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*Astron. Astrophys. 338, 819-839 (1998)*
## Tilting of a disk of self-gravitating rings
**
R.V.E. Lovelace
**
Department of Astronomy, Cornell University, Ithaca, NY
14853-6801, USA (e-mail: rvl1@cornell.edu)
*Received 6 April 1998 / Accepted 6 July 1998*
**Abstract**
The present work represents an attempt to understand the `rules of
behavior' of observed warps in the HI disks of spiral galaxies found
by Briggs (1990). In contrast with most earlier theoretical work, the
present study investigates different initial value problems of a
warped disk in an oblate (or prolate) halo potential, and it
represents the disk warp in terms of *N* independently tilted,
self-gravitating, concentric rings. This representation gives new
insight into the disk warping. The phenomenon of phase-locking of the
lines-of-nodes of nearby rings due to self-gravity is demonstrated. We
consider the influence of dynamical friction due to ring motion
through the halo matter as well as friction between gaseous rings with
different vertical motions due to turbulent viscosity. We first
consider the dynamics of one, two, and three tilted rings of different
radii in a halo potential. We go on to develop dynamical equations for
rings which are most simply expressed in terms of
the complex tilt angles , where
is the actual tilt angle and
the line-of-nodes angle for the
ring (). Relatively small
values of *N* () are sufficient to describe
the warp evolution during the age of a galaxy during which time
discrete modes are not important. The equations for
are solved numerically for four different types
of initial conditions: (1) warp excitation by a passing
satellite, (2) excitation by a sinking compact minor satellite,
(3) warp evolution due to a tilted halo potential, and
(4) warp evolution resulting from an initially tilted disk plane.
The nature of the warps is most clearly shown by the polar plots of
versus .
**Key words:** galaxies: kinematics and
dynamics
galaxies:
spiral
galaxies: structure
SIMBAD Objects
### Contents
© European Southern Observatory (ESO) 1998
Online publication: September 17, 1998
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