1996/02/21 by D. Syer, Dave Syer, Scott Tremaine · 52 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Astrophysics #Axial symmetry #Barotropic fluid #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Differential equation #Differential rotation #Geometry #Geophysics and Gravity Measurements #Inertial frame of reference #Mathematics #Mechanics #Ordinary differential equation #Partial differential equation #Physics #Quantum mechanics #Rotational symmetry #Stars #Symmetry (geometry) #astro-ph
paper · pdf · doi:10.1093/mnras/281.3.925
published in Monthly Notices of the Royal Astronomical Society 281(3), 925-936 (Oxford University Press) · To appear in MNRAS 10 pages, tex, with figures, PostScript version also available at http://www.mpa-garching.mpg.de/~syer/papers/
arxiv created 1996/02/21 · openalex publication_date 1996/08/01 · arxiv updated 2015/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We develop equations to describe the equilibrium state of scale-free, razor-thin barotropic fluid discs, with rotation curve v ∞ R−β, ²ϵ( −1/4,1/2). The discs may be embedded in a scale-free axisymmetric background potential. Nearly axisymmetric discs are constructed analytically, and discs with azimuthal density variations as large as 10:1 are constructed numerically. For small departures from axisymmetry, we find that (i) stationary self-consistent cold or cool discs with m ≥ 2 do not exist; (ii) on a plane whose axes are the Mach number and the strength of the background potential, there are generally two one-parameter sequences of non-axisymmetric discs (one with aligned isodensity contours and one with spiral contours); the spiral sequence exists only for m = 1; (iii) isolated discs with a flat rotation curve (β = 0) support non-axisymmetric equilibrium states at all Mach numbers, and discs with β = 1/4 support a two-parameter family of self-similar spiral patterns.