modes, one by one from the location of the bifurcation point until the whole S-family disappears. This is a generic scenario for all $\lambda \ge 1$ models regardless of the disk temperature controlled by $N$. Solid lines in Figure \[pic:spectrum-m2-unstable\][*b*]{} show the [*eigenfrequency loci*]{} of a model with $(N,\lambda)=(6,1)$ as $\alpha$ increases from $0.2$ to $0.42$. It is evident that mode B1 is destabilized through a pitchfork bifurcation while the loci of modes B2 and C1, and S-modes exhibit a tangent bifurcation. All modes except mode G are stable for $\alpha <0.23$. Surprisingly, mode G resists against stabilization even for very small values of $\alpha$. This indicates that mode G is not characterized by the fraction of dark to luminous matter. In §\[sec:variations-of-lambda\] and §\[sec:variation-of-N\], I will show that this mode is highly sensitive to the variations of $\lambda$ and $N$. According to my computations (e.g., Figure \[pic:spectrum-m2-unstable\][*b*]{}), by increasing $\alpha$ all S-modes are born at the same bifurcation frequency $\omega_{S}\approx 0.43$, but mode B2 comes out from a van Kampen mode with $\omega_{B}\approx 0.83$. This result completely rules out any skepticism that mode B2 is a member of S-family.

Figure \[pic:mode-shape-m2\] displays the wave patterns and amplitude functions of 