Hans-Peter Nollert, Penn State
Modern astrophysics is unthinkable without the input of general relativity. Therefore, the German Astronomical Society (Astronomische Gesellschaft) joined forces with the `Gravitation and Relativity Theory' section of the German Physical Society (DPG) in organizing this school on selected topics in relativistic astrophysics, such as gravitational lensing, gravitational waves, neutron stars and collapsing binaries, and accretion phenomena. The school took place in the physics center of the Deutsche Physikalische Gesellschaft in Bad Honnef from August 19 to 23 1996.
Jürgen Ehlers brought the lectures off to a great start with his comprehensive overview over the basic concepts of general relativity, with emphasis on physical interpretation, on astrophysical relevance, especially for lensing and gravitational radiation, and on the initial value problem for time evolution calculations. He found ways to help even old experts in the field see many things in a new light.
Peter Schneider discussed gravitational lensing: its history in the context of astrophysics, the basic concepts and the wealth of information that can be gained from observations of weak lensing: Mass profiles of galaxies, dark mass concentration, mean distribution of galaxies, even the Hubble constant - and much more. With new telescopes soon becoming operational, he foresees a bright future for his field.
Joachim Wambsganss described the searches for microlensing events. He presented the theoretical background and an overview over the history of the MACHO, EROS, and OGLE projects. The search for dark matter objects, for binaries and planets is the main objective in studying galactic microlensing events. About three times as many events as expected are observed in the galactic bulge, but fewer than expected towards the large Magellanic cloud. A preliminary conclusion states that the galactic halo almost certainly does not consist of brown dwarfs. The focus of attention for extragalactic events is on the determination of size and brightness profile of the sources, and on the detection of compact objects for the lenses and the determination of their masses.
Ute Kraus discussed theory and consequences of light deflection near neutron stars. Geometric effects, such as increased visibility of the star's surface, can have drastic effects for the pulse profiles of radiation emitted on or near the surface of the star. Since her main concern were light curves of X-ray pulsars, it is sufficient to consider photon trajectories in a Schwarzschild metric. In addition to the geometric effects, changes of photon energy and intensity radiation have to be taken into account.
Karsten Danzmann's guide on ``How to build a GEO600 interferometric gravitational wave detector in your back yard with spare change found under your couch cushions'' covered every aspect from using recycling to make your laser light go further, to reducing noise of nearby tractors, to the proper way of welding the vacuum tubes. If you can spare a little more, go for LISA, the heavenly version - you'll be first on the block to have one, and you will be guaranteed a variety of spectacular sources, such as coalescence of massive black holes anywhere in the universe, or white dwarf binaries.
Ed Seidel reported that the Grand Challenge community is getting ready to tackle a new challenge: the fully relativistic, three dimensional treatment of the merger of neutron star binaries. The plan is to use post-Newtonian techniques for the pre-coalescence phase, and then take the results of this as initial data (at a separation of about 8M) for the general relativistic hydrodynamical calculation. The relativistic field equations will be even more difficult to handle than the hydrodynamic equations, requiring the development of suitable algorithms, of adaptive mesh techniques, finding the best gauge conditions, and an effective use of parallel algorithms.
Heinz Herold discussed the effects of various equations of state and of rapid rotation on the equilibrium state of neutron stars. The structure equations can be solved using a variational principle in the form of a minimum surface problem. The numerical treatment is based on a finite element discretization. It turns out that higher mass models allow higher angular velocities. The deformation of the surface of the star was visualized using isometric embedding (for its internal geometry) or ray-tracing (for a view from the outside).
An excursion to the Drachenfels, a nearby hill featuring ancient ruins of a fortress, a grand view over the Rhine river, and a restaurant, provided some welcome diversion for the participants on Tuesday afternoon.
Instabilities of rotating stars can be quite frightening: Lee Lindblom pointed out that in principle, every star, even the earth, shows rotational instability. Luckily, they are usually countered by dissipative effects. Using a Newtonian two-potential technique, he found that the balance may be in favor for the instabilities in the case of neutron stars. However, it is not clear if they can prevail in a relativistic context, since they will be damped by gravitational radiation. At least for realistic equations of state, they may turn out not to be an issue.
Hans-Peter Nollert discussed treating collisions of black holes and neutron stars without the help of supercomputers. He pretended that the two colliding bodies are like a perturbation of the single final object: . The gravitational radiation emitted during and after the collision can then be obtained from linear equations. For black holes, the comparison with the full numerical calculations is remarkably good. He wishes he could do the same trick for neutron stars - if only a good fairy would take care of the initial conditions...
