The nature of one of the fundamental components of the Universe, dark matter, is still unknown. One interesting possibility is that dark matter could exist in the form of a self-interacting Bose–Einstein Condensate (BEC). The fundamental properties of dark matter in this model are determined by two parameters only, the mass and the scattering length of the particle. In the present study we investigate the properties of the galactic rotation curves in the BEC dark matter model, with quadratic self-interaction, by using 173 galaxies from the recently published Spitzer Photomery & Accurate Rotation Curves (SPARC) data. We fit the theoretical predictions of the rotation curves in the slowly rotating BEC models with the SPARC data by using genetic algorithms. We provide an extensive set of figures of the rotation curves, and we obtain estimates of the relevant astrophysical parameters of the BEC dark matter halos (central density, angular velocity and static radius). The density profiles of the dark matter distribution are also obtained. It turns out that the BEC model gives a good description of the SPARC data. The presence of the condensate dark matter could also provide a solution for the core–cusp problem.

The time evolution of a physical quantity associated with a thermodynamic system whose equilibrium fluctuations are modulated in amplitude by a slowly varying phenomenon can be modeled as the product of a Gaussian white noise {Z t} and a stochastic process with strictly positive values {V t} referred to as volatility. The probability density function (pdf) of the process X t =V t Z t is a scale mixture of Gaussian white noises expressed as a time average of Gaussian distributions weighted by the pdf of the volatility. The separation of the two components of {X t} can be achieved by imposing the condition that the absolute values of the estimated white noise be uncorrelated. We apply this method to the time series of the returns of the daily S&P500 index, which has also been analyzed by means of the superstatistics method that imposes the condition that the estimated white noise be Gaussian. The advantage of our method is that this financial time series is processed without partitioning or removal of the extreme events and the estimated white noise becomes almost Gaussian only as result of the uncorrelation condition.

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