The Adiabatic Invariant of Dark Matter in Spiral Galaxies

Abstract

Collisionless dark matter can only expand adiabatically. To test this idea and constrain the properties of dark matter, we study spiral galaxies in the “Spitzer Photometry and Accurate Rotation Curves” (SPARC) sample. Fitting the rotation curves, we obtain the root-mean-square (rms) velocity and density of dark matter in the core of the galaxies. We then calculate the rms velocity v h rms (1) that dark matter particles would have if expanded adiabatically from the core of the galaxies to the present mean density of dark matter in the universe. We obtain this “adiabatic invariant” v h rms (1) for 40 spiral galaxies. The distribution of v h rms (1) has a mean 0.87 km/s and a standard deviation of 0.27 km/s. This low relative dispersion is noteworthy given the wide range of the properties of these galaxies. The adiabatic invariant v h rms (1) may, therefore, have a cosmological origin. In this case, the rms velocity of non-relativistic dark matter particles in the early universe when density perturbations are still linear is v h rms ( a )= v h rms (1)/ a , where a is the expansion parameter. The adiabatic invariant obtains the ratio of dark matter temperature T h (a) to mass m h in the early universe.