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Abstract Low-surface-brightness galaxies are excellent laboratories, where stars and baryonic matter act as tracers of the gravitational potential of the dark matter halo. If dark matter is modeled as a perfect fluid, then spherically symmetric and static dark matter halos in hydrostatic equilibrium demand that dark matter should have an intrinsic pressure that counteracts the gravitational attraction that the dark matter halo exerts on itself. This static fluid (a dark-matter-dominated system, where the presence of baryons is negligible) has a specific equation of state for each rotational velocity profile of the stars in galaxies. In this work, we study the dark matter equation of state needed for the self-gravitating object to produce a gravitational potential such that the tracers follow the universal rotational velocity profile for stars of spiral galaxies proposed by Persic et al. and analyze the properties of the self-gravitating structures that emerge from this equation of state. The resulting configurations explaining the observed rotational speeds are found to be unstable. We conclude that the halo is not in hydrostatic equilibrium, it is nonspherically symmetric, or it is not static if the universal velocity profile should be valid for fitting the rotational velocity curve of the galaxies.
Aceña et al. (Wed,) studied this question.