1) General: Pointed end. A point of transition.
→ polar cusp.
L. cuspis "point, spear, pointed end."
Tizé, noun from tiz "sharp, pointed," from Mid.Pers. tēz, tēž, tigr "sharp," O.Pers. tigra- "pointed," Av. taēža-, tighra- "pointed," Skt. taējas- "the sharp edge (of a knife), piercing (flame)", from tij- "to be sharp, to pierce," Gk. stizein "to prick, puncture," stigma "mark made by a pointed instrument," L. instigare "to goad," P.Gmc. *stik- "to pierce, prick, be sharp," O.H.G. stehhan, Ger. stechen "to prick," O.E. stician "to pierce, stab," E. stick "to pierce;" PIE *st(e)ig- "to stick; pointed".
Fr.: problème des cuspides
A problem encountered by the → cold dark matter (CDM) model of galaxy formation. The numerical simulations with CDM predict a large concentration of dark matter in the center of galaxies, with a peaked density distribution, in contrast to the real, observed galaxies. See also: → angular momentum catastrophe; → missing dwarfs.
Fr.: cuspide de densité
A localized increase in number of → stellar black holes near a → supermassive black hole predicted by models of galactic → stellar dynamics (Bahcall, Wolf, 1976, ApJ, 209, 214). Same as → stellar cusp.
Fr.: cuspide polaire
Fr.: cuspide stellaire
A steeply rising radial profile (→ cusp) in the number density of stars in the central region of a galaxy resulting from the gravitational influence of a central → supermassive black hole, as predicted by theoretical models. An important assumption of all cusp formation models is that the stellar cluster is in dynamical equilibrium in the black hole potential. This radial profile is usually characterized by a power law of the form n(r) ∝ r-γ, with a slope that is steeper than that of a flat isothermal → core. For a single-mass stellar cluster, Bahcall & Wolf (1976) determined the dynamically relaxed cusp will have γ = 7/4. The presence of such a cusp is important observationally because it may represent a simple test for black holes in stellar systems where dynamical mass estimates are difficult, such as in the cores of galaxies. In the case of the Milky Way, several attempts have been done to probe the presence of such a stellar cusp. However, the presence of the cusp is not confirmed. For example, based on the late-type stars alone, Do et al. (2009, ApJ 703, 1323), show that γ is less than 1.0 at the 99.7% confidence level. This is consistent with the nuclear star cluster having no cusp, with a → core profile that is significantly flatter than that predicted by most cusp formation theories, and even allows for the presence of a central hole in the stellar distribution (See also Genzel et al., 2010, Rev.Mod.Phys. 82, 3121, also at astro-ph/1006.0064).