Can dark matter be a Bose-Einstein condensate? (0705.4158v4)

Abstract: We consider the possibility that the dark matter, which is required to explain the dynamics of the neutral hydrogen clouds at large distances from the galactic center, could be in the form of a Bose-Einstein condensate. To study the condensate we use the non-relativistic Gross-Pitaevskii equation. By introducing the Madelung representation of the wave function, we formulate the dynamics of the system in terms of the continuity equation and of the hydrodynamic Euler equations. Hence dark matter can be described as a non-relativistic, Newtonian Bose-Einstein gravitational condensate gas, whose density and pressure are related by a barotropic equation of state. In the case of a condensate with quartic non-linearity, the equation of state is polytropic with index $n=1$. To test the validity of the model we fit the Newtonian tangential velocity equation of the model with a sample of rotation curves of low surface brightness and dwarf galaxies, respectively. We find a very good agreement between the theoretical rotation curves and the observational data for the low surface brightness galaxies. The deflection of photons passing through the dark matter halos is also analyzed, and the bending angle of light is computed. The bending angle obtained for the Bose-Einstein condensate is larger than that predicted by standard general relativistic and dark matter models. Therefore the study of the light deflection by galaxies and the gravitational lensing could discriminate between the Bose-Einstein condensate dark matter model and other dark matter models.

• The paper tests the hypothesis that dark matter is a Bose-Einstein condensate by modeling it with the Gross-Pitaevskii equation and hydrodynamic approximations.
• It employs the Thomas-Fermi and Madelung representations to derive a polytropic state that explains the density distributions and rotation curves of dark matter halos.
• Empirical fits to rotation curves from low surface brightness and dwarf galaxies support the model, indicating its potential in explaining gravitational lensing phenomena.

Bose-Einstein Condensate as a Model for Dark Matter

The paper by Böhmer and Harko addresses an intriguing hypothesis in contemporary astrophysics: whether dark matter, a non-baryonic component necessary to explain observed galactic dynamics, could be a Bose-Einstein condensate (BEC). Using a theoretical framework based on the Gross-Pitaevskii equation, the authors explore how ultralight scalar particles might form a gravitationally bound BEC, consequently influencing galactic rotation curves and gravitational lensing.

Methodology and Key Findings

The paper initiates its exploration by deploying the Gross-Pitaevskii equation with a quartic non-linearity to model the BEC. By utilizing the Madelung representation, the authors recast this quantum system into hydrodynamic equations akin to the Euler and continuity equations, with a barotropic equation of state typically associated with BECs. In particular, for a condensate characterized by quartic non-linearity, this state appears polytropic with index $n = 1$.

In the Thomas-Fermi approximation, which neglects quantum pressure in favor of interaction terms, the density distribution of the condensate halo is shown to resolve into a solvable Lane-Emden equation. The authors demonstrate that the mass and radius of such BEC dark matter halos are functions of the particle's mass and scattering length involved in the condensate.

The authors then test the model against empirical data, comparing theoretical predictions with rotation curves from low surface brightness and dwarf galaxies. Results from these fits show a significant congruence between the model's predictions and observations, suggesting that the BEC model provides a viable explanation for galactic rotation phenomena. Importantly, the analysis discerns that such a model could yield larger deflection angles of light as compared to predictions made traditionally by isothermal sphere models, offering practical implications for gravitational lensing studies.

Implications

The implications of this work extend over both practical and theoretical territories in astrophysics. Practically, this model provides a different avenue for understanding rotational dynamics of galaxies and offers a potentially novel explanation for dark matter's pervasive influence. Theoretically, it highlights the mechanistic richness of BECs, underscoring their ability to emulate gravitational dynamics attributable to dark matter while incorporating quantum field behavior into macroscopic astrophysical phenomena.

Speculation on Future Developments

Future developments based on this paper's methodology could involve refining numerical simulations to better accommodate variable parameters such as temperature dependence and many-body interactions effectively. Moreover, extending this model into a cosmological context—linking BEC-integrated dark matter to cosmic structure formation and behavior—could help address large scale structure alignments and anisotropies in the cosmic microwave background.

Thus, while requiring further observational evidence and theoretical rigor, Böhmer and Harko's proposition opens a promising theoretical front that melds quantum mechanics and astrophysical observations under the ambit of the Bose-Einstein condensate model for dark matter. The results suggest paths forward in both validating and enhancing our conception of dark matter's role and constitution within the universe.