Catastrophic planetesimal collision

A catastrophic planetesimal collision has

Q \geq Q_{D}^{*}

and disperses a substantial fraction of the target mass.

Table of contents

Collision disruption radius under secular stirring ( $a / a_{p} ≳ Q_{D}^{*} a_{p} / (GM e_{p}^{2})$ )

 0  0

A phase-mixed population secularly forced by a distant eccentric planet has typical orbital eccentricity proportional to

e_{p} a / a_{p}

. Consequently a relative speed of order orbital eccentricity times Keplerian speed gives

v_{col}^{2} \sim e_{p}^{2} (a / a_{p}) GM / a_{p}

. Comparing specific impact energy with a catastrophic disruption threshold gives a lower disruption radius

a / a_{p} ≳ Q_{D}^{*} a_{p} / (GM e_{p}^{2})

, up to an order-one coefficient depending on velocity statistics and impact-energy convention. The planet mass sets the secular stirring time, but cancels from this energy scaling.

Catastrophic planetesimal collision rate ( $R_{cc}$ )

 0  0

The catastrophic planetesimal collision rate is the collision rate integrated over impactors large enough to satisfy

Q \geq Q_{D}^{*}

Catastrophic collision mass-loss timescale

 0  0

The catastrophic collision mass-loss timescale is the target mass divided by the rate at which catastrophic impacts remove mass from its largest remnant.