arXiv subjects

Yuk Tung Liu

Publications and source records attributed to Yuk Tung Liu.

At least 37 records · Page 2Linked to original sources

arXiv2007

Magnetorotational collapse of very massive stars to black holes in full general relativity

We perform axisymmetric simulations of the magnetorotational collapse of very massive stars in full general relativity. Our simulations are applicable to the collapse of supermassive stars (M > 10^3M_sun) and to very massive Pop III stars. We model our initial configurations by n=3 polytropes. The ratio of magnetic to rotational kinetic energy in these configurations is chosen to be small (1% and 10%). We find that such magnetic fields do not affect the initial collapse significantly. The core collapses to a black hole, after which black hole excision is employed to continue the evolution long enough for the hole to reach a quasi-stationary state. We find that the black hole mass is M_h = 0.95M and its spin parameter is J_h/M_h^2 = 0.7, with the remaining matter forming a torus around the black hole. We freeze the spacetime metric ("Cowling approximation") and continue to follow the evolution of the torus after the black hole has relaxed to quasi-stationary equilibrium. In the absence of magnetic fields, the torus settles down following ejection of a small amount of matter due to shock heating. When magnetic fields are present, the field lines gradually collimate along the hole's rotation axis. MHD shocks and the MRI generate MHD turbulence in the torus and stochastic accretion onto the central black hole. When the magnetic field is strong, a wind is generated in the torus, and the torus undergoes radial oscillations that drive episodic accretion onto the hole. These oscillations produce long-wavelength gravitational waves potentially detectable by LISA. The final state of the magnetorotational collapse always consists of a central black hole surrounded by a collimated magnetic field and a hot, thick accretion torus. This system is a viable candidate for the central engine of a long-soft gamma-ray burst.

astro-ph↗

arXiv2007

Filling the holes: Evolving excised binary black hole initial data with puncture techniques

We follow the inspiral and merger of equal-mass black holes (BHs) by the moving puncture technique and demonstrate that both the exterior solution and the asymptotic gravitational waveforms are unchanged when the initial interior solution is replaced by constraint-violating ``junk'' initial data. We apply this result to evolve conformal thin-sandwich (CTS) binary BH initial data by filling their excised interiors with arbitrary, but smooth, initial data and evolving with standard puncture gauge choices. The waveforms generated for both puncture and filled-CTS initial data are remarkably similar, and there are only minor differences between irrotational and corotational CTS BH binaries. Even the interior solutions appear to evolve to the same constraint-satisfying solution at late times, independent of the initial data.

gr-qc↗

arXiv2007

Magnetized Hypermassive Neutron Star Collapse: a candidate central engine for short-hard GRBs

Hypermassive neutron stars (HMNSs) are equilibrium configurations supported against collapse by rapid differential rotation and likely form as transient remnants of binary neutron star mergers. Though HMNSs are dynamically stable, secular effects such as viscosity or magnetic fields tend to bring HMNSs into uniform rotation and thus lead to collapse. We simulate the evolution of magnetized HMNSs in axisymmetry using codes which solve the Einstein-Maxwell-MHD system of equations. We find that magnetic braking and the magnetorotational instability (MRI) both contribute to the eventual collapse of HMNSs to rotating black holes surrounded by massive, hot accretion tori and collimated magnetic fields. Such hot tori radiate strongly in neutrinos, and the resulting neutrino-antineutrino annihilation could power short-hard GRBs.

astro-ph↗

arXiv2007

The Final Fate of Binary Neutron Stars: What Happens After the Merger?

