arXiv subjects

David L. Meier

Publications and source records attributed to David L. Meier.

30 records · Page 2Linked to original sources

arXiv2003

Constrained Transport Algorithms for Numerical Relativity. I. Development of a Finite Difference Scheme

A scheme is presented for accurately propagating the gravitational field constraints in finite difference implementations of numerical relativity. The method is based on similar techniques used in astrophysical magnetohydrodynamics and engineering electromagnetics, and has properties of a finite differential calculus on a four-dimensional manifold. It is motivated by the arguments that 1) an evolutionary scheme that naturally satisfies the Bianchi identities will propagate the constraints, and 2) methods in which temporal and spatial derivatives commute will satisfy the Bianchi identities implicitly. The proposed algorithm exactly propagates the constraints in a local Riemann normal coordinate system; {\it i.e.}, all terms in the Bianchi identities (which all vary as $\partial^3 g$) cancel to machine roundoff accuracy at each time step. In a general coordinate basis, these terms, and those that vary as $\partial g\partial^2 g$, also can be made to cancel, but differences of connection terms, proportional to $(\partial g)^3$, will remain, resulting in a net truncation error. Detailed and complex numerical experiments with four-dimensional staggered grids will be needed to completely examine the stability and convergence properties of this method. If such techniques are successful for finite difference implementations of numerical relativity, other implementations, such as finite element (and eventually pseudo-spectral) techniques, might benefit from schemes that use four-dimensional grids and that have temporal and spatial derivatives that commute.

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arXiv2003

Ohm's Law in the Fast Lane: General Relativistic Charge Dynamics

Fully relativistic and causal equations for the flow of charge in curved spacetime are derived. It is believed that this is the first set of equations to be published that correctly describes the flow of charge, and evolution of the electromagnetic field, in highly dynamical relativistic environments on time scales much shorter than the collapse time ($GM/c^3$). The equations will be important for correctly investigating problems such as the dynamical collapse of magnetized stellar cores to black holes and the production of jets and gravitational waves. This system of equations, given the name of `charge dynamics', is analogous to those of hydrodynamics (which describe the flow of {\em mass} in spacetime rather than the flow of charge). The most important one in the system is the relativistic generalized Ohm's law, which is used to compute time-dependent four-current. Unlike previous equations for the current, this one ensures that charge drift velocities remain less than the speed of light, takes into account the finite current rise time, is expressed in a covariant form, and is suitable for general relativistic computations in an arbitrary metric. It includes the standard known effects (Lorentz force, Hall effect, pressure effect, and resistivity) and reduces to known forms of Ohm's law in the appropriate limits. In addition, the plasma particles are allowed to have highly relativistic drift velocities, resulting in an implicit equation for the `current beaming factor' $γ_q$.

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arXiv2003

SIMsim: An End-to-End Simulation of The Space Interferometer Mission

We present the basic elements and first results of an end-to-end simulation package whose purpose is to test the validity of the Space Interferometer Mission design. The fundamental simulation time step is one millisecond, with substructure at 1/8 ms, and the total duration of the simulation is five years. The end product of a given "wide-angle" astrometry run is an estimated grid star catalog over the entire sky with an accuracy of about 4 micro-arcseconds. SIMsim is divided into five separate modules that communicate via data pipes. The first generates the 'truth' data on the spacecraft structure and laser metrology. The second module generates uncorrupted fringes for the three SIM interferometers, based on the current spacecraft orientation, target stars' positions, etc. The third module reads out the CCD white light fringe data at specified times, corrupting that and the metrology data with appropriate errors. The data stream out of this module represents the basic data stream on the simulated spacecraft. The fourth module performs fringe-fitting tasks on this data, recovering the total path delay, and the fifth and final module inverts the entire metrology/delay dataset to ultimately determine the instantaneous path delay on a fiducial baseline fixed in space. (Pathlength feed forward is used every few milliseconds to re-position the interferometer to keep the fringes in the delay window.) The average of all such delays over an integration time (typically 30 s) is reported as one of several hundred thousand measured stellar delays over the five-year period, which are then inverted to produce the simulated catalog. Future plans include taking into account more sources of error from the SIM error budget and including narrow angle observations in the observing plan.

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arXiv2002

The Magnetorotational Instability in Core Collapse Supernova Explosions

We investigate the action of the magnetorotational instability (MRI) in the context of iron-core collapse. Exponential growth of the field on the rotation time scale by the MRI will dominate the linear growth process of field line "wrapping" with the same characteristic time. We examine a variety of initial rotation states, with solid body rotation or a gradient in rotational velocity, that correspond to models in the literature. A relatively modest value of the initial rotation, a period of ~ 10 s, will give a very rapidly rotating PNS and hence strong differential rotation with respect to the infalling matter. We assume conservation of angular momentum on spherical shells. Results are discussed for two examples of saturation fields, a fiducial field that corresponds to Alfven velocity = rotational velocity and a field that corresponds to the maximum growing mode of the MRI. Modest initial rotation velocities of the iron core result in sub-Keplerian rotation and a sub-equipartition magnetic field that nevertheless produce substantial MHD luminosity and hoop stresses: saturation fields of order 10^{15} - 10^{16} G develop within 300 msec after bounce with an associated MHD luminosity of about 10^{52} erg/s. Bi-polar flows driven by this MHD power can affect or even cause the explosions associated with core-collapse supernovae.

