arXiv subjects

D. Lynden-Bell

Publications and source records attributed to D. Lynden-Bell.

At least 19 recordsLinked to original sources

arXiv2017

Komar fluxes of circularly polarized light beams and cylindrical metrics

The mass per unit length of a cylindrical system can be found from its external metric as can its angular momentum. Can the fluxes of energy, momentum and angular momentum along the cylinder also be so found? We derive the metric of a beam of circularly polarized electromagnetic radiation from the Einstein-Maxwell equations. We show how the uniform plane wave solutions miss the angular momentum carried by the wave. We study the energy, momentum, angular momentum and their fluxes along the cylinder both for this beam and in general. The three Killing vectors of any stationary cylindrical system give three Komar flux vectors which in turn give six conserved fluxes. We elucidate Komar's mysterious factor 2 by evaluating Komar integrals for systems that have no trace to their stress tensors. The Tolman-Komar formula gives twice the energy for such systems which also have twice the gravity. For other cylindrical systems their formula gives correct results.

gr-qc↗

arXiv2017

Does Viscosity turn inflation into the CMB and $Λ$

Consideration of the entropy production in the creation of the CMB leads to a simple model of the evolution of the universe during this period which suggests a connection between the small observed acceleration term and the early inflation of a closed universe. From this we find an unexpected relationship between the Omega's of cosmology and calculate the total volume of the universe.

gr-qc↗

arXiv2015

On the Alignment of the Stress Tensor in Galaxies

We show that, provided the principal axes of the second velocity moment tensor of a stellar population are generally unequal and are oriented perpendicular to a set of orthogonal surfaces at each point, then those surfaces must be confocal quadric surfaces and the potential must be separable or Stackel. This is true under the mild assumption that the even part of the distribution function is invariant under time reversal $v_i \rightarrow -v_i$ of each velocity component. In particular, if the second velocity moment tensor is everywhere exactly aligned in spherical polar coordinates, then the potential must be of Stackel form (excepting degenerate cases where two or more of the semiaxes of ellipsoid are everywhere the same). The theorem also has consequences for alignment in cylindrical polar coordinates, which is used in the popular Jeans Anisotropic Models (JAM). We analyse data on the radial velocities and proper motions of a sample of $\sim 7400$ stars in the stellar halo of the Milky Way. We provide the distributions of the tilt angles or misalignments from the spherical polar coordinate systems. We show that in this sample the misalignment is always small (usually within $3^\circ$) for radii between 7 and 12 kpc. The velocity anisotropy is very radially biased ($β\approx 0.7$), and almost invariant across the volume in our study. Finally, we construct a triaxial stellar halo in a triaxial NFW dark matter halo using a made-to-measure method. Despite the triaxiality of the potential, the velocity ellipsoid of the stellar halo is nearly spherically aligned within $\sim6^\circ$ for large regions of space, particularly outside the scale radius of the stellar halo. We conclude that the second velocity moment ellipsoid can be close to spherically aligned for a much wider class of potentials than the strong constraints that arise from exact alignment might suggest.

astro-ph.GA↗

arXiv2014

Variations on the theme of Michel Henon's Isochrone

A variation of Newton's method of mapping Kepler's orbits into orbits in the simple harmonic oscillator is shown to give Henon's Isochrone. The statistical mechanics of a micro-canonical ensemble of isochrone oscillators shows that the temperature reaches a maximum as a function of the energy and then declines to zero at the escape energy. In that declining region adding heat (energy) decreases the temperature, as occurs in star clusters. We then define the internal temperature of an ensemble of binary stars all at the same (negative) energy and show that they too get cooler when heated and hotter when cooled. When the internal temperature of a binary is less that the temperature of the stars it interacts with, then on average heat will flow into it, making it less bound and of still lower temperature. Conversely hard binaries have higher internal temperatures than the local stars, so they lose energy and become hotter and yet more strongly bound, a process invoked by Michel Henon in his explanation of star-cluster evolution. Finally we give an isochronal variation of Newton's exactly soluble N-body problem.

astro-ph.GA↗

arXiv2014

The Torqued Cylinder and Levi-Civita's metric

When a static cylindrical system is subjected to equal and opposite torques top and bottom it transports angular momentum along its axis. The external metric of this static system can be transformed to Levi-Civita's form by using helical coordinates. This gives the external metric of a static cylinder three dimensionless parameters corresponding to the mass per unit length, the total stress along the cylinder, and the total torque. The external vacuum metric of a spherical system is characterised by its mass alone. How many parameters characterise the external metric of a general stationary cylindrical system? Leaving aside the radius of the cylinder which defines the scale we find that there are five parameters, the three above mentioned, to which should be added the momentum along the cylinder per unit length and the angular momentum per unit length. We show how to transform Levi-Civita's one parameter metric to include all five.

