arXiv subjects

William H. Lee

Publications and source records attributed to William H. Lee.

At least 73 records · Page 4Linked to original sources

arXiv2007

What is the optimum stellar rotation rate for a collapsar?

We consider low angular momentum, neutrino cooled accretion flows onto newborn black holes in the context of the collapsar model for long Gamma Ray Bursts, and find a considerable energy release for rotation rates lower than those usually considered. The efficiency for the transformation of gravitational binding energy into radiation is maximized when the equatorial angular momentum l0 ~ 2 Rg c, where Rg is the Schwarzschild radius.

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arXiv2006

Accretion modes in collapsars - prospects for GRB production

We explore low angular momentum accretion flows onto black holes formed after the collapse of massive stellar cores. In particular, we consider the state of the gas falling quasi-spherically onto stellar-mass black holes in the hypercritical regime, where the accretion rates are in the range 0.001 - 0.5 solar masses per second and neutrinos dominate the cooling. Previous studies have assumed that in order to have a black hole switch to a luminous state, the condition l >> r_g c, where l is the specific orbital angular momentum of the infalling gas and r_g is the Schwarszchild radius, needs to be fulfilled. We argue that flows in hyperaccreting, stellar mass disks around black holes are likely to transition to a highly radiative state when their angular momentum is just above the threshold for disk formation, l ~ 2 r_g c. In a range where l lies between r_g c and 2 r_g c, a dwarf disk forms in which gas spirals rapidly into the black hole due to general relativistic effects, without any help from horizontal viscous stresses. For high rotation rates with l greater than 2 r_g c, the luminosity is supplied by large, hot equatorial bubbles around the black hole. The highest neutrino luminosities are obtained for l ~ 2 r_g c, and this value of angular momentum also produces the most energetic neutrinos, and thus also the highest energy deposition rates. Given the range of l explored in this work, we argue that, as long as l is greater than 2 r_g c, low angular momentum cores may in fact be better suited for producing neutrino--driven explosions following core collapse in supernovae and gamma ray bursts.

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arXiv2005

Forced Oscillations in Fluid Tori and Quasi-Periodic Oscillations

The kilo-Hertz Quasi--Periodic Oscillations in X-ray binaries could originate within the accretion flow, and be a signature of non--linear fluid oscillations and mode coupling in strong gravity. The possibility to decipher these systems will impact our knowledge of fundamental parameters such as the neutron star mass, radius, and spin. Thus they offer the possibility to constrain the nuclear equation of state and the rotation parameter of stellar--mass black holes. We review the general properties of these oscillations from a hydrodynamical point of view, when the accretion flow is subject to external perturbations and summarize recent results.

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arXiv2005

A compact binary merger model for the short, hard GRB 050509b

The first X-ray afterglow for a short (~30 ms), hard gamma-ray burst was detected by Swift on 9 May 2005 (GRB 050509b). No optical or radio counterpart was identified in follow-up observations. The tentative association of the GRB with a nearby giant elliptical galaxy at redshift z=0.2248 would imply a total energy release E(gamma, isotropic) ~3 x 10**48 erg, and that the progenitor had traveled several tens of kpc from its point of origin, in agreement with expectations linking these events to the final merger of compact binaries driven by gravitational wave emission. We model the dynamical merger of such a system and the time-dependent evolution of the accretion tori thus created. The resulting energetics, variability, and expected durations are consistent with GRB 050509b originating from the tidal disruption of a neutron star by a stellar mass black hole, or of the merger of two neutron stars followed by prompt gravitational collapse of the massive remnant. We discuss how the available gamma-ray and X-ray data provide a probe for the nature of the relativistic ejecta and the surrounding medium.

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arXiv2005

Dynamical evolution of neutrino--cooled accretion disks: detailed microphysics, lepton-driven convection, and global energetics

We present a detailed, two dimensional numerical study of the microphysical conditions and dynamical evolution of accretion disks around black holes when neutrino emission is the main source of cooling. Such structures are likely to form after the gravitational collapse of massive rotating stellar cores, or the coalescence of two compact objects in a binary (e.g., the Hulse--Taylor system). The physical composition is determined self consistently by considering two regimes: neutrino--opaque and neutrino--transparent, with a detailed equation of state which takes into account neutronization, nuclear statistical equilibrium of a gas of free nucleons and alpha particles, blackbody radiation and a relativistic Fermi gas of arbitrary degeneracy. Various neutrino emission processes are considered, with electron/positron capture onto free nucleons providing the dominant contribution to the cooling rate. We find that important temporal and spatial scales, related to the optically thin/optically thick transition are present in the disk, and manifest themselves clearly in the energy output in neutrinos. This transition produces an inversion of the lepton gradient in the innermost regions of the flow which drives convective motions, and affects the density and disk scale height radial profiles. The electron fraction remains low in the region close to the black hole, and if preserved in an outflow, could give rise to heavy element nucleosynthesis. Our specific initial conditions arise from the binary merger context, and so we explore the implications of our results for the production of gamma ray bursts.