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arXiv2001

Asymmetric Supernovae from Magneto-Centrifugal Jets

Strong toroidal magnetic fields generated in stellar collapse can generate magneto-centrifugal jets in analogy to those found in simulations of black hole accretion and explain why all core collapse supernovae are found to be substantially asymmetric and predominantly bi-polar. We describe two phases: the initial LeBlanc-Wilson jet and a subsequent protopulsar or toroidal jet that propagates at about the core escape velocity. The jets will produce bow shocks that tend to expel matter, including iron and silicon, into equatorial tori, accounting for observations of the element distribution in Cas A. A magnetic ``switch'' mechanism may apply in instances of low density and large magnetic field with subsequent increase in the speed and collimation of the toroidal jet, depositing relatively little momentum. The result could be enough infall to form a black hole with a third, highly relativistic jet that could catch up to the protopulsar jet after it has emerged from the star. The interaction of these two jets could generate internal shocks and explain the presence of iron lines in the afterglow. Recent estimates that typical gamma-ray burst energy is about 3x10^50 erg imply either a very low efficiency for conversion of rotation into jets, or a rather rapid turnoff of the jet process even though the black hole still rotates rapidly. Magnetars and ``hypernovae'' might arise in an intermediate parameter regime of energetic jets that yield larger magnetic fields and provide more energy than the routine case, but that are not so tightly collimated that they yield failed supernova. (slightly abridged)

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arXiv2001

In the Shadow of the Accretion Disk: Higher Resolution Imaging of the Central Parsec in NGC 4261

The physical conditions in the inner parsec of accretion disks believed to orbit the central black holes in active galactic nuclei can be probed by imaging the absorption (by ionized gas in the disk) of background emission from a radio counterjet. We report high angular resolution VLBI observations of the nearby (about 40 Mpc) radio galaxy NGC 4261 that confirm free-free absorption of radio emission from a counterjet by a geometrically thin, nearly edge-on disk at 1.6, 4.8, and 8.4 GHz. The angular width and depth of the absorption appears to increase with decreasing frequency, as expected. We derive an average electron density of ~10E4 per cc at a disk radius of about 0.2 pc, assuming that the inner disk inclination and opening angles are the same as at larger radii. Pressure balance between the thermal gas and the magnetic field in the disk implies an average field strength of 0.1 milligauss at a radius of 0.2 pc. These are the closest-in free-free absorption measurements to date of the conditions in an extragalactic accretion disk orbiting a black hole with a well-determined mass. If a standard advection-dominated accretion flow exists in the disk center, then the transition between thin and thick disk regions must occur at a radius less than 0.2 pc (4000 Schwarzschild radii).

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arXiv2000

The Association of Jet Production with Geometrically Thick Accretion Flows and Black Hole Rotation

A model is presented in which the strongest radio-emitting jet outflows are produced in black hole systems when the accretion is a geometrically thick ($H/R \sim 1$) inflow ({\it e.g.}, ADAF, CDAF) {\em and} if the black hole is rotating. For galactic black hole candidates, the model naturally accounts for the observed correlation of jet outflow with the black hole hard emission state and predicts an association of strong jets with rapid black hole rotation. When extended to the supermassive case, the model accounts for the highest radio galaxy and quasar jet powers and provides additional theoretical support for the ``spin paradigm'', which asserts that radio loud quasars are produced by Kerr holes and radio quiet ones by Schwarzschild holes. In some cases, the angular momentum and energy outflow in the jet may be large enough to significantly alter the structure of the accretion flow from that predicted by current models.

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arXiv1999

Grand Unification of AGN and the Accretion and Spin Paradigms

While attempts to unify certain classes of AGN using orientation and environmental effects have been successful, it is widely recognized that intrinsic properties of the accreting black hole system also must play a role in determining the appearance of such an object. In addition to mass and accretion rate, the angular momentum (or spin) of the black hole can play a crucial role in determining the power of a relativistic jet that is generated by magnetohydrodynamic acceleration near the hole. In this paper a scenario is presented, based on accretion theory and recent models of MHD jet production, in which the primary (although not only) parameter differentiating between radio loud and quiet objects is the black hole spin, and that determining quasar vs. radio galaxy is the accretion rate. A surprising number of desirable features result from these simple concepts and the accompanying equations. In addition, there are several testable predictions that can determine whether this grand unification scheme has further merit.

