Post History

The [shell variant of a Dyson sphere](https://en.wikipedia.org/wiki/Dyson_sphere#Dyson_shell) consists of an artificially-made shell of material about 1 AU in radius encircling a star. The sphere captures most of the star's energy and stores it for future use. Unfortunately, the megastructure will lose energy. It has a non-zero temperature, and therefore it will radiate energy in the form of black body radiation. As with any heat engine, we can assign an efficiency, $\eta$, to it:
$$\eta\equiv1-\frac{T_{\text{DS}}}{T_*}$$
with $T_{\text{DS}}$ the temperature of the shell and $T_\*$ the temperature of the star. [An old paper I found](https://ui.adsabs.harvard.edu/abs/1985IAUS..112..315S/abstract) thinks that a temperature of $T_{\text{DS}}=300\text{ K}$ might be realistic (giving an efficiency $\eta=0.95$), and that the ultimate lower-temperature limit is set by the cosmic microwave background, at $T_{\text{DS}}=2.7\text{ K}$ and $\eta=0.99955$, all assuming a Sun-like star.

I'd bet anything that the true limit is higher and depends on the composition of the shell, but I have no idea what that limit is. Assuming that the structure is built by a [Type II civilization](https://en.wikipedia.org/wiki/Kardashev_scale#Type_II_civilization_methods) but that they don't have access to handwavium or any other magical material, what's the maximum efficiency of a Dyson sphere of this nature?