Theoretical analysis of the interaction between superfluid dark matter and rotating supermassive black holes offers a promising framework for probing quantum effects in ultralight dark matter and its role in galactic structure. We study how black hole rotation influences the state of ultralight bosonic dark matter, focusing on the stability and dynamics of vortex lines. The gravitational effects of both dark matter and the black hole on the physical properties of these vortex lines, including their precession around the black hole, are analyzed. Published by the American Physical Society 2025

We study the effects of superfluid dark matter on the structure of a cosmic string wake, considering both the effects of regular and quantum pressure terms. We consider the total fluid to consist of a combination of baryons and dark matter. Hence, we are also able to study the effects of superfluid dark matter on the distribution of baryons inside the wake. We focus on parameter values for the superfluid dark matter which allow a MONDian explanation of galaxy rotation curves.

We consider a cosmic string moving through a gas of superfluid dark matter (SFDM) particles and analyze how it affects the dark matter distribution. We look at two different cases; first, a cosmic string passing through an already condensed region, and second, through a region that is not yet condensed. In the former, the string induces a weak shock in the superfluid, and the Bose-Einstein condensate (BEC) survives. In the latter, a wake of larger density is formed behind the string, and we study under which conditions a BEC can be formed in the virialized region of the wake. By requiring the thermalization of the DM particles and the overlap of their de Broglie wavelengths inside the wake, we obtain an upper bound on the mass of the dark matter particles on the order of 10 eV, which is compatible with typical SFDM models.

The theory of superfluid dark matter is characterized by self-interacting sub-eV particles that thermalize and condense to form a superfluid core in galaxies. Massive black holes at the center of galaxies, however, modify the dark matter distribution and result in a density enhancement in their vicinity known as dark matter spikes. The presence of these spikes affects the evolution of binary systems by modifying their gravitational wave emission and inducing dynamical friction effects on the orbiting bodies. In this work, we assess the role of dynamical friction for bodies moving through a superfluid core enhanced by a central massive black hole. As a first step, we compute the dynamical friction force experienced by bodies moving in a circular orbit. Then, we estimate the gravitational wave dephasing of the binary, showing that the effect of the superfluid drag force is beyond the reach of space-based experiments like LISA, contrarily to collisionless dark matter, therefore providing an opportunity to distinguish these dark matter models.

Superfluid dark matter (SFDM) is a model that promises to reproduce the successes of both particle dark matter on cosmological scales and those of Modified Newtonian Dynamics (MOND) on galactic scales. SFDM reproduces MOND only up to a certain distance from the galactic center, and only for kinematic observables: it does not affect trajectories of light. We test whether this is consistent with a recent analysis of weak gravitational lensing that has probed accelerations around galaxies to unprecedentedly large radii. This analysis found the data to be close to the prediction of MOND, suggesting they might be difficult to fit with SFDM. To investigate this matter, we solved the equations of motion of the model and compared the result to observational data. Our results show that the SFDM model is incompatible with the weak-lensing observations, at least in its current form.

The idea of self-interacting bosonic dark matter capable of exhibiting superfluidity is revisited. We show that the most interesting parameter space of the theory corresponds to fully thermalized dark matter halos. As a result the entire halo undergoes Bose-Einstein condensation due to high degeneracy. Since it is observationally preferable for the dark matter density profile to be similar to cold dark matter in the outskirts of the halo, we argue that the Jeans wavelength must be at least few times shorter than the virial radius. This entails that, upon condensation, a dark matter halo fragments into superfluid clumps. However, we demonstrate that these would be solitons experience strong tidal disruption and behave as virialized weakly interacting streams. An exception is the central soliton, which can be as large as few tens of kiloparsecs in size without contradicting observational bounds. As a result, in dwarf galaxies, the observed rotation curves can be completely contained within the superfluid soliton. In this case, the dark matter distribution is expected to be strongly sensitive to the baryonic density profile. We argue that the diversity of rotation curves observed for dwarf galaxies is a natural consequence of the superfluid dark matter scenario.

