Open AccessThe curvature condition for self‐consistent scale‐free galaxies
Author(s) -
Jalali Mir Abbas,
De Zeeuw P. Tim
Publication year - 2002
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.1365-8711.2002.05674.x
Subject(s) - physics , curvature , superposition principle , power law , galaxy , astrophysics , classical mechanics , rotational symmetry , orbit (dynamics) , schwarzschild radius , gravitation , geometry , mechanics , quantum mechanics , statistics , mathematics , engineering , aerospace engineering
We modify the curvature condition for the existence of self‐consistent scale‐free discs, introduced by Zhao, Carollo and de Zeeuw. We survey the parameter space of the power‐law discs, and show that the modified curvature condition is in harmony with the results of Schwarzschild's numerical orbit superposition method. We study the orbital structure of the power‐law discs, and find a correlation between the population of centrophobic banana orbits and the non‐self‐consistency index. We apply the curvature condition to other families of scale‐free elongated discs and find that it rules out a large range of power‐law slopes and axis ratios. We generalize the condition and apply it to three‐dimensional scale‐free axisymmetric galaxy models.