MOND implications for spectral line profiles of shell galaxies: shell
  formation history and mass-velocity scaling relations
  Context. Many ellipticals are surrounded by round stellar shells probably
stemming from minor mergers. A new method for constraining gravitational
potential in elliptical galaxies has recently been suggested. It uses the
spectral line profiles of these shells to measure the circular velocity at the
edge of the shell and the expansion velocity of the shell itself. MOND is an
alternative to the dark matter framework aiming to solve the missing mass
problem.
  Aims. We study how the circular and expansion velocities behave in MOND for
large shells.
  Methods. The asymptotic behavior for infinitely large shells is derived
analytically. The applicability of the asymptotic results for finitely sized
shells is studied numerically on a grid of galaxies modeled with S\'ersic
spheres.
  Results. Circular velocity settles asymptotically at a value determined by
the baryonic mass of the galaxy forming the baryonic Tully-Fisher relation
known for disk galaxies. Shell expansion velocity also becomes asymptotically
constant. The expansion velocities of large shells form a multibranched analogy
to the baryonic Tully-Fisher relation, together with the galactic baryonic
masses. For many - but not all - shell galaxies, the asymptotic values of these
two types of velocities are reached under the effective radius. If MOND is
assumed to work in ellipticals, then the shell spectra allow many details of
the history to be revealed about the formation of the shell system, including
its age. The results pertaining to circular velocities apply to all elliptical
galaxies, not only those with shells.
