Multiscale (time and mass) dynamics of space objects Proceedings IAU Symposium No. 364, 2021 A. Celletti, C. Beaug´ e, C. Gales & A. Lemˆaitre, eds. © 2021 International Astronomical Union DOI: 00.0000/X000000000000000X Noise, friction and the radial-orbit instability in anisotropic stellar systems: stochastic N −body simulations Pierfrancesco Di Cintio 1,2,3 and Lapo Casetti 2,3,4 1 Enrico Fermi Research Center (CREF), Via Panisperna 89A, I-00184, Rome, Italy email: pierfrancesco.dicintio@unifi.it 2 INFN, Sezione di Firenze, via G. Sansone 1, I-50019, Sesto Fiorentino (FI), Italy 3 Dipartimento di Fisica e Astronomia, Universit`a di Firenze, via G. Sansone 1, I-50019, Sesto Fiorentino (FI), Italy 4 INAF-Osservatorio astrofisico di Arcetri, largo E. Fermi 5, I-50125, Firenze, Italy Abstract. By means of numerical simulations we study the radial-orbit instability in anisotropic self-gravitating N -body systems under the effect of noise. We find that the presence of additive or multiplicative noise has a different effect on the onset of the instability, depending on the initial value of the orbital anisotropy. Keywords. stellar dynamics, galaxies: kinematics and dynamics, methods: n-body simulations, diffusion. 1. Introduction Spherically symmetric, self-gravitating collisionless equilibrium systems with a large fraction of the kinetic energy stored in low angular momentum orbits are known to be dynamically unstable. The associated instability is known as Radial Orbit Instability (hereafter ROI, see e.g. Polyachenko & Shukhman (2015) and references therein). Usually, the amount of radial anisotropy in a spherical system is quantified by introducing the Fridman-Polyachenko-Shukhman parameter (see Binney & Tremaine (2008)) ξ ≡ 2K r K t , (1.1) where the radial and tangential kinetic energies are given respectively by K r =2π  ρ(r)σ 2 r (r)r 2 dr, K t =2π  ρ(r)σ 2 t (r)r 2 dr, (1.2) ρ is the system density, and σ 2 r and σ 2 t are the radial and tangential phase-space aver- aged square velocity components, respectively. For isotropic systems ξ = 1. Numerical simulations show that the ROI typically occurs for ξ  1.7, even though it is well known that the ”real” critical value of ξ above which the given system is unstable, depends on the specific phase-space structure of the initial condition under consideration. The ROI it is frequently invoked as the mechanism responsible for the triaxiality of the elliptical galaxies and the formation of bars in disk galaxies. However, little is known on the effective nature of the underlying mechanism or its near- or far-field origin (see e.g. Polyachenko & Shukhman (2015), Di Cintio, Ciotti & Nipoti (2017) and references therein). Recently, Marechal & Perez (2010) introduced a novel interpretation of ROI as a (effective) dissipation-induced phenomenon. In this preliminary work we investigate 1 arXiv:2110.11026v1 [astro-ph.GA] 21 Oct 2021