7,446 research outputs found
Light curve of a source orbiting around a black hole: A fitting-formula
A simple, analytical fitting-formula for a photometric light curve of a
source of light orbiting around a black hole is presented. The formula is
applicable for sources on a circular orbit with radius smaller than 45
gravitational radii from the black hole. This range of radii requires
gravitational focusation of light rays and the Doppler effect to be taken into
account with care. The fitting-formula is therefore useful for modelling the
X-ray variability of inner regions in active galactic nuclei.Comment: 12 pages, requires aasms.sty, to appear in The Astrophysical Journal,
Vol. 470 (October 20, 1996), figures available upon request from the Author,
or at http://otokar.troja.mff.cuni.cz/user/karas/au_www/karas/papers.ht
Strong-gravity effects acting on polarization from orbiting spots
Accretion onto black holes often proceeds via an accretion disc or a
temporary disc-like pattern. Variability features, observed in the light curves
of such objects, and theoretical models of accretion flows suggest that
accretion discs are inhomogeneous and non-axisymmetric. Fast orbital motion of
the individual clumps can modulate the observed signal. If the emission from
these clumps is partially polarized, which is likely the case, then rapid
polarization changes of the observed signal are expected as a result of general
relativity effects.Comment: 6 pages, 2 figures; proceedings of "The Coming of Age of X-ray
Polarimetry," Rome, Italy, April 27-30, 200
Stellar capture by an accretion disc
Long-term evolution of a stellar orbit captured by a massive galactic center
via successive interactions with an accretion disc has been examined. An
analytical solution describing evolution of the stellar orbital parameters
during the initial stage of the capture was found. Our results are applicable
to thin Keplerian discs with an arbitrary radial distribution of density and
rather general prescription for the star-disc interaction. Temporal evolution
is given in the form of quadrature which can be carried out numerically.Comment: Letter to MNRAS, 5 pages and 3 figures; also available at
http://otokar.troja.mff.cuni.cz/user/karas/au_www/karas/papers.ht
On multidegree of tame and wild automorphisms of C^3
In this note we show that the set mdeg(Aut(C^3)) mdeg(Tame(C^3)) is not
empty. Moreover we show that this set has infinitely many elements. Since for
the famous Nagata's example N of wild automorphism, mdeg N =(5,3,1) is an
element of mdeg(Tame(C^3)) and since for other known examples of wild
automorphisms the multidegree is of the form (1,d_2,d_3) (after permutation if
neccesary), then we give the very first exmple of wild automorphism F of C^3
such that mdeg F does not belong to mdeg(Tame(C^3)).
We also show that, if d_1,d_2 are odd numbers such that gcd (d_1,d_2) =1,
then (d_1,d_2,d_3) belongs to mdeg(Tame(C^3)) if and only if d_3 is a linear
combination of d_1,d_2 with natural coefficients. This a crucial fact that we
use in the proof of the main result
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