Critical Dynamics under the Vlassov-Poisson Equations: Critical Exponents and Scaling of the Distribution Function near the Point of a Marginal Stability

Details Critical Dynamics under the Vlassov-Poisson Equations: Critical Exponents and Scaling of the Distribution Function near the Point of a Marginal Stability Critical Dynamics under the Vlassov-Poisson Equations: Critical Exponents and Scaling of the Distribution Function near the Point of a Marginal Stability

Apr 2001

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2001apj...550..622i&link_type=abstract

The Astrophysical Journal, Volume 550, Issue 2, pp. 622-634.

Astronomy and Astrophysics

Astronomy

3

Chaos, Galaxies: Spiral, Galaxies: Structure, Gravitation, Instabilities

Scientific paper

Using direct integration of the Vlassov equation in configurational space, nonlinear dynamics of a model one-dimensional periodic self-gravitating system are investigated near the point of a marginal stability. The critical velocity dispersion σ2cr, corresponding to a marginal stability of the Jeans mode with the least k, is assumed as the critical point. The peak amplitude of the Jeans mode computed in a run is assumed as the order parameter. In the neighborhood of the critical point, the dynamics can be described by a set of the power laws typical for a system undergoing a second-order phase transition. For the order parameter, this is A~-θβ, where β=1.907+/-0.006 and θ=(σ2- σ2cr)/σ2cr<0. At θ=0 the response depends on the strain F1 of external drive as A~F1/δ1, where δ=1.544+/-0.002. The susceptibility χ=∂A/∂F1, F1-->0, diverges as χ~|θ|-γ+/- as θ-->+/-0, γ-=1.020+/-0.008 for θ<0, and γ+=0.995+/-0.020 for θ>0. Under this accuracy, these critical exponents satisfy the equality γ+/-=β(δ-1). For a gravitating system, its existence is a direct consequence of scaling invariance of the distribution function at |θ|<<1 i.e., f(λatt, x, λavv, λaθθ, λaA0A0, λaFF1)=λf(t, x, v, θ, A0, F1). These critical exponents indicate a wide critical area where critical phenomena may determine macroscopic dynamics. The random external drive field of a small amplitude causes anomalous growth of the marginally stable Jeans perturbation into a spatially coherent structure.

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