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.
