Core-cusp revisited and dark matter phase transition constrained at O(0.1) eV with low surface brightness rotation curve

Recently a new particle physics model called bound dark matter (BDM) has been proposed [A. de la Macorra, Astropart. Phys. 33, 195 (2010).] in which dark matter (DM) particles are massless above a threshold energy (E-c) and acquire mass below it due to nonperturbative methods. Therefore, the BDM model describes DM particles which are relativistic, hot dark matter (HDM) in the inner regions of galaxies and describes nonrelativistic, cold dark matter (CDM) where halo density is below rho(c) E-c(4). To realize this idea in galaxies, we use a particular DM cored profile that contains three parameters: a typical scale length (r(s)) and density (rho(0)) of the halo, and a core radius (r(c)) stemming from the relativistic nature of the BDM model. We test this model by fitting rotation curves of 17 low surface brightness (LSB) galaxies from The HI Nearby Galaxy Survey (THINGS). Since the energy E-c parametrizes the phase transition due to the underlying particle physics model, it is not dependent on the details of galaxy and/or structure formation and therefore the DM profile parameters r(s), r(c), E-c are constrained, leaving only two free parameters. The high spatial and velocity resolution of this sample allows one to derive the model parameters through the numerical implementation of the chi(2)-goodness-of-fit test to the mass models. We compare the fittings with those of Navarro-Frenk-White (NFW), Burkert, and pseudoisothermal (ISO) profiles. Through the results, we conclude that the BDM profile fits better, or equally well, than NFW, Burkert, and ISO profiles and agree with previous results implying that cored profiles are preferred over the N-body motivated cuspy profiles. We also compute two-dimensional likelihoods of the BDM parameters r(c) and E-c for the different galaxies and matter contents, and find an average galaxy core radius r(c) = 300 pc and a transition energy between hot and cold dark matter at E-c = 0.11(-0.07) (+0.21) eV when the DM halo is the only component and therefore the maximum dark matter contribution in galaxies. In a more realistic analysis, as in the Kroupa mass model, we obtain a core r(c) = 1.48 kpc, and energy E-c = 0.06(-0.03) (+0.07) eV.