187 research outputs found
l=1::Weinberg's weakly damped mode in an N-body model of a spherical stellar system
Spherical stellar systems such as King models, in which the distribution
function is a decreasing function of energy and depends on no other invariant,
are stable in the sense of collisionless dynamics. But Weinberg showed, by a
clever application of the matrix method of linear stability, that they may be
nearly unstable, in the sense of possessing {\sl weakly} damped modes of
oscillation. He also demonstrated the presence of such a mode in an -body
model by endowing it with initial conditions generated from his perturbative
solution. In the present paper we provide evidence for the presence of this
same mode in -body simulations of the King model, in which the
initial conditions are generated by the usual Monte Carlo sampling of the King
distribution function. It is shown that the oscillation of the density centre
correlates with variations in the structure of the system out to a radius of
about 1 virial radius, but anticorrelates with variations beyond that radius.
Though the oscillations appear to be continually reexcited (presumably by the
motions of the particles) we show by calculation of power spectra that
Weinberg's estimate of the period (strictly, divided by the real part of
the eigenfrequency) lies within the range where the power is largest. In
addition, however, the power spectrum displays another very prominent feature
at shorter periods, around 5 crossing times.Comment: 9 pages, 6 figures, footnote added in Sec.3.2, no other change to the
version published in MNRA
The Kinematic Richness of Star Clusters - II. Stability of Spherical Anisotropic Models with Rotation
International audienc
Black box probabilistic numerics
Peer reviewe
Mapping the stability of stellar rotating spheres via linear response theory
Rotation is ubiquitous in the Universe, and recent kinematic surveys have
shown that early type galaxies and globular clusters are no exception. Yet the
linear response of spheroidal rotating stellar systems has seldom been studied.
This paper takes a step in this direction by considering the behaviour of
spherically symmetric systems with differential rotation. Specifically, the
stability of several sequences of Plummer spheres is investigated, in which the
total angular momentum, as well as the degree and flavour of anisotropy in the
velocity space are varied. To that end, the response matrix method is
customised to spherical rotating equilibria. The shapes, pattern speeds and
growth rates of the systems' unstable modes are computed. Detailed comparisons
to appropriate N-body measurements are also presented. The marginal stability
boundary is charted in the parameter space of velocity anisotropy and rotation
rate. When rotation is introduced, two sequences of growing modes are
identified corresponding to radially and tangentially-biased anisotropic
spheres respectively. For radially anisotropic spheres, growing modes occur on
two intersecting surfaces (in the parameter space of anisotropy and rotation),
which correspond to fast and slow modes, depending on the net rotation rate.
Generalised, approximate stability criteria are finally presented.Comment: 18 pages, 20 figures. Submitted to MNRA
Gravothermal oscillations in multi-component models of star clusters
In this paper, gravothermal oscillations are investigated in multi-component
star clusters which have power law initial mass functions (IMF). For the power
law IMFs, the minimum masses () were fixed and three different maximum
stellar masses () were used along with different power-law exponents
() ranging from 0 to -2.35 (Salpeter). The critical number of stars at
which gravothermal oscillations first appear with increasing was found
using the multi-component gas code SPEDI. The total mass () is seen to
give an approximate stability condition for power law IMFs with fixed values of
and independent of . The value is shown to give an approximate stability condition which is also
independent of , though the critical value is somewhat higher for the
steepest IMF that was studied. For appropriately chosen cases, direct N-body
runs were carried out in order to check the results obtained from SPEDI.
Finally, evidence of the gravothermal nature of the oscillations found in the
N-body runs is presented.Comment: 9 pages, 3 figures, 8 tables. Accepted for publication in MNRA
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