arXiv subjects

Tjonnie Guang Feng Li

Publications and source records attributed to Tjonnie Guang Feng Li.

17 recordsLinked to original sources

arXiv2026

A Multidimensional General-Relativistic Boltzmann Solver for Neutrino Transport: Implementation, Discretization and Optimization

We present the implementation of a multidimensional general-relativistic Boltzmann solver for neutrino transport using the finite volume method. We extend the general-relativistic magnetohydrodynamics solver \texttt{Gmunu} to discretize the full $6$D phase space. We discretize the momentum space in spherical coordinates in the comoving frame, and the position space in the lab frame in Cartesian, cylindrical or spherical coordinates. As in the M1 scheme, we expand the interaction kernels up to first order in a Legendre series. We present a discretization scheme that ensures consistency between the number-conservative and non-conservative formulations in empty flat spacetime, multiple dimensions and coordinate systems, conserves energy to $\sim 1\%$ with $20$ energy bins in 1D tests. We discuss optimizations of the implicit solver for stiff source terms to minimize its computational cost. In particular, we introduce a method that leverages the Legendre expansion of the kernels to reduce the dimensionality of the problem. In a 1D core-collapse supernova snapshot, our method yields a speed-up factor of $300$ compared to a full-matrix LU method for $14$ angular bins when including energy- and species-coupling interactions. Finally, we validate our implementation on standard test cases and report quadratic convergence in space, energy and propagation angles. We compare our solver to the M1 scheme in simplified 1D configurations and find differences of about $10\%$ in the free-streaming luminosities in relaxation test cases, which we attribute primarily to the M1 closure relation. The average energies, on the other hand, agree between the two methods. We compare both methods on a core-collapse supernova test case and find an overall good agreement in the fluid variables' profiles at the time of core bounce for $20$ energy bins.

astro-ph.HE↗

arXiv2025

Fundamental modes of rotating neutron stars with various degrees of differential rotation in dynamical spacetimes

Violent astrophysical events, including core-collapse supernovae and binary neutron star mergers, can result in rotating neutron stars with diverse degrees of differential rotation. Oscillation modes of these neutron stars could be excited and emit strong gravitational waves. Detecting these modes may provide information about neutron stars, including their structures and dynamics. Hence, dynamical simulations were employed to construct relations for quantifying the oscillation mode frequency in previous studies. Specifically, linear relations for the frequencies of fundamental $l=0$ quasi-radial mode $f_{F}$ and fundamental $l=2$ quadrupolar mode $f_{^2f}$ were constructed by simulations with the Cowling approximation. Nevertheless, these relations can overestimate $f_{F}$ and underestimate $f_{^2f}$ up to $\sim 30\%$. Furthermore, it has yet to be fully studied how the degree of differential rotation affects $f_{F}$ and $f_{^2f}$. Here, for the first time, we consider both various degrees of differential rotation $\Tilde{A}$ and dynamical spacetime to construct linear relations for quantifying $f_{F}$ and $f_{^2f}$. Through 2D axisymmetric simulations, we first show that both $f_{F}$ and $f_{^2f}$ scale almost linearly with the stellar compactness $M/R$ for different values of $\Tilde{A}$. We also observe the quasi-linear relations for both $f_{F}$ and $f_{^2f}$ with the kinetic-to-binding energy ratio $T/|W|$ for different $\Tilde{A}$ values. Finally, we constructed linear fits that can quantify $f_{F}$ and $f_{^2f}$ by $T/|W|$. Consequently, this work updated the relations for the fundamental modes of rotating neutron stars with differential rotations in dynamical spacetime.

