Statistical deprojection of intervelocities, interdistances and masses in the Isolated Galaxy Pair Catalog

In order to study the internal dynamics of actual galaxy pairs, we need to derive the probability distribution function (PDF) of true 3D (orbital) intervelocities and interdistances between pair members from their observed (projected) values, and of the pair masses from Kepler's third law. Our Isolated Galaxy Pair Catalog (IGPC) of 13114 pairs \cite{Nottale2018a} is used here for this research. The algorithms of statistical deprojection elaborated in \cite{Nottale2018b} are applied to these observational data. We derive the orbital velocity PDFs for the whole catalog and for several selected subsamples. The interdistance PDF is deprojected and compared to analytical profiles which are expected from semi-theoretical arguments. The PDF of deprojected pair orbital velocities is characterized by the existence of a main probability peak around $\approx 150$ km.s$^{-1}$ for all subsamples of the IGPC as well as for the UGC pair catalog \cite{Chamaraux2016}. The interdistance PDFs of both the projected and deprojected data are described at large distances by the same power law with exponent $\approx -2$. The whole distributions, including their cores, are fairly fitted by King profiles. The mass deprojection yields a mass/luminosity ratio for the pairs of $M/L=(30 \pm 5)$ in Solar units. The orbital velocity probability peak is observed at the same value, $\approx 150$ km/s, as the main exoplanet velocity peak, which points toward a possible universality of Keplerian structures, whatever the scale. The pair $M/L$ ratio is just 5 times the standard ratio for luminous matter, which does not require the existence of non-baryonic dark matter in these systems.