Quaoar: A rock in the Kuiper Belt

My compliments to Wesley Fraser and Mike Brown for publishing an academic journal article with a title piquant enough to serve as the title of a blog entry! And I suppose I ought to compliment them, too, for discovering the densest yet known object in the Kuiper belt.

Quaoar was discovered in 2002 by Chad Trujillo and Mike Brown. It's one of the larger Kuiper belt objects and was estimated in 2004 to have a diameter of more than 1,200 kilometers (which would make it similar in size to Pluto's moon Charon); however, later Spitzer observations have suggested that it is less than 900 kilometers across (smaller than Ceres).

The paper I'm writing about today, "Quaoar: a Rock in the Kuiper Belt," is based upon seven sets of Hubble Space Telescope WFPC2 observations of Quaoar and its recently-named moon, Weywot. The discovery of a moon was great news, because the orbital characteristics of a moon have a very direct relationship to the mass of the primary. So, to get at Quaoar's mass, Fraser and Brown just had to figure out Weywot's orbit, watching it go around Quaoar.

Which isn't as easy as it sounds; Quaoar is very far away, and Weywot is very dim, 5 magnitudes dimmer than Quaoar. (That, in itself, is informative: if Quaoar and Weywot are made of the same stuff, then Weywot would be about 1/12 the diameter of Quaoar and have about 1/2000th of its mass.)

In their seven sets of observations, they managed to find Weywot five times, but in two sets, they couldn't see the faint moon, which probably means that it was too close to Quaoar for the WFPC2 pictures to be able to resolve it as a separate object. And hey, since I just figured out how to dig into the Hubble data, I was able to unearth (unquaoar?) two of the relevant Hubble photos. Even better, I was able to find two photos taken eight days apart in which I could line up the background stars, blinking them to see if I could spot Quaoar. I think I spotted Quaoar (and therefore presumably Weywot as well). It helped to assume that they tried to place Quaoar on the higher-resolution PC part of the WFPC2 camera. But take the animation below with a grain of salt, because I'm not 100% certain that I identified the correct blip.

Each of the seven sets of observations contained more than one photo, but they couldn't see any statistically significant motion of Weywot from the first to last photo in each observation set. They measured the positions of Weywot relative to Quaoar as seen (or not seen) in each of the seven observations and then wrote code to come up with a best-fit orbit for Weywot.

Fraser and Brown derived an elliptical orbit for Weywot with an orbital period of 12.4 days — pretty leisurely — and a semi-major axis of 14,500 kilometers (that is, the path that Weywot traces around Quaoar would snugly encircle two Earths side-by-side). With a little bit of help from Kepler and Newton, they determined the total mass of the Quaoar-Weywot system to be 1.6 ± 0.3 × 10²¹ kilograms, which is, they state, roughly 12% that of Eris, the largest object in the Kuiper belt. 12% of Eris may sound small, but that's a matter of perspective. Mars has less than 11% the mass of Earth! And remember, they figured Weywot accounted for 1/2000 of this, a negligible amount; that system mass is basically identical to Quaoar's mass.

OK, so they have Quaoar's mass, which is interesting in itself, but they wanted to figure out its density, because density can tell you quite a lot about what a planet is made of. To get density, they needed Quaoar's volume, which is related to its diameter. But, as I said above, there's been quite a range of estimates for Quaoar's diameter. So they had to address that range in the paper. The Hubble Space Telescope's high-powered cameras actually can resolve Quaoar as an object spanning a couple of pixels, so it seems they should be able to directly measure the diameter. But there are various things that make this a very difficult thing to do; you have to make assumptions about how the disk of Quaoar appears to get darker as you look closer and closer to its limb. The original estimate, of 1200+ kilometers, was based on the assumed behavior of a Lambertian surface, one where the brightness of the surface doesn't depend upon the observer's point of view. (A Lambertian surface has no specular reflection whatsoever.)

But subsequent work on Quaoar has shown that it's not Lambertian; in fact, it can be argued that its surface is very similar to those of the icy moons of Uranus and Neptune. These objects have high albedos, have measurable opposition surges, and, most importantly, darken less rapidly toward their limbs than Lambertian surfaces do. That means that the first diameter estimate was likely 40% too large. With the assumption that Quaoar's surface looks like those of the Uranian satellites, Fraser and Brown calculate a diameter that's in much better agreement with the Spitzer measurements: 890 ± 70 kilometers. That's a bit smaller than Ceres, and about 3/4 the diameter of the icy moons of Uranus, Ariel and Umbriel, that it's now assumed to appear similar to.

Mass and diameter give you density. And that density turns out to be 4.2 ± 0.3 g/cm³ — in other words, with all the uncertainties taken into account, the density could be anywhere from 2.9 to 5.5 grams per cubic centimeter. These numbers may not mean a lot to most of you, but to me it's really quite surprising; shocking, even. These outer solar system worlds are supposed to be icy, and indeed most Kuiper belt objects have densities that aren't too different from water, which is 1 gram per cubic centimeter. The densest previously known one was Haumea, at a density of 2.6 grams per cubic centimeter; that would be consistent with a body that had some rock and some ice. But 2.9 to 5.5 means you really have to have quite a lot of rock. In fact, since the densities of typical rocks range from about 2.6 to about 3.5 grams per cubic centimeter, most of the range of possible densities for Quaoar exclude the possibility of it containing any significant amount of ice at all.

Now, Quaoar has got to have some ice, because you can see ice (not just water but also methane and ethane ice) on its surface in spectral data. But its density makes it otherwise more similar to asteroids than the other Kuiper belt objects.

How can this be? Fraser and Brown say that if planetary dynamics could put Kuiper belt objects into the asteroid belt, maybe they could likewise have tossed an asteroid into a stable, circular orbit in the Kuiper belt. (I'll have to follow up with Hal Levison on that suggestion.) Or maybe some ancient impact managed to blast away all of Quaoar's ice component. Their various suggestions are interesting, but exploring their likelihood isn't the topic of the paper; they leave that to the dynamicists. (It should be noted, however, that they acknowledge having discussed the subject with Hal Levison.)

In the end, this paper is an example of what makes science so fun. With careful observations and methods that have their roots in 400-year-old physics, we can successfully answer questions like: how big is that thing out there? Yet every answered question spawns more questions and sometimes turns things we thought we understood back into puzzles: how the heck did a giant rock get way out there? Does my fairy tale story about how the solar system first formed make sense anymore, knowing that there's at least one giant rock out there? Science is a perpetual motion machine! There will always be more questions to answer.