Context. The compact radio source Sagittarius A * (Sgr A * ) at the centre of our Galaxy harbours a supermassive black hole, whose mass (≈3.7 × 10 6 M ) has been measured from stellar orbital motions. Sgr A * is therefore the nearest laboratory where super-massive black hole astrophysics can be tested, and the environment of black holes can be investigated. Since it is not an active galactic nucleus, it also offers the possibility of observing the capture of small objects that may orbit the central black hole. Aims. We study the effects of the strong gravitational field of the black hole on small objects, such as a comet or an asteroid. We also explore the idea that the flares detected in Sgr A * might be produced by the final accretion of single, dense objects with mass of the order of 10 20 g, and that their timing is not a characteristic of the sources, but rather of the space-time of the central galactic black hole in which they are moving. Methods. The problem of tidal disruption of small objects by a black hole is studied numerically, using ray-tracing techniques, in a Schwarzschild background. Results. We find that tidal effects are strong enough to melt sufficiently massive, solid objects, and present calculations of the temporal evolution of the light curve of infalling objects as a function of various parameters. Our modelling of tidal disruption suggests that during tidal squeezing, the conditions for synchrotron radiation can be met. We show that the light curve of a flare can be deduced from dynamical properties of geodesic orbits around black holes and that it depends only weakly on the physical properties of the source.
Context. Low-mass satellites, like asteroids and comets, are expected to be present around the black hole at the Galactic center. We consider small bodies orbiting a black hole, and we study the evolution of their orbits due to tidal interaction with the black hole. Aims. In this paper we investigate the consequences of the existence of plunging orbits when a black hole is present. We are interested in finding the conditions that exist when capture occurs. Methods. Earlier analysis of the evolution of classical Keplerian orbits was extended to relativistic orbits around a Schwarzschild black hole. Results. The main difference between the Keplerian and black hole cases is in the existence of plunging orbits. Orbital evolution, leading from bound to plunging orbits, goes through a "final" unstable circular orbit. On this orbit, tidal energy is released on a characteristic black hole timescale. Conclusions. This process may be relevant for explaining how small, compact clumps of material can be brought onto plunging orbits, where they may produce individual short duration accretion events. The available energy and the characteristic timescale are consistent with energy released and the timescale typical of Galactic flares.
Low Mass X-ray Binaries (LMXB s) with either a black hole or a neutron star show power spectra characterised by Quasi Periodic Oscillations (QPOs). Twin peak high frequency QPOs are characterised by frequencies that are typical for matter orbiting within 10 fg from the compact object. We consider clumps of material orbiting a Schwarzschild black hole, that are deformed by tidal interaction. We present some preliminary calculations of corresponding light curves and power spectra. We were able to fit the simulated power spectra with the high frequency part of the power spectra observed in the LMXB XTE J1550-564 containing ablackhole. Ournumerical simulations reproduce the twin high frequency QPOs and the power-law. The lower peak corresponds to the Keplerian frequency, the upper one to the sum of the Keplerian and the radial frequency.
Realistic modelling of radiation transfer in and from variable accretion disks around black holes requires the solution of the problem: find the constants of motion and equation of motion of a light-like geodesic connecting two arbitrary points in space. Here we give the complete solution of this problem in the Schwarzschild space-time.
In this article we model a Global Navigation Satellite System (GNSS) in a Schwarzschild spacetime, as a first approximation of the relativistic geometry around the Earth. The closed time-like and scattering light-like geodesics are obtained analytically, describing respectively trajectories of satellites and electromagnetic signals. We implement an algorithm to calculate Schwarzschild coordinates of a GNSS user who receives proper times sent by four satellites, knowing their orbital parameters; the inverse procedure is implemented to check for consistency. The constellation of satellites therefore realizes a geocentric inertial reference system with no a priori realization of a terrestrial reference frame. We show that the calculation is very fast and could be implemented in a real GNSS, as an alternative to usual post-Newtonian corrections. Effects of non-gravitational perturbations on positioning errors are assessed, and methods to reduce them are sketched. In particular, inter-links between satellites could greatly enhance stability and accuracy of the positioning system.
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