Summaries of NRTE and URTE are presented in Appendix A and Appendix B, respectively. If, however, the dominant dark matter-dark matter interaction is gravity, then the time constant to approach NRTE is much greater than the age of the universe, and non-relativistic dark matter retains the URTE distribution. If these interactions are sufficiently strong, dark matter acquires the NRTE distribution, either Fermi-Dirac or Bose-Einstein. The momentum distribution of the non-relativistic dark matter particles approaches non-relativistic thermal equilibrium (NRTE) due to dark matter-dark matter elastic interactions. As the universe expands and cools, dark matter becomes non-relativistic. In the no freeze-in and no freeze-out scenario, the ultra-relativistic dark matter is in ultra-relativistic thermal equilibrium (URTE), either Fermi-Dirac, or Bose-Einstein. A convenient overview of these studies, and a discussion of the (apparent?) disagreements with current limits, are presented in. This no freeze-in and no freeze-out scenario is the result of measurements presented in. In particular, we assume that dark matter has zero chemical potential Thus we arrive at the following scenario: in the early universe dark matter is in diffusive and thermal equilibrium with the standard model sector, and decouples (from the standard model sector, and from self annihilation) while still ultra-relativistic. This result is either a coincidence, or strong evidence that the chemical potential of dark matter has the very special value It turns out that the measured value ofĬorresponds to thermal equilibrium between dark matter and the standard model sector in the early universe if Separately, we need one more constraint, e.g. Note that dark matter becomes non-relativistic at expansion parameter To be of cosmological origin: it determines the ratio of dark matter temperature In 10 galaxies of the THINGS sample, and 46 different galaxies in the SPARC sample, obtain results consistent within statistical and systematic uncertainties.
The issue of possible phase-space dilution due to galaxy structure formation appears to be secondary, since measurements of Remains constant so long as the mean number of dark matter particles per orbital remains constant, as expected for non-interacting dark matter.
) The interest in Equation (1) lies in the ability to measureīy fitting spiral galaxy rotation curves.
(We use the standard notation in cosmology as defined in. Is the density of dark matter in the core of the galaxy. Is the root-mean-square velocity of dark matter particles in the core of the galaxy, and This observer feels no gravity, observes dark matter expanding adiabatically, reaching maximum expansion, and then collapsing adiabatically into the core of a galaxy.
BOSON X DARK X BOSON FREE
Now consider a free observer in a density peak. (Throughout, the sub-index “h” stands for the halo of dark matter.) Note that , and a particle root-mean-square (rms) velocity Non-relativistic dark matter in the early universe has a density