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arXiv2025

Magnetic effects on fundamental modes in rotating neutron stars with a purely toroidal magnetic field

Electromagnetic and gravitational-wave signals from neutron stars are shaped by rapid rotation and strong magnetic fields. Determining these properties is essential to interpret such signals, but current measurements are limited: rotation estimates rely on electromagnetic detections and assume uniform rotation, while inferring interior magnetic fields remains ambiguous due to a lack of direct observations. Measuring the excited fundamental modes of neutron stars in gravitational-wave signals offers a promising solution, as these modes encode information about stellar composition, structure, and dynamics. Previous studies have examined the individual effects of rotation and magnetic fields on these modes, identifying magnetic suppression and establishing linear relations for the frequencies of the fundamental $l=0$ quasi-radial mode $f_F$ and $l=2$ quadrupolar mode $f_{^2f}$. However, few have investigated the combined influence of rotation and magnetic fields. Here, for the first time, we consider both rotation and a toroidal magnetic field to construct linear relations for quantifying $f_F$ and $f_{^2f}$, showing that their combined effects can be constrained by detecting these modes. Using 2D axisymmetric simulations, we demonstrate that quasi-linear relations between $f_F$, $f_{^2f}$, stellar compactness $M/R$, and kinetic-to-binding energy ratio $T/|W|$ persist even with a toroidal magnetic field. The slope of these relations depends on the toroidal magnetization constant $K_\mathrm{m}$. Additionally, measuring the frequency ratio $f_{^2f}/f_F$ enables inference of $T/|W|$ and the maximum magnetic field strength $\mathcal{B}_\mathrm{max}$. Lastly, we show that differential rotation causes only minor deviations from predictions for uniform rotation. Thus, this work demonstrates that rotational and magnetic properties of neutron stars can be inferred from their fundamental modes.

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arXiv2025

Gravitational wave signatures from the phase-transition-induced collapse of a magnetized neutron star

Strong magnetic fields make neutron stars potential sources of detectable electromagnetic and gravitational-wave signals. Hence, inferring these magnetic fields is critical to understand the emissions of neutron stars. However, due to the lack of direct observational evidence, the interior magnetic field configuration remains ambiguous. Here, for the first time, we show that the internal magnetic field strength along with the composition of a neutron star can be directly constrained by detecting the gravitational waves from the \emph{phase-transition-induced collapse} of a magnetized neutron star. By dynamically simulating this collapsing event, we first find that the dominant peaks in the gravitational waveform are the fundamental $l=0$ quasi-radial $F$ mode and the fundamental $l=2$ quadrupolar $^2f$ mode. We next show that the maximum gravitational wave amplitude $|h|_\mathrm{max}$ increases with the maximum magnetic field strength of the interior toroidal field $\mathcal{B}_\mathrm{max}$ until the maximum rest-mass density at bounce $ρ_\mathrm{max,b}$ decreases due to the increasing $\mathcal{B}_\mathrm{max}$. We then demonstrated that the magnetic suppression of fundamental modes found in our previous work remains valid for the hybrid stars formed after the phase-transition-induced collapses. We finally show that measuring the frequency ratio between the two fundamental modes $f_{^2f}/f_{F}$ allows one to infer $\mathcal{B}_\mathrm{max}$ and the baryonic mass fraction of matter in the mixed phase $M_\mathrm{mp} / M_{0}$ of the resulting hybrid star. Consequently, taking $\mathcal{B}_\mathrm{max}$ and $M_\mathrm{mp} / M_{0}$ as examples, this work has demonstrated that much information inside neutron stars could be extracted similarly through measuring the oscillation modes of the stars.

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arXiv2024

Formation of a magnetized hybrid star with a purely toroidal field from phase-transition-induced collapse

