1,084 research outputs found
Disk heating by more than one spiral density wave
We consider a differentially rotating, 2D stellar disk perturbed by two
steady state spiral density waves moving at different patterns speeds. Our
investigation is based on direct numerical integration of initially circular
test-particle orbits. We examine a range of spiral strengths and spiral speeds
and show that stars in this time dependent gravitational field can be heated
(their random motions increased).This is particularly noticeable in the
simultaneous propagation of a 2-armed spiral density wave near the corotation
resonance (CR), and a weak 4-armed one near the inner and outer 4:1 Lindblad
resonances. In simulations with 2 spiral waves moving at different pattern
speeds we find: (1) the variance of the radial velocity, sigma_R^2, exceeds the
sum of the variances measured from simulations with each individual pattern;
(2) sigma_R^2 can grow with time throughout the entire simulation; (3)
sigma_R^2 is increased over a wider range of radii compared to that seen with
one spiral pattern; (4) particles diffuse radially in real space whereas they
don't when only one spiral density wave is present. Near the CR with the
stronger, 2-armed pattern, test particles are observed to migrate radially.
These effects take place at or near resonances of both spirals so we interpret
them as the result of stochastic motions. This provides a possible new
mechanism for increasing the stellar velocity dispersion in galactic disks. If
multiple spiral patterns are present in the Galaxy we predict that there should
be large variations in the stellar velocity dispersion as a function of radius.Comment: 20 pages, 13 figures. Submitted to MNRA
Harmonic Twistor Formalism and Transgression on Hyperk\"ahler manifolds
In this paper we continue our study of the fourth order transgression on
hyper\"ahler manifolds introduced in the previous paper. We give a local
construction for the fourth-order transgression of the Chern character form of
an arbitrary vector bundle supplied with a self-dual connection on a four
dimensional hyperk\"ahler manifold. The construction is based on the harmonic
twistor formalism. Remarkably, the resulted expression for the fourth order
transgression is given in terms of the determinant of the
-operator defined on fibers of the twistor fibration.Comment: 10pp., Late
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