Testing modified gravity with dwarf spheroidal galaxies

Abstract

The observed velocity dispersion of the classical dwarf spheroidal (dSph)\ngalaxies of the Milky Way (MW) requires the Newtonian stellar mass-to-light\n($M_*/L$) ratios in the range of about 10 to more than 100 solar units that are\nwell outside the acceptable limit predicted by stellar population synthesis\nmodels. Using Jeans analysis, we calculate the line-of-sight velocity\ndispersion ($\\sigma_{\\emph{los}}$) of stars in eight MW dSphs in the context of\nthe modified gravity (MOG) theory of Moffat, assuming a constant $M_*/L$ ratio\nwithout invoking the exotic cold dark matter. First, we use the weak field\napproximation of MOG and assume the two parameters $ \\alpha $ and $ \\mu $ of\nthe theory to be constant as has already been inferred from fitting to the\nobserved rotational data of The HI Nearby Galaxy Survey catalogue of galaxies.\nWe find that the derived $M_*/L$ ratios for almost all dSphs are too large to\nbe explained by the stellar population values. In order to fit the\nline-of-sight velocity dispersions of the dSph with reasonable $M_*/L$ values,\nwe must vary $\\alpha$ and $\\mu$ on a case by case basis. A common pair of\nvalues cannot be found for all dSphs. Comparing with the values found from\nrotation curve fitting, it appears that $\\mu$ correlates strongly with galaxy\nluminosity, shedding doubt on it as a universal constant.\n