The case against scale-invariant central halo densities: implications for the self-interacting dark matter scenarios in the context of the two-component virial theorem

It has been argued in the literature that present day central halo densities are probably scale-invariant with respect to mass, although the data from which this conclusion has been reached is statistically poor. We present estimates of the central dark matter halo densities (r0) for a large data sample ranging from dwarf ellipticals to clusters of galaxies, based on the application of the two-component virial theorem (2VT) to these systems. We find that the scaling relations defined by the properties of these objects seem to be ruled by a dark-to-luminous density ratio parameter which naturally emerges in this framework. We analyze how sensitive our 2VT estimates are with respect to the use of different models for the halo and luminous component. We show that the results are inconsistent with a scale-invariant central halo density. Namely, the dark matter central halo density of galaxies in general is ~3 orders of magnitude greater than that of groups and clusters of galaxies, forming therefore a significant 'gap' between these systems (galaxies and groups/clusters). Considered separately, halos of galaxies fit by the 2VT do present an almost scale-invariant r0, but those of groups and clusters of galaxies seem to follow r0~M-1/4, where M is the effective mass of the system. Taken all systems together, a derived crude scaling is r0~M-3/4. We briefly expose possible consequences of a scale-dependent r0 on self-interacting dark matter scenarios.