arXiv subjects

Andrew J. S. Hamilton

Publications and source records attributed to Andrew J. S. Hamilton.

At least 37 records · Page 2Linked to original sources

arXiv2012

The interior structure of rotating black holes 2. Uncharged black holes

(Abridged) A solution is obtained for the interior structure of an uncharged rotating black hole that accretes a collisionless fluid. The solution is conformally stationary, axisymmetric, and conformally separable, possessing a conformal Killing tensor. Hyper-relativistic counter-streaming between collisionless ingoing and outgoing streams drives inflation at (just above) the inner horizon, followed by collapse. As ingoing and outgoing streams approach the inner horizon, they focus into twin narrow beams directed along the ingoing and outgoing principal null directions, regardless of the initial angular motions of the streams. The radial energy-momentum of the counter-streaming beams gravitationally accelerates the streams even faster along the principal directions, leading to exponential growth in the streaming density and pressure, and in the Weyl curvature and mass function. At exponentially large density and curvature, inflation stalls, and the spacetime collapses. As the spacetime collapses, the angular motions of the freely-falling streams grow. When the angular motion has become comparable to the radial motion, which happens when the conformal factor has shrunk to an exponentially tiny scale, conformal separability breaks down, and the solution fails. The condition of conformal separability prescribes the form of the ingoing and outgoing accretion flows incident on the inner horizon. The dominant radial part of the solution holds provided that the densities of ingoing and outgoing streams incident on the inner horizon are uniform, independent of latitude; that is, the accretion flow is "monopole." The sub-dominant angular part of the solution requires a special non-radial pattern of angular motion of streams incident on the inner horizon. The prescribed angular pattern cannot be achieved if the collisionless streams fall freely from outside the horizon.

gr-qc↗

arXiv2012

The interior structure of rotating black holes 3. Charged black holes

This paper extends to the case of charged rotating black holes the conformally stationary, axisymmetric, conformally separable solutions presented for uncharged rotating black holes in a companion paper. In the present paper, the collisionless fluid accreted by the black hole may be charged. The charge of the black hole is determined self-consistently by the charge accretion rate. As in the uncharged case, hyper-relativistc counter-streaming between ingoing and outgoing streams drives inflation at (just above) the inner horizon, followed by collapse. If both ingoing and outgoing streams are charged, then conformal separability holds during early inflation, but fails as inflation develops. If conformal separability is imposed throughout inflation and collapse, then only one of the ingoing and outgoing streams can be charged: the other must be neutral. Conformal separability prescribes a hierarchy of boundary conditions on the ingoing and outgoing streams incident on the inner horizon. The dominant radial boundary conditions require that the incident ingoing and outgoing number densities be uniform with latitude, but the charge per particle must vary with latitude such that the incident charge densities vary in proportion to the radial electric field. The sub-dominant angular boundary conditions require specific forms of the incident number- and charge-weighted angular motions. If the streams fall freely from outside the horizon, then the prescribed angular conditions can be achieved by the charged stream, but not by the neutral stream. Thus, as in the case of an uncharged black hole, the neutral stream must be considered to be delivered ad hoc to just above the inner horizon.

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arXiv2011

Time Evolution of the Reverse Shock in SN 1006

The Schweizer-Middleditch star, located behind the SN 1006 remnant and near its center in projection, provides the opportunity to study cold, expanding ejecta within the SN 1006 shell through UV absorption. Especially notable is an extremely sharp red edge to the Si II 1260 Angstrom feature, which stems from the fastest moving ejecta on the far side of the SN 1006 shell--material that is just encountering the reverse shock. Comparing HST far-UV spectra obtained with COS in 2010 and with STIS in 1999, we have measured the change in this feature over the intervening 10.5-year baseline. We find that the sharp red edge of the Si II feature has shifted blueward by 0.19 +/- 0.05 Angstroms, which means that the material hitting the reverse shock in 2010 was moving slower by 44 +/- 11 km/s than the material that was hitting it in 1999, a change corresponding to - 4.2 +/- 1.0 km/s/yr. This is the first observational confirmation of a long-predicted dynamic effect for a reverse shock: that the shock will work its way inward through expanding supernova ejecta and encounter ever slower material as it proceeds. We also find that the column density of shocked Si II (material that has passed through the reverse shock) has decreased by 7 +/- 2% over the ten-year period. The decrease could indicate that in this direction the reverse shock has been ploughing through a dense clump of Si,leading to pressure and density transients.

