Left: difference of the adiabatic exponent, Γ₁, from 4/3 as a function of M_r/M for selected models. Solid and dashed lines indicate unstable and stable models against the GR instability, respectively. Accretion rates are color-coded, as is indicated. Right: quantity, Q, defined in Eq. (12) is plotted as a function of M_r/M for the structures of SMSs with various accretion rates. Unstable and stable structures are plotted with solid and short-dashed lines, respectively. These curves are compared with the long-dashed black line representing Q_crit (Eq. (13)) that corresponds to the Q for the critical n = 3 polytrope.