Modelling the light-curves of objects tidally disrupted by a black hole

Tidal disruption by massive black holes is a phenomenon, during which a large part of gravitational energy can be released on a very short time-scale. The time-scales and energies involved during X-ray and IR flares observed in Galactic centre suggest that they may be related to tidal disruption events. Furthermore, aftermath of a tidal disruption of a star by super-massive black hole has been observed in some galaxies, e.g. RX J1242.6-1119A. All these discoveries increased the demand for tools for tidal disruption study in curved space-time. Here we summarise our study of general relativistic effects on tidal deformation of stars and compact objects.Comment: 2 pages, to appear in the proceedings of the JENAM 2008, Symposium 7: "Grand Challenges in Computational Astrophysics

Diagnostics of plasma in the ionospheric D-region: detection and study of different ionospheric disturbance types

Here we discuss our recent investigations of the ionospheric plasma by using very low and low frequency (VLF/LF) radio waves. We give a review of how to detect different low ionospheric reactions (sudden ionospheric disturbances) to various terrestrial and extra-terrestrial events, show their classification according to intensity and time duration, and present some methods for their detections in time and frequency domains. Investigations of detection in time domain are carried out for intensive long-lasting perturbations induced by solar X-ray flares and for short-lasting perturbations caused by gamma ray bursts. We also analyze time variations of signals used in the low ionospheric monitoring after earthquake events. In addition, we describe a procedure for the detection of acoustic and gravity waves from the VLF/LF signal analysis in frequency domain. The research of the low ionospheric plasma is based on data collected by the VLF/LF receivers located in Belgrade, Serbia

What brakes the Crab pulsar?

Optical observations provide convincing evidence that the optical phase of the Crab pulsar follows the radio one closely. Since optical data do not depend on dispersion measure variations, they provide a robust and independent confirmation of the radio timing solution. The aim of this paper is to find a global mathematical description of Crab pulsar's phase as a function of time for the complete set of published Jodrell Bank radio ephemerides (JBE) in the period 1988-2014. We apply the mathematical techniques developed for analyzing optical observations to the analysis of JBE. We break the whole period into a series of episodes and express the phase of the pulsar in each episode as the sum of two analytical functions. The first function is the best-fitting local braking index law, and the second function represents small residuals from this law with an amplitude of only a few turns, which rapidly relaxes to the local braking index law. From our analysis, we demonstrate that the power law index undergoes "instantaneous" changes at the time of observed jumps in rotational frequency (glitches). We find that the phase evolution of the Crab pulsar is dominated by a series of constant braking law episodes, with the braking index changing abruptly after each episode in the range of values between 2.1 and 2.6. Deviations from such a regular phase description behave as oscillations triggered by glitches and amount to fewer than 40 turns during the above period, in which the pulsar has made more than 2.0e10 turns. Our analysis does not favor the explanation that glitches are connected to phenomena occurring in the interior of the pulsar. On the contrary, timing irregularities and changes in slow down rate seem to point to electromagnetic interaction of the pulsar with the surrounding environment.Comment: 11 pages, 8 figures, 3 tables; accepted for publication in Astronomy & Astrophysic

Non-adiabatically driven electron in quantum wire with spin-orbit interaction

An exact solution is derived for the wave function of an electron in a semiconductor quantum wire with spin-orbit interaction and driven by external time dependent harmonic confining potential. The formalism allows analytical expressions for various quantities to be derived, such as spin and pseudo-spin rotations, energy and occupation probabilities for excited states. It is demonstrated how perfect spin and pseudo-spin flips can be achieved at high frequencies of order \omega, the confining potential level spacing. By an appropriately chosen driving term, spin manipulation can be exactly performed far into the non-adiabatic regime. Implications for spin-polarised emission and spin-dependent transport are also discussed.Comment: 11 pages, 3 figure

Optical phase coherent timing of the Crab nebula pulsar with Iqueye at the ESO New Technology Telescope

