Physical interpretation of the mass-luminosity relation of dwarf spheroidal galaxies

We discuss a physical interpretation of the relation between M-vir/L and M-vir of dwarf spheroidal galaxies (dSphs), where M-vir and L are the virial mass and the total luminosity of a dSph, respectively. We used 11 dSphs in the Local Group as the sample. We find two distinct sequences on the M-vir/L-M-vir plane: M-vir/L proportional to M-vir(2.0) for dSphs with M-vir < 10(8) M., whereas M-vir/L is approximately constant for M-vir > 10(8) M.. A "discontinuity" is seen at M-vir similar or equal to 10(8) M.. We interpret the discontinuity as the threshold for the gas in dSphs to be blown away by successive supernovae. If a dSph has virial mass (most of which is dark mass) less than 10(8) M., the gas is blown away, while in a dSph of larger mass, the deep potential well prevents the blow-away mechanism from working effectively. Thus, a large mass ratio of dark matter to baryonic matter (i.e., large M-vir/L) is realized in a low-mass (M-vir < 10(8) M.) dSph through gas depletion, whereas M-vir/L becomes lower in high-mass (M-vir > 10(8) M.) dSphs. We further make an attempt to explain the above relation for the low-mass dSphs, M-vir/L proportional to M-vir(2.0), based on an estimate of cooling time, using the scaling laws of virial temperature, virial mass, and radius of a dSph and assuming that the heating by OB star radiation terminates the star formation activity. We succeed in deriving the above relation for the mass-to-light ratio and luminosity.