Modified-dynamics Predictions Agree with Observations of the Hi Kinematics in Faint Dwarf Galaxies Contrary to the Conclusions of Lo Sargent and Young

Lo, Sargent, and Young (1993) have recently published an analysis of the HI kinematics of nine faint dwarf galaxies. Among other things, they conclude that the masses of these systems, as deduced by the modified dynamics (MOND) from the observed velocity dispersions, are systematically smaller than even the HI masses that are observed in these systems, by a factor of ten or more. Such a state of things would speak strongly against MOND. We show here that the MOND mass estimator used by Lo et al. is smaller than the proper expression, by a factor of about twenty. We derive the proper mass estimator as an exact virial-like relation between the 3-D rms velocity, 〈v〉, and the total mass, M , of an arbitrary, self-gravitating system, made of light constituents, that is everywhere in the very-low-acceleration regime of MOND. This reads M = (9/4)〈v2〉2/Gao. (For a system that is not stationary, 〈v〉 involves also an average over time.) We do this in the Bekenstein-Milgrom formulation of MOND as a modification of gravity. This relation has been known before for the special case of a stationary, spherical system. We further generalize this relation to cases with constituent masses that are not small compared with that of the whole system. We discuss various applications of the M − v relation; inter alia, we derive an expression for the two-body force law in the large-distance limit. With the correct estimator the predictions of MOND are, by and large, in good agreement with the total observed masses (the observed gas mass plus a stellar mass corresponding to an M/L of order one solar unit).