The merger of two neutron stars usually produces a remnant with a mass significantly above the single (nonrotating) neutron star maximum mass. In some cases, the remnant will be stabilized against collapse by rapid, differential rotation. MHD-driven angular momentum transport eventually leads to the collapse of the remnant's core, resulting in a black hole surrounded by a massive accretion torus. Here we present simulations of this process. The plausibility of generating short duration gamma ray bursts through this scenario is discussed.

gr-qc↗

arXiv2006

Magnetorotational collapse of massive stellar cores to neutron stars: Simulations in full general relativity

We study magnetohydrodynamic (MHD) effects arising in the collapse of magnetized, rotating, massive stellar cores to proto-neutron stars (PNSs). We perform axisymmetric numerical simulations in full general relativity with a hybrid equation of state. The formation and early evolution of a PNS are followed with a grid of 2500 x 2500 zones, which provides better resolution than in previous (Newtonian) studies. We confirm that significant differential rotation results even when the rotation of the progenitor is initially uniform. Consequently, the magnetic field is amplified both by magnetic winding and the magnetorotational instability (MRI). Even if the magnetic energy E_EM is much smaller than the rotational kinetic energy T_rot at the time of PNS formation, the ratio E_EM/T_rot increases to 0.1-0.2 by the magnetic winding. Following PNS formation, MHD outflows lead to losses of rest mass, energy, and angular momentum from the system. The earliest outflow is produced primarily by the increasing magnetic stress caused by magnetic winding. The MRI amplifies the poloidal field and increases the magnetic stress, causing further angular momentum transport and helping to drive the outflow. After the magnetic field saturates, a nearly stationary, collimated magnetic field forms near the rotation axis and a Blandford-Payne type outflow develops along the field lines. These outflows remove angular momentum from the PNS at a rate given by \dot{J} \sim ηE_EM C_B, where ηis a constant of order 0.1 and C_B is a typical ratio of poloidal to toroidal field strength. As a result, the rotation period quickly increases for a strongly magnetized PNS until the degree of differential rotation decreases. Our simulations suggest that rapidly rotating, magnetized PNSs may not give rise to rapidly rotating neutron stars.

astro-ph↗

arXiv2006

Collapse and black hole formation in magnetized, differentially rotating neutron stars

The capacity to model magnetohydrodynamical (MHD) flows in dynamical, strongly curved spacetimes significantly extends the reach of numerical relativity in addressing many problems at the forefront of theoretical astrophysics. We have developed and tested an evolution code for the coupled Einstein-Maxwell-MHD equations which combines a BSSN solver with a high resolution shock capturing scheme. As one application, we evolve magnetized, differentially rotating neutron stars under the influence of a small seed magnetic field. Of particular significance is the behavior found for hypermassive neutron stars (HMNSs), which have rest masses greater the mass limit allowed by uniform rotation for a given equation of state. The remnant of a binary neutron star merger is likely to be a HMNS. We find that magnetic braking and the magnetorotational instability lead to the collapse of HMNSs and the formation of rotating black holes surrounded by massive, hot accretion tori and collimated magnetic field lines. Such tori radiate strongly in neutrinos, and the resulting neutrino-antineutrino annihilation (possibly in concert with energy extraction by MHD effects) could provide enough energy to power short-hard gamma-ray bursts. To explore the range of outcomes, we also evolve differentially rotating neutron stars with lower masses and angular momenta than the HMNS models. Instead of collapsing, the non-hypermassive models form nearly uniformly rotating central objects which, in cases with significant angular momentum, are surrounded by massive tori.

gr-qc↗

arXiv2006

General Relativistic Simulations of Slowly and Differentially Rotating Magnetized Neutron Stars

We present long-term (~10^4 M) axisymmetric simulations of differentially rotating, magnetized neutron stars in the slow-rotation, weak magnetic field limit using a perturbative metric evolution technique. Although this approach yields results comparable to those obtained via nonperturbative (BSSN) evolution techniques, simulations performed with the perturbative metric solver require about 1/4 the computational resources at a given resolution. This computational efficiency enables us to observe and analyze the effects of magnetic braking and the magnetorotational instability (MRI) at very high resolution. Our simulations demonstrate that (1) MRI is not observed unless the fastest-growing mode wavelength is resolved by more than about 10 gridpoints; (2) as resolution is improved, the MRI growth rate converges, but due to the small-scale turbulent nature of MRI, the maximum growth amplitude increases, but does not exhibit convergence, even at the highest resolution; and (3) independent of resolution, magnetic braking drives the star toward uniform rotation as energy is sapped from differential rotation by winding magnetic fields.