The Crab nebula pulsar was observed in 2009 January and December with a novel very fast optical photon counter, Iqueye, mounted at the ESO 3.5 m New Technology Telescope. Thanks to the exquisite quality of the Iqueye data, we computed accurate phase coherent timing solutions for the two observing runs and over the entire year 2009. Our statistical uncertainty on the determination of the phase of the main pulse and the rotational period of the pulsar for short (a few days) time intervals are $\approx 1 \, \mu$s and ~0.5 ps, respectively. Comparison with the Jodrell Bank radio ephemerides shows that the optical pulse leads the radio one by ~240 $\mu$s in January and ~160 $\mu$s in December, in agreement with a number of other measurements performed after 1996. A third-order polynomial fit adequately describes the spin-down for the 2009 January plus December optical observations. The phase noise is consistent with being Gaussian distributed with a dispersion $\sigma$ of $\approx 15 \, \mu$s in most observations, in agreement with theoretical expectations for photon noise-induced phase variability.Comment: 10 pages, 5 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Spectroscopy and 3D imaging of the Crab nebula

Spectroscopy of the Crab nebula along different slit directions reveals the 3 dimensional structure of the optical nebula. On the basis of the linear radial expansion result first discovered by Trimble (1968), we make a 3D model of the optical emission. Results from a limited number of slit directions suggest that optical lines originate from a complicated array of wisps that are located in a rather thin shell, pierced by a jet. The jet is certainly not prominent in optical emission lines, but the direction of the piercing is consistent with the direction of the X-ray and radio jet. The shell's effective radius is ~ 79 seconds of arc, its thickness about a third of the radius and it is moving out with an average velocity 1160 km/s.Comment: 21 pages, 14 figures, submitted to ApJ, 3D movie of the Crab nebula available at http://www.fiz.uni-lj.si/~vidrih

Analytical time-like geodesics

Time-like orbits in Schwarzschild space-time are presented and classified in a very transparent and straightforward way into four types. The analytical solutions to orbit, time, and proper time equations are given for all orbit types in the form r=r(\lambda), t=t(\chi), and \tau=\tau(\chi), where \lambda\ is the true anomaly and \chi\ is a parameter along the orbit. A very simple relation between \lambda\ and \chi\ is also shown. These solutions are very useful for modeling temporal evolution of transient phenomena near black holes since they are expressed with Jacobi elliptic functions and elliptic integrals, which can be calculated very efficiently and accurately.Comment: 15 pages, 10 figures, accepted by General Relativity and Gravitatio

Effects of Kerr Spacetime on Spectral Features from X-Ray Illuminated Accretion Discs

We performed detailed calculations of the relativistic effects acting on both the reflection continuum and the iron line from accretion discs around rotating black holes. Fully relativistic transfer of both illuminating and reprocessed photons has been considered in Kerr spacetime. We calculated overall spectra, line profiles and integral quantities, and present their dependences on the black hole angular momentum. We show that the observed EW of the lines is substantially enlarged when the black hole rotates rapidly and/or the source of illumination is near above the hole. Therefore, such calculations provide a way to distinguish among different models of the central source.Comment: 9 pages, latex, 13 figures, 3 Tables; accepted for publication in MNRA

On the tidal evolution of the orbits of low-mass satellites around black holes

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. 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. 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. 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.Comment: 7 pages, 6 figure

Optical Spectrum of Main-, Inter- and Off-pulse Emission from Crab Pulsar

A dedicated stroboscopic device was used to obtain optical spectra of the Crab main-pulse and inter-pulse as well as the spectrum of the underlying nebula when the pulsar is turned off. As the nebular emission is very inhomogeneous, our ability to effectively subtract the nebular background signal is crucial. No spectral lines intrinsic to the pulsar are detected. The main-pulse and the inter-pulse behave as power laws, both with the same de-reddened index Alpha = +0.2 +- 0.1. This value was obtained by subtracting the nebular spectrum at the exact position of the pulsar. The underlying nebula is redder, Alpha = -0.4 +- 0.1. Its emission lines are split into approaching (sim. -1200 km/s) and receding (sim. +600 km/s) components. The strength of emission line components and the flux in nebular continuum vary on arcsec scale. The nebular line and continuum intensities along the N-S slit are given.Comment: Accepted for publication in the Astrophysical Journal. 10 pages, 3 Tables, 4 Figure