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arXiv2005

Oscillations of Thick Accretion Discs Around Black Holes - II

We present a numerical study of the global modes of oscillation of thick accretion discs around black holes. We have previously studied the case of constant distributions of specific angular momentum. In this second paper, we investigate (i) how the size of the disc affects the oscillation eigenfrequencies, and (ii) the effect of power-law distributions of angular momentum on the oscillations. In particular, we compare the oscillations of the disc with the epicyclic eigenfrequencies of a test particle with different angular momentum distributions orbiting around the central object. We find that there is a frequency shift away from the epicyclic eigenfrequency of the test particle to lower values as the size of the tori is increased. We have also studied the response of a thick accretion disc to a localized external perturbation using non constant specific angular momentum distributions within the disc. We find that in this case it is also possible (as reported previously for constant angular momentum distributions) to efficiently excite internal modes of oscillation. In fact we show here that the local perturbations excite global oscillations (acoustic p modes) closely related to the epicyclic oscillations of test particles. Our results are particularly relevant in the context of low mass X-ray binaries and microquasars, and the high frequency Quasi-Periodic Oscillations (QPOs) observed in them. Our computations make use of a Smooth Particle Hydrodynamics (SPH) code in azimuthal symmetry, and use a gravitational potential that mimics the effects of strong gravity.

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arXiv2004

Oscillations of Thick Accretion Discs Around Black Holes

We present a numerical study of the response of a thick accretion disc to a localized, external perturbation with the aim of exciting internal modes of oscillation. We find that the perturbations efficiently excite global modes recently identified as acoustic p--modes, and closely related to the epicyclic oscillations of test particles. The two strongest modes occur at eigenfrequencies which are in a 3:2 ratio. We have assumed a constant specific angular momentum distribution within the disc. Our models are in principle scale--free and can be used to simulate accretion tori around stellar or super massive black holes.

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arXiv2004

Opaque or transparent? A link between neutrino optical depths and the characteristic duration of short gamma-ray bursts

Cosmological gamma ray bursts (GRBs) are thought to occur from violent hypercritical accretion onto stellar mass black holes, either following core collapse in massive stars or compact binary mergers. This dichotomy may be reflected in the two classes of bursts having different durations. Dynamical calculations of the evolution of these systems are essential if one is to establish characteristic, relevant timescales. We show here for the first time the result of dynamical simulations, lasting approximately one second, of post--merger accretion disks around black holes, using a realistic equation of state and considering neutrino emission processes. We find that the inclusion of neutrino optical depth effects produces important qualitative temporal and spatial transitions in the evolution and structure of the disk, which may directly reflect upon the duration and variability of short GRBs.

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arXiv2004

Resonance in Forced Oscillations of an Accretion Disk and Kilohertz Quasi Periodic Oscillations

We have performed numerical simulations of a radially perturbed "accretion" torus around a black hole or neutron star and find that the torus performs radial and vertical motions at the appropriate epicyclic frequencies. We find clear evidence that vertical motions are excited in a non-linear resonance when the applied perturbation is periodic in time. The strongest resonant response occurs when the frequency difference of the two oscillations is equal to one-half the forcing frequency, precisely as recently observed in the accreting pulsar, SAX J1808.4-3658, where the observed kHz QPO peak separation is half the spin frequency of 401 Hz.

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arXiv2004

High-frequency QPOs as a problem in physics: non-linear resonance

The presence of a kHz frequency in LMXBs has been expected from scaling laws, by analogy with the QPO phenomenon in HMXB X-ray pulsars. Interpretation of the two kHz frequencies, observed in accreting neutron stars, in terms of non-linear resonance in strong-field gravity led to the prediction of twin QPOs in black hole systems, in a definite frequency ratio (such as 2/3). The imprint of a subharmonic of the 401 Hz rotation rate in the frequencies of the QPOs detected in the accreting millisecond pulsar is at once a signature of non-linear resonance and of coupling between accretion disk modes and the neutron star spin.

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arXiv2003

Dynamical consequences of CDM merger trees

Within the context of the standard structure formation scenario, massive present day elliptical galaxies are sometimes thought of as the result of a major merger of spiral systems. Through extensive SPH simulations of merging spirals, we have explored these processes with the aim of quantifying their relaxation times. This is important, as it sets a minimum time interval between the onset of a merger, and the appearance of an elliptical galaxy. We then compare this constraint with predictions of the hierarchical scenario, computed through Press-Schechter merger trees. We find evidence for elliptical systems which appear not to have been formed by a major merger of spirals.

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arXiv2003

Non-linear resonance in the accretion disk of a millisecond pulsar

Twin quasi-periodic millisecond modulations of the X-ray flux (kHz QPOs) have recently been reported from an accreting 2.5 ms X-ray pulsar. We identify modes of disk oscillations whose frequencies are in agreement with the observed ones when the rotating neutron star is modeled with realistic equations of state. The frequency difference of the twin QPOs, equal to about one half of the neutron-star spin rate, clearly indicates that resonant oscillations of the accretion disk have been observed. Similar non-linear resonances may also be spontaneously excited in the accretion disk. The two QPO frequencies in the pulsar system are close to a 5:7 ratio and this suggests a link with the QPOs in black hole systems, where frequency ratios of 2:3 and 3:5 have been reported.

