Evolution of globular-cluster systems of ultra-diffuse galaxies due to
  dynamical friction in MOND gravity
  (Abridged) Dynamical friction can be used to distinguish Newtonian gravity
and modified Newtonian dynamics (MOND) because it works differently in these
frameworks. This concept, however, has yet to be explored very much with MOND.
Previous simulations showed weaker dynamical friction during major mergers for
MOND than for Newtonian gravity with dark matter. Analytic arguments suggest
the opposite for minor mergers. In this work, we verify the analytic
predictions for MOND by high-resolution $N$-body simulations of globular
clusters (GCs) moving in isolated ultra-diffuse galaxies (UDGs). We test the
MOND analog of the Chandrasekhar formula for the dynamical friction proposed by
S\'anchez-Salcedo on a single GC. We also explore whether MOND allows GC
systems of isolated UDGs to survive without sinking into nuclear star clusters.
The simulations are run using the adaptive-mesh-refinement code Phantom of
Ramses. The mass resolution is $20\,M_\odot$ and the spatial resolution
$50\,$pc. The GCs are modeled as point masses. Simulations including a single
GC reveal that, as long as the apocenter of the GC is over about 0.5 effective
radii, the S\'anchez-Salcedo formula works excellently, with an effective
Coulomb logarithm increasing with orbital circularity. Once the GC reaches the
central kiloparsec, its sinking virtually stops, likely because of the core
stalling mechanism. In simulations with multiple GCs, many of them sink toward
the center, but the core stalling effect seems to prevent them from forming a
nuclear star cluster. The GC system ends up with a lower velocity dispersion
than the stars of the galaxy. By scaling the simulations, we extend these
results to most UDG parameters, as long as these UDGs are not external-field
dominated.
