Stellar Occultation Investigations of Pluto's Atmosphere

Colette Salyk

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21 2

Stellar Occultation Investigations of Pluto's Atmosphere

Colette Salyk

Submitted to the department of Earth, Atmospheric and Planetary Sciences in Partial Fulfillment of the Requirements for the Degree of Bachelor of Science in Earth, Atmospheric and Planetary Sciences

ABSTRACT

We investigate the shape of Pluto's atmosphere using data from the occultation of the V=15.7 star P131.1 by Pluto on 2002 Aug 21 (UT). We find that Pluto's atmosphere, as projected onto the sky, is noticeably non-circular. This implies an overall ellipsoidal shape, which could be an indication of high winds and/or latitudinal stratification. We decide to compare our results to those obtained from datasets of the occultation of P8 by Pluto on 1988 June 9 (UT). Previous analyses of these datasets by Millis et al. (1993) had led to the conclusion that Pluto's atmospheric shape did not deviate from that of a sphere. However, we find that the 1988 datasets do not conclusively demonstrate that this is the case. We conclude that Pluto's atmosphere is currently non-spherical and could have been non- spherical at the time of the 1988 occultation. Implications for high winds and/or latitudinal stratification present exciting possibilities to be investigated by the upcoming New Horizons mission to Pluto.

Thesis Supervisor: James L. Elliot Professor of Earth, Atmospheric and Planetary Sciences Professor of Physics 3

1. Introduction

The planet Pluto, discovered in the year 1930, is the furthest solar system planet from our sun. With an apparent magnitude of -15 at the time of discovery, it was difficult to observe with available techniques, and remained, for many years, an object of interest and speculation. As early as 1994, Kuiper (1944) used stability considerations to propose that

Pluto may have an atmosphere. Other speculations about the possible presence of or characteristics of an atmosphere on Pluto arose in the early 1970's. A pair of papers proposed and discussed an atmosphere composed primarily of Ne, with an additional brief

mention of the possibility of an N 2 atmosphere (Hart, 1974, Golitsyn, 1975). The first observational results about Pluto came in 1976, when methane frost was detected by spectroscopy (Cruikshank 1976). Stem, Trafton and Gladstone (1987) used this information, as well as observations that Pluto's albedo changed with both time and location, to argue that

Pluto should have an atmosphere. This result was to be confirmed in 1988.

In 1988, an observed stellar occultation by Pluto confirmed the presence of an atmosphere. Stellar occultations are one of the most important observational techniques for studying distant planets, because they return extremely high spatial resolution information about a body's atmosphere or rings. Occultations occur when a planet passes in front of a star as viewed from Earth. If we measure the received starlight as the star is occulted and an atmosphere surrounds the body, we observe a reduction in starlight because the atmosphere refracts the starlight away from our line of sight. Because the star is essentially a point source, the spatial resolution of the observations are limited only by Fresnel diffraction, which translates to a resolution of just a few kilometers at Pluto. Observers of the 1988 occultation by Pluto saw a reduction in starlight due to refraction and concluded that Pluto did, indeed, possess a thin atmosphere, which they believed to be composed of CH4, but 4

mentioned that it was also consistent with a primarily N 2 atmosphere (Elliot et al. 1989). In

addition, they noted that Pluto's atmosphere had a roughly isothermal upper layer as well as a

lower layer that either acted as an extinction layer, or had a radically different scale height

from the upper atmosphere. The shape of Pluto's atmosphere was also investigated and

determined to be circular (Millis et al. 1993).

Succeeding the exciting discovery of Pluto's atmosphere, Yelle and Lunine (1989)

determined, theoretically, that a predominantly CH4 atmosphere was not consistent with the

occultation results. Owen et al. (1993) soon after detected N2 , CH4 , and CO on Pluto's

surface, and reasoned that due to N2 being both the most abundant and most volatile of the

three molecules, N 2 should be the most abundant atmospheric constituent. After these significant studies, our knowledge of Pluto's atmosphere did not have a chance to expand until the occurrence of the next stellar occultation. Because the probability of a stellar occultation occurrence depends directly on the area of sky subtended by the occulting body, stellar occultations by Pluto are rare. The next occultation by Pluto occurred in summer

2002.