gr-qc↗

arXiv2012

Effects of rotating gravitational waves

We study gravitational waves to first and second order in amplitude in vacuum asymptotically flat spacetimes. The Einstein equations are solved to first order and these solutions are superposed to form a time-symmetric ingoing and then outgoing pulse regular everywhere. The waves are assumed to have odd-parity and a non-vanishing angular momentum which keeps them away from the axis at all times. The averaged energy of the waves is evaluated. The relevant Einstein equation is then solved to second order in the amplitude. The influence of the angular momentum of the waves on the rotation of local inertial frames with respect to the frames at great distances is analyzed. The rotation of the frames occurs even in the region around the origin where spacetime is almost flat. The rotation is without time delay as it follows from the constraint equation. The results are illustrated graphically for various values of the "harmonic index m" corresponding to azimuthal rotation and the "harmonic index l" describing the latitudinal rotation of the waves. The apparent motions of the fixed stars on the celestial sphere as seen through rotating waves from the local inertial frame are calculated and displayed.

gr-qc↗

arXiv2012

On Fast Linear Gravitational Dragging

A new formula is given for the fast linear gravitational dragging of the inertial frame within a rapidly accelerated spherical shell of deep potential. The shell is charged and is electrically accelerated by an electric field whose sources are included in the solution.

gr-qc↗

arXiv2010

Corotating light cylinders and Alfvén waves

Exact relativistic force free fields with cylindrical symmetry are explored. Such fields are generated in the interstellar gas via their connection to pulsar magnetospheres both inside and outside their light cylinders. The possibility of much enhanced interstellar fields wound on cylinders of Solar system dimensions is discussed but these are most likely unstable.

astro-ph.HE↗

arXiv2009

Does the Universe Accelerate Equally in all Directions?

We employ the Union compilation of Type Ia supernovae with a maximum likelihood analysis to search for a dark energy dipole. To approach this problem, we present a simple, computationally efficient, and largely model independent method. We opted to weight each SN by its observed error estimate, so poorly measured SNe that deviate substantially from the Hubble law do not produce spurious results. We find, with very low significance, a dipole in the cosmic acceleration directed roughly towards the cosmic microwave background dipole, but this is almost certainly coincidental.

astro-ph.CO↗

arXiv2008

Fields from a relativistic magnetic explosion

Following Prendergast we study the relativistically expanding electromagnetic fields generated by an axisymmetric explosion of magnetic energy in a small volume. The magnetic field expands uniformly either within a cone or in all directions and it is therefore accompanied by an electric field. In the highly conducting plasma the charges move to annul the electric field in the frame of the moving plasma. The solutions presented are analytical and semi-analytical. We find that the time-scale for the winding up of the initial magnetic field is crucial, as short time-scales lead to strong radiant fields. Assuming a magnetic field of $10^{13}Gauss$ emerging from a magnetosphere of $10^{9}cm$ we end with a jet when confined by a pressure environment that falls more slowly than $r^{-4}$. The jet carries energy of $10^{51}erg$, which is mostly due to differential rotation at the base.

astro-ph↗

arXiv2007

Are Complex A and the Orphan Stream related?

We consider the possibility that the Galactic neutral hydrogen stream Complex A and the stellar Orphan stream are related, and use this hypothesis to determine possible distances to Complex A and the Orphan stream, and line-of-sight velocities for the latter. The method presented uses our current knowledge of the projected positions of the streams, as well as line-of-sight velocities for Complex A, and we show that a solution exists in which the two streams share the same orbit. If Complex A and the Orphan stream are on this orbit, our calculations suggest the Orphan stream to be at an average distance of 20 kpc, with heliocentric radial velocities of approximately -110 km/s. Complex A would be ahead of the Orphan stream in the same wrap of the orbit, with an average distance of 10 kpc, which is consistent with the distance constraints determined through interstellar absorption line techniques.

astro-ph↗

arXiv2007

Electromagnetic Fields in Jets

The magnetic fields and energy flows in an astronomical jet described by our earlier model are calculated in detail. Though the field distribution varies with the external pressure function p(z), it depends only weakly on the other boundary conditions. Individual fieldlines were plotted; the lines become nearly vertical at the bottom and are twisted at the top. An animation of a fieldline's motion was made, which shows the line being wound up by the accretion disc's differential rotation and rising as a result of this. The distribution of Poynting flux within the jet indicates that much of the energy flows up the jet from the inside of the accretion disc but a substantial fraction flows back down to the outside.

