Understanding local dwarf spheroidals and their scaling relations under MOdified Newtonian Dynamics
We use a specific form of the interpolation function in the MOND formalism, which optimally accounts for the internal structure of dwarf spheroidal (dSph) galaxies, to explore the consequences it has on the scaling relations seen in these systems. The particular form of the interpolation function we used leads to a law of gravity that does not degrade the good fit of the MOND proposal on galactic scales, and in fact, slightly improves the accordance with observations on dSph scales. This formalism yields a good description of gravitational phenomena without the need of invoking any still undetected and hypothetically dominant dark matter, in the weak field regime probed by local dSph galaxies. Isothermal equilibrium density profiles then yield projected surface density profiles for the local dSph galaxies in very good agreement with observational determinations, for values of the relevant parameters as inferred from recent observations of these Galactic satellites. The observed scaling relations for these systems are also naturally accounted for within the proposed scheme, including a previously unrecognised correlation of the inferred mass-to-light ratios of local dSph's with the ages of their stellar populations, which is natural in modified gravity schemes in the absence of dark matter. The results shed some light on the form that the MOND interpolating function may have in the most challenging regime, which occurs at moderate accelerations and intermediate mass-weighted lengths.