Superfluid dark matter, consisting of self-interacting light particles that thermalize and condense to form a superfluid in galaxies, provides a novel theory that matches the success of the standard ΛCDM model on cosmological scales while simultaneously offering a rich phenomenology on galactic scales. Within galaxies, the dark matter density profile consists of a nearly homogeneous superfluid core surrounded by an isothermal envelope. In this work we compute the density profile of superfluid dark matter around supermassive black holes at the center of galaxies. We show that, depending on the fluid equation of state, the dark matter profile presents distinct power-law behaviors, which can be used to distinguish it from the standard results for collisionless dark matter.

The Lambda-Cold Dark Matter model explains cosmological observations most accurately till date. However, it is still plagued with various shortcomings at galactic scales. Models of dark matter such as superfluid dark matter, Bose-Einstein Condensate(BEC) dark matter and fuzzy dark matter have been proposed to overcome some of these drawbacks. In this work, we probe these models using the current constraint on the gravitational wave (GW) propagation speed coming from the binary neutron star GW170817 detection by LIGO-Virgo detector network and use it to study the allowed parameter space for these three models for Advanced LIGO+Virgo, LISA, IPTA and SKA detection frequencies. The speed of GW has been shown to depend upon the refractive index of the medium, which in turn, depends on the dark matter model parameters through the density profile of the galactic halo. We constrain the parameter space for these models using the bounds coming from GW speed measurement and the Milky Way radius bound. Our findings suggest that with Advanced LIGO-Virgo detector sensitivity, the three models considered here remain unconstrained. A meaningful constraint can only be obtained for detection frequencies ≤ 10-9 Hz, which falls in the detection range of radio telescopes such as IPTA and SKA. Considering this best possible case, we find that out of the three condensate models, the fuzzy dark matter model is the most feasible scenario to be falsified/validated in near future.

A preference for cold dark matter over Superfluid Dark Matter in local Milky Way data

ABSTRACT We assume dark matter to be a cosmological self-gravitating Bose–Einstein condensate of non-relativistic ultralight scalar particles with competing gravitational and repulsive contact interactions and investigate the observational implications of such model. The system is unstable to the formation of stationary self-bound structures that minimize the energy functional. These cosmological superfluid droplets, which are the smallest possible gravitationally bound dark matter structures, exhibit a universal mass profile and a corresponding universal rotation curve. Assuming a hierarchical structure formation scenario where granular dark matter haloes grow around these primordial stationary droplets, the model predicts cored haloes with rotation curves that obey a single universal equation in the inner region ($r\, \lesssim \, 1$ kpc). A simultaneous fit to a selection of galaxies from the SPARC data base chosen with the sole criterion of being strongly dark matter dominated even within the innermost region, indicates that the observational data are consistent with the presence of a Bose–Einstein condensate of ultralight scalar particles of mass m ≃ 2.2 × 10−22 eV c−2 and repulsive self-interactions characterized by a scattering length as ≃ 7.8 × 10−77 m. Such small self-interactions have profound consequences on cosmological scales. They induce a natural minimum scale length for the size of dark matter structures that makes all cores similar in length (∼1 kpc) and contributes to lower their central densities.

We derive the equation of state of a Bose gas with contact interactions using relativistic quantum field theory. The calculation accounts for both thermal and quantum corrections up to one-loop order. We work in the Hartree-Fock-Bogoliubov approximation and follow Yukalov's prescription of introducing two chemical potentials, one for the condensed phase and another one for the excited phase, to circumvent the well-known Hohenberg-Martin dilemma. As a check on the formalism, we take the nonrelativistic limit and reproduce the known results. Finally, we translate our results to the hydrodynamical, two-fluid model for finite-temperature superfluids. Our results are relevant for the phenomenology of Bose-Einstein condensate and superfluid dark matter candidates, as well as the color-flavor locking phase of quark matter in neutron stars.

