My guess (not involving differential equations) is that the sphere is the initial shape least likely to end up as a bowling pin. The beauty of siravan's result is it shows that even a sphere can do so.

Re the blog post - I have no problem with it. An asteroid that has had a low perihelion for a long time will have finished any comet-like behaviour and be cooked dry. On the other hand one that has more recently been perturbed so as to lower its perihelion might still be comet-like.

I'm also very dubious about that statement concerning Hartley-2's effluent composition. For one thing, the nucleus is extremely active, and unless it's very, very anomalously enriched in CO2 the bulk of those jets has to consist of water vapor.

Not buying it.

I think we'll find plenty of water in the asteroids. (Looking forward to Vesta snd Ceres!) I think that the asteroid belt and the Kuiper belt are parts of a continuum, albeit one that has had a large swathe carved though it by the giant planets making intermediate objects rare.

On the subject of bowling pins (or dumbells) here's another: http://t2.gstatic.com/images?q=tbn:ANd9GcT...vwBbwQkdYu8MoU=
http://www.google.co.uk/imgres?imgurl=http...280&bih=825

As ngunn mentioned, the reason I started from a sphere was to show that even in absence of any asymmetry except in rotational axis, it is possible to get a complex shape just as a result of sublimation. I haven't run the simulation for other initial shapes, but my guess is that for a wide range of shapes (reasonably convex and smooth), the final result would be more or less the same.

Now, the case for Hartley 2 is much more complex. If I interpret what A'Hearn said during the press conference correctly, Hartley 2 rotational axis is not aligned with its symmetry axis, rather it is spinning in a complex fashion, probably even chaotic. Also, most of the jets are localized at the two ends rather that in the middle. This is probably because the smooth area is a dust trap and all that dust protects this area from sublimation. The reason that the waist is a dust trap is the complex gravitational potential of such an asymmetrical shape. I have attached a quick surface potential calculation for Hartley 2 (assuming uniform mass distribution); the smooth area is located at the bottom of the gravity well.

I think you have here discovered the reason for the ubiquity of 'contact binaries' in the asteroid and Kuiper belts. They don't form by two objects coalescing from a very gentle mutual orbital dance. They form, they must form, by the erosion of larger bodies.

Siravan, quick write a paper. Even a small one. G

One comment on Siravan's model: It suggests that the bilobate shape would only exist for a short time late in the object's evolution - for most of the time it's a prolate spheroid. And presumably soon after the object takes that shape it disintegrates entirely. If it only has that shape for (say) 10% of its life it suggests we should only see 10% of objects looking like that. If we see a lot of these objects, another theory might be needed.

Phil

One comment on the real world situation: as a body narrows, it's likely to change its spin axis - not continue rotating along its long axis. This would suggest, over time, the trend of continued sublimation on a spherical body would be for it to stay spherical.

I think.

Andy

I'm not so sure of that. As shrinkage is driven initially by sublimation, presumably the residue gets progressively more ice-poor until there is negligible sublimation. Subsequent shrinkage would proceed only by the much slower process of micrometeorite erosion. I think a 'dead' comet could survive in dumbell form for a very long time, looking and behaving exactly like some asteroids. Even after the original neck broke the two lobes would just roll together in a new configuration.

It was a simplified models. In reality, there are many other factors involved in determining the sublimation rate. For example:

1. When the comet nucleus becomes bilobate, the waist becomes a dust trap which prevents further sublimation from the waist.
2. A bilobate shape is concave and has complex shadowing.
3. A solid and spinning object tends to align its spin axis with the axis of maximum angular inertia, which for an elongated shape is perpendicular to the long axis.
4. Most comets, including Hartley 2, vent both H20 and CO2 (among other things), which of course have different sublimation temperatures.
5. many other factors...

My pure speculation is that a bolibate shape is pseudo-stable, i.e. for a large subset of initial conditions, the comet nucleus reaches a bilobate shape in some point in its evolution and from this point on the net results of all the different factors is to keep in more or less in the same shape.

Wild 2 and Tempel 1 do not subscribe to this model. What does that say about them, and the model?

I couldn't help but notice that Tempel 1 and Wild 2 do in fact resemble the more oblate shapes in siravan's graphic.

(images shamelessly stolen from the Ted/Emily chart)

I checked the perihelia since that is one factor that must have a bearing on sublimation: Wild 1.592, Tempel 1.509, Borelly 1.35, Hartley 1.05, Halley 0.587.

One possible explanation is that both Wild 2 and Temple 1 have a lower eccentricity orbit compared to the rest. One assumption of the model is that sublimation primarily happens close to perihelion. For a more "circular" orbit, sublimation is more or less yearlong and the model doesn't work.

Except for the peanut case, where the axis is vertical to the plane of orbit, since it will retain the same orientation all the way round.