On July 27 2002, Pluto occulted the R=12.3 star P126A. Unfortunately, due to difficulties in predicting the occultation's location, only a couple of mobile telescopes were able to collect data (Buie et al. 2002). Luckily, another occultation occurred shortly afterwards on the 2 111 of August. This occultation was observed at six different observatories and on ten telescopes. Four telescopes were located on Mauna Kea; observers at these telescopes were focused on providing an explanation for the lower atmospheric layer observed in 1988 and noting any differences from the observed features of the 1988 occultation (Elliot et al. 2003). The other five locations were used to provide a large spatial baseline across the globe, and therefore, across Pluto's disk as seen from Earth. This baseline 5

is essential for correctly determining the location of the star's path along Pluto's disk. It also

provides a means for investigating the shape of Pluto's atmosphere.

The shape of a planet's atmosphere can be determined by observing an occultation from several different locations on Earth. The shape, in turn, gives us information about the atmospheric structure, from which one may infer wind speeds, if the oblateness is not likely to be caused by the rotation of the planet. Stellar occultation measurements of Saturn's moon

Titan resulted in the surprising finding of a significantly ellipsoidal atmosphere (ellipticity -

0.016), implying very high winds and a possibly latitudinally-stratified wind structure

(Hubbard et al. 1993). Stellar occultation measurements of Neptune's moon Triton in the

90's showed that its atmosphere was even more ellipsoidal (ellipticity ~ 0.040) than Titan's

(Elliot et al. 2000). Looking back at the Pluto occultation of 1998, we find that, although similar analyses were performed by Millis et al. (1993), the possibility of an ellipsoidal atmosphere was not mentioned. We investigate here the shape of Pluto's atmosphere by using 2002 occultation data as well as by re-examining the data points from the 1998 occultation.

2. Observations

The occultation of the V = 15.7 star P13 1.1 by Pluto occurred on 2002 Aug 8 at approximately 6:59 (UT) (Elliot et al. 2003). The total event duration, from immersion to emersion, was about five minutes. The details of all observations, including locations, telescopes, event times and instrumentation specifics can be found in Table 1. For our purposes, we note that observers on Mauna Kea observed in several different wavelength bands and with generally high S/N ratios. Other, smaller telescopes, despite necessarily 6 lower signal collecting abilities, were utilized at several different locations to maximize the spatial coverage of the event. The data interpreted in our analysis include datasets from

Haleakala Observatory on Maui, Lick and Palomar Observatories in California and Lowell

Observatory in Arizona, along with one high S/N dataset from Mauna Kea, obtained on the

University of Hawaii's 2.2m telescope.

Each dataset consisted of a series of CCD frames that captured images of both P13 1.1 and Pluto. In general, each dataset spanned a time period beginning at least several minutes before the starlight's immersion into Pluto's atmosphere, and ending several minutes afterwards. A notable exception is the dataset taken at Haleakala. Because of instrument- setup problems, observers were only able to capture the emersion portion of the event.

Image integration times and cycle times (the time required for the reading out of the CCD chip) varied from location to location; the time resolution, therefore, ranged from 0.0001 seconds to 2.4 seconds. (These details can also be found in Table 1).

3. Light Curves and Model Fitting

The first step in reducing the image datasets is to construct occultation lightcurves. A lightcurve, in its simplest form, is simply a plot of received starlight as a function of time.

However, as the star and its occulting body are not resolvable for this event, it is easiest to construct a lightcurve of the starlight plus planet-light as a function of time. Furthermore, to minimize the effects of time-variable atmospheric conditions, the observed light is generally divided by the light of a non-variable reference star, preferably observed on the same frame.

We applied both of these techniques to our datasets. We performed aperture photometry, using one aperture that encompassed both Pluto and P131.1 and a second aperture that 7

encompassed the reference star, and then calculated the ratio of the combined Pluto and star

signals to the reference starlight. By accounting for the relative brightness of Pluto and

P131.1, the signal from Pluto was removed, leaving a plot of received starlight as a function

of time. The five relevant lightcurves are displayed in Fig. 1. Occultation lightcurves from

Haleakala, Lick, Lowell, Palomar and the UH 2.2m telescope were fit using the least-squares

method and a light curve model for an occultation by a small body with a possible

atmospheric thermal gradient, haze layer, and limb cutoff (Elliot and Young 1992). In

general, the quality of the fits was very good, with the possible exception of Palomar, whose low signal quality is clearly apparent in Figure 1.

