An Infinite Family of Generalized Kalnajs Disks

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.