astro-ph.GA↗

arXiv2011

Towards a general description of the interior structure of rotating black holes

The purpose of this paper is to present a number of proposals about the interior structure of a rotating black hole that is accreting slowly, but in an arbitrary time- and space-dependent fashion. The proposals could potentially be tested with numerical simulations. Outgoing and ingoing particles free-falling in the parent Kerr geometry become highly focused along the principal outgoing and ingoing null directions as they approach the inner horizon, triggering the mass inflation instability. The original arguments of Barrabes, Israel & Poisson (1990) regarding inflation in rotating black holes are reviewed, and shown to be based on Raychauduri's equation applied along the outgoing and ingoing null directions. It is argued that gravitational waves should behave in the geometric optics limit, and consequently that the spacetime should be almost shear-free. A full set of shear-free equations is derived. A specific line-element is proposed, which is argued should provide a satisfactory approximation during early inflation. Finally, it is argued that super-Planckian collisions between outgoing and ingoing particles will lead to entropy production, bringing inflation to an end, and precipitating collapse.

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arXiv2011

Intergalactic Filaments as Isothermal Gas Cylinders

Using a cosmological simulation at redshift 5, we find that the baryon-rich cores of intergalactic filaments extending outward from galaxies commonly form isothermal gas cylinders in regions favorable to their formation. The central gas density is typically about 500 times the cosmic mean total density, and the temperature is typically 1-2 times 10^4 K, just above the Lyman alpha cooling floor. These findings argue that the hydrodynamic properties of the gas are more important than the dark matter in determining this structure. It is noteworthy that the temperature and ionization state of the gas completely determine a finite total mass per unit length of an isothermal cylinder. Our findings may have implications for understanding the "cold mode" mechanism of gas transport into galaxies.

astro-ph.CO↗

arXiv2010

Stereoscopic visualization in curved spacetime: seeing deep inside a black hole

Stereoscopic visualization adds an additional dimension to the viewer's experience, giving them a sense of distance. In a general relativistic visualization, distance can be measured in a variety of ways. We argue that the affine distance, which matches the usual notion of distance in flat spacetime, is a natural distance to use in curved spacetime. As an example, we apply affine distance to the visualization of the interior of a black hole. Affine distance is not the distance perceived with normal binocular vision in curved spacetime. However, the failure of binocular vision is simply a limitation of animals who have evolved in flat spacetime, not a fundamental obstacle to depth perception in curved spacetime. Trinocular vision would provide superior depth perception.

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arXiv2010

The physics of the relativistic counter-streaming instability that drives mass inflation inside black holes

If you fall into a real astronomical black hole (choosing a supermassive black hole, to make sure that the tidal forces don't get you first), then you will probably meet your fate not at a central singularity, but rather in the exponentially growing, relativistic counter-streaming instability at the inner horizon first pointed out by Poisson & Israel (1990), who called it mass inflation. The chief purpose of this paper is to present a clear exposition of the physical cause and consequence of inflation in spherical, charged black holes. Inflation acts like a particle accelerator in that it accelerates cold ingoing and outgoing streams through each other to prodigiously high energies. Inflation feeds on itself: the acceleration is powered by the gravity produced by the streaming energy. The paper: (1) uses physical arguments to develop simple approximations that follow the evolution of inflation from ignition, through inflation itself, to collapse; (2) confirms that the simple approximations capture accurately the results of fully nonlinear one- and two-fluid self-similar models; (3) demonstrates that, counter-intuitively, the smaller the accretion rate, the more rapidly inflation exponentiates; (4) shows that in single perfect-fluid models, inflation occurs only if the sound speed equals the speed of light, supporting the physical idea that inflation in single fluids is driven by relativistic counter-streaming of waves; (5) shows that what happens during inflation up to the Planck curvature depends not on the distant past or future, but rather on events happening only a few hundred black hole crossing times into the past or future; (6) shows that, if quantum gravity does not intervene, then the generic end result of inflation is not a general relativistic null singularity, but rather a spacelike singularity at zero radius.

