Recent studies have shown that dark matter with a superfluid phase in which phonons mediate a long-distance force gives rise to the phenomenologically well-established regularities of Modified Newtonian Dynamics (mond). Superfluid dark matter, therefore, has emerged as a promising explanation for astrophysical observations by combining the benefits of both particle dark matter and mond, or its relativistic completions, respectively. We here investigate whether superfluid dark matter can reproduce the observed Milky Way rotation curve for $R < 25\, \rm {kpc}$ and are able to answer this question in the affirmative. Our analysis demonstrates that superfluid dark matter fits the data well with parameters in reasonable ranges. The most notable difference between superfluid dark matter and mond is that superfluid dark matter requires about $20\%$ less total baryonic mass (with a suitable interpolation function). The total baryonic mass is then 5.96 · 1010 M⊙, of which 1.03 · 1010 M⊙ are from the bulge, 3.95 · 1010 M⊙ are from the stellar disk, and 0.98 · 1010 M⊙ are from the gas disk. Our analysis further allows us to estimate the radius of the Milky Way’s superfluid core (concretely, the so-called nfw and thermal radii) and the total mass of dark matter in both the superfluid and the normal phase. By varying the boundary conditions of the superfluid to give virial masses $M_{200}^{\rm {DM}}$ in the range 0.5 − 3.0 · 1012 M⊙, we find that the nfw radius RNFW varies between $65\, \rm {kpc}$ and $73\, \rm {kpc}$, while the thermal radius RT varies between about $67\, \rm {kpc}$ and $105\, \rm {kpc}$. This is the first such treatment of a non-spherically-symmetric system in superfluid dark matter.

In superfluid dark matter (SFDM), the phonon field plays a double role: it carries the superfluid's energy density and it mediates the MOND-like phonon force. We show that these two roles are in tension with each other on galactic scales: a MOND-like phonon force is in tension with a superfluid in equilibrium and with a significant superfluid energy density. To avoid these tensions, we propose a model where the two roles are split between two different fields. This also allows us to solve a stability problem in a more elegant way than standard SFDM. We argue that the standard estimates for the size of a galaxy's superfluid core need to be revisited.

In superfluid dark matter the exchange of phonons can create an additional force that has an effect similar to Modified Newtonian Dynamics (MOND). To test whether this hypothesis is compatible with observation, we study a set of strong gravitational lenses from the SLACS survey and check whether the measurements can be explained by a superfluid in the central region of galaxies.Concretely, we try to simultaneously fit each lens's Einstein radius and velocity dispersion with a spherically symmetric density profile of a fluid that has both a normal and a superfluid component. We demonstrate that we can successfully fit all galaxies except one, and that the fits have reasonable stellar mass-to-light-ratios. We conclude that strong gravitational lensing does not pose a challenge for the idea that superfluid dark matter mimics modified gravity.

Modified Newtonian Dynamics has one free parameter and requires an interpolation function to recover the normal Newtonian limit. We here show that this interpolation function is unnecessary in a recently proposed covariant completion of Erik Verlinde's emergent gravity, and that Verlinde's approach moreover fixes the function's one free parameter. The so-derived correlation between the observed acceleration (inferred from rotation curves) and the gravitational acceleration due to merely the baryonic matter fits well with data. We then argue that the redshiftdependence of galactic rotation curves could offer a way to tell apart different versions of modified gravity from particle dark matter.

Superfluid dark matter postulates that the centers of galaxies contain superfluid condensates. An important quantity regarding these superfluids is their chemical potential µ. Here, we discuss two issues related to this chemical potential. First, there is no exactly conserved quantity associated with this chemical potential due to the symmetry-breaking baryon-phonon coupling. Second, µ is sometimes introduced by shifting the phonon field by µ · t which -again due to the symmetrybreaking baryon-phonon coupling -introduces an explicit time dependence in the Lagrangian. We investigate under which conditions introducing a chemical potential is nevertheless justified and show how to correctly introduce it when these conditions are met. We further propose a model that recovers superfluid dark matter's zero-temperature equations of motion including a chemical potential even if the aforementioned conditions for justifying a chemical potential are not met.The chemical potential of superfluid dark matter U (1) symmetry usually associated with superfluidity [19]. This causes two problems regarding SFDM's chemical potential.The first problem is that SFDM might not have a chemical potential at all. This is because the U (1) symmetry is broken in SFDM and chemical potentials as a statistical physics concept are a consequence of conserved quantities. This problem requires a solution, since SFDM needs a chemical potential for its phenomenology on galactic scales.The other problem is that SFDM's chemical potential µ is sometimes introduced by shifting the phonon field by µ · t (see e.g. Ref.[1] below Eq. (6) for an explicit example). This leads to an explicit time dependence in the U (1)-breaking baryon-phonon coupling. Phenomenologically, this may or may not be problematic depending on the size of µ and the details of the model. But conceptually, a chemical potential is an equilibrium quantity from statistical physics and should not be associated with an explicit time dependence. This problem requires an explanation.The aim of this paper is to clarify these issues regarding SFDM's chemical potential. In the following, we employ units with c = = 1 and the metric signature (+, −, −, −). Small Greek indices run from 0 to 3 and denote spacetime dimensions.We start with an introduction to SFDM in Sec. 2. In Sec. 3, we discuss the nonconservation of the U (1) charge of SFDM and the conditions under which a chemical potential may nevertheless be introduced. We then show how to correctly introduce a chemical potential in case these conditions are met in Sec. 4. Using these results, we distinguish two different non-relativistic limits which may be taken in SFDM in Sec. 5. In Sec. 6, we address possible confusions regarding SFDM's equilibrium energy-momentum tensor. Finally, we propose an alternative model which avoids the problems of SFDM regarding its chemical potential in Sec. 7. We conclude in Sec. 8.