Evidence of Absence of Tidal Features in the Outskirts of Ultra Diffuse
  Galaxies in the Coma Cluster
  We study the presence of tidal features associated with ultra diffuse
galaxies (UDGs) in galaxy clusters. Specifically, we stack deep Subaru images
of UDGs in the Coma cluster to determine whether they show position angle
twists at large radii. Selecting galaxies with central surface brightness
(g-band) >24 magarcsec^{-2} and projected half-light radius >1.5 kpc, we
identify 287 UDGs in the Yagi et al. 2016 catalog of low surface brightness
Coma objects. The UDGs have apparent spheroidal shapes with median Sersic index
~ 0.8 and median axis-ratio ~ 0.7. The images are processed by masking all
background objects and rotating to align the major axis before stacking them in
bins of properties such as axis ratio, angle of major axis with respect to the
cluster center and separation from cluster center. Our image stacks reach
further than 7 kpc (~4r_e). Analysis of the isophotes of the stacks reveal that
the ellipticity remains constant up to the last measured point, which means
that the individual galaxies have a non-varying position angle and axis ratio
and show no evidence for tidal disruption out to ~ 4r_e. We demonstrate this
explicitly by comparing our stacks with stacks of model UDGs with and without
tidal features in their outskirts. We infer that the average tidal radius of
the Coma UDGs is >7 kpc and estimate that the average dark matter fraction
within the tidal radius of the UDGs inhabiting the innermost 0.5 Mpc of Coma is
> 99%.