4. Pluto's Atmospheric Figure from the P131.1 occultation

Best-fit lightcurve models were then used to investigate the shape of Pluto's atmosphere. The procedure for determining an atmospheric figure using occultation observations can be described roughly as follows. The starlight signal received on Earth diminishes as the star's path crosses the planet's path because of the refraction of light rays by the planet's atmosphere. Because the drop in starlight is caused by refraction, the amount of starlight received on Earth is an indication of the pressure depth reached by the light rays that graze the planet's disk. Since we know the geometry of the observed events (i.e. we know Pluto's, the star's and our location at all times), we also know at which location along the planet's disk we are observing this pressure level. By observing at several locations on

Earth, and thereby observing the immergence and emergence of the star at several locations on the planet's disk, one can determine the shape of a given pressure contour. 8

A common procedure is to determine, for each station, the time at which the starlight reached its half-light level (where the starlight's signal was at 50% of its full level) and use

these times to model the pressure contour (Elliot et al. 2000). In the case of the P131.1 occultation by Pluto, however, Lowell observatory was far enough away from the center of the occultation shadow that the star's path only grazed Pluto's atmosphere. Consequently, the refraction of starlight resulted in a drop in signal of only about 6% (see Fig 1). Rather than model Pluto's half-light level, we instead determined the time at which the Lowell lightcurve reached its lowest level of 94% stellar signal and also found the times at which

94% light was reached at all other locations. We used the results of the lightcurve model fits to determine the times of 94% light, during immersion and emersion, at Lowell Observatory,

Lick Observatory, Palomar Observatory, Haleakala, and the UH 2.2 meter telescope on

Mauna Kea. This resulted in 8 reference times, as observers at Haleakala did not observe immersion, and Lowell only provided one reference point. A summary of locations and 94% light times are shown in Table 2. The errors listed are derived from the errors in the least- squares-fit parameters, and are most directly related to the error in fitted midtime.

The next step after determining 94% light times was to determine how these times related to positions with respect to Pluto's disk. With knowledge of the star's right ascension and declination, as well as each telescope's latitude, longitude and altitude, it is possible to translate each immersion or emersion 94% light point onto a plane parallel to the viewable disk of Pluto. In this coordinate system, known as the 'fgh" coordinate system (Elliot et al.

1993),f points East, g points North and h points in the direction of the occulted star. All three coordinates are measured in kilometers. With this transformation complete, we can now fit a shape to the available immersion and emersion points. This shape would represent a 2D projection of Pluto's atmosphere onto the plane of the sky. 9

Before performing these fits, it was necessary to determine the error of each point's position in the "fgh " system, both to be able to apply appropriate weights to the points when

fitting as well as to determine the goodness-of-fit parameter X2. We have assumed that the dominant error for each point is the error in the exact timing of 94% light. To translate this error in time to an error in distance, one can simply multiply the timing error by the velocity of the star's motion across the planet's disk at each location. We thereby obtain errors lying along the occultation chords- the lines defined by each immersion/emersion pair representing the path of the star behind Pluto as seen from a given station. However, we plan on fitting circles (or ellipses) to these points by minimizing the sum of the distances from each point to the edge of the circle. Therefore, only the components of the error pointing towards the center of the circle are to be taken into account in the fits. We determined approximate coordinates for the center of the disk and an approximate radius by performing a preliminary, unweighted fit, and used these to determine the distance errors projected towards the center of the circle. The projected error is calculated as the error along the chord times the cosine of the angle between the chord and the line defined by the center of the circle and the point.

Using simple geometry, the correct error is found to be approximately:

Ar= vAtL/(2 R) where v is the velocity of the event, At is the timing error from Table 2, L is the length of the chord connecting one point with its corresponding pair and R is the approximated radius of the circle. Clearly L was not determinable for Maui, since only emersion was observed; we have used the chord length for the UH 2.2m observations as an approximate value, since

Haleakala and Mauna Kea lie close together, both on Earth and in (f g) space. In addition, note that L must be zero for Lowell, since we chose the 94% light level to be the lowest level of starlight observed at Lowell and therefore have only one Lowell point and no chord length. We recognize that it is not reasonable to assume that the Lowell point has zero error 10

and a correspondingly infinite weight, and we have subsequently left it out of all fits that

used projected errors to determine weights.

