Back when I first took statistics, I was impressed by how reliably and scientifically you could measure something as seemingly uncertain as uncertainty. Statistics was all about quantifying uncertainty — the "statistical" kind of uncertainty, that is. . . not the kind about whether or not she really loves you. Or about whether you maybe bumped the photometer on the back of the telescope with your elbow, so that all of its readings are off systematically.
This comes to mind because researchers mining Hubble Space Telescope data have announced — by relying heavily on bit-by-bit statistics — that they have detected the smallest Kuiper Belt object yet observed.
In the December 17th Nature, Hilke Schlichting (Caltech) and her colleagues report finding the signature of a star being briefly occulted by something, as seen by one of Hubble's Fine Guidance Sensors (FGSs). The three FGSs watch selected guidestars to provide high-precision navigational information to Hubble's attitude controls. The group searched 12,000 hours of FGS data for signs of any star briefly disappearing.
The researchers found just one apparent case, lasting about 0.3 second. (The FGSs sample a star's light 40 times a second.) However, it wasn't a clean disappearance and reappearance like the asteroid occultations that amateurs often seek to observe. The occulting object was apparently so small, and so far away, that the event was dominated by the diffraction pattern the object imposed on the starlight passing around it, as shown in the graph below.
By assuming that the object was in a circular orbit, the group was able to estimated its distance based on the duration of the occultation. They came up with a distance of about 45 a.u., similar to the mean distance of Pluto and many other Kuiper Belt objects from the Sun. Also, the amount of diffraction-dimming gave an estimate of the object's size: about 1 kilometer (0.6 mile) across.
All of this — even whether an occultation really happened at all — depends on close statistical analysis of the graph above. The center of each red error bar is the star's observed brightness during an interval 1/40 of a second long. The error bar extends one standard deviation (in statistics talk, one sigma) above and below each point.
How well do these match the theoretically predicted pink squares, overall? Pretty darn well, the authors say. They find only a 2% chance that a correlation this good would happen in the FGS data by chance.
But that could depend on various assumptions, and other specialists are not yet convinced. And there have been other claims of momentary Kuiper Belt occultations in the past that did not pan out on closer analysis.
If this finding is true, it matters, because of another statistical inference. Finding one object 1 km in diameter in a data set this size indicates a dearth of small Kuiper Belt objects compared to what would naturally be expected from the number of large ones. This, in turn, suggests that small Kuiper Belt objects get ground down by the same kind of collisions that are creating dust rings around some other stars, in the stars' own Kuiper-Belt-like zones. When it comes to small-number statistics, one data point is about as small a number as you can get — but it does tell you something.
To try to find more occultations, the team plans to analyze the remaining FGS data for nearly the full duration of Hubble's operations since its launch in 1990.
For more information, see the group's paper.