An Infinite Family of Generalized Kalnajs Disks

TL;DR

This paper introduces an infinite family of axially symmetric thin disk models, extending the Kalnajs disk, with varied mass distributions and rotation profiles, useful for astrophysical applications.

Contribution

It develops a method to generate an infinite family of generalized Kalnajs disks with diverse density and velocity profiles, expanding the set of available disk models.

Findings

The first disk is uniformly rotating with velocity proportional to radius.

Higher-order disks have velocity profiles that peak near the center and decrease outward.

Surface density peaks at the center and tapers to zero at the edge.

Abstract

An infinite family of axially symmetric thin disks of finite radius is presented. The family of disks is obtained by means of a method developed by Hunter and contains, as its first member, the Kalnajs disk. The surface densities of the disks present a maximum at the center of the disk and then decrease smoothly to zero at the edge, in such a way that the mass distribution of the higher members of the family is more concentrated at the center. The first member of the family have a circular velocity proportional to the radius, representing thus a uniformly rotating disk. On the other hand, the circular velocities of the other members of the family increases from a value of zero at the center of the disks until a maximum and then decreases smoothly until a finite value at the edge of the disks, in such a way that for the higher members of the family the maximum value of the circular velocity is attained nearest the center of the disks.