astro-ph↗

arXiv2006

Evolution of magnetized, differentially rotating neutron stars: Simulations in full general relativity

We study the effects of magnetic fields on the evolution of differentially rotating neutron stars, which can form in stellar core collapse or binary neutron star coalescence. Magnetic braking and the magnetorotational instability (MRI) both redistribute angular momentum; the outcome of the evolution depends on the star's mass and spin. Simulations are carried out in axisymmetry using our recently developed codes which integrate the coupled Einstein-Maxwell-MHD equations. For initial data, we consider three categories of differentially rotating, equilibrium configurations, which we label normal, hypermassive and ultraspinning. Hypermassive stars have rest masses exceeding the mass limit for uniform rotation. Ultraspinning stars are not hypermassive, but have angular momentum exceeding the maximum for uniform rotation at the same rest mass. We show that a normal star will evolve to a uniformly rotating equilibrium configuration. An ultraspinning star evolves to an equilibrium state consisting of a nearly uniformly rotating central core, surrounded by a differentially rotating torus with constant angular velocity along magnetic field lines, so that differential rotation ceases to wind the magnetic field. In addition, the final state is stable against the MRI, although it has differential rotation. For a hypermassive neutron star, the MHD-driven angular momentum transport leads to catastrophic collapse of the core. The resulting rotating black hole is surrounded by a hot, massive, magnetized torus undergoing quasistationary accretion, and a magnetic field collimated along the spin axis--a promising candidate for the central engine of a short gamma-ray burst. (Abridged)

astro-ph↗

arXiv2005

Collapse of magnetized hypermassive neutron stars in general relativity

Hypermassive neutron stars (HMNSs) -- equilibrium configurations supported against collapse by rapid differential rotation -- are possible transient remnants of binary neutron star mergers. Using newly developed codes for magnetohydrodynamic simulations in dynamical spacetimes, we are able to track the evolution of a magnetized HMNS in full general relativity for the first time. We find that secular angular momentum transport due to magnetic braking and the magnetorotational instability results in the collapse of an HMNS to a rotating black hole, accompanied by a gravitational wave burst. The nascent black hole is surrounded by a hot, massive torus undergoing quasistationary accretion and a collimated magnetic field. This scenario suggests that HMNS collapse is a possible candidate for the central engine of short gamma-ray bursts.

astro-ph↗

arXiv2005

Magnetized hypermassive neutron star collapse: a central engine for short gamma-ray bursts

A hypermassive neutron star (HMNS) is a possible transient formed after the merger of a neutron star binary. In the latest magnetohydrodynamic simulations in full general relativity, we find that a magnetized HMNS undergoes `delayed' collapse to a rotating black hole (BH) as a result of angular momentum transport via magnetic braking and the magnetorotational instability. The outcome is a BH surrounded by a massive, hot torus with a collimated magnetic field. The torus accretes onto the BH at a quasi-steady accretion rate ~10 solar mass/s; the lifetime of the torus is ~10 ms. The torus has a temperature \sim 10^{12} K, leading to copious neutrino-antineutrino thermal radiation. Therefore, the collapse of an HMNS is a promising scenario for generating short-duration gamma-ray bursts and an accompanying burst of gravitational waves and neutrinos.

astro-ph↗

arXiv2005

Relativistic Magnetohydrodynamics In Dynamical Spacetimes: Numerical Methods And Tests

