Abstract
Context.Recent study of SDSS J1257+3419 has revealed that this stellar system is either a faint and small dwarf galaxy or a faint and widely extended globular cluster (see also arXiv:0709.0327 [astro-ph]). Aims.In this short note, the author suggests that this system is one of the smallest dwarf spheroidals (dSphs) in the Milky Way. Methods.We re-examine some observational quantities of this object and check whether it can be bound system. Results. As a result, we find the mass of SDSS J1257+3419 is the lowest of dSphs in the Milky Way, and its mass density is typical of dSphs. Important is that the tidal radius of SDSS J1257+3419 is much larger than its half-light radius. That is, this very small dSph can be bound by its own gravity.
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