Velocity-density twin transforms in thin disk model
arXiv:1411.0197 · doi:10.1093/mnras/stv1265
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.
arXiv comment3 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
References in corpus (6)
- Is dark matter present in NGC4736? An iterative spectral method for finding mass distribution in spiral galaxies
- Modeling the Newtonian Dynamics for Rotation Curve Analysis of Thin-Disk Galaxies
- Gravitational microlensing as a test of a finite-width disk model of the Galaxy
- On the axisymmetric thin disk model of flattened galaxies
- Constraining the vertical structure of the Milky Way rotation by microlensing in a finite-width global disk model
- A new method for reconstructing the density distribution of matter in the disks of spiral galaxies from the rotation velocity curve in it