Dark matter may be composed of light bosons, m b ∼ 10 −22 eV, with a de Broglie wavelength λ ∼ 1 kpc in typical galactic potentials. Such "fuzzy" dark matter (FDM) behaves like cold dark matter (CDM) on much larger scales than the de Broglie wavelength, but may resolve some of the challenges faced by CDM in explaining the properties of galaxies on small scales ( 10 kpc). Because of its wave nature, FDM exhibits stochastic density fluctuations on the scale of the de Broglie wavelength that never damp. The gravitational field from these fluctuations scatters stars and black holes, causing their orbits to diffuse through phase space. We show that this relaxation process can be analyzed quantitatively with the same tools used to analyze classical two-body relaxation in an N -body system, and can be described by treating the FDM fluctuations as quasiparticles, with effective mass ∼ 10 7 M ⊙ (1 kpc/r) 2 (10 −22 eV/m b ) 3 in a galaxy with a constant circular speed of 200 km s −1 .This novel relaxation mechanism may stall the inspiral of supermassive black holes or globular clusters due to dynamical friction at radii of a few hundred parsecs, and can heat and expand the central regions of galaxies. These processes can be used to constrain the mass of the light bosons that might comprise FDM. * Hubble Fellow

The secular evolution of an infinitely thin tepid isolated galactic disc made of a finite number of particles is investigated using the inhomogeneous Balescu-Lenard equation expressed in terms of angle-action variables. The matrix method is implemented numerically in order to model the induced gravitational polarisation. Special care is taken to account for the amplification of potential fluctuations of mutually resonant orbits and the unwinding of the induced swing amplified transients. Quantitative comparisons with N-body simulations yield consistent scalings with the number of particles and with the self-gravity of the disc: the fewer the particles and the colder the disc, the faster the secular evolution. Secular evolution is driven by resonances, but does not depend on the initial phases of the disc. For a Mestel disc with Q ∼ 1.5, the polarisation cloud around each star boosts its secular effect by a factor of a thousand or more, accordingly promoting the dynamical relevance of self-induced collisional secular evolution. The position and shape of the induced resonant ridge are found to be in very good agreement with the prediction of the Balescu-Lenard equation, which scales with the square of the susceptibility of the disc. In astrophysics, the inhomogeneous Balescu-Lenard equation may describe the secular diffusion of giant molecular clouds in galactic discs, the secular migration and segregation of planetesimals in proto-planetary discs, or even the long-term evolution of population of stars within the Galactic centre. It could be used as a valuable check of the accuracy of N-body integrators on secular timescales.

AM CVn binaries consist of a WD accreting from a hydrogen-deficient star (or WD) companion (Warner, 1995;Solheim, 2010). In their formation history (Fig. 1.6 and Section 1.3.1.1), AM CVns form after at least one CE phase of their progenitor system. The current RLO is initiated, due to orbital damping caused by GW radiation, at orbital periods of typically 5−20 min (depending on the nature and the temperature of the companion star), and the mass-transfer rate is determined