Physical Interpretation of the Mass-Luminosity Relation of Dwarf Spheroidal Galaxies
We discuss a physical interpretation of the relation between $M_{\rm vir}/L$ and $M_{\rm vir}$ of dwarf spheroidal galaxies (dSphs), where $M_{\rm vir}$ 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 $M_{\rm vir}/L$--$M_{\rm vir}$ plane: $M_{\rm vir}/L\propto M_{\rm vir}^{2.0}$ for dSphs with $M_{\rm vir}<10^8M_\odot$, whereas $M_{\rm vir}/L\simeq$ constant for $M_{\rm vir}>10^8M_\odot$. A ``discontinuity'' is seen at $M_{\rm vir}\simeq 10^8M_\odot$. 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 $10^8M_\odot$, 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, large mass ratio of dark matter (DM) to baryonic matter (i.e., large $M_{\rm vir}/L$) is realized in a low-mass ($M_{\rm vir}<10^8M_\odot$) dSph through the gas depletion, whereas $M_{\rm vir}/L$ becomes lower in high-mass ($M_{\rm vir}>10^8M_\odot$) dSphs. We further make an attempt to explain the above relation for the low-mass dSphs, $M_{\rm vir}/L\propto M_{\rm vir}^{2.0}$, based on 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.