Dynamical Evolution of Elliptical Galaxies with Central Singularities

Abstract

We study the effect of a massive central singularity on the structure of a triaxial galaxy using N-body simulations. Starting from a single initial model, we grow black holes with various final masses Mh and at various rates, ranging from impulsive to adiabatic. In all cases, the galaxy achieves a final shape that is nearly spherical at the center and close to axisymmetric throughout. However, the rate of change of the galaxy's shape depends strongly on the ratio Mh/Mg of black hole mass to galaxy mass. When Mh/Mg < 0.3%, the galaxy evolves in shape on a timescale that exceeds 100 orbital periods, or roughly a galaxy lifetime. When Mh/Mg > 2%, the galaxy becomes axisymmetric in little more than a crossing time. We propose that the rapid evolution toward axisymmetric shapes that occurs when Mh/Mg > 2% provides a negative feedback mechanism which limits the mass of central black holes by cutting off their supply of fuel.Comment: 27 Latex pages, 9 Postscript figures, uses aastex.sty. Accepted for Publication in The Astrophysical Journal, Nov. 26, 199

Black holes and galaxy metamorphosis

“…Hence, the destruction of these centrophilic orbits breaks the backbone of the triaxial model and the system evolves toward axisymmetry. This effect has been shown in numerous computational and analytic studies [10][11][12][13][14][15]. In fact, the main controversies are whether the galaxy becomes axisymmetric locally or globally, and whether the transformation occurs in a few crossing times or over many Hubble times.…”

“…However, most self-consistent N-body simulations which have studied this effect have employed astrophysically unrealistic galaxy models [10,13]. For example, the models have been highly flattened, maximally triaxial models, while observations indicate that ellipticals are most likely mildly triaxial and not very flattened.…”

On the Effect of Chaotic Orbits on Dynamical Friction

“…The expressions of the gravitational potential and the components of the force corresponding to the c-models with c \ 0 (Merritt & Fridman 1996) were evaluated numerically using the Gaussian integration (Press et al 1992). Following Merritt & Quinlan (1998), we adopted the maximum possible value for the black hole mass, When the m h \ 0.02M. mass of a central black hole exceeds roughly 2% of the mass of the host galaxy, there is a transition to global chaoticity (the boxlike orbits lose their characteristic shapes) and the galaxy responds by rapidly becoming axisymmetric.…”

“…The chosen value allowed us to obtain a considerable percentage of chaotic orbits with short di †usion times. It was not possible to adopt a softening parameter, as small as the ones used e h , by Merritt & Quinlan (1998 , Table 1), however, because it would have demanded the use of extremely small integration time steps and, consequently, prohibitively long integration times, so that we adopted e h \ 0.08.…”

“…The central cusp models used by Merritt & Fridman (1996) are adequate candidates for the present purpose, particularly considering that our use of nonÈself-consistent methods prevents any evolution of the system toward axisymmetry (Merritt & Fridman 1996 ;Valluri & Merritt 1998 ;Merritt & Quinlan 1998) with the possible decrease of the percentage of chaotic orbits. Another way of perturbing the system is by means of rotation, which may yield a high degree of chaoticity (CMW ; Muzzio et al 2000aMuzzio et al , 2000b.…”