tokens: effect saturates in the DML, so MOND can provide only a limited amount of additional stability even for a galaxy with arbitrarily low surface density. This might explain why low surface brightness disk galaxies often have spiral features (McGaugh et al. 1995 ), usually taken as a sign that disk self-gravity is important (Lin Shu 1964 ; Das et al. 2020 ). The global stability of disks thus offers a promising way to break the CDM-modified gravity degeneracy in galaxies. M33 is one of the nearest galaxies with a rather low surface brightness. S19 recently conducted isolated N -body and hydrodynamical (hydro) simulations of M33 in the CDM context. As with many other galaxies, its observed RC required them to use a cored DM profile. They found it rather difficult to explain the weak observed bar together with the two-armed spiral (Corbelli Walterbos 2007 ) in the presence of a live CDM halo. Weak bars are also observed in many other galaxies (Cuomo et al. 2019 ). They are problematic in the CDM picture because a bar in the baryons creates a response in the live DM halo, which would cause a resonant effect (Athanassoula 2002 ). This was demonstrated explicitly by S19 , who compared their live halo simulations to a “frozen halo” simulation in which the DM particles provide a fixed gravitational potential. 7 7 This can be thought of as the DM particles providing gravity but not moving. S19 showed that M33 would be more stable in a frozen halo, leading to a weak bar similar to that in the observed M33. Such a model is of course unphysical in the ΛCDM context, but useful to better understand the dynamics. Interestingly, a frozen halo is somewhat similar to gravity theories like MOND where galaxies lack hypothetical DM. This is because features in the disk very rapidly become irrelevant to the potential as one moves away from its plane. Consequently, perturbations in the disk have very little effect on the Milgromian “phantom DM” (PDM) halo because its density depends only on the local potential. 8 8 PDM is the DM density distribution that would be needed for the Newtonian gravitational field to equal the MOND one of the baryons alone. The PDM distribution of thin exponential disks was visualized in, e.g., Lüghausen et al. ( 2013 , 2015 ). Indeed, this is why a bare disk can be stable in MOND. The lack of an actual DM halo automatically removes the possibility of bar–halo angular momentum exchange. However, disk self-gravity is enhanced in MOND compared to the case of a frozen DM halo. The presence of an EFE would slightly decrease this enhancement, but would also decrease the spheroidal potential support from the PDM. In general, it would also break the axisymmetry and up–down symmetry of the problem. Clearly, numerical simulations are needed to properly understand how disk stability is influenced by a fundamental modification to the gravity law. Several MOND N -body simulations have considered isolated disks, starting with the seminal work of Brada
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