gr-qc↗

arXiv2010

Measuring Gas Accretion and Angular Momentum near Simulated Supermassive Black Holes

Using cosmological simulations with a dynamic range in excess of 10 million, we study the transport of gas mass and angular momentum through the circumnuclear region of a disk galaxy containing a supermassive black hole (SMBH). The simulations follow fueling over relatively quiescent phases of the galaxy's evolution (no mergers) and without feedback from active galactic nuclei (AGNs), as part of the first stage of using state-of-the-art, high-resolution cosmological simulations to model galaxy and black hole co-evolution. We present results from simulations at different redshifts (z=6, 4, and 3) and three different black hole masses (30 million, 90 million, and 300 million solar masses; at z=4), as well as a simulation including a prescription that approximates optically thick cooling in the densest regions. The interior gas mass throughout the circumnuclear disk shows transient and chaotic behavior as a function of time. The Fourier transform of the interior gas mass follows a power law with slope -1 throughout the region, indicating that, in the absence of the effects of galaxy mergers and AGN feedback, mass fluctuations are stochastic with no preferred timescale for accretion over the duration of each simulation (~ 1-2 Myr). The angular momentum of the gas disk changes direction relative to the disk on kiloparsec scales over timescales less than 1 Myr, reflecting the chaotic and transient gas dynamics of the circumnuclear region. Infalling clumps of gas, which are driven inward as a result of the dynamical state of the circumnuclear disk, may play an important role in determining the spin evolution of an SMBH, as has been suggested in stochastic accretion scenarios.

astro-ph.CO↗

arXiv2009

Entropy creation inside black holes points to observer complementarity

Heating processes inside large black holes can produce tremendous amounts of entropy. Locality requires that this entropy adds on space-like surfaces, but the resulting entropy (10^10 times the Bekenstein-Hawking entropy in an example presented in the companion paper) exceeds the maximum entropy that can be accommodated by the black hole's degrees of freedom. Observer complementarity, which proposes a proliferation of non-local identifications inside the black hole, allows the entropy to be accommodated as long as individual observers inside the black hole see less than the Bekenstein-Hawking entropy. In the specific model considered with huge entropy production, we show that individual observers do see less than the Bekenstein-Hawking entropy, offering strong support for observer complementarity.

gr-qc↗

arXiv2009

Huge entropy production inside black holes

We show that the entropy created by Ohmic dissipation inside an accreting charged black hole may exceed the Bekenstein-Hawking entropy by a large factor. If the black hole subsequently evaporates, radiating only the Bekenstein-Hawking entropy, then the black hole appears to destroy entropy, violating the second law of thermodynamics. A companion paper discusses the implications of this startling result. Bousso's covariant entropy bound is not violated.

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arXiv2009

The interior structure of slowly rotating black holes

The internal structure of a slowly rotating, charged black hole that is undergoing mass inflation at its inner horizon is derived. The equations governing the angular behavior decouple from the radial behavior, so all conclusions regarding inflation in a spherical charged black hole carry through unchanged for a slowly-rotating black hole. Quantities inflate only in the radial direction, not in the angular direction. Exact self-similar solutions are obtained. For sufficiently small accretion rates, the instantaneous angular motion of the accretion flow has negligible effect on the angular spacetime structure of the black hole, even if the instantaneous angular momentum of the accretion flow is large and arbitrarily oriented.