Context. We make rotation curve fits to test the superfluid dark matter model. Aims. In addition to verifying that the resulting fits match the rotation curve data reasonably well, we aim to evaluate how satisfactory they are with respect to two criteria, namely, how reasonable the resulting stellar mass-to-light ratios are and whether the fits end up in the regime of superfluid dark matter where the model resembles modified Newtonian dynamics (MOND). Methods. We fitted the superfluid dark matter model to the rotation curves of 169 galaxies in the SPARC sample. Results. We found that the mass-to-light ratios obtained with superfluid dark matter are generally acceptable in terms of stellar populations. However, the best-fit mass-to-light ratios have an unnatural dependence on the size of the galaxy in that giant galaxies have systematically lower mass-to-light ratios than dwarf galaxies. A second finding is that the superfluid often fits the rotation curves best in the regime where the superfluid’s force cannot resemble that of MOND without adjusting a boundary condition separately for each galaxy. In that case, we can no longer expect superfluid dark matter to reproduce the phenomenologically observed scaling relations that make MOND appealing. If, on the other hand, we consider only solutions whose force approximates MOND well, then the total mass of the superfluid is in tension with gravitational lensing data. Conclusions. We conclude that even the best fits with superfluid dark matter are still unsatisfactory for two reasons. First, the resulting stellar mass-to-light ratios show an unnatural trend with galaxy size. Second, the fits do not end up in the regime that automatically resembles MOND, and if we force the fits to do so, the total dark matter mass is in tension with strong lensing data.

The predicted size of dark matter substructures in kilo-parsec scales is model-dependent. Therefore, if the correlations between dark matter mass densities as a function of the distances between them are measured via observations, we can scrutinize dark matter scenarios. In this paper, we present an assessment procedure of dark matter scenarios. First, we use Gaia’s data to infer the single-body phase-space density of the stars in the Fornax dwarf spheroidal galaxy. The latter, together with the Jeans equation, after eliminating the gravitational potential using the Poisson equation, reveals the mass density of dark matter as a function of its position in the galaxy. We derive the correlations between dark matter mass densities as a function of distances between them. No statistically significant correlation is observed. Second, for the sake of comparison with the standard cold dark matter, we also compute the correlations between dark matter mass densities in a small halo of the Eagle hydrodynamics simulation. We show that the correlations from the simulation and from Gaia are in agreement. Third, we show that Gaia observations can be used to limit the parameter space of the Ginzburg–Landau statistical field theory of dark matter mass densities and subsequently shrink the parameter space of any dark matter model. As two examples, we show how to leave limitations on (i) a classic gas dark matter and (ii) a superfluid dark matter.

In 2015 Berezhiani & Khoury proposed a Superfluid Dark Matter (SFDM) model where dark matter condenses and forms a superfluid on galactic scales. In the superfluid state phonons interact with baryons, resulting in a behavior similar to that of Modified Newtonian Dynamics (MOND). If one assumes that the DM condensate rotates along with the galaxy, a grid of vortices should form throughout the superfluid component if the rotation is fast enough. We aim to investigate the size and impact of the vortices on surrounding baryons, and to further investigate the parameter space of the model. We also look for a possible vortex solution of the Lagrangian presented for the SFDM theory. We first take a simple approach and investigate vortex properties in a constant density DM halo, applying knowledge from condensed matter physics. We then use the zero-temperature condensate density profile as a template to vary the DM particle mass and the energy scale, Λ, of the SFDM model. Further, we attempt to find a vortex solution of the theory by extracting the Euler-Lagrange equation with respect to the modulus of the condensate wavefunction from the full relativistic SFDM Lagrangian. For the constant density approach we find that the vortices are on millimeter scale, and separated by distances ∼0.002 AU. The parameter space of the model is found to be substantial and a reduction in the DM particle mass leads to larger vortices with a higher energy. However, none of the parameter combinations explored here give both realistic values of Λ and vortices energetic enough to have an observational impact on the galaxy as a whole. The vortex equation extracted from the Lagrangian of the model is unstable, and no solution exhibiting the standard properties of a vortex solution is found.

