Debris disk

A debris disk is an optically thin circumstellar population of dust and larger solid bodies maintained mainly by collisions.

The fractional luminosity is $f=L_{\mathrm{disk}}/L_{\ast }$; for blackbody grains in an optically thin belt at radius $r$, it equals their total geometric cross-section divided by $4\pi r^2$.

A collisional cascade transfers mass from large bodies to progressively smaller fragments. A steady cascade has a size distribution whose mass flux through logarithmic size bins is independent of size.

A differential power-law size distribution has $n(D)dD=k{D}^{-\alpha }dD$ objects with sizes between $D$ and $D+dD$.

The catastrophic disruption threshold is the impact energy per unit target mass required both to shatter a body and to disperse enough fragments against self-gravity.

A rubblising collision shatters a body but does not supply enough energy to disperse its fragments against self-gravity, leaving a gravitationally bound rubble pile.