Many problems at the forefront of theoretical astrophysics require the treatment of magnetized fluids in dynamical, strongly curved spacetimes. Such problems include the origin of gamma-ray bursts, magnetic braking of differential rotation in nascent neutron stars arising from stellar core collapse or binary neutron star merger, the formation of jets and magnetized disks around newborn black holes, etc. To model these phenomena, all of which involve both general relativity (GR) and magnetohydrodynamics (MHD), we have developed a GRMHD code capable of evolving MHD fluids in dynamical spacetimes. Our code solves the Einstein-Maxwell-MHD system of coupled equations in axisymmetry and in full 3+1 dimensions. We evolve the metric by integrating the BSSN equations, and use a conservative, shock-capturing scheme to evolve the MHD equations. Our code gives accurate results in standard MHD code-test problems, including magnetized shocks and magnetized Bondi flow. To test our code's ability to evolve the MHD equations in a dynamical spacetime, we study the perturbations of a homogeneous, magnetized fluid excited by a gravitational plane wave, and we find good agreement between the analytic and numerical solutions.

astro-ph↗

arXiv2005

Excitation Of MHD Modes With Gravitational Waves: A Testbed For Numerical Codes

We consider a gravitational wave oscillating in an initially homogeneous, magnetized fluid. The fluid is perfectly conducting and isentropic, and the magnetic field is initially uniform. We find analytic solutions for the case in which the gravitational wave is linear and unaffected by the background fluid and field. Our solutions show how gravitational waves can excite three magnetohydrodynamic (MHD) modes in the fluid: Alfven waves, and both fast and slow magnetosonic waves. Our analytic solutions are particularly useful for testing numerical codes designed to treat general relativistic MHD in dynamical spacetimes, as we demonstrate in a companion paper.

astro-ph↗

arXiv2004

General relativistic hydrodynamics with viscosity: contraction, catastrophic collapse, and disk formation in hypermassive neutron stars

Viscosity and magnetic fields drive differentially rotating stars toward uniform rotation, which has important consequences in many astrophysical contexts. For example, merging binary neutron stars can form a "hypermassive" remnant, i.e. a differentially rotating star with a mass greater than the maximum allowed by uniform rotation. The removal of the centrifugal support provided by differential rotation can lead to delayed collapse of the remnant to a black hole, accompanied by a burst of gravitational radiation. Both magnetic fields and viscosity alter the structure of differentially rotating stars on secular timescales, making numerical tracking of the evolution difficult. Here, we present the first simulations of rapidly rotating stars with shear viscosity in full general relativity. We self-consistently include viscosity in our relativistic hydrodynamic code to solve the relativistic Navier-Stokes equations both in axisymmetry and in full 3+1 dimensions. In axisymmetry, we follow secular evolution with high resolution over dozens of rotation periods (thousands of M). We find that viscosity operating in a hypermassive star generically leads to the formation of a compact, uniformly rotating core surrounded by a low-density disk. These uniformly rotating cores are often, but not always, unstable to gravitational collapse. In the unstable cases, we follow the collapse and determine the mass and the spin of the final black hole and ambient disk. In all cases studied, the rest mass of the resulting disk is found to be 10-20% of the original star, whether surrounding a uniformly rotating core or a rotating black hole. This study foreshadows more detailed, future simulations of secular processes, including magnetic effects, in relativistic stars.

astro-ph↗

arXiv2003

Magnetic Braking in Differentially Rotating, Relativistic Stars

We study the magnetic braking and viscous damping of differential rotation in incompressible, uniform density stars in general relativity. Differentially rotating stars can support significantly more mass in equilibrium than nonrotating or uniformly rotating stars. The remnant of a binary neutron star merger or supernova core collapse may produce such a "hypermassive" neutron star. Although a hypermassive neutron star may be stable on a dynamical timescale, magnetic braking and viscous damping of differential rotation will ultimately alter the equilibrium structure, possibly leading to delayed catastrophic collapse. Here we consider the slow-rotation, weak-magnetic field limit in which E_rot << E_mag << W, where E_rot is the rotational kinetic energy, E_mag is the magnetic energy, and W is the gravitational binding energy of the star. We assume the system to be axisymmetric and solve the MHD equations in both Newtonian gravitation and general relativity. Toroidal magnetic fields are generated whenever the angular velocity varies along the initial poloidal field lines. We find that the toroidal fields and angular velocities oscillate independently along each poloidal field line, which enables us to transform the original 2+1 equations into 1+1 form and solve them along each field line independently. The incoherent oscillations on different field lines stir up turbulent-like motion in tens of Alfven timescales ("phase mixing"). In the presence of viscosity, the stars eventually are driven to uniform rotation, with the energy contained in the initial differential rotation going into heat. Our evolution calculations serve as qualitative guides and benchmarks for future, more realistic MHD simulations in full 3+1 general relativity.