The immersion and emersion points in Pluto's disk plane roughly define the shape of

a circle, as one should expect if Pluto is close to being a spherical body. We therefore chose

to begin with the simplest case, by fitting these points with a circle. We performed 3 fits: one

with all points equally weighted, a second with each point weighted by its Signal/Noise level

squared, and a third with each point weighted by the inverse of the square of its projected

error as calculated above. The fit was performed by varying the circle's center and radius to

minimize the sum of the squared distances from each point to the circle's edge. The fitted

parameter values and reduced chi-squared value for each of these three fits are shown as

rows 1-3 in Table 3. The best fit is achieved with the third fit, in which the weights were

dependent on the projected timing errors. A plot of the 94% light points and this best-fit

circle is shown in Figure 2. Note that despite the reasonable reduced X2 Of 0.87, the fit is

clearly overshooting both Palomar points, as well as the Lowell point, which was not

included in the fit. This was an indication that a circle may not provide an adequate fit. We

decided to try fitting the figure with an ellipse.

We performed three elliptical fits to these data, using the same three sets of weights, respectively, as were used in the circular fits. The results of these fits can be seen as fits 5-7 in Table 3. Fit 7 is statistically the best fit and is shown in Figure 3. The ellipse properly approaches the Southeastern-most points, and is also consistent with the Lowell point, although this was given zero weight in the fitting. This ellipse has ellipticity 0.076. Note, however, that the reduced X2 of this fit is 0.076 and, in fact, all of the elliptical fits have reduced X2 values of much less than 1, which is the approximate value we would expect for a reasonable fit. In addition, it can be seen in Figure 3 that the ellipse falls well within the 11

plotted error bars for most points. We wondered, therefore, if we had, perhaps,

overestimated our projected errors.

Luckily, we had an independent means to determine whether or not our error bars

were an accurate representation of the actual uncertainty. If, indeed, we had overestimated the error bars, we would expect that if we determined the error bars of 94% light times from all of the Mauna Kea telescopes, the error bars would be larger than the scatter in 94% light times. (Note, that we are here assuming that these telescopes are close enough together so as to have a negligible intrinsic difference in 94% light time) In order to investigate whether such a discrepancy existed, we began by determining the 94% light times from the lightcurves obtained with UKIRT, the UH 0.6m and the IRTF. Because four separate passbands were used at the IRTF, the IRTF observations produced four lightcurves.

Including these four lightcurves with the two from the other Mauna Kea telescopes meant that we obtained six independent measures of 94% light, upon each of immersion and emersion, each with a timing error as determined from errors in fitted model parameters.

Shown in Figure 4 are the immersion and emersion 94% light times, plotted with timing errors. We have, additionally, plotted the weighted mean of the 94% light times for each of immersion and emersion. It is apparent, especially upon immersion, that the mean is a much better approximation to the actual values than the error bars would suggest. Put quantitatively, the reduced x2 values for immersion and emersion are 0.17 and 0.29, respectively, both much lower than the expected value of 1. The reduced x2 value for the two sets combined is 0.21. We believe, therefore, that we have somewhere unintentionally inflated our errors, such that they no longer properly represent the actual uncertainty in our data. In an attempt to adjust for this unknown discrepancy, we determined that to produce a reduced X2 of 1 for the fit of mean 94% light time to all Mauna Kea 94% light times would require that all timing errors be divided by -2.2. We have applied this correction to the error 12

bars in the third of our circular and elliptical fits. The fits with these adjusted error bars and

their respective reduced x2 's are shown as fits 4 and 8 in Table 3. These corrected error bars

yield a much more probable X2 for the elliptical fit, and demonstrate that the circular fit was,

indeed, not properly fitting the data. We conclude that, based on our observations of the

P131.1/Pluto occultation, Pluto's projected atmospheric shape deviates significantly from that of a circle.

5. Re-examination of Pluto's figure from 1988 dataset

Upon noting that Pluto's 2002 atmospheric figure was noticeably non-spherical, we decided to re-examine the 1988 occultation results of Millis et al. (1993) who had previously reported no deviation from sphericity in Pluto's atmosphere. Their data were derived from observations of the occultation of P8 by Pluto on 1998 June 9, (UT). We had two issues in mind as we looked back at these data. Firstly, we wanted to be sure that our method was consistent with theirs by showing we could reproduce their results. Secondly, we wanted to find out whether in 1998 Pluto's atmosphere had shown no sign of ellipticity, or whether indications of ellipticity had, instead, been overlooked. Either result would be quite enlightening- either indicating a drastic change in Pluto's atmosphere or confirming our conclusion that Pluto's atmosphere is not spherical.

Our first goal was to try to recreate the results of Millis et al. using our fitting methods with their immersion and emersion times to ensure consistency. Their paper included a list of telescopes and the times at which 76.4% light, the minimum light observed at the Mt. John telescope, was reached. We began by simply attempting to recreate their plot of 76.4% light times in (f g) space and quickly realized that one of the published times, that 13

of the Mt. Tamborine station, was not consistent with their figure. And, indeed, the

published time had a misprint that made it one second off from the correct time (L.

