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.

## Comments

Dennis F. Hyde

December 25, 2009 at 2:41 pm

I am continually amazed at the beauty and clarity of the photos taken by Hubble. Will be a sad day when this great telescope meets its demize. Hope there is something in the works to replace it.

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WR

December 26, 2009 at 8:42 am

Hi

Statistics also says that with the shown 23 measurements 3.8 of them should lie above the +/- 1 sigma range and 3.8 should lie below the +/- 1 sigma range (in each case ~ 1/6th of the measurements). This rule of thumb is not really harmed by the shown measurements. Effectivly they base there result on 3 measurements that would else have to be rejected as outliers.

If they find only a 2% chance that a correlation this good would happen in the FGS data by chance and they searched 12000 hours of FGS data (giving nearly half a million data points), I would wonder if they wouldn't find such an appeart event that looks real just by chance.

All in all I'm pretty sceptical if this is a real event and not just normal noise that by chance looks like a real event.

The Nature paper can be read via:

http://adsabs.harvard.edu/abs/2009Natur.462..895S

http://arxiv.org/abs/0912.2996

Merry Christmas

WR

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WR

December 26, 2009 at 11:34 am

Hi

When looking at Fig. 1a of the paper and deriving the mean and stddev from the +2 and -2 sigma lines (7.3 measurements each of the 160 measurements in the 4 sec data set above and below the +/- 2 sigma band) one can derice a mean of ~ 150.8 counts +/- ~ 10.8 counts for the stddev. This stddev is about in the correct range as the uncertainty bars in the above plot and Fig. 1b of the paper.

But the model in the 0.6 sec data set around "mid eclipse" in the above plot and Fig. 1b of the paper assumes a significantly higher "uneclipsed mean" of ~ 157.5 counts. This is IMO not OK.

Its IMO strange that the actual measurements were not as obviously marked as the calculated model "measurements" as their difference actually define the goodness of fit of the model.

Further the last measurement in time was omitted in the above plot and Fig. 1b of the paper although there is enough space to show it. With ~ 125 counts it would have been considered as an other outlier and would have made the plot much less convincing. Doinmg so is IMO not OK either.

CS

WR

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Richard

December 29, 2009 at 8:53 am

Video-taping asteroid occultations has been a fascinating hobby of mine for the past several years. I use my hand made 16" Newtonian reflector, GPS time base and a QIWI On Screen Display unit to time these events to +/- 17 milliseconds. I am always amazed how such difficult predictions can actually be made with the precision that I have found to be the case.

I do have a question on the portion of the article quoted 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."

If the distance, speed, and size of an unseen object are unknown, is it really possible to calculate all three of these parameters with any reasonable degree of accuracy?

I thought the only way ordinary asteroid occultations provide the size of the objects, is the fact that the distance and speed are pretty well known. Therefore, the length of time of the occultation provides a clue to the size of the object. Multiple observations are still required to prevent certain ambiguities.

Am I missing something here?

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