Table of Contents

As a crude attempt to describe the velocity field of a galaxy with an oval distortion we have made a simple kinematical model, based on a suggestion by Dr. A. Toomre (note that this model was made in 1974, before more elaborate, and physically better founded, models were constructed by others. It should not be-taken too seriously; and is only meant as a guideline to determine the geometry of the system).

Consider a circular orbit at radius r in the plane of the
galaxy. We deform this circle into an ellipse by stretching it along the
x-axis and squeezing it along the y-axis. The Cartesian co-ordinates (x, y)
of a point P on the circle transform to (x’, y’) with:

x’ = x*f ; y’ = y/fa is the semi-major axis of the ellipse, b is the semi-minor axis. The circular velocity vector at P is (u, v) = (- Vc sin(phi) , Vc cos(phi) ), with phi = arctan y / x and Vc the amplitude of the circular velocity at radius r. We can eliminate phi and transform this vector also with equations (1) . Then we give the resulting ovals a constant pattern speed Omegap, but we reduce the angular velocity at each mean radius to compensate for this. We then have:

u’ = .... ; v’ = ....where r^2 = x^2f^2 + y^2/f^2 and Vc is taken at r.

**in=**- Input file name, a snapshot. No default.
**out=**- Output file name, a snapshot, no default.
**f=**- Factor to squash by. A number larger than 1 will stretch along the X axis, and squash the Y axis. [1.0]
**omega=**- Pattern Speed [0.0].
**times=**- Times to select snapshots from [all]

mkdisk disk1 100000 rmax=2 mass=1 snapsquash disk1 disk2 1.1 1 snaprotate disk2 disk3 30,60 zx snapgrid disk3 ccd3 moment=-1 ccdplot ccd3 or if you like NEMO’s pipe method, it can be done in one line: mkdisk - 100000 rmax=2 mass=1 |\If you have ds9, the commandsnapsquash - - 1/1.1 1 |\snaprotate - - 30,60 zy |\snapgrid - bosma-vel.ccd moment=-1 ccdplot bosma-vel.ccd nds9 bosma-vel.ccd

This can be compared in the same projection with the f=1 case, or now leaving out the programs and options we don’t need anymore:

mkdisk - 100000 rmax=2 mass=1 |\snaprotate - - 60 y |\snapgrid - bosma0-vel.ccd moment=-1 ccdplot bosma0-vel.ccd nds9 bosma0-vel.ccd

28-Jul-06V1.0 CreatedPJT/AB 23-oct-2021adjusted examplePJT