2013/08/20 by Petra Suková, P. Suková, O. Semerák · 49 citations
Physics and Astronomy · #Accretion (finance) #Astrophysical Phenomena and Observations #Astrophysics #Astrophysics and Star Formation Studies #Black hole (networking) #Classical mechanics #Galactic Center #Galaxy #General relativity #Geodesic #Geometry #Gravitation #Physics #Pulsars and Gravitational Waves Research #RADIUS #Schwarzschild metric #Schwarzschild radius #Supermassive black hole #astro-ph.GA #gr-qc #nlin.CD
paper · pdf · doi:10.1093/mnras/stt1587
published in Monthly Notices of the Royal Astronomical Society 436(2), 978-996 (Oxford University Press) · 19 pages, 10 figures; accepted in MNRAS
arxiv created 2013/08/20 · openalex publication_date 2013/10/15 · arxiv updated 2013/11/15 · openalex created_date 2022/05/12 · openalex updated_date 2026/08/05
We continue the study of time-like geodesic dynamics in exact static, axially and reflection symmetric space–times describing the fields of a Schwarzschild black hole surrounded by thin discs or rings. In the first paper of this series, the rise (and decline) of geodesic chaos with ring/disc mass and position and with test particle energy was revealed on Poincaré sections and on time series of position or velocity and their power spectra. In the second paper, we compared these results with those obtained by two recurrence methods, focusing on ‘sticky’ orbits whose different parts show different degrees of chaoticity. Here, we complement the analysis by using several Lyapunov-type coefficients which quantify the rate of orbital divergence. After comparing the results with those obtained by the previous methods, we specifically consider a system involving a black hole surrounded by a small thin disc or a large ring, having in mind the configuration which probably occurs in galactic nuclei. Within the range of parameters which roughly corresponds to our Galactic centre, we found that the black hole accretion disc does not have a significant gravitational effect on the dynamics of free motion at larger radii, while the inner circumnuclear molecular ring (concentrated above 1 pc radius) can only induce some irregularity in motion of stars (‘particles’) on smaller radii if its mass reaches 10 to 30 per cent of the central black hole (which is the upper estimate given in the literature), if it is sufficiently compact (which does not hold but maybe for its inner rim) and if the stars can get to its close vicinity. The outer dust ring between 60 and 100 pc appears to be less important for the geodesic dynamics in its interior.