The age of the main population of the Sagittarius dwarf spheroidal galaxy. Solving the "M giant conundrum"

We present a statistically decontaminated Color Magnitude Diagram of a 1°× 1° field in the core of the Sagittarius dSph galaxy. Coupling this CMD with the most recent metallicity distributions obtained from high resolution spectroscopy we derive robust constraints on the mean age of the stellar population that dominates the galaxy (Pop A). Using three different sets of theoretical isochrones in the metallicity range -0.4≤ [M/H]≤ -0.7 and taking into consideration distance moduli in the range 16.90≤ (m-M)_0≤ 17.20 we find that the mean age of Pop A is larger than 5 Gyr, and the best-fit value is age = 8.0± 1.5 Gyr. Since Pop A provides the vast majority of the M giants that traces the tidal stream of Sgr dSph all over the sky, our estimate resolves the so called "M giant conundrum" (Majewski et al. 2003, ApJ, 599, 1082). The time needed by the M giants that currently populates the stream to diffuse within the main body of Sgr and to reach the extremes of the tidal tails once torn apart from the parent galaxy (≃3{-}4 Gyr) can be easily accommodated into the time lapsed since their birth (≃5.5{-}9.5 Gyr).