astro-ph↗

arXiv2007

Energy and angular momentum densities of stationary gravity fields

We give physical explanations of explicit invariant expressions for the energy and angular momentum densities of gravitational fields in stationary space-times. These expressions involve non-locally defined conformal factors. In certain coordinates these become locally defined in terms of the metric. These results are derived via expressions for total gravitational potential energy from the difference between the total energy and the mechanical energy. The latter involves kinetic energy seen in the frame of static observers. When in the axially symmetric case we consider zero angular momentum observers (who move orthogonally to surfaces of constant time), we find that the angular momentum they attribute to the gravitational field is solely due to their motion.

gr-qc↗

arXiv2006

An Orphan in the "Field of Streams"

We use Sloan Digital Sky Survey Data Release 5 photometry and spectroscopy to study a tidal stream that extends over 50 degrees in the North Galactic Cap. From the analysis of the path of the stream and the colors and magnitudes of its stars, the stream is about 20 kpc away at its nearest detection (the celestial equator). We detect a distance gradient -- the stream is farther away from us at higher declination. The contents of the stream are made up from a predominantly old and metal-poor population that is similar to the globular clusters M13 and M92. The integrated absolute magnitude of the stream stars is estimated to be M_r = -7.5. There istentative evidence for a velocity signature, with the stream moving at -40 km/s at low declinations and +100 km/s at high declinations. The stream lies on the same great circle as Complex A, a roughly linear association of HI high velocity clouds stretching over 30 degrees on the sky, and as Ursa Major II, a recently discovered dwarf spheroidal galaxy. Lying close to the same great circle are a number of anomalous, young and metal-poor globular clusters, including Palomar 1 and Ruprecht 106.

astro-ph↗

arXiv2006

Lattice Melting and Rotation in Perpetually Pulsating Equilibria

Systems whose potential energies consists of pieces that scale as r^-2 together with pieces that scale as r^2, show no violent relaxation to Virial equilibrium but may pulsate at considerable amplitude for ever. Despite this pulsation these systems form lattices when the non-pulsational `energy' is low, and these disintegrate as that energy is increased. The `specific heats' show the expected halving as the `solid' is gradually replaced by the `fluid' of independent particles. The forms of the lattices are described here for N ~ 20 and they become hexagonal close packed for large N. In the larger N limit, a shell structure is formed. Their large N behaviour is analogous to a gamma=5/3 polytropic fluid with a quasi-gravity such that every element of fluid attracts every other in proportion to their separation. For such a fluid, we study the `rotating pulsating equilibria' and their relaxation back to uniform but pulsating rotation. We also compare the rotating pulsating fluid to its discrete counter part, and study the rate at which the rotating crystal redistributes angular momentum and mixes as a function of extra heat content.

astro-ph↗

arXiv2006

Hamilton's Eccentricity Vector Generalised to Newton Wonders

The vectorial velocity is given as a function of the position of a particle in orbit when a Newtonian central force is supplemented by an inverse cubic force as in Newton's theorem on revolving orbits. Such expressions are useful in fitting orbits to radial velocities of orbital streams. The Hamilton-Laplace-Runge-Lenz eccentricity vector is generalised to give a constant of the motion for these systems and an approximate constant for orbits in general central potentials. A related vector is found for Hooke's centred ellipse.

astro-ph↗

arXiv2006

Magnetic Jets from Swirling Disks

A broad swathe of astrophysical phenomena, ranging from tubular planetary nebulae through Herbig-Haro objects, radio-galaxy and quasar emissions to gamma-ray bursts and perhaps high-energy cosmic rays, may be driven by magnetically-dominated jets emanating from accretion disks. We give a self-contained account of the analytic theory of non-relativistic magnetically dominated jets wound up by a swirling disk and making a magnetic cavity in a background medium of any prescribed pressure, p(z). We solve the time-dependent problem for any specified distribution of magnetic flux P(R,0) emerging from the disk at z=0, with any specified disk angular velocity Omega_d(R). The physics required to do this involves only the freezing of the lines of force to the conducting medium and the principle of minimum energy.

astro-ph↗

arXiv2005

Inconsistency in theories of violent-relaxation

We examine an inconsistency in theories of violent-relaxation by Lynden-Bell and Nakamura. The inconsistency arises from the non-transitive nature of these theories: a system that under goes a violent-relaxation, relaxes and then upon an addition of energy, undergoes violent-relaxation once again would settle in an equilibrium state that is different from the one that is predicted had the system would go directly from the initial to the final states. We conclude that a proper description of the violent-relaxation process cannot be achieved by equilibrium statistical mechanics approach, but instead a dynamical theory for the coarse-grained phase-space density is needed.

astro-ph↗