Binary galaxies and alternative physics. I. A qualitative application of MOND and Mannheim-Kazanas gravity

Binary galaxies are modeled as point-masses obeying the non-Newtonian MOND and Mannheim-Kazanas (MKG) theories of gravity. Random samples of such systems are generated by means of Monte Carlo simulations of binary orbits. Model pairs have total masses and mass ratios similar to pairs in the cataloged sample used in the analysis. General features of synthetic samples are derived from a comparison with observed data of galaxy pairs in $R \times \Delta V/(L_1+L_2)^{1/2} $ space. Both MOND and Mannheim-Kazanas binaries either on circular or low-eccentricity orbits cannot be the source of observations because they require extremely high $M\mathrm{/}L$ values ($\approx$ 45 solar units). Both MOND and MKG binaries on high-eccentricity orbits and reasonable $M\mathrm{/}L$ values (5 solar units) produce envelopes of $R\times \mathrm{\Delta }V\mathrm{/}(L_1+L_2{)}^{1\mathrm{/}2}$ consistent with the observations, but the distribution of separations is inconsistent with the observed data, unless strong selection effects are at work. A definite answer to the issue whether one or another model is suitable to explain real binary galaxy dynamics will be only possible when {\it a large sample containing a significant fraction of wide pairs, determined with velocity-blind selection procedures, is investigated} under a rigorous statistical analysis, taking into account sample selection biases and contamination by non-physical pairs.