[ExI] The strange star that has serious scientists talking about an alien megastructure

[Anders Sandberg]

This is a nice presentation and paper
http://orfe.princeton.edu/~rvdb/tex/talks/PACM07/RingTalk.pdf
http://orfe.princeton.edu/~rvdb/tex/saturn/ms.pdf
that show Maxwell was right about the ring stability.

A ring of n objects with mass m orbiting a mass M will remain stable is  
m < 2.298 M/n^3. So if each Dysonlet is square with side s, area density 
rho and orbits at distance R, then: rho < [2.298/8 pi^3] M s /R^3. That 
is, the Dysonlets need to become much larger in a large sphere. If we 
take rho to be 0.0271 kg/m^2 (aluminium foil), at R=1 AU the smallest 
stable Dysonlet has side 4.9 km. Note that you can stabilize things by 
moving half out to a slightly wider orbit (n^3 drops by a factor of 8) 
but you will have to deal with the different periods producing 
self-shadowing.

If an abandoned ring has some breakup (say meteor damage), then it seems 
likely that the appearance of smaller fragments can destabilize the 
whole array. In fact, the Kessler syndrome 
http://webpages.charter.net/dkessler/files/Collision%20Frequency.pdf in 
this case might be *way* nastier than around Earth, since we are talking 
about a thick soup of collectors: almost half of the directions 
available for a debris piece will intersect with something else. Once 
there are smaller fragments, they will start gravitating towards larger 
densities and destabilize the overall structure.

The growth of a perturbation is roughly X''= omega^2 X + [nonlinear 
stuff] (omega is angular frequency), so once the array destabilizes it 
will go bad in about one rotation. But as the simulations on Vanderbei's 
page show, it may take a long while for the disaster to trigger.


-- 
Dr Anders Sandberg
Future of Humanity Institute
Oxford Martin School
Oxford University