V. Bozza

Gravitational lensing in the strong field limit

We provide an analytic method to discriminate among different types of black holes on the grounds of their strong field gravitational lensing properties. We expand the deflection angle of the photon in the neighborhood of complete capture, defining a strong field limit, in opposition to the standard weak field limit. This expansion is worked out for a completely generic spherically symmetric spacetime, without any reference to the field equations and just assuming that the light ray follows the geodesics equation. We prove that the deflection angle always diverges logarithmically when the minimum impact parameter is reached. We apply this general ¯ . ,

Strong Field Limit of Black Hole Gravitational Lensing

We give the formulation of the gravitational lensing theory in the strong field limit for a Schwarzschild black hole as a counterpart to the weak field approach. It is possible to expand the full black hole lens equation to work a simple analytical theory that describes the physics in the strong field limit at a high accuracy degree. In this way, we derive compact and reliable mathematical formulae for the position of additional critical curves, relativistic images and their magnification, arising in this limit.

Gravitational Lensing by Black Holes

We review the theoretical aspects of gravitational lensing by black holes, and discuss the perspectives for realistic observations. We will first treat lensing by spherically symmetric black holes, in which the formation of infinite sequences of higher order images emerges in the clearest way. We will then consider the effects of the spin of the black hole, with the formation of giant higher order caustics and multiple images. Finally, we will consider the perspectives for observations of black hole lensing, from the detection of secondary images of stellar sources and spots on the accretion disk to the interpretation of iron K-lines and direct imaging of the shadow of the black hole.

High-precision photometry by telescope defocussing - II. The transiting planetary system WASP-4

We present high-precision photometry of two transit events of the extrasolar planetary system WASP-5, obtained with the Danish 1.54 m telescope at ESO La Silla. In order to minimise both random and flat-fielding errors, we defocussed the telescope so its point spread function approximated an annulus of diameter 40 pixels (16 00 ). Data reduction was undertaken using standard aperture photometry plus an algorithm for optimally combining the ensemble of comparison stars. The resulting light curves have point-to-point scatters of 0.50 mmag for the first transit and 0.59 mmag for the second. We construct detailed signal to noise calculations for defocussed photometry, and apply them to our observations. We model the light curves with the JKTEBOP code and combine the results with tabulated predictions from theoretical stellar evolutionary models to derive the physical properties of the WASP-5 system. We find that the planet has a mass of Mb = 1.637± 0.075± 0.033 MJup, a radius of Rb = 1.171± 0.056± 0.012 RJup, a large surface gravity of gb = 29.6± 2.8 m s i2 and a density of rb = 1.02±0.14±0.01 rJup (statistical and systematic uncertainties). The planet’s high equilibrium temperature of Teq = 1732± 80 K, makes it a good candidate for detecting secondary eclipses.

Quasiequatorial gravitational lensing by spinning black holes in the strong field limit

Spherically symmetric black holes produce, by strong field lensing, two infinite series of relativistic images, formed by light rays winding around the black hole at distances comparable to the gravitational radius. In this paper, we address the relevance of the black hole spin for the strong field lensing phenomenology, focusing on trajectories close to the equatorial plane for simplicity. In this approximation, we derive a two-dimensional lens equation and formulae for the position and the magnification of the relativistic images in the strong field limit. The most outstanding effect is the generation of a non trivial caustic structure. Caustics drift away from the optical axis and acquire finite extension. For a high enough black hole spin, depending on the source extension, we can practically observe only one image rather than two infinite series of relativistic images. In this regime, additional non equatorial images may play an important role in the phenomenology.

Analytic Kerr black hole lensing for equatorial observers in the strong deflection limit

In this paper we present an analytical treatment of gravitational lensing by Kerr black holes in the limit of very large deflection angles, restricting to observers in the equatorial plane. We accomplish our objective starting from the Schwarzschild black hole and adding corrections up to second order in the black hole spin. This is sufficient to provide a full description of all caustics and the inversion of lens mapping for sources near them. On the basis of these formulae we argue that relativistic images of low mass x-ray binaries around Sgr

Kerr black hole lensing for generic observers in the strong deflection limit

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High-precision photometry by telescope defocusing - III. The transiting planetary system WASP-2★: High-precision defocused photometry of WASP-2

are very likely to be seen by future x-ray interferometry missions.

High-precision photometry by telescope defocusing – IV. Confirmation of the huge radius of WASP-17 b†

We generalize our previous work on gravitational lensing by a Kerr black hole in the strong deflection limit, removing the restriction to observers on the equatorial plane. Starting from the Schwarzschild solution and adding corrections up to the second order in the black hole spin, we perform a complete analytical study of the lens equation for relativistic images created by photons passing very close to a Kerr black hole. We find out that, to the lowest order, all observables (including shape and shift of the black hole shadow, caustic drift and size, images position and magnification) depend on the projection of the spin on a plane orthogonal to the line of sight. In order to break the degeneracy between the black hole spin and its inclination relative to the observer, it is necessary to push the expansion to higher orders. In terms of future very-long base line interferometry observations, this implies that very accurate measures are needed to determine these two parameters separately.

Spitzer as a microlens parallax satellite : mass and distance measurements of the binary lens system OGLE-2014-BLG-1050L

We present high-precision photometry of three transits of t he extrasolar planetary system WASP-2, obtained by defocussing the telescope, and achievi ng point-to-point scatters of between 0.42 and 0.73 mmag. These data are modelled using the JKTEBOP code, and taking into account the light from the recently-discovered faint s tar close to the system. The physical properties of the WASP-2 system are derived using tabulated pr ictions from five different sets of stellar evolutionary models, allowing both statist ical and systematic errorbars to be specified. We find the mass and radius of the planet to be M = 0.847± 0.038± 0.024MJup andRb = 1.044± 0.029± 0.015RJup. It has a low equilibrium temperature of 1280± 21K, in agreement with a recent finding that it does not have an atmo spheric temperature inversion. The first of our transit datasets has a scatter of only 0.42 mma g with respect to the best-fitting light curve model, which to our knowledge is a record for grou nd-based observations of a transiting extrasolar planet.