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arXiv1999

General Relativistic Simulations of Jet Formation by a Rapidly Rotating Black Hole

Recent observations of Galactic Black Hole Candidates (BHCs) suggest that those that are superluminal jet sources have more rapid black hole spin rates than otherwise normal BHCs. This provides observational support for models of relativistic jet formation that extract rotational energy of the central black hole. To investigate this mechanism, we have developed a new general relativistic magnetohydrodynamic code in Kerr geometry. Here we report on the first numerical simulation of the formation of a relativistic jet in a rapidly-rotating (a=0.95) Kerr black hole magnetosphere. We assume that the initial velocity of the disk is zero. We find that the maximum velocity of the jet reaches 0.93c (Lorentz factor, 2.7) and the terminal velocity of the jet is 0.85c (Lorentz factor, 1.9). On the other hand, for a non-rotating (a=0) Schwarzschild black hole, the maximum outflow velocity is less than 0.6c for initial magnetospheric conditions similar to to those of the Kerr black hole case. These numerical results show the importance of the rapidly rotating black hole for the relativistic jet formation.

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arXiv1999

A Magnetically-Switched, Rotating Black Hole Model For the Production of Extragalactic Radio Jets and the Fanaroff and Riley Class Division

A model is presented in which both Fanaroff and Riley class I and II extragalactic jets are produced by magnetized accretion disk coronae in the ergospheres of rotating black holes. While the jets are produced in the accretion disk itself, the output power still is an increasing function of the black hole angular momentum. For high enough spin, the black hole triggers the magnetic switch, producing highly-relativistic, kinetic-energy-dominated jets instead of Poynting-flux-dominated ones for lower spin. The coronal mass densities needed to trigger the switch at the observed FR break power are quite small ($\sim 10^{-15} g cm^{-3}$), implying that the source of the jet material may be either a pair plasma or very tenuous electron-proton corona, not the main accretion disk itself. The model explains the differences in morphology and Mach number between FR I and II sources and the observed trend for massive galaxies to undergo the FR I/II transition at higher radio power. It also is consistent with the energy content of extended radio lobes and explains why, because of black hole spindown, the space density of FR II sources should evolve more rapidly than that of FR I sources. If the present model is correct, then the ensemble average speed of parsec-scale jets in sources distinguished by their FR I morphology (not luminosity) should be distinctly slower than that for sources with FR II morphology. The model also suggests the existence of a population of high-redshift, sub-mJy FR I and II radio sources associated with spiral or pre-spiral galaxies that flared once when their black holes were formed but were never again re-kindled by mergers.

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arXiv1999

General Relativistic Simulations of Jet Formation in a Rapidly Rotating Black Hole Magnetosphere

To investigate the formation mechanism of relativistic jets in active galactic nuclei and micro-quasars, we have developed a new general relativistic magnetohydrodynamic code in Kerr geometry. Here we report on the first numerical simulation of jet formation in a rapidly-rotating (a=0.95) Kerr black hole magnetosphere. We study cases in which the Keplerian accretion disk is both co-rotating and counter-rotating with respect to the black hole rotation. In the co-rotating disk case, our results are almost the same as those in Schwarzschild black hole cases: a gas pressure-driven jet is formed by a shock in the disk, and a weaker magnetically-driven jet is also generated outside the gas pressure-driven jet. On the other hand, in the counter-rotating disk case, a new powerful magnetically-driven jet is formed inside the gas pressure-driven jet. The newly found magnetically-driven jet in the latter case is accelerated by a strong magnetic field created by frame dragging in the ergosphere. Through this process, the magnetic field extracts the energy of the black hole rotation.

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arXiv1998

Multi-Dimensional Astrophysical Structural and Dynamical Analysis I. Development of a Nonlinear Finite Element Approach

A new field of numerical astrophysics is introduced which addresses the solution of large, multidimensional structural or slowly-evolving problems (rotating stars, interacting binaries, thick advective accretion disks, four dimensional spacetimes, etc.). The technique employed is the Finite Element Method (FEM), commonly used to solve engineering structural problems. The approach developed herein has the following key features: 1. The computational mesh can extend into the time dimension, as well as space, perhaps only a few cells, or throughout spacetime. 2. Virtually all equations describing the astrophysics of continuous media, including the field equations, can be written in a compact form similar to that routinely solved by most engineering finite element codes. 3. The transformations that occur naturally in the four-dimensional FEM possess both coordinate and boost features, such that (a) although the computational mesh may have a complex, non-analytic, curvilinear structure, the physical equations still can be written in a simple coordinate system independent of the mesh geometry. (b) if the mesh has a complex flow velocity with respect to coordinate space, the transformations will form the proper arbitrary Lagrangian- Eulerian advective derivatives automatically. 4. The complex difference equations on the arbitrary curvilinear grid are generated automatically from encoded differential equations. This first paper concentrates on developing a robust and widely-applicable set of techniques using the nonlinear FEM and presents some examples.

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