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