Open AccessDensity cusps: restrictions on non‐axisymmetric models
Author(s) -
Zhao HongSheng
Publication year - 1998
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1998.01413.x
Subject(s) - physics , rotational symmetry , phase space , space (punctuation) , work (physics) , classical mechanics , sequence (biology) , scale (ratio) , statistical physics , mechanics , quantum mechanics , philosophy , linguistics , biology , genetics
Galactic nuclei are now generally thought to have density cusps in their centres, and the evidence is mounting that as a consequence they are unlikely to be triaxial. Self‐consistent stellar dynamical models of non‐axisymmetric cusps would be an interesting counter‐argument to this conclusion. We consider 2D analogues of triaxial cusps: a sequence of non‐axisymmetric, cuspy discs first described by Sridhar & Touma. Scale‐free models with potential Φ ∝ r α are examined in detail. It is shown analytically for 0 < α ≲ 0.43 that self‐consistent models with positive phase‐space density do not exist. Numerical solutions of the combined Vlasov and Poisson equations suggest that the whole sequence of models with 0 < α < 1 are also unphysical. Together with existing work on cusps, we conclude on purely theoretical grounds that galactic nuclei are not expected to be triaxial.