot represents the relationship between the fractional change in angular velocity $\Delta\Omega/\Omega$ and a normalized energy density of the string tension $\mu/\mu_0$. This plot demonstrates a power-law relationship due to the linear trend on the log-log scale and the fit function models an increasing power law. The consistency of the data points across various EoSs suggests that this relationship holds over a wide range of conditions, making it a robust characteristic.
• Figure 3: (left panel) The plot illustrates a time-based analysis of the change in the angular velocity of the NS $\Delta\Omega$ measured in $10^{-5}$ s$^{-1}$. The plot consists of two distinct time regimes: pre-spin-up and post-spin-up events. At $t=0$ s, a significant change in $\Delta\Omega$ is initiated due to the appearance of a TD, marking the onset of a spin-up event. The spin-up event induce a perturbation or decay behavior in $\Delta\Omega$ indicating the influence of a damping mechanism due to the gravitational wave damping from CS cusps, which affects the system’s angular velocity. The fit function used effectively models this decay, and can be used as a predictive tool for analyzing similar phenomena. (right panel) The plot shows analysis of changes in $\Delta\Omega$ as a function of time, for family of curves each with different angular velocity change and damping rate (corresponding to particular $G\mu$ and gravitational radiation rate). Several pulsars are overlapped and labeled, with curves representing their behaviors during and after a "glitch" event. The very slow decay in pre-spin-up indicates a gradual energy loss, due to dipole radiation.
• Figure 4: The plot presents a comparison between continuous gravitational waves (GW) and gravitational wave bursts, focusing on the strain amplitude $h_+/h_0$ as a function of time. The upper section shows sensitivity limits for gravitational wave detection, particularly from advLIGO, with varying values of $G\mu$. The blue waveform represents continuous gravitational waves (GW) over time due to rotating NS. The red vertical lines indicate the presence of gravitational wave bursts due to CS cusps at around $t=5$ s, $t=10$ s, and $t=20$ s (shown at different times only for comparison) for $G\mu=10^{-7}$, $10^{-8}$ and $10^{-9}$ respectively.