Strongly magnetized neutron stars are popular candidates for producing detectable electromagnetic and gravitational-wave signals. Gravitational collapses of neutron stars triggered by a phase transition from hadrons to deconfined quarks in the cores could also release a considerable amount of energy in the form of gravitational waves and neutrinos. Hence, the formation of a magnetized hybrid star from such a \emph{phase-transition-induced collapse} is an interesting scenario for detecting all these signals. These detections may provide essential probes for the magnetic field and composition of such stars. Thus far, a dynamical study of the formation of a magnetized hybrid star from a \emph{phase-transition-induced collapse} has yet to be realized. Here, we investigate the formation of a magnetized hybrid star with a purely toroidal field and its properties through dynamical simulations. We find that the maximum values of rest-mass density and magnetic field strength increase slightly and these two quantities are coupled in phase during the formation. We then demonstrate that all microscopic and macroscopic quantities of the resulting hybrid star vary drastically when the maximum magnetic field strength goes beyond a threshold of $\sim 5 \times 10^{17}$ G but they are insensitive to the magnetic field below this threshold. Specifically, the magnetic deformation makes the rest-mass density drop significantly, suppressing the matter fraction in the mixed phase. These behaviors agree with those in the equilibrium models of previous studies. Therefore, this work provides a solid support for the magnetic effects on a hybrid star.

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arXiv2023

General-relativistic radiation transport scheme in Gmunu II: Implementation of novel microphysical library for neutrino radiation -- Weakhub

We introduce \texttt{Weakhub}, a novel neutrino microphysics library that provides opacities and kernels beyond conventional interactions used in the literature. This library includes neutrino-matter, neutrino-photon, and neutrino-neutrino interactions, along with corresponding weak and strong corrections. A full kinematics approach is adopted for the calculations of $β$-processes, incorporating various weak corrections and medium modifications due to the nuclear equation of state. Calculations of plasma processes, electron neutrino-antineutrino annihilation, and nuclear de-excitation are included. We also present the detailed derivations of weak interactions and the coupling of them to the two-moment based general-relativistic multi-group radiation transport in the \texttt{G}eneral-relativistic \texttt{mu}ltigrid \texttt{nu}merical (\texttt{Gmunu}) code. We compare the neutrino opacity spectra for all interactions and estimate their contributions at hydrodynamical points in core-collapse supernova and binary neutron star postmerger remnant, and predict the effects of improved opacities in comparison to conventional ones for a binary neutron star postmerger at a specific hydrodynamical point. We test the implementation of the conventional set of interactions by comparing it to an open-source neutrino library \texttt{NuLib} in a core-collapse supernova simulation. We demonstrate good agreement with discrepancies of less than $\sim 10\%$ in luminosity for all neutrino species, while also highlighting the reasons contributing to the differences. To compare the advanced interactions to the conventional set in core-collapse supernova modelling, we perform simulations to analyze their impacts on neutrino signatures, hydrodynamical behaviors, and shock dynamics, showing significant deviations.

astro-ph.HE↗

arXiv2023

General-relativistic radiation transport scheme in $\texttt{Gmunu}$ I: Implementation of two-moment based multi-frequency radiative transfer and code tests

We present the implementation of two-moment based general-relativistic multi-group radiation transport module in the $\texttt{G}$eneral-relativistic $\texttt{mu}$ltigrid $\texttt{nu}$merical ($\texttt{Gmunu}$) code. On top of solving the general-relativistic magnetohydrodynamics and the Einstein equations with conformally flat approximations, the code solves the evolution equations of the zeroth- and first-order moments of the radiations. Analytic closure relation is used to obtain the higher order moments and close the system. The finite-volume discretisation has been adopted for the radiation moments. The advection in spatial and frequency spaces are handled explicitly. In addition, the radiation-matter interaction terms, which are very stiff in the optically thick region, are solved implicitly. Implicit-explicit Runge-Kutta schemes are adopted for time integration. We test the implementation with a number of numerical benchmarks from frequency-integrated to frequency dependent cases. Furthermore, we also illustrate the astrophysical applications in hot neutron star and core-collapse supernovae modellings, and compare with other neutrino transport codes.

