Using the theory describing the evolution of a galaxy halo due to stochastic fluctuations developed in the companion paper, we show that a halo quickly evolves toward the same self-similar profile, independent of its initial profile and concentration. The selfsimilar part of profile takes the form of a double power law with inner and outer exponents taking the values near −1.5 and −3 respectively. The precise value of the inner exponent depends on the magnitude and duration of the noisy epoch and most likely on form of the inner profile to start. The outer exponent is the result of evolution dominated by the external l = 1 multipole resulting from the inner halo’s response to noise. Three different noise processes are studied: (1) a bombardment by blobs of mass small compared to the halo mass (‘shrapnel’); (2) orbital evolution of substructure by dynamical friction (‘satellites’); and (3) noise caused by the orbit of blobs in the halo (‘black holes’). The power spectra in the shrapnel and satellite cases is continuous and results in the double power law form, independent of initial conditions. The power spectrum for black holes is discrete and has a different form with a much slower rate of evolution. A generic prediction of this study is that noise from transient processes will drive evolution toward the same double power law with only weak constraints on the noise source and initial conditions.
Weinberg, Martin D., "Noise-driven Evolution in Stellar Systems: A Universal Halo Profile" (2008). Astronomy Department Faculty Publication Series. 17.