On the rotation curves for axially symmetric disc solutions of the Vlasov–Poisson system

Abstract

A large class of flat axially symmetric solutions to the VlasovPoisson system is constructed with the property that the corresponding rotation curves are approximately flat, slightly decreasing or slightly increasing. The rotation curves are compared with measurements from real galaxies and satisfactory agreement is obtained. These facts raise the question whether the observed rotation curves for disk galaxies may be explained without introducing dark matter. Furthermore, it is shown that for the ansatz we consider stars on circular orbits do not exist in the neighborhood of the boundary of the steady state.

On axisymmetric and stationary solutions of the self-gravitating Vlasov system

“…This is particularly evident in the spherically symmetric case, where the stability of equilibrium solutions has been numerically investigated [15]. We also note that a similar relation has been observed in the work of Andréasson and Rein in the flat case [22], where a similar algorithm is used.…”

“…While several authors have constructed disk-models in which the matter is confined to the plane [28,22], our aim here is to find fully three-dimensional solutions whose spatial density distributions are as close to planar as possible.…”

“…In this section we investigate solutions to the Vlasov-Poisson and Einstein-Vlasov systems with flattened spheroidal spatial density profiles, which can provide models for disk-like galaxies. While several authors have constructed disk-models in which the matter is confined to the plane [28,22], our aim here is to find fully three-dimensional solutions whose spatial density distributions are as close to planar as possible.…”

How the Spirals in the Milky Way's ISM form

“…The distribution function in our model is a function of the third component of the angular momentum and the energy only and our technique can easily be extended to construct a self-consistent, multiphase model for the whole galaxy; a task that was elusive up to now (Binney 2020). Our technique is based on a fixed-point like algorithm, which is an improved version of the algorithm from Andréasson & Rein (2015), plus a good understanding of how distribution functions, which match observations, must look like. The resulting distribution function is comparable with the one of a cut-out Mestel disc like it is, e.g., studied in Zang (1976), Toomre (1981) or Sellwood & Carlberg (2019).…”

Analytical models of finite thin disks in a magnetic field

“…The models are constructed using a method developed by Hunter [20] based on obtaining solutions of Laplace equation in terms of oblate spheroidal coordinates, which are ideally suited to the study of flat disks of finite extension. Several classes of analytical models corresponding to thin disks have been obtained by different authors [21][22][23][24][25][26][27][28]. Thin disks with electromagnetic fields, specially in curved spacetimes, also have been studied extensively [29][30][31][32][33][34][35][36][37].…”