SEGAL:The  Secular Evolution of GALaxies

  1. I.Proposal’s context, positioning and objective(s) 

A         Objectives and research hypothesis


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:

i) First, new ground-based or space instruments like Muse, Gravity, MaNGA/SAMI and Gaia are collecting an unprecedented wealth of data probing the long-term dynamical state of galaxies on all scales. We now have access to precision astrometric data on the phase-space structure of our Milky Way (literally billions of stars), complemented by statistical samples of kinetic information on large populations of galaxies;

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;

iii) Finally, recent theoretical breakthroughs in our understanding of the kinetic theory of self-gravitating systems allow us for the first time to follow the effects of gravitationally-amplified external and internal perturbation on the orbital structure of galaxies over cosmic time. In particular, we now have self-consistent integro-differential equations describing the quasi-linear evolution of a given system under the effect of self-induced (e.g. through the system’s own graininess) or externally-driven fluctuations.  

        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):


In a stellar/collisionless “fluid”, this diffusion coefficient (which drives the secular distortion of its orbital structure, following the dissipation-fluctuation theorem) is amplified by the square of its inverse gravitational susceptibility, ε, evaluated at the natural frequencies of the system. If the perturbation hits these natural frequencies while the system is not far from marginal stability, anisotropic diffusion along that resonance can be extremely efficient and cause rapid changes.

Whether they are external or self-induced, the long-term resonant effects of potential perturbations on galaxies can therefore now be accounted for in detail, by quantifying their spectral properties on small (central cluster), intermediate (disc) and large (halo, globular cluster system) scales. This distinction between processes specific to each scale is made possible by the chosen dichotomy between external and internal fluctuations. It is a requirement to capture secularly the many scales involved.

The distinction also allows us to disentangle their respective roles in sourcing secular evolution, as we quantify the diffusion signatures and the characteristic timescales associated with each source of fluctuations.