38 research outputs found
Kerr black hole lensing for generic observers in the strong deflection limit
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 VLBI observations, this implies that very accurate
measures are needed to determine these two parameters separately.Comment: 17 pages, 4 figures, one section added, to appear on Physical Review
Kerr-Sen dilaton-axion black hole lensing in the strong deflection limit
In the present work we study numerically quasi-equatorial lensing by the
charged, stationary, axially-symmetric Kerr-Sen dilaton-axion black hole in the
strong deflection limit. In this approximation we compute the magnification and
the positions of the relativistic images. The most outstanding effect is that
the Kerr-Sen black hole caustics drift away from the optical axis and shift in
clockwise direction with respect to the Kerr caustics. The intersections of the
critical curves on the equatorial plane as a function of the black hole angular
momentum are found, and it is shown that they decrease with the increase of the
parameter . All of the lensing quantities are compared to particular
cases as Schwarzschild, Kerr and Gibbons-Maeda black holes.Comment: 31 pages, 17 figures; V2 references added, some typos corrected, V3
references added, language corrections, V4 table added, minor technical
correction
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 at a high accuracy degree the physics
in the strong field limit. 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.Comment: 11 pages, 3 figure
Quasi-Equatorial 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.Comment: 13 pages, 9 figures. Improved version with detailed physical
discussio
Gravitational lensing in the strong field limit
We provide an analytic method to discriminate among different types of black
holes on the ground of their strong field gravitational lensing properties. We
expand the deflection angle of the photon in the neighbourhood 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 formalism to Schwarzschild,
Reissner-Nordstrom and Janis-Newman-Winicour black holes. We then compare the
coefficients characterizing these metrics and find that different collapsed
objects are characterized by different strong field limits. The strong field
limit coefficients are directly connected to the observables, such as the
position and the magnification of the relativistic images. As a concrete
example, we consider the black hole at the centre of our galaxy and estimate
the optical resolution needed to investigate its strong field behaviour through
its relativistic images.Comment: 10 pages, 5 figures, in press on Physical Review
An extended scheme for fitting X-ray data with accretion disk spectra in the strong gravity regime
Accreting black holes are believed to emit X-rays which then mediate
information about strong gravity in the vicinity of the emission region. We
report on a set of new routines for the Xspec package for analysing X-ray
spectra of black-hole accretion disks. The new computational tool significantly
extends the capabilities of the currently available fitting procedures that
include the effects of strong gravity, and allows one to systematically explore
the constraints on more model parameters than previously possible (for example
black-hole angular momentum). Moreover, axial symmetry of the disk intrinsic
emissivity is not assumed, although it can be imposed to speed up the
computations. The new routines can be used also as a stand-alone and flexible
code with the capability of handling time-resolved spectra in the regime of
strong gravity. We have used the new code to analyse the mean X-ray spectrum
from the long XMM--Newton 2001 campaign of the Seyfert 1 galaxy MCG--6-30-15.
Consistent with previous findings, we obtained a good fit to the broad Fe K
line profile for a radial line intrinsic emissivity law in the disk which is
not a simple power law, and for near maximal value of black hole angular
momentum. However, equally good fits can be obtained also for small values of
the black hole angular momentum. The code has been developed with the aim of
allowing precise modelling of relativistic effects. Although we find that
current data cannot constrain the parameters of black-hole/accretion disk
system well, the approach allows, for a given source or situation, detailed
investigations of what features of the data future studies should be focused on
in order to achieve the goal of uniquely isolating the parameters of such
systems.Comment: Accepted for publication in ApJ S
Profiles of emission lines generated by rings orbiting braneworld Kerr black holes
In the framework of the braneworld models, rotating black holes can be
described by the Kerr metric with a tidal charge representing the influence of
the non-local gravitational (tidal) effects of the bulk space Weyl tensor onto
the black hole spacetime. We study the influence of the tidal charge onto
profiled spectral lines generated by radiating tori orbiting in vicinity of a
rotating black hole. We show that with lowering the negative tidal charge of
the black hole, the profiled line becomes to be flatter and wider keeping their
standard character with flux stronger at the blue edge of the profiled line.
The extension of the line grows with radius falling and inclination angle
growing. With growing inclination angle a small hump appears in the profiled
lines due to the strong lensing effect of photons coming from regions behind
the black hole. For positive tidal charge () and high inclination angles
two small humps appear in the profiled lines close to the red and blue edge of
the lines due to the strong lensing effect. We can conclude that for all values
of , the strongest effect on the profiled lines shape (extension) is caused
by the changes of the inclination angle.Comment: Accepted by General Relativity and Gravitatio
Gravitating discs around black holes
Fluid discs and tori around black holes are discussed within different
approaches and with the emphasis on the role of disc gravity. First reviewed
are the prospects of investigating the gravitational field of a black
hole--disc system by analytical solutions of stationary, axially symmetric
Einstein's equations. Then, more detailed considerations are focused to middle
and outer parts of extended disc-like configurations where relativistic effects
are small and the Newtonian description is adequate.
Within general relativity, only a static case has been analysed in detail.
Results are often very inspiring, however, simplifying assumptions must be
imposed: ad hoc profiles of the disc density are commonly assumed and the
effects of frame-dragging and completely lacking. Astrophysical discs (e.g.
accretion discs in active galactic nuclei) typically extend far beyond the
relativistic domain and are fairly diluted. However, self-gravity is still
essential for their structure and evolution, as well as for their radiation
emission and the impact on the environment around. For example, a nuclear star
cluster in a galactic centre may bear various imprints of mutual star--disc
interactions, which can be recognised in observational properties, such as the
relation between the central mass and stellar velocity dispersion.Comment: Accepted for publication in CQG; high-resolution figures will be
available from http://www.iop.org/EJ/journal/CQ
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.Comment: Invited article for the GRG special issue on lensing (P. Jetzer, Y.
Mellier and V. Perlick Eds.). 31 pages, 12 figure
The response of temperate aquatic ecosystems to global warming: novel insights from a multidisciplinary project
This article serves as an introduction to this special issue of Marine Biology, but also as a review of the key findings of the AQUASHIFT research program which is the source of the articles published in this issue. AQUASHIFT is an interdisciplinary research program targeted to analyze the response of temperate zone aquatic ecosystems (both marine and freshwater) to global warming. The main conclusions of AQUASHIFT relate to (a) shifts in geographic distribution, (b) shifts in seasonality, (c) temporal mismatch in food chains, (d) biomass responses to warming, (e) responses of body size, (f) harmful bloom intensity, (f), changes of biodiversity, and (g) the dependence of shifts to temperature changes during critical seasonal windows