1,057 research outputs found
Reflected Iron Line From a Source Above a Kerr Black Hole Accretion Disc
In this paper we present a fully relativistic approach to modelling both the
continuum emission and the reflected fluorescent iron line from a primary X-ray
source near a Kerr black hole. The X-ray source is located above an accretion
disc orbiting around the black hole. The source is assumed to be a static point
source located on an arbitrary position above the disc, on or off the axis of
rotation. We carry out Monte Carlo simulations in order to estimate the iron
line spectrum as well as its equivalent width. Because of the gravitational
lensing effect, an enhancement of the iron line is expected when the primary
source is located close to the central black hole. We find that for a source
located on the axis of rotation the enhancement is relatively modest. An
observer at inclination 30 degrees would measure an equivalent width of ~300eV
in the extreme case of a maximally rotating black hole and a source located at
height 1.5 gravitational radius from the centre. This corresponds to an
equivalent width enhancement factor of about 2 compared to the classical value
where no lensing effect comes into play. However, when allowing the source to
be located off the axis of rotation, much stronger enhancement can be obtained.
In the extreme case of a maximally rotating black hole and a source located
just above the approaching side of the disc, an observer at inclination 30d
egrees could measure an equivalent width as high as ~1.5 keV (i.e. ~10 times
the classical value). We also find that observers located at high inclination
angles observe a stronger line than observers at low inclination angles.Comment: 11 pages, 13 figures. Submitted to Monthly Notices of the Royal
Astronomical Society (MNRAS
A new form of the Kerr solution
A new form of the Kerr solution is presented. The solution involves a time
coordinate which represents the local proper time for free-falling observers on
a set of simple trajectories. Many physical phenomena are particularly clear
when related to this time coordinate. The chosen coordinates also ensure that
the solution is well behaved at the horizon. The solution is well suited to the
tetrad formalism and a convenient null tetrad is presented. The Dirac
Hamiltonian in a Kerr background is also given and, for one choice of tetrad,
it takes on a simple, Hermitian form.Comment: 8 pages, LaTeX, no figures. Corrected and improved version. To appear
in Phys. Rev.
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Calculating the Rotor Between Conformal Objects
Abstract: In this paper we will address the problem of recovering covariant transformations between objects—specifically; lines, planes, circles, spheres and point pairs. Using the covariant language of conformal geometric algebra (CGA), we will derive such transformations in a very simple manner. In CGA, rotations, translations, dilations and inversions can be written as a single rotor, which is itself an element of the algebra. We will show that the rotor which takes a line to a line (or plane to a plane etc) can easily be formed and we will investigate the nature of the rotors formed in this way. If we can recover the rotor between one object and another of the same type, a useable metric which tells us how close one line (plane etc) is to another, can be a function of how close this rotor is to the identity. Using these ideas, we find that we can define metrics for a number of common problems, specifically recovering the transformation between sets of noisy objects
Do wavelets really detect non-Gaussianity in the 4-year COBE data?
We investigate the detection of non-Gaussianity in the 4-year COBE data
reported by Pando, Valls-Gabaud & Fang (1998), using a technique based on the
discrete wavelet transform. Their analysis was performed on the two DMR faces
centred on the North and South Galactic poles respectively, using the
Daubechies 4 wavelet basis. We show that these results depend critically on the
orientation of the data, and so should be treated with caution. For two
distinct orientations of the data, we calculate unbiased estimates of the
skewness, kurtosis and scale-scale correlation of the corresponding wavelet
coefficients in all of the available scale domains of the transform. We obtain
several detections of non-Gaussianity in the DMR-DSMB map at greater than the
99 per cent confidence level, but most of these occur on pixel-pixel scales and
are therefore not cosmological in origin. Indeed, after removing all multipoles
beyond from the COBE maps, only one robust detection remains.
Moreover, using Monte-Carlo simulations, we find that the probability of
obtaining such a detection by chance is 0.59. We repeat the analysis for the
53+90 GHz coadded COBE map. In this case, after removing
multipoles, two non-Gaussian detections at the 99 per cent level remain.
Nevertheless, again using Monte-Carlo simulations, we find that the probability
of obtaining two such detections by chance is 0.28. Thus, we conclude the
wavelet technique does {\em not} yield strong evidence for non-Gaussianity of
cosmological origin in the 4-year COBE data.Comment: 7 pages, 5 figures. Revised version including discussion of
orientation sensitivity of the wavelet decomposition. MNRAS submitte
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