**AAS 204th Meeting, June 2004**

*Session 40 Galaxies*

Poster, Tuesday, June 1, 2004, 10:00am-7:00pm, Ballroom
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## [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(k_{o} r) where k_{o} =
2\pi/\lambda_{o} and the'wavelength' \lambda_{o} 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 (k_{o} r)/r]
[\Sigma a_{2n} P_{2n}(sin b)], where the a_{2n} are
coefficients determined by the mass distribution and the
P_{2n} 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.

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Bulletin of the American Astronomical Society, **36** #2

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