Whatever the central source of a gamma ray burster actually is, there has to be a fireball - unless gamma ray bursters are local, i.e. less than 200pc away. With this premise, Peter Mészáros gave theoretical explanations for many observed features of these elusive objects, based on the expansion of the fireball and the dissipation of its energy.
Harald Riffert provided the necessary ingredients for a model of thin accretion disks around black holes: Solve the gas dynamics in the equatorial plane of a Kerr background metric, build the energy-momentum tensor from an ideal fluid, viscous stress, and radiation flux, assume the disk to be stationary and rotationally symmetric, with velocities dominant in the direction. Integrating over the height of the disk, the vertical structure equations decouple from the radial part. The radial disk structure can be solved analytically, and the vertical equations have the same form as in the Newtonian case. The resulting model spectra can be fit to the UV-soft X-ray continuum of AGN.
When it comes to rapidly rotating relativistic systems, most work has concentrated on black holes and neutron stars, with little attention payed to other systems. Jim Ipser studied rapidly rotating accretion disks around compact objects, using a quasinormal mode analysis for perturbations of a simple equilibrium model. As a clever trick, he uses the perturbed Euler equation to eliminate the velocity perturbations. Relying on the Cowling approximation eliminates the metric perturbations, resulting in a single equation for a potential-like fluid variable. Taking into account frame dragging, his model provides a possible source for quasi-periodic oscillations in black hole X-ray binaries, giving a counter-argument to the objection that sources showing QPO's cannot be candidates for black holes.
Are quasars supermassive black holes or star clusters at the centers of galaxies? After reviewing an impressive collection of observational data, Max Camenzind favored the black hole scenario. In order to explain the central machine providing the power and accelerating the observed jets, magnetic fields are required. Consequently, the magnetohydrodynamics of disks in the background field of rapidly rotating stars was the topic of the second part of his lecture.
Fred Rasio presented a three dimensional Newtonian treatment of the merger phase of binary neutron star coalescence, using smoothed particle hydrodynamics. A Newtonian treatment is interesting in its own right: The hydrodynamics contain enough challenging physics, and they dominate the dynamics of the merger. The results can thus serve as preliminary estimates for the gravitational radiation emitted during the merger. When fully numerical codes become available, the Newtonian results can serve as a test case. In the future, nuclear physics, strong relativistic effects, and turbulent viscosity should be included for a more realistic treatment.
Pablo Laguna studied the evolution of matter in curved spacetime, using a smoothed particle approach on a fixed relativistic background. The SPH simulation reproduces the results of length scale estimates if the artificial viscosity is suitably adjusted. In particular, he examined the tidal disruption of stars by massive black holes. This scenario can be regarded as the fuelling process of active galactic nuclei: A dense star cluster in the vicinity of a central, supermassive black hole provides the necessary raw material.
A cosmic perspective was provided by Andreas Tammann, who reviewed observations determining the Hubble constant. Since measurements of redshifts are generally undisputed, most of his talk concentrated on determining cosmic distances. He used SNe Ia supernovae calibrated by cepheids, the Virgo cluster, and field galaxies. Including independent methods such as growth of supernovae shells, gravitational lenses, or fluctuations of the microwave background, he arrived at a value of . He warned the audience to be critical of headlines which will soon appear in popular newspapers, claiming that a new distance determination of the Fornax cluster in the southern hemisphere leads to , since this value may be based on improper identification of distances. He discussed estimates for the age of the universe, which he puts at yrs, compatible with his favored value of .
Michael Soffel reviewed experiments relating to gravity: Is there a fifth force (pronounced dead), does the gravitational constant depend on time (not to within one part in ), and what is its numerical value (the worst known physical constant)? He discussed the weak equivalence principle, the Einstein EP, and the strong EP. All are very well confirmed by various experiment; improved measurements are desirable with respect to some quantizations of gravity, which might cause tiny deviations (). With regard to general relativity, he discussed perihelion advance, light deflection, timing delay, and the Lense-Thirring effect.
The proceedings of the school will be published by Vieweg in early 1997.
The organizers, Hanns Ruder, Harald Riffert, and Hans-Peter Nollert for the Astronomische Gesellschaft and Friedrich Hehl for the Deutsche Physikalische Gesellschaft, wish to acknowledge the generous financial support from the WE-Heraeus Foundation which made this school possible.
We wish to point out that the names of the organizers of last year's school on ``Relativity and scientific computing'', Friedrich Hehl and Roland Puntigam for the Deutsche Physikalische Gesellschaft and Hanns Ruder for the Astronomische Gesellschaft, were inadvertently left out of the report on this school in the last issue of Matters of Gravity.