On the Gravitational Stability of the Maclaurin Disk

Abstract

We study the global gravitational stability of a gaseous self-gravitating Maclaurin disk in the absence of a halo. Further, we replace Newtonian gravity with the specific Modified gravity theory known as MOG in the relevant literature. MOG is an alternative theory for addressing the dark matter problem without invoking exotic dark matter particles, and possesses two free parameters α and µ 0 in the weak field limit. We derive the equilibrium gravitational potential of the Maclaurin disk in MOG and develop a semi-analytic method for studying the response of the disk to linear non-axysymmetric perturbations. The eigenvalue spectrum of the normal modes of the disk is obtained and its physical meaning has been explored. We show that Maclaurin disks are less stable in MOG than in Newtonian gravity. In fact both parameters (α, µ 0 ) have destabilizing effects on the disk. Interestingly µ 0 excites only the bar mode m = 2 while α affects all the modes. More specifically, when α > 1, the bar mode is strongly unstable and unlike in Newtonian gravity can not be avoided, at least in the weak field limit, with increasing the pressure support of the disk.

Local stability of galactic discs in modified dynamics

“…Another challenge facing modified gravity/dynamics models is the problem of global stability. For example, Roshan et al (2016) develop a semi-analytic method to study the response of a Maclaurin disc to linear nonaxisymmetric perturbations for the theory of MOG. Their results show that Maclaurin discs are less stable in MOG compared to Newtonian gravity and especially the bar mode, i.e.…”

“…For example, Milgrom (1989) investigates local stabilities of discs governed by MOND dynamics, Roshan & Abbassi (2014, 2015a) study the effects of MOG while the implications of f (R) have been surveyed by Roshan & Abbassi (2015b). Also Roshan et al (2016) and Ghafourian & Roshan (2017) study the global stability of galactic discs under MOG from theoretical and numerical point of view respectively.…”

Global stability of self-gravitating discs in modified gravity

“…Let us start with the potential and the corresponding rotation curve for Mestel disc in MOG. To do so, we mention that in the cylindrical coordinate system, solutions of (3) and (4) can be expended with respect to Bessel functions as, for more details see Roshan et al (2016)…”

Self-gravity in Magnetized Neutrino-dominated Accretion Disks

“…Toomre Parameter There are several numerical theoretical studies and simulations that describe a massive unstable discin Newtonian gravity (e.g., Bonnell (1994); Matsumoto et al (2003)) or even in Modified Gravity (e.g., Roshan et al (2015); Roshan et al (2016)). However, considering existing numerical simulations, it is not possible simply to say that all massive discs fragment because, to our knowledge, not only do current numerical simulations suffer from their own limitations, but they also do not generally give a fully consistent picture of global fragmentation.…”