Velocity-density twin transforms in thin disk model

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.

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

References in corpus (2)

• Is dark matter present in NGC4736? An iterative spectral method for finding mass distribution in spiral galaxies
• Constraining the vertical structure of the Milky Way rotation by microlensing in a finite-width global disk model