Galaxies lacking dark matter in the Illustris simulation
  (Abridged) Any viable cosmological model in which galaxies interact predicts
the existence of primordial and tidal dwarf galaxies (TDGs). In particular, in
the standard model of cosmology ($\Lambda$CDM), according to the dual dwarf
galaxy theorem, there must exist both primordial dark matter-dominated and dark
matter-free TDGs with different radii. We study the frequency, evolution, and
properties of TDGs in a $\Lambda$CDM cosmology. We use the hydrodynamical
cosmological Illustris-1 simulation to identify tidal dwarf galaxy candidates
(TDGCs) and study their present-day physical properties. We also present movies
on the formation of a few galaxies lacking dark matter, confirming their tidal
dwarf nature. TDGCs can however also be formed via other mechanisms, such as
from ram-pressure-stripped material or, speculatively, from cold-accreted gas.
We find 97 TDGCs with $M_{stellar} >5 \times 10^7 M_\odot$ at redshift $z = 0$,
corresponding to a co-moving number density of $2.3 \times 10^{-4} h^3
cMpc^{-3}$. The most massive TDGC has $M_{total} = 3.1 \times 10^9 M_\odot$,
comparable to that of the Large Magellanic Cloud. TDGCs are
phase-space-correlated, reach high metallicities, and are typically younger
than dark matter-rich dwarf galaxies. We report for the first time the
verification of the dual dwarf theorem in a self-consistent $\Lambda$CDM
cosmological simulation. Simulated TDGCs and dark matter-dominated galaxies
populate different regions in the radius-mass diagram in disagreement with
observations of early-type galaxies. The dark matter-poor galaxies formed in
Illustris-1 have comparable radii to observed dwarf galaxies and to TDGs formed
in other galaxy-encounter simulations. In Illustris-1, only 0.17% of all
selected galaxies with $M_{stellar} = 5 \times 10^7-10^9 M_\odot$ are TDGCs or
dark matter-poor dwarf galaxies. The occurrence of NGC 1052-DF2-type objects is
discussed.
