AAS 204th Meeting, June 2004
Session 40 Galaxies
Poster, Tuesday, June 1, 2004, 10:00am-7:00pm, Ballroom

## [40.06] The Sinusoidal Potential and Spiral Galaxies

G. R. Wilson, D. F. Bartlett ()

In the sinusoidal potential (Bartlett, 2001) the numerator of Newton's law is replaced by GM cos(ko r) where ko = 2\pi/\lambdao and the'wavelength' \lambdao is 425 pc. When this potential is used with an extended mass distribution, the distant potential from any multipole moment diminishes simply as 1/r. Suppose the mass distribution to be azimuthally symmetric and symmetric about the galactic equator. Then the distant potential factors into radial and angular parts, \phi(r,b)= [cos (ko r)/r] [\Sigma a2n P2n(sin b)], where the a2n are coefficients determined by the mass distribution and the P2n are the Legendre polynomials. The summation stops at about n=6 for the Milky Way.

We will show that the potential depends critically on whether or not odd n's as well as even contribute to the sum. In the latter case the galaxy is likely to have a substantial bulge and to have strong distant potentials near the poles as well as on the equator. This is the case for the Milky Way, where we relate the strong polar potential to the break-up of the Sagittarius Dwarf Spheroidal.

Alternatively, a disk-only galaxy, such as M33, has contributions from both odd and even terms and no strong distant potential away from the equator. If any galaxy has just an exponential disk, the predicted dependence of the rotation velocity on the luminosity and the decay length of the disk is particularly simple.

Bulletin of the American Astronomical Society, 36 #2
© YEAR. The American Astronomical Soceity.