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On the fundamental issue of dark matter in galaxies there is a substantial difference between spheroidals and disk systems. Let us notice that also the latter statement shows that, although we are focused on DM halos, nonetheless, we must discuss galaxy morphology. And this has been the leitmotiv of this review: the DM component enters in aspects apparently of pertinence of the luminous matter and vice versa.

We have started to point out that the luminosity or a reference velocity is the tag that defines the dark and luminous mass distribution in galaxies. However, very recent results have proven that in spirals, “dd” and LSBs, the universal rotation curve, when expressed in physical units, needs two statistically independent controlling parameters: the luminosity and the compactness. It must be specified that we are not just flagging some empirical relationships: we have three structural properties of the stellar discs that enter in close relation with the three structural properties of the DM halos.

In elliptical galaxies, the situation is still very open. They also show regularities in their total mass distributions: its logarithmic derivative from r = 0 to r = Re and beyond is very near to 1, despite that in this region the galaxies pass from a totally LM dominated regime to one with a relevant fraction of dark matter. The fundamental plane of ellipticals and S0 entangles two quantities of the luminous world, the luminosity/stellar spheroidal mass, and the half-light ratio and a hybrid one: the dispersion velocity, which is rooted in both luminous and dark worlds. Universality in the distribution of matter in ellipticals has not been established yet. We believe that this is due to the insufficient quality and quantity of proper and useful probes of their gravitational potentials. We also have to notice that also for these systems there are evidences of cored DM distributions.

Dwarf spheroidals, despite their limited number, are becoming always more crucial in the investigation of dark matter. Each of these dark spheres, lying at the lowest mass boundary of the cosmological structures harboring stars, is a wealth of information on the dark particle. Unfortunately, we can probe their gravitational field only very near to their centers, with tracers that provide data that are difficult to be unambiguously interpreted. It is worth saying, however, that also for this population of galaxies, there are evidences of cored DM halos with properties similar to those of the disk systems and ellipticals.

The non-gravitational nature of DM remains a mystery (Bertone 2010, de Swart et al. 2017). It seems impossible to explain the observational evidences gathered so far in a simple dark matter framework. In my opinion, they are portals to the new physics that seems to lurk behind the phenomenon called “dark matter”. I think that it will be important to recognize our prejudices and confront them head on, also if this means to end our fascination with the Λ CDM Weakly Interacting Massive Particles scenario.

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