gr-qc↗

arXiv2008

Methods for Rapidly Processing Angular Masks of Next-Generation Galaxy Surveys

As galaxy surveys become larger and more complex, keeping track of the completeness, magnitude limit, and other survey parameters as a function of direction on the sky becomes an increasingly challenging computational task. For example, typical angular masks of the Sloan Digital Sky Survey contain about N=300,000 distinct spherical polygons. Managing masks with such large numbers of polygons becomes intractably slow, particularly for tasks that run in time O(N^2) with a naive algorithm, such as finding which polygons overlap each other. Here we present a "divide-and-conquer" solution to this challenge: we first split the angular mask into predefined regions called "pixels," such that each polygon is in only one pixel, and then perform further computations, such as checking for overlap, on the polygons within each pixel separately. This reduces O(N^2) tasks to O(N), and also reduces the important task of determining in which polygon(s) a point on the sky lies from O(N) to O(1), resulting in significant computational speedup. Additionally, we present a method to efficiently convert any angular mask to and from the popular HEALPix format. This method can be generically applied to convert to and from any desired spherical pixelization. We have implemented these techniques in a new version of the mangle software package, which is freely available at http://space.mit.edu/home/tegmark/mangle/, along with complete documentation and example applications. These new methods should prove quite useful to the astronomical community, and since mangle is a generic tool for managing angular masks on a sphere, it has the potential to benefit terrestrial mapmaking applications as well.

astro-ph↗

arXiv2008

Intergalactic baryon-rich regions at high redshift

Using a high resolution cosmological simulation of reionization we have examined the differing structures formed by gas and dark matter at a redshift of 5.1. Baryon-rich regions form a small number of filaments, which connect the largest galaxies in the simulation. More detailed examination of the ten largest galaxies reveals long, slender gaseous filaments about 5 proper kpc in width radiating from the galaxy centers. Extending out from each filament are a few smooth, thin, nearly planar gaseous sheets. By contrast, the dark matter concentrates into quasi-spherical bodies. The results have implications for our understanding of structure formation in the early universe and of the Lyman alpha forest.

astro-ph↗

arXiv2007

Resolving Gas Dynamics in the Circumnuclear Region of a Disk Galaxy in a Cosmological Simulation

Using a hydrodynamic adaptive mesh refinement code, we simulate the growth and evolution of a galaxy, which could potentially host a supermassive black hole, within a cosmological volume. Reaching a dynamical range in excess of 10 million, the simulation follows the evolution of the gas structure from super-galactic scales all the way down to the outer edge of the accretion disk. Here, we focus on global instabilities in the self-gravitating, cold, turbulence-supported, molecular gas disk at the center of the model galaxy, which provide a natural mechanism for angular momentum transport down to sub-pc scales. The gas density profile follows a power-law scaling as r^-8/3, consistent with an analytic description of turbulence in a quasi-stationary circumnuclear disk. We analyze the properties of the disk which contribute to the instabilities, and investigate the significance of instability for the galaxy's evolution and the growth of a supermassive black hole at the center.

astro-ph↗

arXiv2006

The Chemical Distribution in a Subluminous Type Ia Supernova: HST Images of the SN 1885 Remnant

We present HST images of the remnant of SN 1885 seen in absorption against M31's bulge via resonance lines of Ca I, Ca II, Fe I, and Fe II. Viewed in CaII H & K line absorption, the remnant appears as a nearly black circular spot with an outermost angular radius of 0.40" +/- 0.025" implying r = 1.52 pc and a 120 yr average expansion velocity of 12400 +/-1400 km/s. The strongest Ca II absorption is organized in a broken ring structure with a radius of 0.20" (=6000 km/s) with several apparent absorption `clumps' of an angular size near the pixel scale of 0.05" (= 1500 km/s). The detection of Ca II clumps is the first direct evidence for some instabilities and the existence of a deflagration phase in SNe Ia or, alternatively, mixing induced by radioactive decay of 56^Ni over time scales of seconds or days. However, the degree of mixing allowed by the observed images is much smaller than current 3D calculations for Rayleigh-Taylor dominated deflagration fronts. The images also require a central region of no or little Ca but iron group elements indicative of burning under sufficiently high densities for electron capture taking place, i.e., burning prior to a significant pre-expansion of the WD.

