MONDian predictions for Newtonian M/L ratios for ultrafaint dSphs

Abstract

Under Newtonian gravity total masses for dSph galaxies will scale as $M_{T} \propto R_{e} \sigma^{2}$, with $R_{e}$ the effective radius and $\sigma$ their velocity dispersion. When both of the above quantities are available, the resulting masses are compared to observed stellar luminosities to derive Newtonian mass to light ratios, given a physically motivated proportionality constant in the above expression. For local dSphs and the growing sample of ultrafaint such systems, the above results in the largest mass to light ratios of any galactic systems known, with values in the hundreds and even thousands being common. The standard interpretation is for a dominant presence of an as yet undetected dark matter component. If however, reality is closer to a MONDian theory at the extremely low accelerations relevant to such systems, $\sigma$ will scale with { stellar mass} $M_{*}^{1/4}$. This yields an expression for the mass to light ratio which will be obtained under Newtonian assumptions of $(M/L)_{N}=120 R_{e}(\Upsilon_{*}/L)^{1/2}$. Here we compare $(M/L)_{N}$ values from this expression to Newtonian inferences for this ratios for the actual $(R_{e}, \sigma, L)$ observed values for a sample of recently observed ultrafaint dSphs, obtaining good agreement. Then, for systems where no $\sigma$ values have been reported, we give predictions for the $(M/L)_{N}$ values which under a MONDian scheme are expected once kinematical observations become available. For the recently studied Dragonfly 44 { and Crater II systems}, reported $(M/L)_{N}$ values are also in good agreement with MONDian expectations.