Strength-dependent steady collisional-cascade slope ($\alpha =(21+b)/(6+b)$)

With size-independent collision speed and catastrophic disruption threshold $Q_D^{\ast }\propto D^b$, the catastrophic planetesimal collision rate scales as $R\propto D^{3-\alpha +b(1-\alpha )/3}$. Multiplying by mass per logarithmic size bin gives processed mass proportional to $D^{7-2\alpha +b(1-\alpha )/3}$. Constant mass flux in a collisional cascade sets the exponent to zero, yielding the displayed differential-number index when $b\ne -6$. This is the zero-velocity-exponent case of a velocity-dependent collisional cascade.