= Solution
At fixed masses, the <equal-mass circular-binary quadrupole luminosity> grows as $R^{-5}$. The binary's Newtonian binding energy is $-GM^2/(4R)$, so reducing the separation increases both the binding and the radiated power. Equivalently, its luminosity scaling is
$$
P=\frac25\frac{c^5}{G}\left(\frac{GM}{Rc^2}\right)^5,
$$
which makes the importance of <orbital compactness> explicit.
Ordinary extended stars cannot remain separate at very small orbital radii: contact, mass transfer and <tidal disruption> intervene. A <neutron star> or <black hole> can remain a compact orbiting object down to separations of order a few gravitational radii, allowing high orbital speeds, rapidly changing <mass quadrupole moments> and strong <gravitational waves>. Thus compact, tightly bound binaries are especially efficient emitters. The Newtonian <quadrupole formula> explains the scaling; precision predictions near merger require relativistic dynamics, where that approximation itself ceases to be reliable.
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