Gravitational instability of polytropic spheres containing region of trapped null geodesics: a possible explanation of central supermassive black holes in galactic halos

Journal Article · Thu Jun 01 04:00:00 EDT 2017 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2017/06/056· OSTI ID:22676131

Stuchlík, Zdeněk; Schee, Jan; Toshmatov, Bobir; Hladík, Jan; Novotný, Jan ^[1]

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1. Institute of Physics and Research Centre of Theoretical Physics and Astrophysics, Faculty of Philosophy and Science, Silesian University in Opava, Bezručovo náměstí 13, CZ-74601 Opava (Czech Republic)

We study behaviour of gravitational waves in the recently introduced general relativistic polytropic spheres containing a region of trapped null geodesics extended around radius of the stable null circular geodesic that can exist for the polytropic index N > 2.138 and the relativistic parameter, giving ratio of the central pressure p {sub c} to the central energy density ρ{sub c}, higher than σ = 0.677. In the trapping zones of such polytropes, the effective potential of the axial gravitational wave perturbations resembles those related to the ultracompact uniform density objects, giving thus similar long-lived axial gravitational modes. These long-lived linear perturbations are related to the stable circular null geodesic and due to additional non-linear phenomena could lead to conversion of the trapping zone to a black hole. We give in the eikonal limit examples of the long-lived gravitational modes, their oscillatory frequencies and slow damping rates, for the trapping zones of the polytropes with N element of (2.138,4). However, in the trapping polytropes the long-lived damped modes exist only for very large values of the multipole number ℓ > 50, while for smaller values of ℓ the numerical calculations indicate existence of fast growing unstable axial gravitational modes. We demonstrate that for polytropes with N ≥ 3.78, the trapping region is by many orders smaller than extension of the polytrope, and the mass contained in the trapping zone is about 10{sup −3} of the total mass of the polytrope. Therefore, the gravitational instability of such trapping zones could serve as a model explaining creation of central supermassive black holes in galactic halos or galaxy clusters.

• OSTI ID: 22676131
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 06 Vol. 2017; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
BLACK HOLES
CONVERSION
DAMPING
DENSITY
DISTURBANCES
EIKONAL APPROXIMATION
ENERGY DENSITY
GALAXIES
GALAXY CLUSTERS
GRAVITATIONAL INSTABILITY
GRAVITATIONAL WAVES
MASS
MULTIPOLES
NONLINEAR PROBLEMS
PERTURBATION THEORY
RELATIVISTIC RANGE
SUPERMASSIVE STARS
TRAPPING