Roughly how long could an 'Oumuamua type object get?
Roughly how long could an 'Oumuamua type object get if created naturally or if created artificially using fused rock? What would be the limiting factor governing the length of such objects?
Oumaumau was a strange elongated object that entered the Solar System in 2017. It is believed to have formed from a series of molten blobs of rock following a very close encounter with a star.
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Based on the current state of thinking, somewhere in the vicinity of a couple hundred kilometers.
This particular formation theory (Zhang & Lin 2020) is a variant of an idea that's been kicked around for a couple of years. The basic principle is that early in the history of a planetary system, newly-formed planetesimals drift too close to the star and are torn apart by tidal forces. Some of the resulting fragments are, through mechanisms like three-body interactions, ejected into interstellar space, resulting in 'Oumuamua-like objects. (See Ćuk 2018 and Raymond et al. 2018 for a start - Zhang & Lin's idea is an interesting twist on older work.)
The maximum size of these fragments is dictated by the same thing that produced them - tidal forces. After a planetesimal breaks up, tidal stresses continually act on the fragments. Some of these bodies will travel closer to the star, and therefore experience even stronger tidal forces. Each fragment will continue to break up until internal forces can resist gravity and the so-called crack propagation stops.
As part of their analysis of planetesimal fragmentation around white dwarfs, Rafikov 2018 modeled the distribution of fragment sizes. The peak sizes depend on the composition of the planetesimals; iron planetoids should produce minimum and maximum radii of $R_f^{\text{min}}=350$ m and $R_f^{\text{max}}=250$ km. Rocky planetoids should be slightly smaller, at $R_f^{\text{min}}=100$ m and $R_f^{\text{max}}=200$ km. It appears that fragmentation of either type should produce significant numbers of 'Oumuamua-sized objects, at $R_f=100$ m to $1$ km. This is partly why we think these models may be true: they produce 'Oumuamua-like objects. Our dataset is currently extremely limited; it only contains 'Oumuamua and Comet 2I/Borisov.
Most other astronomers use similar limits in their models; we can safely that say that the fragments should have maximum sizes on the order of $\sim100$ km. I should note that these fragments, regardless of size, will not necessarily have the same dimensions as 'Oumuamua, but I'm not aware of any authors who have also conducted that sort of analysis.
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