There has been much interest in novel models of dark matter that exhibit interesting behavior on galactic scales. A primary motivation is the observed Baryonic Tully-Fisher Relation in which the mass of galaxies increases as the quartic power of rotation speed. This scaling is not obviously accounted for by standard cold dark matter. This has prompted the development of dark matter models that exhibit some form of so-called MONDian phenomenology to account for this galactic scaling, while also recovering the success of cold dark matter on large scales. A beautiful example of this are the so-called superfluid dark matter models, in which a complex bosonic field undergoes spontaneous symmetry breaking on galactic scales, entering a superfluid phase with a 3/2 kinetic scaling in the low energy effective theory, that mediates a long-ranged MONDian force. In this work we examine the causality and locality properties of these and other related models. We show that the Lorentz invariant completions of the superfluid models exhibit high energy perturbations that violate global hyperbolicity of the equations of motion in the MOND regime and can be superluminal in other parts of phase space. We also examine a range of alternate models, finding that they also exhibit forms of non-locality.

Aims. The aim of the present work is to better understand the gravitational drag forces, also referred to as dynamical friction, acting on massive objects moving through a self-interacting Bose-Einstein condensate, also known as a superfluid, at finite temperatures. This is relevant for models of dark matter consisting of light scalar particles with weak self-interactions that require nonzero temperatures, or that have been heated inside galaxies. Methods. We derived expressions for dynamical friction using linear perturbation theory, and compared these to numerical simulations in which nonlinear effects are included. After testing the linear result, it was applied to the Fornax dwarf spheroidal galaxy, and two of its gravitationally bound globular clusters. Dwarf spheroidals are well-suited for indirectly probing properties of dark matter, and so by estimating the rate at which these globular clusters are expected to sink into their host halo due to dynamical friction, we inferred limits on the superfluid dark matter parameter space. Results. The dynamical friction in a finite-temperature superfluid is found to behave very similarly to the zero-temperature limit, even when the thermal contributions are large. However, when a critical velocity for the superfluid flow is included, the friction force can transition from the zero-temperature value to the value in a conventional thermal fluid. Increasing the mass of the perturbing object induces a similar transition to when lowering the critical velocity. When applied to two of Fornax’s globular clusters, we find that the parameter space preferred in the literature for a zero-temperature superfluid yields decay times that are in agreement with observations. However, the present work suggests that increasing the temperature, which is expected to change the preferred parameter space, may lead to very small decay times, and therefore pose a problem for finite-temperature superfluid models of 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.

Dark matter = modified gravity? Scrutinising the spacetime–matter distinction through the modified gravity/ dark matter lens

Cartography of the space of theories: An interpretational chart for fields that are both (dark) matter and spacetime

ABSTRACT 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 $R \lt 25\, \rm {kpc}$ 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 $20{{\ \rm per\ cent}}$ less total baryonic mass (with a suitable interpolation function). The total baryonic mass is then $5.96 \times 10^{10}\, \mathrm{ M}_\odot$, of which $1.03 \times 10^{10}\, \mathrm{ M}_\odot$ are from the bulge, $3.95 \times 10^{10}\, \mathrm{ M}_\odot$ are from the stellar disc, and $0.98 \times 10^{10}\, \mathrm{ M}_\odot$ are from the gas disc. 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 of $0.5\!-\!3.0 \times 10^{12}\, \mathrm{ M}_\odot$, we find that the Navarro, Frenk, and White (nfw) radius RNFW varies between $65$ and $73\, \rm {kpc}$, while the thermal radius RT varies between about $67$ and $105\, \rm {kpc}$. This is the first such treatment of a non-spherically symmetric system in superfluid dark matter.