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arXiv2003

Accretion disk assembly and survival during the disruption of a neutron star by a black hole

We study the formation of accretion disks resulting from dynamical three dimensional binary coalescence calculations, where a neutron star is tidally disrupted before being swallowed by its black hole companion. By subsequently assuming azimuthal symmetry we are able to follow the time dependence of the disk structure for a few tenths of a second. Although the disruption of a neutron star leads to a situation where violent instabilities redistribute mass and angular momentum within a few dynamical timescales, enough gas mass remains in the orbiting debris to catalyse the extraction of energy from the hole at a rate adequate to power a short-lived gamma ray burst.

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arXiv2002

The swallowing of a quark star by a black hole

In 3-d SPH simulations of the coalescence of a quark star with a pseudo-Newtonian black hole all of the quark matter is quickly accreted by the black hole. The Madsen-Caldwell-Friedman argument against the existence of quark stars may need to be re-examined.

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arXiv2002

Accretion disks around black holes: dynamical evolution, meridional circulations and gamma ray bursts

We study the hydrodynamical evolution of massive accretion disks around black holes, formed when a neutron star is disrupted by a black hole in a binary system. Initial conditions are taken from 3D calculations of coalescing binaries. Assuming azimuthal symmetry, we follow the time dependence of the disk structure for 0.2 seconds. We use an ideal gas e.o.s., and assume that all the dissipated energy is radiated away. The disks evolve due to viscous stresses, modeled with an alpha law. We study the disk structure, and the strong meridional circulations that are established and persist throughout our calculations. These consist of strong outflows along the equatorial plane that reverse direction close to the surface of the disk and converge on the accretor. In the context of GRBs, we estimate the energy released from the system in neutrinos and through magnetic-dominated mechanisms, and find it can be as high as 10^52 erg and 10^51 erg respectively, during an estimated timescale of 0.1-0.2 seconds. neutrino-anti neutrino annihilation is likely to produce bursts from only an impulsive energy input (the annihilation luminosity scales as t^(-5/2)) and so would be unable to account for a large fraction of bursts with complicated light curves. However a gas mass ~0.1-0.25 Msun survives in the orbiting debris, enabling strong magnetic fields (~10^16 Gauss) to be anchored in the dense matter long enough to power short GRBs. We also investigate the continuous energy injection that arises as the black hole slowly swallows the rest of the disk and discuss its consequences on the GRB afterglow emission.

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arXiv2002

Binary coalescence of a strange star with a black hole: Newtonian results

We present Newtonian three-dimensional hydrodynamical simulations of the merger of quark stars with black holes. The initial conditions correspond to non-spinning stars in Keplerian orbits, the code includes gravitational radiation reaction in the quadrupole approximation for point masses. We find that the quark star is disrupted, forming transient accretion structures around the black hole, but 0.03 of the original stellar mass survives the initial encounter and remains in an elongated orbit as a rapidly rotating quark starlet, in all cases. No resolvable amount of mass is dynamically ejected during the encounters--the black hole eventually accretes 99.99% +/- 0.01% of the quark matter initially present.

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arXiv2001

Newtonian hydrodynamics of the coalescence of black holes with neutron stars IV: Irrotational binaries with a soft equation of state

We present the results of three-dimensional hydrodynamical simulations of the final stages of inspiral in a black hole-neutron star binary, when the separation is comparable to the stellar radius. We use a Newtonian Smooth Particle Hydrodynamics (SPH) code to model the evolution of the system, and take the neutron star to be a polytrope with a soft (adiabatic index G=2 and G=5/3) equation of state and the black hole to be a Newtonian point mass. The only non-Newtonian effect we include is a gravitational radiation back reaction force, computed in the quadrupole approximation for point masses. We use irrotational binaries as initial conditions for our dynamical simulations, which are begun when the system is on the verge of initiating mass transfer and followed for approximately 23 ms. For all the cases studied we find that the star is disrupted on a dynamical time-scale, and forms a massive (the disc mass is approximately 0.2 solar masses) accretion torus around the spinning (Kerr) black hole. The rotation axis is clear of baryons (less than 1.e-5 solar masses within 10 degrees) to an extent that would not preclude the formation of a relativistic fireball capable of powering a cosmological gamma ray burst. Some mass (the specific amount is sensitive to the stiffness of the equation of state) may be dynamically ejected from the system during the coalescence and could undergo r-process nucleosynthesis. We calculate the waveforms, luminosities and energy spectra of the gravitational radiation signal and show how they reflect the global outcome of the coalescence process.

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arXiv2001

Coalescence of a strange star with a black hole

We present the first numerical results on the binary coalescence of a quark star with a black hole, obtained with a 3-D Newtonian smooth particle hydro (SPH) code. The star is initially represented by 17,000 particles modeling a self-gravitating fluid with the equation of state P= (rho - rho0)c**2/3, and the black hole by a point mass with an absorbing boundary at the Schwarzschild radius. As in similar calculations carried out for a stiff polytrope, the stellar core survives the initial episode of mass transfer, but here an accretion disk is clearly formed as well.

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