SEGAL:The Secular Evolution of GALaxies

Context: Galaxies are unique laboratories to test the universal law of gravity, the driving force from their inner cores to their outskirts. Astronomers have recently focused significant amounts of theoretical, computational and observational efforts to understand and explain their cosmic evolution. This rising interest can be explained by the alignment of three transformational shifts:

ii) Second, the steady increase in computing power allows us to perform numerical simulations of resolution and complexity greater than ever before in the context of the Cold Dark Matter (CDM) paradigm. Such a framework is now well-established and successfully describes the formation of structures on large scales, but several challenges are still present on the smaller ones. In this respect, the development of progressively more accurate numerical simulations is essential. This applies not only to isolated and idealised setups, but also to account statistically for the fluctuating environment on different scales, from galactic centers to the outskirts of dark halos. These self-gravitating astrophysical systems can therefore now be considered nested, embedded in their own lively environment, with which they interact throughout their lifetime;

Building upon the seminal works describing the linear response of self-gravitating systems (by Goldreich, Lynden-Bell, Toomre, Kalnajs and others), the development in kinetic theory of a self-consistent framework to characterise their quasi-linear response (Weinberg’01) now offers us a unique opportunity to follow galaxies over cosmic timescales. As for the Earth, galaxies are indeed subject to ‘weather’ and ‘climate’. The former is driven by transients (which reflect recent disturbances which have not yet phase mixed), while the latter encodes distinctive features specifically in orbital space generated over long (secular) timescales. Quasi-linear theory captures the latter. It is, therefore, ideally suited to describe galaxies on large and small scales, because their dynamical times are very short compared to a Hubble time. For galaxies, the most significant (non serendipitous) processes are secular in nature. This motivates the present proposal: through the corresponding stochastic differential equations (SDE), galactic dynamics can now make statistical predictions over cosmic times.

The kinetic developments
rely on the inhomogeneous
Balescu-Lenard (IBL) equation (Heyvaerts’10,
and Figure 1 below), i.e. the master equation describing self-induced
fluctuations on the one hand, and a proper accounting of
environmentally- driven fluctuations and their gravitational
amplification, captured by the dressed Fokker-Planck (dFP) equation on
the other hand1.
These equations allow us to gauge the
respective roles of nature
vs. nurture in
establishing the long term observed kinetic properties of galaxies,
relying on stochastic processes which capture all sources of
fluctuations. The corresponding extended kinetic theories (see e.g.
Fouvry+’15,’18
and footnote 1 for a mini review) define a computational framework to
quantify statistically the long-term evolution of self-gravitating
systems, complementing (commonly used) N-body methods. Qualitatively,
these kinetic equations all involve diffusion coefficients in orbital
(action) space, Dm(J),
scaling like the power spectrum of the dressed potential fluctuations
projected along the unperturbed trajectories (with m
the harmonic number of the resonance, J
the action and Ω
the frequencies):