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).
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) = (- V 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.
mkdisk disk1 10000 rmax=2 mass=1 snapsquash disk1 disk2 1.1 1 snaprotate disk2 disk3 30,60 zx snapgrid disk3 ccd3 moment=-1 ccdplot ccd3If you have ds9, the command nds9 will send this image into the ds9 display server.
28-Jul-06 V1.0 Created PJT/AB
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