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A recent study has revealed SDSS J1257+3419 is either a faint and small dwarfgalaxy or a faint and widely extended globular cluster. In this Letter, theauthor suggests this stellar system is a dwarf spheroidal (dSph). Adopting anobservational relation between binding energy and mass of old stellar systems,we derive a relation between mass and size of dSphs by assuming that they aredark matter dominated and virialized objects. Letting half-light radiusrepresent size of SDSS J1257+3419, we find that its mass is $\sim 7\times 10^6$solar mass. This indicates mass-to-light ratio ($M/L$) of SDSS J1257+3419 isabout 1000 in the solar unit. This large $M/L$ is expected from a Mateo plot ofdSphs. Thus, we insist SDSS J1257+3419 is a dSph.

The Faint Stellar Object SDSS J1257+3419 is a Dark Matter Dominated System