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arXiv2023

Oscillations of Highly Magnetized Non-rotating Neutron Stars

Highly magnetized neutron stars are promising candidates to explain some of the most peculiar astronomical phenomena, for instance, fast radio bursts, gamma-ray bursts, and superluminous supernovae. Pulsations of these highly magnetized neutron stars are also speculated to produce detectable gravitational waves. In addition, pulsations are important probes of the structure and equation of state of the neutron stars. The major challenge in studying the pulsations of highly magnetized neutron stars is the demanding numerical cost of consistently solving the nonlinear Einstein and Maxwell equations under minimum assumptions. With the recent breakthroughs in numerical solvers, we investigate pulsation modes of non-rotating neutron stars which harbour strong purely toroidal magnetic fields of $10^{15-17}$ G through two-dimensional axisymmetric general-relativistic magnetohydrodynamics simulations. We show that stellar oscillations are insensitive to magnetization effects until the magnetic to binding energy ratio goes beyond 10%, where the pulsation mode frequencies are strongly suppressed. We further show that this is the direct consequence of the decrease in stellar compactness when the extreme magnetic fields introduce strong deformations of the neutron stars.

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arXiv2022

An extension of Gmunu: General-relativistic resistive magnetohydrodynamics based on staggered-meshed constrained transport with elliptic cleaning

We present the implementation of general-relativistic resistive magnetohydrodynamics solvers and three divergence-free handling approaches adopted in the General-relativistic multigrid numerical (Gmunu) code. In particular, implicit-explicit Runge-Kutta schemes are used to deal with the stiff terms in the evolution equations for small resistivity. Three divergence-free handling methods are (i) hyperbolic divergence cleaning through a generalised Lagrange multiplier (GLM); (ii) staggered-meshed constrained transport (CT) schemes and (iii) elliptic cleaning though multigrid (MG) solver which is applicable in both cell-centred and face-centred (stagger grid) magnetic field. The implementation has been test with a number of numerical benchmarks from special-relativistic to general-relativistic cases. We demonstrate that our code can robustly recover a very wide range of resistivity. We also illustrate the applications in modelling magnetised neutron stars, and compare how different divergence-free handling affects the evolution of the stars. Furthermore, we show that the preservation of the divergence-free condition of magnetic field when staggered-meshed constrained transport schemes can be significantly improved by applying elliptic cleaning.

astro-ph.IM↗

arXiv2021

Lensing of Gravitational Waves as a Novel Probe of Graviton Mass

The diffraction patterns of lensed gravitational waves encode information about their propagation speeds. If gravitons have mass, the dispersion relation and speed of gravitational waves will be affected in a frequency-dependent manner, which would leave traces in the diffraction pattern if the waves are lensed. In this paper, we study how the alternative dispersion relation induced by massive gravitons affects gravitational waves lensed by point-mass lenses, such as intermediate-mass black holes. We find that the waveform morphology of lensed dispersive gravitational waves depends on the graviton mass more sensitively than their unlensed counterpart. Together with lensing amplification, the waveform-morphology modifications due to lensing can improve the measurement accuracy of the graviton mass. A single lensed gravitational-wave signal enables us to measure the graviton mass with an accuracy comparable with the combined measurement across $\mathcal{O}(10^3)$ unlensed signals. Our method allows us to incorporate lensed gravitational-wave signals into existing graviton-mass measurements. Our method can also be generalized to other lens types, gravitational-wave sources, and detector networks, preparing ourselves for thoroughly understanding the nature of gravitational waves in the era of lensed gravitational-wave astronomy.

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arXiv2021

Gmunu: Paralleled, grid-adaptive, general-relativistic magnetohydrodynamics in curvilinear geometries in dynamical spacetimes

We present an update of the General-relativistic multigrid numerical (Gmunu) code, a parallelized, multi-dimensional curvilinear, general relativistic magnetohydrodynamics code with an efficient non-linear cell-centred multigrid (CCMG) elliptic solver, which is fully coupled with an efficient block-based adaptive mesh refinement modules. Currently, Gmunu is able to solve the elliptic metric equations in the conformally flat condition (CFC) approximation with the multigrid approach and the equations of ideal general-relativistic magnetohydrodynamics by means of high-resolution shock-capturing finite volume method with reference-metric formularise multi-dimensionally in cartesian, cylindrical or spherical geometries. To guarantee the absence of magnetic monopoles during the evolution, we have developed an elliptical divergence cleaning method by using multigrid solver. In this paper, we present the methodology, full evolution equations and implementation details of our code Gmunu and its properties and performance in some benchmarking and challenging relativistic magnetohydrodynamics problems.