Wasserman, personal communication). Their observation summary table is recreated here as

Table 4, with the corrected Mt. Tamborine time.

In Millis et al., 8 circular fits were performed, each using different numbers of data

points and/or a different weighting scheme. We have here reproduced what they had chosen

as their best fit. This fit includes only points with S/N > 10 and gives precisely equal weight

to each of these points. Our fit reproduced the Millis et al. radius with a difference of -1 km.

It is not clear why the two fits have this small discrepancy, but the results are well within the fitted radius's error, and we are therefore satisfied that we've reproduced the Millis et al. result. In order to quantify the goodness of this fit, we determined errors projected towards the center of the circle following the procedure outlined in section IV. Using these projected errors, we found a reduced x2 of 8.76, indicating that this is likely not a very good fit to the data. The results of this fit are shown as Fit 1 in Table 5. However, it is not surprising that an equal-weight scheme should yield an inappropriate fit, as an appropriate fit should give greater weight to the more accurate points. So we performed a second circular fit, this time using the inverse square of the projected errors as weights. We again used only points with

S/N >10, but had to exclude the Mt. John point as well, as its projected error is zero (as was the case with the Lowell Observatory point in 2002). As shown in Table 5, we achieved a 2 of 1.77- a great improvement over the previous fit. (Interestingly, Millis et al. did not publish a fit of this type.) We have shown this circular fit as Figure 5 a. However, as the x2 was still significantly higher than 1, we decided to investigate the relevance of elliptical fits.

We began with two elliptical fits of the points with S/N > 10 - one in which the data were weighted evenly, and one in which the data were weighted using the inverse square of their projected errors. These fits are listed as fits 3 and 4 in Table 5, and it is apparent that 14 the second of these elliptical fits is the better fit of the two and that the second elliptical fit also has a lower x value than the best fit circle. This best-fit ellipse is shown as Figure 5 b.

However, we decided to check the consistency of this fit with the data points which were not used in the fit (see Figure 5 c), and found that the ellipse was likely "over-flattened" by the absence of the Toowoomba and Mt. Tamborine points. Because of the obvious inconsistency between the pairs of points derived from Toowomba and Mt. Tamborine, we performed one fit with each pair. All of these fits are included in Table 5. It can be clearly seen that some parameters, most notably semi-major axis and ellipticity, varied greatly from fit to fit. We therefore hesitate to make any firm conclusions about the quality of these fits. However, we believe that these fits demonstrate that one cannot rule out the possibility of a non-spherical atmosphere on Pluto at the time of the 1988 occultation. We thereby demonstrate that our results from the P131.1 occultation are not inconsistent with the results of Millis et al., and that in 1988 signs of non-sphericity were likely overlooked, perhaps with the thought that they had been introduced by errors, rather than representative of the actual state of Pluto's atmosphere.

Table 6 briefly compares the best-fit ellipses from 1988 and 2002.

6. Discussion

We believe we have found significant evidence for non-sphericity in Pluto's atmosphere and take our best-fit ellipticity of 0.076 as a means for discussing its implications. The ellipticity of an atmospheric surface rotating as a whole at velocity v is given by 15

e = 3/2 J2+ v2/(2 a g)

(Elliot et al. 2000 ) where J2 is the planet's mass quadrupole moment, g is its atmospheric

gravity, and a is the average radius of the given pressure level. If we assume Pluto is a solid

spherical body spinning at its orbital period of -6.4, we would expect a deviation from

sphericity of its solid body to be no more than a few hundred meters. We therefore set J2 to be - 0. Using e = 0.076, a = 1385.8 km (see Table 3, fit 7) and g = 0.58 m/s 2 and, we can solve for v. We find that the velocity of the layer, v - 350 m/s. The speed of sound in a diatomic gas is given by

*( 7/5 R Ti/) where R is the universal gas constant, T is the temperature and pt is the molecular mass. We find, assuming Pluto's atmosphere is composed primarily of Nitrogen gas and using T = 104

K (Elliot et al. 2003) as an approximation for the temperature at this atmospheric level, we find that the speed of sound is -207 m/s. Thus, the atmospheric velocities required to maintain an ellipticity of 0.076 would need to be more than one and one-half times the speed of sound.

