Modified Gravity Theories in Light of the Anomalous Velocity Dispersion
  of NGC1052-DF2
  Recent observations of ultra-dwarf galaxy NGC1052-DF2 started an interesting
discussion between dark matter hypothesis and modified gravity theories.
Reported low velocity dispersion (< 10.5 km/s at 90% confidence level) derived
from the kinematic data of 10 globular clusters in the galaxy points towards an
extraordinarily low dynamical mass ($\sim$ $3.4 \times 10^{8} M_{\odot}$) which
is of the same order of the luminous mass ($\sim$ $2.0 \times 10^{8}
M_{\odot}$) in the galaxy. This has been interpreted as the first evidence of a
galaxy `without Dark Matter'. It has been argued that dark matter is not
necessarily coupled to the the baryonic mass on the galactic scale and poses a
challenge to modified gravity theories. We explore the dynamics of NGC1052-DF2
within the context of four popular alternative theories of gravity [Modified
Newtonian Dynamcies (MOND), Weyl Conformal gravity, Modified gravity
(MOG)/Scalar-Tensor-Vector Gravity (STVG) and Verlinde's Emergent gravity] and
present the analysis of detailed radial variation of the velocity dispersion.
We demonstrate that the dispersion data of NGC1052-DF2 is fully consistent with
modified gravity paradigm (as well as with general relativity without dark
matter). We reach similar conclusion for the ultra-dwarf NGC1052-DF4 which has
been claimed to be the second candidate for galaxies `without Dark Matter'.
