## Galactic Halos

#### Secular-H: Restructuring live and open halos

**WPH1 The cusp-core problem of galactic halos** Dark matter (DM) only simulations favour the formation of a cusp in the inner region of DM haloes (Dubinski+’91; Navarro+’97), following what appears to be a universal cuspy profile, the NFW profile. However, observations tend to recover profiles more consistent with a shallower core (Moore’94; de Blok+’02). This discrepancy between the cuspy profile predicted by direct DM-only simulations and the core profile inferred from observations is an important challenge in cosmology, coined the cusp-core problem. Various solutions have been proposed to resolve this discrepancy. A first set of solutions involves modifying the dynamical properties of the collisionless DM, preventing it from collapsing into cuspy profile in the first place. Examples include the possibility of warm dark matter (Kuzio de Naray+’10) or of self-interacting dark matter (Spergel+’00). Another set of investigations rely on the idea that not accounting self-consistently for the baryonic physics and its back-reactions on the DM may also be at the origin of the discrepancy. These mechanisms can be divided into three broad categories. The first one relies on dynamical friction from infalling baryonic clumps and disc instabilities (El-Zant+’01; Weinberg+’02; Goerdt+’10; Del Popolo+’16). A second mechanism is associated with AGN-driven feedback (Peirani+’08; Martizzi+’12; Dubois+’16). Finally, a third option involves the long-term fluctuations associated with supernova-driven feedback (Binney+’01; Penarrubia+ '12). The collisionless diffusion equation is the ideal framework to investigate in detail their role on the secular evolution of DM haloes.
In SEGAL, the first step will be to characterise these fluctuations. To do so, we will rely on hydrodynamical simulations, see Fig. 6.

In order to decouple the source of perturbations, i.e. the disc, from the perturbed system, i.e. the halo, these simulations are performed while using a static and inert halo. Such a setup allows us to measure and characterise the statistical properties of the fluctuations induced by the disc directly from simulations. Because the DM halo is analytical, this also prevents any shot noise associated with using a finite number of DM particles. Once these fluctuations are estimated, their effects on the DM halo may then be quantified using the secular collisionless diffusion equation. In order to characterise these fluctuations, we will consider an analytic NFW halo profile, and embed within it a gaseous and stellar disc, after preparing the system in a quasi-stationary state. In addition, we will implement supernova feedback allowing for the release of energy from the supernova into the interstellar medium. Figure 5 illustrates two successive snapshots of such a hydrodynamical simulation. In this figure, one can note that because of supernova feedback, the gas density fluctuates. These fluctuations in the potential due to the gas will be felt by the DM halo and may therefore drive resonant secular diffusion in the DM halo. We will ensemble-average various realisations of this same physical setup. The same approach will allow us to investigate how much this diffusion depends on the strength of the feedback, while changing the recipes (e.g. cooling/heating, etc.) used in the hydrodynamical simulations. We will quantify the typical fluctuation power spectrum and find quantitative bounds on feedback strengths sufficient to induce a softening of the DM halo’s profile. Similarly, the diffusion efficiency w.r.t. the disc and halo masses will also be investigated. Finally, the efficiency of AGN feedback to induce secular diffusion on larger scales in more massive DM halo will also be quantified with the same toolbox.

**WPH2: The cosmic fate of open halos and galaxies** It now appears clearly that the dynamical (azimuthal instabilities, warps, accretion), physical (heating, cooling) and secular (radial migration) evolution of galaxies are processes which are in part driven by the nature of their live halo, in particular by the boundary conditions imposed by their cosmic environment (e.g. Stewart+’16).It is therefore of prime importance to quantify the secular response of a galaxy or a halo induced by its interaction with this near environment. Interaction should be understood in a general sense and involve tidal potential interactions (like that corresponding to a satellite orbiting around the galaxy), shot noise (e.g. the population of globular clusters within the halo), and infall, where external components (virialized or not) are advected into the halo (Weinberg’93).

Halo transmission and amplification can then foster communication between spatially separated regions through gravitational wakes (see e.g. Murali’99) and continuously excites the galactic structure. For example, spirals can be induced by encounters with satellites and/or by mass injection (e.g. Toomre +’72; Howard+’90), while warps result from torque interactions with the surrounding matter (Jiang+’99).

The statistical link between the inner properties of galactic haloes, and their cosmic boundary can be reversed to attempt and constrain the strength of infall while investigating their secular evolution. Following Pichon+’06, the dressed Fokker Planck equation will be extended in SEGAL and applied to systems open to their cosmic environment. We will derive the kinetic equation which governs the quasi-linear evolution of DM profiles induced by cosmic infall. Under the assumption of ergodicity, we will relate the corresponding source, drift and diffusion coefficients of the ensemble-average distribution to the underlying cosmic two-point statistics of the infall. We will also account for the slow evolution of the underlying equilibrium over half a Hubble time (see also Aubert+’07), and quantify cold gas infall towards the disc (cf WPD1). Finally SEGAL will revisit the Balescu equation in a context where the system’s number of particles gets to evolve during secular evolution, to describe for example the dissolution of over-densities via phase mixing and tidal stripping. A connection with chemical potentials and (later stages of) violent relaxation will be addressed (see also WPT3).

**WPH3: The phase space structure of tidal streams and their progenitor clusters.T**he stellar streams within our MW’s dark halo as seen by GAIA will be analysed in terms of an impulsive diffusion process which will allow us to constrain the dark halo’s shape, its flattening and its clumpiness, (since each stream provides an estimate of the local diffusion tensor, which in turn scales like the local power-spectrum of the (dark+visible) potential). All quantities are of interest to constrain the ΛCDM paradigm on Galactic scales. One additional goal will be investigate the subtle connection between the structural and kinematic properties of the stars in the tidal tails and the phase space properties of the progenitor star clusters (Varri+ '18). It has important implications on the morphology and dynamics of the streams, as recently demonstrated by the complex outer structures of the globular cluster omega Centari, for which the modelling of the internal rotation has been crucial (Ibata+ '19, Nature). A key aspect will be the continuation of our current investigation of the fundamental role played by 'kinematic complexity' in the evolution of collisional stellar systems (Breen+ '17, 19, Rozier+ '19, Hamilton+ '19.

*Results & Deliverables:* Measurement of the power-spectrum of the potential fluctuations induced by the supernova feedback from a galactic disc, as a function of a galaxy's properties (e.g. SFR or radial profile). Implementation of the diffusion equation to constrain the timescale for the cusp-core transformation from inner baryonic perturbations, as a function of a halo's properties (e.g. mass or concentration). Measurement of the power-spectrum of fluctuations induced by a DM halo, as a function of a halo's properties (e.g. cold DM vs. fuzzy DM, role of the large-scale structures). Computation of the galactic disc heating induced by the DM halo perturbations. Formulation of a theory of angular momentum diffusion in collisional stellar systems. Characterization of the phase space properties of tidal streams resulting from progenitor clusters modelled with direct summation N-body simulations, including rotation and pressure anisotropy. Computation of the dissolution time of stellar streams from DM halo perturbations, and comparisons with constraints from GAIA measurements. Construction of a theory of inflow-driven diffusion to account for the statistics of inflows on galactic scales.