The imprint of the MOND external field effect on the Oort cloud comets aphelia distribution

Milgromian dynamics (MD or MOND) is a promising physical description excelling especially in galaxies. When formulated as a modified gravity theory, it leads to the so called external field effect (EFE). In the case of the solar system this means that bodies orbiting the Sun are influenced, beyond its tidal effect, by the external gravitational field of the Galaxy with magnitude $\sim2\times10^{-10}$ m s$^{-2}$ and time-varying direction. Aphelia of intermediate outer Oort cloud (OC) comets ($30<X<60,~X\equiv 10^{6}/a[\text{au}]$, where $a$ is semimajor axis) are distributed non-uniformly on the celestial sphere, showing an apparent concentration around a great circle centered at Galactic longitudes $L=-45$ and 135 deg. Such non-uniformity is beyond that attributable to the classical injectors of comets, stellar encounters and the Galactic tides, as well as the expected observational biases. We investigated a hypothesis that the great circle concentration of aphelia is a consequence of the long-term action of EFE in the framework of MD. We considered exclusively quasi-linear MOND (QUMOND) theory. We built our model of the OC in MD on an analytical approximation of the QUMOND potential for a point mass in the dominant external field of constant magnitude. The model is well applicable at heliocentric distances $r\gtrsim10~000$ au. Constraints on the strength of EFE found by the analysis of the Cassini radio-tracking data were taken into account. We demonstrated characteristic imprint of the EFE on the distribution of aphelia of candidate outer OC comets that migrated down to $r=10~000$ au. By both analytical and numerical calculations, we showed that the combined effect of EFE and the Galactic tides could qualitatively account for the characteristic features seen in the observed distribution of aphelia of the outer OC comets.