Galactic Discs

Secular-D: the cosmic fate of galactic discs 

WPD1:Radial migration via churning and blurring Most stars, perhaps all, are born in stellar discs. Major mergers destroyed some of these discs quite early in the history of the universe, but some discs have survived up to the present day, including the Milky Way. Understanding the secular dynamics of stellar discs therefore appears as an essential ingredient of cosmology, as the discs’ cosmological environments are now firmly established in the ΛCDM model. Self-gravitating stellar discs are cold responsive dynamical systems in which rotation provides an important reservoir of free energy and where orbital resonances play a key role. The availability of free energy leads to some stimuli being strongly amplified, while resonances tend to localise their dissipation, with the net result that even a very small perturbation can lead to discs evolving to significantly distinct equilibria. These discs are embedded in various sources of gravitational noise, from shot noise arising from the finite number of giant molecular clouds in the interstellar medium to globular clusters and substructures orbiting around the galaxy.

Spiral arms in the gas distribution also provide another source of fluctuations, while the central bar of the disc offers yet another coherent stimuli. The history of galactic discs likely comprises the joint responses to all these various stimuli (internal and external). 
One can find in the solar neighbourhood at least three illustrations of such effects. First, the random velocity of each coeval cohort of stars increases with the cohort’s age (Wielen,’77; Aumer+’09). In addition, the velocity distribution around the Sun exhibits several ‘streams’ of stars (Dehnen,’98). Each of these streams contains stars of various ages and chemistries, which are all responding to some stimulus in a similar fashion (Famaey+’05). Finally, in the two-dimensional action-space, resonant ridges form and play an important role in the secular dynamics of razor-thin stellar discs, as argued in Sellwood+’14. Indeed, Gaia’DR2 has revealed a very rich structure in local velocity space, which is related to resonances with multiple non-axisymmetric patterns (including the bar) and possibly to incomplete phase-mixing. In terms of in-plane motions, this rich structure is also seen as ridges in the actions of the axisymmetric background potential of the Galaxy. We have preliminary shown (Monari+’19) that a second prominent ridge in action space then corresponds to the 4:1 outer resonance of the m = 4 mode of such a bar, and that the velocity structure seen as an arch at high azimuthal velocities in Gaia data can be related to its 2:1 outer Lindblad resonance. Direct numerical simulations of thin stellar discs over secular timescales are very challenging because their two dimensional geometry combined with their responsiveness causes discreteness noise to be important unless very large number of particles is employed. It is only recently that it became possible to simulate a disc with a sufficient number of particles for Poisson shot noise to be dynamically unimportant for many orbital times. A complementary approach to understand their dynamics is therefore to rely on extended kinetic theory via a stochastic framework. This will be the topic of this WP, relying on in WPT2 for validation. SEGAL will follow up on Fouvry+’15 and evolve both kinetic equations in this context, accounting for mass and angular momentum inflow within the disc, and modeling self-consistently churning (drift in guiding center) and blurring (heating) over a Hubble time, while accounting for secular cold gas infall from the large-scale-structure environment (Pichon+’11, Kimm+’11), see WPH2. A realistic radial profile of accreted cold gas is a requirement for the chemo-dynamical modelling of the Milky Way.