astro-ph.IM↗

arXiv2021

Ringdown Spectroscopy of Rotating Black Holes Pierced by Cosmic Strings

Multiple gauge theories predict the presence of cosmic strings with different mass densities $Gμ/c^2$. We derive an equation governing the perturbations of a rotating black hole pierced by a straight, infinitely long cosmic string along its axis of rotation and calculate the quasinormal-mode frequencies of such a black hole. We then carry out parameter estimation on the first detected gravitational-wave event, GW150914, by hypothesizing that there is a string piercing through the remnant, yielding a constraint of $Gμ/c^2 <3.8\times 10^{-3}$ at the 90\% confidence interval with a comparable Bayes factor with an analysis for a Kerr black hole without a string. In contrast to existing studies which focus on the mutual intersection of cosmic strings, or the cosmic string network, our work focuses on the intersection of a cosmic string with a black hole, with characteristics which can be identified in binary coalescence signals.

gr-qc↗

arXiv2020

Gravitational-wave asteroseismology with f-modes from neutron star binaries at the merger phase

Gravitational-wave signals from coalescing binary neutron stars can yield important information about the properties of nuclear-matter equation of state from the early part of the signal through tidal effects to the properties and oscillation frequencies of the merger product. We investigate a direct link between the properties of isolated neutron stars and their merger, by comparing the frequency of the fundamental oscillation mode ($f$-mode) of neutron stars with the gravitational-wave frequency associated with the merger of two neutron stars. We calculate the quadrupolar ($l=2$) $f$-mode oscillation ($f_{2f}$) of non-rotating and rotating neutron stars using a nonlinear hydrodynamics code in the conformally-flat approximation and obtain the gravitational-wave frequency associated with the peak amplitude ($f_{\rm max}$) of binary-neutron stars from a set of publicly available simulations. We find that $f_{\rm max}$ and $f_{2f}$ differ by about 1\%, on average, across forty-five equal-mass systems with different total mass and equations of state. Assuming that the gravitational-wave frequency is still approximately equal to twice the orbital frequency $Ω$ near the merger, the result indicates that the condition for tidal resonance $|m|Ω= f_{2f}$ is satisfied to high accuracy near the merger, where $m=2$ is the azimuthal quantum number. Moreover, the well established universal relation between $f_{\rm max}$ and the tidal deformability of equal-mass binary systems can now be explained by a similar relation between $f_{2f}$ and the tidal deformability of isolated neutron stars, which has been demonstrated to be associated with the nearly incompressible properties of neutron stars. Our findings suggest that it is possible to relate the gravitational-wave signal at the merger of a binary neutron star system directly to the fundamental oscillation modes and the mass ratio.

astro-ph.HE↗

arXiv2020

Probing the Purely Ingoing Nature of the Black-hole Event Horizon

One of the most fundamental results of general relativity is that the event horizon of black hole is purely ingoing. On the other hand, semiclassical-gravity effects, such as particle creation and the quantization of black-hole area, suggest that black holes can emit energy. Since a black hole is characterized by the presence of the event horizon, the emitted energy must be extracted from the black hole through its horizon. These considerations provide a motivation to test the validity of the purely ingoing nature of black-hole horizon. In this paper, we propose a novel test of the purely ingoing nature of black-hole horizon through gravitational-wave detection. We study the effects of hypothetical out-going gravitational waves to a perturbed black hole by supplementing the boundary condition of gravitational waves at the horizon with a phenomenological outgoing part. We show that this leads to extra excitation of the usual quasinormal modes of a perturbed black hole and continuous emission of gravitational waves. These additional signatures enable us to test the boundary condition(s) of the black-hole event horizon through gravitational-wave detection. Reanalysing the merger remnant of GW150914, we constrain the intensity of the outgoing gravitational-horizon flux to be $ < 10^{40} \rm W$, which is roughly $ 10^{-9} $ of peak luminosity of GW150914.

