The dynamical phase transitions of stellar systems and the corresponding kinematics

Abstract

External fields in Migromian dynamics (MD or MOND, Milgrom 1983) break the Strong Equivalence Principle (SEP) and change the dynamics of self-bound stellar systems moving in space-varying background gravitational fields. We study two kinds of re-virialisation of the stellar systems: the violent phase transition and the adiabatic phase transition for systems moving on radial orbits, where the external field evolves from strong to weak and whose corresponding dynamics changes from Newtonian to Milgromian. We find that the time scale for the phase tranformation from Newtonian to Milgromian gravity lies only within one to a few crossing times for low density globular clusters with masses ranging from $10^4\msun$ to $10^6\msun$. Thus a globular cluster can appear frozen in the Newtonian regime despite being in the Milgromian regime for not longer than a few crossing times. We also study the kinematics and anisotropy profiles of the systems. The velocity dispersions of the systems are larger after the phase transitions, especially for the outer regions of the stellar systems. Moreover, the isotropic systems become radially anisotropic, especially for the outer parts, after the process caused by the dynamical phase transition. Deeper Milgromian systems have more radially anisotropic velocity dispersion functions. We also find that the final profiles of density, velocity dispersion and anisotropy do not depend on the details of the phase transition. I.e., the mass distribution and kinematics of the end-states of the globular clusters do not depend on the rapidity of the transition from Newtonian to Milgromian gravity. Thus, the transition from the Newtonian to the Milgromian regime naturally induces a significant radially anisotropic velocity distribution in a globular cluster.