WPD2: Galactic disc thickening/settling The problem of explaining the origin of thick discs in our Galaxy has been around for some time (e.g. Gilmore+’83). The interest for this dynamical question has been revived recently in the light of the APOGEE survey (Eisenstein+’11) and Gaia data. Star formation within stellar discs typically occurs on the circular orbits of the gas, so that young stars should form a very thin disc (Wielen’77). However, chemo-kinematic observations of old stars within our Milky Way (Jurić+’08; Bovy+’12) or in other galactic discs (Burstein’79; Comerón+’11) have all shown that thick components are very common. Yet the formation of thickened stellar discs remains a significant puzzle for galactic formation theory. Various dynamical mechanisms, either internal or external, have been proposed to explain the observed thickening, but their respective impacts and roles remain to be quantified. First, some violent major events could be at the origin of the vertically extended distribution of stars in disc galaxies: accretion of galaxy satellites (Meza+’05; Abadi+’03), major mergers of gas-rich systems (Brook+’04), or even gravitational instabilities in gas-rich turbulent clumpy discs (Noguchi’98). Violent mergers definitely have a strong impact on galactic structure, but thickened stellar discs could also originate from the slow and continuous heating of pre-existing thin discs, via for example galactic infall leading to multiple minor mergers (Toth+’92; Villalobos+’08). Spiral density waves (Sellwood+’84; Monari+’16) are also possible candidates to increase the disc's velocity dispersion, which can be converted into vertical motion through deflections from giant molecular clouds (GMCs) (Spitzer+’53; Hänninen+’02). In addition, radial migration could also play an important rol­e in the secular evolution of stellar discs. This migration could be induced by spiral-bar coupling (Minchev+’10), transient spiral structures (Barbanis+’67; Solway+’12), or perturbations induced by minor mergers (Bird+’12). Finally, recent large numerical simulations are now attempted in a self-consistent cosmological setup (Grand+’16), to probe the interplay between these competing mechanisms (Fig. 5). All investigations can be broadly characterised as induced by an external or internal source of fluctuations to trigger a vertical orbital reshuffling in the disc. SEGAL will quantify in WPD2 the expected cosmic evolution of the vertical structure of the disc and its population, relying on the multi-component generality of the kinetic formalism. This will involve building perturbatively thickened equilibria with a mapping in action-space from an integrable to a non-integrable model via fits of generating functions (Kaasalainen+’94, see WPT1 below). We will then solve the exact field equations, construct an appropriate basis of potentials, and deal with the full response matrix in order to solve for the corresponding Balescu-Lenard and Fokker Planck equations. Validation will be done in WPT2. We will finally derive the corresponding global kinetic observables: age-vertical dispersion gradients and 3D velocity ellipsoid as a function of position and cosmic age and population, etc.

WPD3: Galactic bar buckling/ dissolution Gaia data viewed in action-space is, as predicted, fairly structured in the solar neighbourhood (see Fig 2). Some of these ridges are possibly transients, while others are of secular nature (Fig. 4). For instance, the impact of the recurrent Galactic bar falls within the formalism of resonant relaxation captured by the Fokker Planck and possibly the Balescu-Lenard equa-tions. In connection with WPT1 and our recent work on IBL for the Hamiltonian mean field model (Benetti+’17, Artemyev+’18), an abstraction for resonances near a bar, we will study how collisional-driven separatrix crossing can explain dissolution and/or buckling (Antoja+’18, Khoperskov+’01). It would be of interest to revisit – in the context of kinetic theory –Binney+19, who relied on an ‘impulse approximation’ while neglecting the self-gravity of the disc, possibly missing the partly self-sustained vertical perturbation present up to 3 Gyr after bar buckling (Khoperskov+’18).

Results & Deliverables: Computations of the timescale for disc thickening, while accounting for self-gravity, as induced by, e.g. DM halo fluctuations, GMCs, passing-by satellites. Computations of the diffusion coefficients in orbital space for churning (diffusion in angular momentum) and blurring (diffusion in eccentricity), while accounting for self-gravity, as induced by different heating mechanisms, e.g. bars, spiral arms, GMCs, passing-by satellites, and DM halo fluctuations. Characterisation of diffusion in extended phase space, i.e. accounting for metallicity and age, and the respective signatures associated with the different heating sources. Global asymptotic and steady-state solution for exponential discs. Characterisation of the orbital diffusion signatures in the vicinity of the Sun, as traced by GAIA DR2 via marginals of DF(J,τ) and the corresponding kinetic estimators. Theory for bar dissolution and buckling. Self-consistent model for cosmic disc settling.