gr-qc↗

arXiv2019

Numerical studies on core collapse supernova in self-interacting massive scalar-tensor gravity

We investigate stellar core collapse in scalar-tensor theory with a massive self-interacting scalar field. In these theories, strong long-lived inverse chirp signals could be induced during the stellar core collapse, which provides us with several potential smoking-gun signatures that could be found using current ground-based detectors. We show that the existence of self-interaction in the potential of the scalar field can significantly suppress spontaneous scalarization and the amplitude of the monopole gravitational-wave radiation. Moreover, this suppression due to self-interaction is frequency dependent and may be discernible in LIGO/Virgo's sensitive band. Therefore, self-interaction should be considered when constraining scalar-tensor coupling parameters with gravitational-wave detections. Alternatively, if such monopole gravitational-wave signals are detected, then one may be able to infer the presence of self-interaction.

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arXiv2019

Phenomenological Inclusion of Alternative Dispersion Relations to the Teukolsky Equation and its Application to Bounding the Graviton Mass with Gravitational-wave Measurements

Existing constraints on the graviton mass from gravitational-wave detections rely on the phase difference developed between different frequencies during the propagation. Effects on the quasinormal-mode frequencies of the black-hole ringdown due to the graviton mass are often ignored. While perturbation theories of black holes have been well developed in the context of general relativity, this is not the case for modified gravity theories. We propose a phenomenological modification to the Teukolsky equation of perturbed black holes to include the dispersion relation due to a gravitational field of nonzero mass. Solving this modified Teukolsky equation by logarithmic perturbation theory, we compute the shift of the quasinormal-mode frequencies due to the presence of a graviton mass. This hypothetical shift can be used to constrain the graviton mass with ringdown signals, either standalone or in conjunction with the phase difference accumulated due to the wave propagation. We estimate that constraints on the graviton mass of $m_g \lesssim 10^{-15}\,\textrm{eV}$ can be put with a detection of the ringdown signal alone by second generation gravitational-wave detectors.

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arXiv2018

Constraining black-hole horizon effects by LIGO-Virgo detections of inspiralling binary black holes

General relativity predicts mass and spin growth of an inspiralling black hole due to an energy-momentum flux flowing through the black-hole horizon. The leading-order terms of this horizon flux introduce 2.5 and 3.5 post-Newtonian corrections to inspiral motions of binary black holes. The corrections may be measurable by gravitational waves detectors. Since the proper improvements to general relativity is still a mystery, it is possible that the true modified gravity theory introduces negligible direct corrections to the geodesics of test masses, while near horizon corrections are observable. We introduce a parameterization to describe arbitrary mass and spin growth of inspiralling black holes. Comparing signals of gravitational waves and a waveform model with parameterized horizon flux corrections, deviations from general relativity can be constrained. We simulate a set of gravitational waves signals following an astrophysical distribution with horizon flux modifications. Then, we perform a Bayesian analysis to obtain the expected constraints from the simulated response of the Advanced LIGO-Virgo detector network to the simulated signals. We show that the constraint can be improved by stacking multiple detections. The constraints of modified horizon flux can be used to test a specific class of modified gravity theories which predict dominant corrections near black-hole horizons over other types of corrections to general relativity. To support Hawking's area theorem at 90\% confidence level, over 10000 LIGO-Virgo detections are required. Within the lifetime of LIGO and Einstein Telescope, a future ground-based gravitational wave detector, near horizon corrections of modified gravity theories are potentially detectable if one of the modified gravity theory is true and the theory predicts a strong correction.

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