astro-ph↗

arXiv2006

The river model of black holes

This paper presents an under-appreciated way to conceptualize stationary black holes, which we call the river model. The river model is mathematically sound, yet simple enough that the basic picture can be understood by non-experts. %that can by understood by non-experts. In the river model, space itself flows like a river through a flat background, while objects move through the river according to the rules of special relativity. In a spherical black hole, the river of space falls into the black hole at the Newtonian escape velocity, hitting the speed of light at the horizon. Inside the horizon, the river flows inward faster than light, carrying everything with it. We show that the river model works also for rotating (Kerr-Newman) black holes, though with a surprising twist. As in the spherical case, the river of space can be regarded as moving through a flat background. However, the river does not spiral inward, as one might have anticipated, but rather falls inward with no azimuthal swirl at all. Instead, the river has at each point not only a velocity but also a rotation, or twist. That is, the river has a Lorentz structure, characterized by six numbers (velocity and rotation), not just three (velocity). As an object moves through the river, it changes its velocity and rotation in response to tidal changes in the velocity and twist of the river along its path. An explicit expression is given for the river field, a six-component bivector field that encodes the velocity and twist of the river at each point, and that encapsulates all the properties of a stationary rotating black hole.

gr-qc↗

arXiv2006

Probing Multiple Sight Lines through the SN 1006 Remnant by UV Absorption Spectroscopy

Absorption-line spectroscopy is an effective probe for cold ejecta within an SNR, provided that suitable background UV sources can be identified. For the SN 1006 remnant we have identified four such sources, in addition to the much-studied Schweitzer-Middleditch (SM) star. We have used STIS on HST to obtain UV spectra of all four sources, to study "core samples" of the SN 1006 interior. The line of sight closest to the center of the SNR shell, passing only 2.0 arcmin away, is to a V = 19.5 QSO at z = 1.026. Its spectrum shows broad Fe II absorption lines, asymmetric with red wings broader than blue. The similarity of these profiles to those seen in the SM star, which is 2.8 arcmin from the center in the opposite direction, confirms the existence of a bulge on the far side of SN 1006. The Fe II equivalent widths in the QSO spectrum are ~ 50% greater than in the SM star, suggesting that somewhat more iron may be present within SN 1006 than studies of the SM star alone have indicated, but this is still far short of what most SNIa models require. The absorption spectrum against a brighter z = 0.337 QSO seen at 57% of the shell radius shows broad silicon absorption lines but no iron other than narrow, probably interstellar lines. The cold iron expanding in this direction must be confined within v <~ 5200 km/s, also consistent with a high-velocity bulge on the far side only. The broad silicon lines indicate that the silicon layer has expanded beyond this point, and that it has probably been heated by a reverse shock. Finally, the spectra of two ~ A0V stars near the southern shell rim show no broad or unusually strong absorption lines, suggesting that the low-ionization ejecta are confined within 83% of the shell radius, at least at the azimuths of these background sources.

astro-ph↗

arXiv2006

A high resolution UV absorption spectrum of supernova ejecta in SN1006

We report a high resolution, far-ultraviolet, STIS E140M spectrum of the strong, broad Si II, III, and IV features produced by the ejecta of SN1006 seen in absorption against the background Schweizer-Middleditch star. The spectrum confirms the extreme sharpness of the red edge of the redshifted Si II 1260 A feature, supporting the idea that this edge represents the location of the reverse shock moving into the freely expanding ejecta. The expansion velocity of ejecta at the reverse shock is measured to be 7026 +-3(relative) +-10(absolute) km/s. If the shock model is correct, then the expansion velocity should be decreasing at the observable rate of 2.7 +-0.1 km/s per year. The pre-shock velocity, post-shock velocity, and post-shock velocity dispersion are all measured from the Si II 1260 A feature, and consistency of these velocities with the shock jump conditions implies that there is little or no electron heating in this fast (2680 km/s) Si-rich shock.

astro-ph↗