astro-ph↗

arXiv2002

Post-Newtonian Models of Differentially Rotating Neutron Stars

A self-consistent field method is developed, which can be used to construct models of differentially rotating stars to first post-Newtonian order. The rotation law is specified by the specific angular momentum distribution j(m), where m is the baryonic mass fraction inside the surface of constant specific angular momentum. The method is then used to compute models of the nascent neutron stars resulting from the accretion induced collapse of white dwarfs. The result shows that the ratios of kinetic energy to gravitational binding energy of the relativistic models are slightly smaller than the corresponding values of the Newtonian models.

gr-qc↗

arXiv2002

Dynamical instability of new-born neutron stars as sources of gravitational radiation

The dynamical instability of new-born neutron stars is studied by evolving the linearized hydrodynamical equations. The neutron stars considered in this paper are those produced by the accretion induced collapse of rigidly rotating white dwarfs. A dynamical bar-mode (m=2) instability is observed when the ratio of rotational kinetic energy to gravitational potential energy $β$ of the neutron star is greater than the critical value $β_d \approx 0.25$. This bar-mode instability leads to the emission of gravitational radiation that could be detected by gravitational wave detectors. However, these sources are unlikely to be detected by LIGO II interferometers if the event rate is less than $10^{-6}$ per year per galaxy. Nevertheless, if a significant fraction of the pre-supernova cores are rapidly rotating, there would be a substantial number of neutron stars produced by the core collapse undergoing bar-mode instability. This would greatly increase the chance of detecting the gravitational radiation.

gr-qc↗

arXiv2001

On the tidally induced gravitational collapse of a particle cluster

An important issue in the dynamics of neutron star binaries is whether tidal interaction can cause the individual stars to collapse into black holes during inspiral. To understand this issue better, we study the dynamics of a cluster of collisionless particles orbiting a non-rotating black hole, which is part of a widely separated circular binary. The companion body's electric- and magnetic-type tidal fields distort the black hole and perturb the cluster, eventually causing the cluster to collapse into the hole as the companion spirals in under the influence of gravitational radiation reaction. We find that magnetic-type tidal forces do not significantly influence the evolution of the cluster as a whole. However, individual orbits can be strongly affected by these forces. For example, some orbits are destabilized due to the addition of magnetic-type tidal forces. We find that the most stable orbits are close to the companion's orbital plane and retrograde with respect to the companion's orbit.

gr-qc↗

arXiv2001

Models of Rapidly Rotating Neutron Stars: Remnants of Accretion Induced Collapse

Equilibrium models of differentially rotating nascent neutron stars are constructed, which represent the result of the accretion induced collapse of rapidly rotating white dwarfs. The models are built in a two-step procedure: (1) a rapidly rotating pre-collapse white dwarf model is constructed; (2) a stationary axisymmetric neutron star having the same total mass and angular momentum distribution as the white dwarf is constructed. The resulting collapsed objects consist of a high density central core of size roughly 20 km, surrounded by a massive accretion torus extending over 1000 km from the rotation axis. The ratio of the rotational kinetic energy to the gravitational potential energy of these neutron stars ranges from 0.13 to 0.26, suggesting that some of these objects may have a non-axisymmetric dynamical instability that could emit a significant amount of gravitational radiation.

astro-ph↗