= Transit dimming by an optically thin orbital wire
{title2=$\Delta F/F_\star$}
For an <edge-on orbit> crossing the centre of a uniformly bright stellar disk at distance $r\gg R_\star$, projected speed is $h/r$ and chord time is $2R_\star r/h$. A steady <cross-sectional-area current> $J_\sigma=2fh$ therefore places area $4fR_\star r$ in front of the <star>, giving
$$
\frac{\Delta F}{F_\star}=\frac4\pi\frac r{R_\star}f.
$$
This requires a geometrically narrow, <optically thin> wire with negligible overlap. A noncentral chord, <limb darkening>, finite angular extent and large <optical depth> change the estimate; it cannot predict dimming greater than one.
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