Testing MOG/Non-local/MOND gravity with rotation curve of dwarf galaxies

The MOdified Gravity (MOG) and Non-local Gravity are two different alternative theories to General Relativity where in the limit of weak filed approximation behave almost in similarly way and are able to play the role of dark matter and explain the rotation curve of spiral galaxies and cluster of galaxies (Moffat & Rahvar 2013, 2014, Rahvar & Mashhoon 2014). The effective gravitational potential in these theories compose of two terms, (i) Newtonian gravity with an enhanced gravitational constant and (ii) the second term with Yukawa type repulsive force which is defined with the length scale of $1/\mu$. In this work we analysis the rotation curve of dwarf galaxies in the LITTLE THINGS catalog and compare them with MOG/Non-local gravity and Modified Newtonian Dynamics (MOND). We obtain almost the same $\alpha$ factor as in our analysis of the spiral galaxy and cluster of galaxies, however we need a smaller length scale of ${\mu} =2.77 kpc^{-1}$ to describe the rotation curve of dwarf galaxies compare to ${\mu} =0.042 kpc^{-1}$ for the larger scales. This result guides us for the possibility of a running $\mu$-parameter as a function of scale of structures in these theories. For the case of MOND, the best value for the characteristic acceleration of this model is consistent with the Millgrom's value (Milgrom 1983).