On feathers, bifurcations and shells: the dynamics of tidal streams across the mass scale

I present an organic description of the spectrum of regimes of collisionless tidal streams and define the orderings between the relevant physical quantities that shape their morphology. Three fundamental dichotomies are identified and described in the form of dimensionless inequalities. These govern (i) the speed of the stream's growth, (ii) the internal coherence of the stream and (iii) its thickness or opening angle, within and outside the orbital plane. The mechanisms through which such main qualitative properties are regulated and the relevant limiting cases are analysed. For example, the slope of the host's density profile strongly influences the speed of the stream's growth, in both length and width, as steeper density profiles enhance differential streaming. Internal coherence is the natural requirement for the appearance of substructure and overdensities in tidal debris, and I concentrate on the characteristic 'feathering' typical of streams of star clusters. Overdensities and substructures are associated with minima in the relative streaming velocity of the stream members. For streams with high circularity, these are caused by the epicyclic oscillations of stars; however, for highly non-circular progenitor's orbits, internal substructure is caused by the oscillating differences in energy and actions with which material is shed at different orbital phases of the progenitor. This modulation results in different streaming speeds along the tidal arm: the streakline of material shed between two successive apocentric passages is folded along its length, pulled at its centre by the faster differential streaming of particles released near pericentre, which are therefore more widely scattered. When the stream is coherent enough, the same mechanism is potentially capable of generating a bimodal profile in the density distributions of the longer wraps of more massive progenitors, which I dub 'bifurcations'. The conditions that allow streams to be internally coherent are explored and I comment on the cases of Palomar 5, Willman 1, the Anticenter and Sagittarius' streams. Analytical methods are accompanied by numerical experiments, performed using a purposely built generative model, also presented here.