Light-crossing size bound for a variable source ($L\lesssim c\Delta t$)

If a single approximately stationary emitting region changes coherently through a causal disturbance, a disturbance travelling no faster than the speed of light takes at least $L/c$ to coordinate a scale $L$. Light-travel differences also smear simultaneous emission from different depths. Under those assumptions, observed intrinsic variability on a time scale $\Delta t$ suggests $L\lesssim c\Delta t$.

For a chosen example $\Delta t=0.010\mathrm{s}$, multiplication by $c=299,792.458\mathrm{km}{\mathrm{s}}^{-1}$ gives $L\lesssim 2998\mathrm{km}$. This is an order-of-magnitude causality bound on a coordinated emitting scale. It is not a measured stellar radius, and even the relation between $L$ and a diameter depends on geometry. A pulsar beam crossing is a geometric clock, and pulsar dispersion delay, scattering and instrumental response can broaden its observed pulse. The recurrence period, observed pulse width and intrinsic variability time must therefore be distinguished before applying the bound. Relativistically moving emitters require further arrival-time corrections.