Transient Spiral Arms from Far Out-of-equilibrium Gravitational Evolution

Abstract

We describe how a simple class out-of-equilibrium, rotating, and asymmetrical mass distributions evolve under their self-gravity to produce a quasi-planar spiral structure surrounding a virialized core, qualitatively resembling a spiral galaxy. The spiral structure is transient, but can survive tens of dynamical times, and further reproduces qualitatively noted features of spiral galaxies such as the predominance of trailing two-armed spirals and large pitch angles. As our models are highly idealized, a detailed comparison with observations is not appropriate, but generic features of the velocity distributions can be identified to be the potential observational signatures of such a mechanism. Indeed, the mechanism leads generically to a characteristic transition from predominantly rotational motion, in a region outside the core, to radial ballistic motion in the outermost parts. Such radial motions are excluded in our Galaxy up to 15 kpc, but could be detected at larger scales in the future by GAIA. We explore the apparent motions seen by external observers of the velocity distributions of our toy galaxies, and find that it is difficult to distinguish them from those of a rotating disk with sub-dominant radial motions at levels typically inferred from observations. These simple models illustrate the possibility that the observed apparent motions of spiral galaxies might be explained by non-trivial nonstationary mass and velocity distributions without invoking a dark matter halo or modification of Newtonian gravity. In this scenario the observed phenomenological relation between the centripetal and gravitational acceleration of the visible baryonic mass could have a simple explanation.

Violent relaxation in the Hamiltonian mean field model: I. Cold collapse and effective dissipation

“…We are admittedly still far from a comprehensive theory of violent relaxation predicting the shape of galaxies, yet the approach we have described here might give some hints towards this goal. Finally, it is worth recalling that the quasi-stationary state reached after the violent relaxation might not be the whole story, as it has been recently shown by means of numerical simulations of self-gravitating particles that structures like spiral arms and rings very similar to those observed in real galaxies may appear as longliving transients during the violent relaxation itself, when the initial conditions are not completely symmetric and the initial angular momentum does not vanish [38]. This is a further indication that a deeper theoretical understanding of violent relaxation in long-range-interacting system is needed and could prove fruitful.…”

“…In fact Eqs. (38) stem from the Vlasov equation for the HMF model (15) in the harmonic approximation (i.e., with sin ϑ ≈ ϑ) and with m = µ. In this case the evolution in phase space reduces to a rigid rotation, i.e., to a periodic motion.…”

Formation of spiral structure from the violent relaxation of self‐gravitating disks

“…These characteristic motion and longevity are different from those of the arms in real galaxies that are dominated by the differential rotation, and it is believed that they will dissolve after a number of rotations. Although the properties of our spiral arms are incompatible with the observed arms, the fact that this kind of spiral structure (and also those in Benhaiem et al (2017)) is obtainable through the violent gravitational collapse lets us speculate that this type of spiral structure could arise in the realm where the galaxy relaxes straight from a monolithic collapse. For an unstable protogalactic cloud that possesses some amount of rotation, our mechanism suggests that the spiral structure can potentially emerge out.…”

“…While the majority of studies principally addresses the ellipticity and the density profile of the QSS, a recent work by Benhaiem et al (2017) proposes that the formation of a long‐lived nonstationary spiral structure through the violent relaxation is possible if one starts from gravitationally unstable rotating ellipsoids. This provides an alternative scenario from the standard framework of this issue, which believes that the spiral pattern is the perturbed component of the disk or bulge in equilibrium (Goldreich & Lynden‐Bell 1965; Lin & Shu 1964) or the tidal tails by the passage of a companion object (Toomre & Toomre 1972).…”

Long-lived transient structure in collisionless self-gravitating systems

“…Extensive observational study over decades, using different tracers, has placed much constraint on such motions [51], and indicates that motion in the outer parts of such galaxies is in fact very predominantly rotational [51,52], although a significant radial motions have been detected in many objects [53]. As discussed in [36] for the results based on simple ellipsoidal IC, it turns out that the naive expectation that such motions are excluded by observations is not confirmed. The reason is that our velocity fields have a very particular spatial (anisotropic) spatial structure which makes it difficult to distinguish them in projection from rotating disc models.…”