Velocity-density twin transforms in thin disk model
Astrophysics of Galaxies
2015-07-02 v3
Abstract
Ring mass density and the corresponding circular velocity in thin disk model are known to be integral transforms of one another. But it may be less familiar that the transforms can be reduced to one-fold integrals with identical weight functions. It may be of practical value that the integral for the surface density does not involve the velocity derivative, unlike the equivalent and widely known Toomre's formula.
Cite
@article{arxiv.1411.0197,
title = {Velocity-density twin transforms in thin disk model},
author = {Łukasz Bratek and Szymon Sikora and Joanna Jałocha and Marek Kutschera},
journal= {arXiv preprint arXiv:1411.0197},
year = {2015}
}
Comments
3 pages; 1 figure (a separate file); v2: added a derivation of w(x) from an infinitely flattened spheroid; v3 improvement/correction of the derivation in v2 + minor corr. in the text