arXiv subjects

Jun Yan Lau

Publications and source records attributed to Jun Yan Lau.

6 recordsLinked to original sources

arXiv2026

Boltzmann Equation Field Theory I: Ensemble Averages

I present an unbiased method of mapping particles to distribution functions and vice versa. This method alone defines the canonical formulation of statistical mechanics, since it can be used to derive the principle of maximum entropy in both Boltzmann's paradigm and Gibbs' paradigm. A rigorous definition of the macrostate enables application of this statistical mechanical theory to self-gravitating systems, by decoupling time-averages and ensemble averages. I compute two-point correlation functions for self-gravitating and electrostatic systems.

astro-ph.GA↗

arXiv2026

Velocities of Free Floaters in a Sea of Stars

We investigate the velocity evolution of free-floating planets and interstellar objects (``free floaters'') through gravitational scatterings by field stars (with the stellar mass $m$ much larger than the mass of the floater, $m_p$). We show that the equilibrium velocity -- where dynamical friction balances stochastic acceleration -- is given by $σ\sqrt{2\ln(m/m_p)}$ (where $σ$ is the velocity disperson of the field stars), diverging from the standard energy equipartition scaling. While the timescale to reach this equilibrium is prohibitively long, we find that slow floaters ($v \lesssim σ$) undergo mass-independent acceleration, doubling their velocities within a few relaxation times. Consequently, free floaters initially following the Maxwellian distribution of their parent stars develop distinctly non-Maxwellian velocity distributions on a relaxation timescale. Since the relaxation time of the Galactic disk is longer than the age, our results suggest that the kinematics of low-mass free floaters in the disk may preserve signatures of their parent stars and ejection history.

astro-ph.EP↗

arXiv2021

Modes of a stellar system II: non-ergodic systems

An equation is derived for the energy of a small disturbance in a system that is generated by a distribution function (DF) of the form $f(\vJ)$ -- most galaxies and star clusters can be closely approximated by such a DF. The theory of van Kampen modes is extended to such general systems. An inner product on the space of DFs is defined such that the energy of a disturbance is its norm under this product. It is shown that van Kampen modes that differ in frequency are then orthogonal, with the consequence that the energies of van Kampen modes are additive. Consequently, most of the insight into the dynamics of ergodic systems that was gained in a recent paper on the van Kampen modes of ergodic systems applies to real clusters and galaxies.

astro-ph.GA↗

arXiv2021

Probabilistic distribution functions

Observed clusters should be modelled by considering the distribution function to be a random variable that quantifies the degree of excitation of the system's normal modes. A system of canonical coordinates for the space of DFs is identified so DFs can be weighted in a consistent way.

astro-ph.GA↗

arXiv2021

Modes of a stellar system I: ergodic systems

The excursions of star clusters and galaxies around statistical equilibria are studied. For a stable ergodic model Antonov's Hermitian operator on six-dimensional phase space has the normal modes as its eigenfunctions. The excitation energy of the system is just the sum of the (positive) energies associated with each normal mode. Formulae are given for the DFs of modes, which are of the type first described by van Kampen rather than Landau, and Landau `modes' can be expressed as sums of van Kampen modes. Each van Kampen mode comprises the response of non-resonant stars to driving by the gravitational field of stars on a group of resonant tori, so its structure is sensitive to the degree of self gravity. The emergence of global distortions in N-body models when particles are started from an analytical equilibrium is explained in terms of the interplay of normal modes. The positivity of modal energies opens the way to modelling the thermal properties of clusters in close analogy with those of crystals.

astro-ph.GA↗

arXiv2019

Relaxation of spherical stellar systems

10,000 simulations of 1000-particle realisations of the same cluster are computed by direct force summation. Over three crossing times the original Poisson noise is amplified more than tenfold by self-gravity. The cluster's fundamental dipole mode is strongly excited by Poisson noise, and this mode makes a major contribution to driving diffusion of stars in energy. The diffusive flow through action space is computed for the simulations and compared with the predictions of both local-scattering theory and the Balescu-Lenard (BL) equation. The predictions of local-scattering theory are qualitatively wrong because the latter neglects self-gravity. These results imply that local-scattering theory is of little value. Future work on cluster evolution should employ either N-body simulation or the BL equation. However, significant code development will be required to make use of the BL equation practicable.

astro-ph.GA↗