A new preprint examines the stability of galaxy-likes structures under a variety of modified gravity theories and finds that some are more stable than they would be with Newtonian dynamics and no dark matter, while others are less stable.
The local stability of stellar and fluid discs, under a new modified dynamical model, is surveyed by using WKB approximation. The exact form of the modified Toomre criterion is derived for both types of systems and it is shown that the new model is, in all situations, more locally stable than Newtonian model. In addition, it has been proved that the central surface density of the galaxies plays an important role in the local stability in the sense that LSB galaxies are more stable than HSBs. Furthermore, the growth rate in the new model is found to be lower than the Newtonian one. We found that, according to this model, the local instability is related to the ratio of surface density of the disc to a critical surface density Σ cr it . We provide observational evidence to support this result based on star formation rate in HSBs and LSBs.Hossein Shenavar, Neda Ghafourian, "Local Stability of Galactic Discs in Modified Dynamics"
(February 5, 2019).
From the conclusion:
In this work, we considered the local stability of a modified dynamical model which is based on imposing Neumann BC on GR field equations. Both fluid and stellar discs in this model are found to be locally more stable compared to pure Newtonian discs. For the gaseous (stellar) discs, when βg ( β⋆) increases the maximum value that is needed for Q to make the system stable decreases. Thus, regions with larger βg or β⋆ are more stable. Also, LSB galaxies which show a high value of Freeman ratio RF ≡ Σ† Σ0 are predicted to be more stable than HSBs. The growth rate were found to be smaller than Newtonian model for both fluid and stellar discs. We tested the model by using THINGS data of (Leroy et. al. 2008) and showed that the general behaviour of star formation rate per surface density (ΣSFR) agrees with the predictions of the model.
Other modified theories too have tried to explain the issue of local stability and many interesting results have been reported. For example, Milgrom (1989) reports that MONDian discs are more stable than Newtonian ones. Also, in the deep MOND limit the stability criteria becomes independent of the acceleration. Furthermore, Milgrom (1989) argues that when Σ ≫ Σ†, or equivalently when RF is small, the Newtonian regime prevails and the disc becomes unstable. It is then proposed that the rarity of discs with small RF is due to their unstable nature. Using Lelli, McGaugh & Schombert (2016) data, we observed the same behaviour here as shown in Fig. 6. Also, Fig. 6 provided a chance to compare the role of Σ† in MOND and the present model.
Roshan & Abbassi (2015a, 2014) show that although MOG provides more attracting force compared to Newtonian theory, it is interestingly less stable than Newtonian case. However, they argue that the difference between the two theories is too small to be detected at galactic scale. This is shown by introducing a parameter βMOG ≡ µ0v/κ, counterpart to β in this work, in which µ0 = 0.042 ± 0.004 kpc−1 is a fundamental constant of MOG derived by Moffat & Rahvar (2013). Any difference between the stability of MOG and Newtonian models is proportional to βMOG, and it would be negligible because of the smallness of µ0 at galactic scales. If, however, this parameter is dependent to the system, say for instance µ0 ∝ 1/Rd in analogy with our analysis, then the instability of MOG could be studied at galactic scales. In fact, Haghi & Amiri (2016) suggest that to fit MOG to the observed velocity dispersion of dwarf spheroidal galaxies, one needs to consider µ0 as a varying parameter. This possibility, however, complicates the MOG model even more. In the case of f (R) theories, on the other hand, Roshan & Abbassi (2015b) show that the discs in a specific class of these theories are generally more stable than Newtonian discs.
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. m = 2, is strongly unstable and unlike in Newtonian gravity cannot be avoided. Also Ghafourian & Roshan (2017) study the global stability of Mestel and exponential discs in MOG from numerical point of view. In future works, we will examine the global stability of the present model in analytical and numerical studies. The equilibrium configuration of our model is reported in Shenavar (2018).Despite slower galaxy growth, structure formation is not necessarily slower.