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'.