726 research outputs found
Dynamics of One-dimensional Self-gravitating Systems Using Hermite-Legendre Polynomials
The current paradigm for understanding galaxy formation in the universe
depends on the existence of self-gravitating collisionless dark matter.
Modeling such dark matter systems has been a major focus of astrophysicists,
with much of that effort directed at computational techniques. Not
surprisingly, a comprehensive understanding of the evolution of these
self-gravitating systems still eludes us, since it involves the collective
nonlinear dynamics of many-particle systems interacting via long-range forces
described by the Vlasov equation. As a step towards developing a clearer
picture of collisionless self-gravitating relaxation, we analyze the linearized
dynamics of isolated one-dimensional systems near thermal equilibrium by
expanding their phase space distribution functions f(x,v) in terms of Hermite
functions in the velocity variable, and Legendre functions involving the
position variable. This approach produces a picture of phase-space evolution in
terms of expansion coefficients, rather than spatial and velocity variables. We
obtain equations of motion for the expansion coefficients for both
test-particle distributions and self-gravitating linear perturbations of
thermal equilibrium. N-body simulations of perturbed equilibria are performed
and found to be in excellent agreement with the expansion coefficient approach
over a time duration that depends on the size of the expansion series used.Comment: 12 pages, accepted for publication in MNRA
Semi-analytical dark matter halos and the Jeans equation
Although N-body studies of dark matter halos show that the density profiles,
rho(r), are not simple power-laws, the quantity rho/sigma^3, where sigma(r) is
the velocity dispersion, is in fact a featureless power-law over ~3 decades in
radius. In the first part of the paper we demonstrate, using the semi-analytic
Extended Secondary Infall Model (ESIM), that the nearly scale-free nature of
rho/sigma^3 is a robust feature of virialized halos in equilibrium. By
examining the processes in common between numerical N-body and semi-analytic
approaches, we argue that the scale-free nature of rho/sigma^3 cannot be the
result of hierarchical merging, rather it must be an outcome of violent
relaxation. The empirical results of the first part of the paper motivate the
analytical work of the second part of the paper, where we use rho/sigma^3
proportional to r^{-alpha} as an additional constraint in the isotropic Jeans
equation of hydrostatic equilibrium. Our analysis shows that the constrained
Jeans equation has different types of solutions, and in particular, it admits a
unique ``periodic'' solution with alpha=1.9444. We derive the analytic
expression for this density profile, which asymptotes to inner and outer
profiles of rho ~ r^{-0.78}, and rho ~ r^{-3.44}, respectively.Comment: 37 pg, 14 fig. Accepted to ApJ: added two figures and extended
discussion. Note that an earlier related paper (conference proceedings)
astro-ph/0412442 has a mistake in eq.(2.2); the correct version is eq.(5) of
the present submissio
The Radial Orbit Instability in Collisionless N-Body Simulations
Using a suite of self-gravitating, collisionless N-body models, we
systematically explore a parameter space relevant to the onset and behavior of
the radial orbit instability (ROI), whose strength is measured by the systemic
axis ratios of the models. We show that a combination of two initial
conditions, namely the velocity anisotropy and the virial ratio, determines
whether a system will undergo ROI and exactly how triaxial the system will
become. A third initial condition, the radial shape of the density profile,
plays a smaller, but noticeable role. Regarding the dynamical development of
the ROI, the instability a) begins after systems collapse to their most compact
configuration and b) evolves fastest when a majority of the particles have
radially anisotropic orbits while there is a lack of centrally-concentrated
isotropic orbits. We argue that this is further evidence that self-reinforcing
torques are the key to the onset of the ROI. Our findings support the idea that
a separate orbit instability plays a role in halting the ROI.Comment: accepted for publication in ApJ. 9 figures in emulateapj styl
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