Dynamical friction is a very interesting physical phenomenon, with important applications in astrophysics. At the simplest level, it can be described as the slowing down (“cooling”) of a test particle moving in a sea of field particles due to the cumulative effects of long-range interactions (no geometric collisions are considered). Several approaches have been devised to understand the underlying physics (which is intriguing, as the final result is an irreversible process produced by a time-reversible dynamics; e.g., see Bertin 2014; Binney and Tremaine 2008; Chandrasekhar 1960; Ogorodnikov 1965; Shu 1999; Spitzer 1987). In this chapter, the dynamical friction time is derived in the Chandrasekhar approach by using the impulsive approximation discussed in Chapter 7.

The fourth variant of Milgrom’s theory (T3) is due to Justin Khoury and Lasha Berezhiani. These researchers made a change to Milgrom’s postulates in order to address the failings of theory variants T0–T2. They introduced dark matter into the theory, but postulated that, on scales corresponding to galaxies, the dark matter acts like a superfluid condensate. By adjusting the equation of state of the superfluid, they showed that the interaction of the dark matter with normal matter – via Newtonian gravity, but also via coupling of the superfluid phonons – can result in an acceleration that approximates Milgrom’s modified dynamics in the low-acceleration regime. On large scales, the dark matter would behave like the dark matter in the standard model. Although still in an early stage of development, Khoury and Berezhiani’s theory has not yet demonstrated an increase in testable content compared withT0–T2, and in fact much of the content of the earlier theory variants is lost.