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Bariego-Quintana, A., & Llanes-Estrada, F. J. (2026). No evidence for Keplerian taper of far-out galactic rotation in the SPARC galaxy database. New Astron., 126, 102537–13pp.
Abstract: We present a statistical analysis of the 175 SPARC galactic rotation curves to test the hypothesis of whether V the Keplerian velocity tapering at large radii (V(r) proportional to 1/ r) germane to a convergent mass distribution in typical spherical halo models agrees with observational data. The null hypothesis is Rubin's flat-rotation curve, V(r) = constant-such as can be obtained from a spherical, isothermal-like density profile, or alternatively with a very prolate halo-. To decide whether we adopt the null (Rubin behaviour) or alternative (Keplerian behaviour) hypothesis, we evaluate the derivative in each galaxy of V(r) with its last data points. The test is model independent inasmuch we are testing for the slope of the dark matter rotation curve, whether it is or not compatible with zero. We conclude that the data is presently compatible with the null hypothesis-no taper off, no decline of V(r) is seen. Separately, beyond SPARC, our own Milky Way galaxy, for which recent data sets have been reported, does show clear V(r) fall-off at the level of 20%.
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Capozziello, S., Harko, T., Koivisto, T. S., Lobo, F. S. N., & Olmo, G. J. (2013). Galactic rotation curves in hybrid metric-Palatini gravity. Astropart Phys., 50-52, 65–75.
Abstract: Generally, the dynamics of test particles around galaxies, as well as the corresponding mass deficit, is explained by postulating the existence of a hypothetical dark matter. In fact, the behavior of the rotation curves shows the existence of a constant velocity region, near the baryonic matter distribution, followed by a quick decay at large distances. In this work, we consider the possibility that the behavior of the rotational velocities of test particles gravitating around galaxies can be explained within the framework of the recently proposed hybrid metric-Palatini gravitational theory. The latter is constructed by modifying the metric Einstein-Hilbert action with an f(R) term in the Palatini formalism. It was shown that the theory unifies local constraints and the late-time cosmic acceleration, even if the scalar field is very light. In the intermediate galactic scale, we show explicitly that in the hybrid metric-Palatini model the tangential velocity can be explicitly obtained as a function of the scalar field of the equivalent scalar-tensor description. The model predictions are compared model with a small sample of rotation curves of low surface brightness galaxies, respectively, and a good agreement between the theoretical rotation Curves and the observational data is found. The possibility of constraining the form of the scalar field and the parameters of the model by using the stellar velocity dispersions is also analyzed. Furthermore, the Doppler velocity shifts are also obtained in terms of the scalar field. All the physical and geometrical quantities and the numerical parameters in the hybrid metric-Palatini model can be expressed in terms of observable/measurable parameters, such as the tangential velocity, the baryonic mass of the galaxy, the Doppler frequency shifts, and the stellar dispersion velocity, respectively. Therefore, the obtained results open the possibility of testing the hybrid metric-Palatini gravitational models at the galactic or extra-galactic scale by using direct astronomical and astrophysical observations.
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