arXiv subjects

J. Perez

Publications and source records attributed to J. Perez.

23 records · Page 2Linked to original sources

arXiv2003

Dissipationless collapse of a set of N massive particles

The formation of self-gravitating systems is studied by simulating the collapse of a set of N particles which are generated from several distribution functions. We first establish that the results of such simulations depend on N for small values of N. We complete a previous work by Aguilar and Merritt concerning the morphological segregation between spherical and elliptical equilibria. We find and interpret two new segregations: one concerns the equilibrium core size and the other the equilibrium temperature. All these features are used to explain some of the global properties of self-gravitating objects: origin of globular clusters and central black hole or shape of elliptical galaxies.

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arXiv1999

Stability of rotating spherical stellar systems

We study the stability of rotating collisionless self-gravitating spherical systems by using high resolution N-body experiments on a Connection Machine CM-5. We added rotation to Ossipkov-Merritt (hereafter OM) anisotropic spherical systems by using two methods. The first method conserves the anisotropy of the distribution function defined in the OM algorithm. The second method distorts the systems in velocity space. We then show that the stability of systems depends both on their anisotropy and on the value of the ratio between the total kinetic energy and the rotational kinetic energy. We also test the relevance of the stability parameters introduced by Perez et al. (1996) for the case of rotating systems.

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arXiv1995

A symplectic approach to gravitational instability

We present a global approach of non-dissipative physics. Based on symplectic mechanics this technique allows us to obtain the solution of a very large class of problems in terms of a Taylor expand. We apply this method to the problem of gravitational instability and we obtain a general expression of the gravitational potential, solution of the Vlasov- Poisson gravitational potential, solution of the Vlasov-Poisson system, as a function of time in the context of Newtonian dust cosmology.

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arXiv1995

Stability of spherical stellar systems I : Analytical results

The so-called ``symplectic method'' is used for studying the linear stability of a self-gravitating collisionless stellar system, in which the particles are also submitted to an external potential. The system is steady and spherically symmetric, and its distribution function $f_0$ thus depends only on the energy $E$ and the squarred angular momentum $L^2$ of a particle. Assuming that $\partial f_0 / \partial E < 0$, it is first shown that stability holds with respect to all the spherical perturbations -- a statement which turns out to be also valid for a rotating spherical system. Thus it is proven that the energy of an arbitrary aspherical perturbation associated to a ``preserving generator" $δg_1$ [i.e., one satisfying $\partial f_0 / \partial L^2 \{ δg_1, L^2 \} = 0$] is always positive if $\partial f_0 / \partial L^2 \leq 0$ and the external mass density is a decreasing function of the distance $r$ to the center. This implies in particular (under the latter condition) the stability of an isotropic system with respect to all the perturbations. Some new remarks on the relation between the symmetry of the system and the form of $f_0$ are also reported. It is argued in particular that a system with a distribution function of the form $f_0 = f_0 (E,L^2)$ is necessarily spherically symmetric.

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arXiv1995

Stability of spherical stellar systems II : Numerical results

We have performed a series of high resolution N-body experiments on a Connection Machine CM-5 in order to study the stability of collisionless self-gravitating spherical systems. We interpret our results in the framework of symplectic mechanics, which provides the definition of a new class of particular perturbations: The preserving perturbations, which are a generalization of the radial ones. Using models defined by the Ossipkov-Merritt algorithm, we show that the stability of a spherical anisotropic system is directly related to the preserving or non-preserving nature of the perturbations acting on the system. We then generalize our results to all spherical systems. Since the ``isotropic component'' of the linear variation of the distribution function cannot be used to predict the stability or instability of a spherical system, we propose a more useful stability parameter which is derived from the ``anisotropic'' component of the linear variation.

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