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.