Similar results, namely unphysically high winds, have been found by analysis of occultations on both Titan (Hubbard et al. 1993) and Triton (Elliot et al. 2000). Hubbard et al. demonstrate that such ellipticity could be explained by an atmosphere with latitudinal bands of various wind speeds, some of which reach ~ 1/2 of the value calculated using occultations. In our case, since Pluto's oblateness is difficult to determine with even the best telescopes, we have the additional possibility that Pluto's mass quadrupole moment, J2, is significantly different from zero. However, it seems likely that the elliptical shape would then be reflective of the position of Pluto's rotational axis, which is clearly not the case in

Figure 3. 16

7. Conclusion

We conclude based on the results of the 2003 occultation of P131.1 by Pluto, that

Pluto's atmosphere demonstrates significant deviation from sphericity, which may be caused

by high-speed winds that change speed with latitude. In addition, we find that Pluto's

atmosphere showed some signs of non-sphericity in 1988, but that inconsistencies in the data

made it difficult to firmly determine its shape. Any speculations about the presence of high-

speed winds rest on the assumption that Pluto is not a significantly oblate solid planet. This

assumption, as well as any indications of the presence of high winds may be investigated by close-up observations, such as those performed with spacecraft. We eagerly await the findings of the upcoming New Horizons mission to Pluto (Stern, 2002). Table 1 Observations *

Site:Telescope East Latitude Altitude Instrument Wavelength Recording interval Cycle Time Integration SNR** Observers (aperture, m) Longitude (i) or Detector (21 Aug. 2002 UT) (s) Time (s) Haleakala -156 15 24 2042 24 3,054 Marconi Bessel I 06:51:10-07:04:44 1.4-2.4 1.0-2.0 105 LCR, DTH AEOS (3.67) CCD37-10 Lick -121 38 14 37 20 34 1,290 PCCD Visiblet 06:34:00-07:03:58 1.0 1.0 16 EWD, CBO Shane (3.0) Lowell -111 329 350549 2,219 PCCD Visiblet 06:40:00-06:47:59 1.5 1.5 53 MWB, BWT, SDK Perkins (1.8) Mauna Kea -155 28 19 194934 4,168 SpeX 0.8-2.5 Am 06:29:09-07:11:20 12.7-15.5 10.0 57 JLE, KBC, JTR IRTF (0.3) UH (2.2) -1552816 194918 4,186 PCCD Visiblet 06:34:26-07:11:25 7.0-8.0 5.0 24 MJP, SQ UH (0.6) -155 28 10 1949 23 4,214 EEV Visiblet 06:39:49-06:59:49 0.5 0.5 103 JMP, BAB, DRT CCD02 UKIRT (3.8) -155 28 13 19 49 21 4,199 IRCAM H 04:58:41-06:55:21 3.3-4.8 1.5 39 DJT, DJO, SKL Palomar -11651 47 33 21 22 1,706 CHISDAS Visiblet 04:58:41-06:55:21 0.0001 0.0001 57 ASB, SSE, DSM, Hale (5.1) SEL Pomona -1174050 342255 2,286 Apogee Visiblet 06:14:37-07:06:14 60.0 40.0 2 BEP, AA Pomona AP47p (1.0)

* Table taken from Elliot et al. 1993 ** "SNR" is the signal-to-noise for the unocculted star for a time interval corresponding to 60 km (about a scale height) of shadow motion t "visible" means an unfiltered CCD was used, except for CHISDAS, which used an unfiltered PMT with an xx photocathode response 18

Fig 1. P131.1/Pluto occultation light curves and fitted models. Plots show normalized stellar flux versus time, as observed at each of 5 telescopes. Note that at Lowell Observatory the stellar signal never drops below -94% of its unocculted value. (data from Elliot et al. 2003, Pasachoff et al. 2003 in preparation, Elliot et al. 2004 in preparation)

1.15 2.5 1,1 2 1.05 Normalized 1.5 V- Normalized 1 Fiux 1 Flux 0.95 0.5 0.9 0 Uck 0.85 Lowell -0.5 250 500 750 1000 1250 1500 1750 2000 600 700 800 900 1000 Seconds after 2002 08 21 06 30 00 Seconds after 2002 08 210630 00

1.2 0..

Normalized 0.6 Normalized 0.6 Flux 0.4 Flux 04

0.2 0.2' Maui, emersion UH 2.2m 0 0 600 800 1000 1200 1400 1600 1600 1400 1600 1000 2000 Secondsafter 20020821 063000 Secondsafter 20020821063000

1.2 .-

Normalized - - Flux 0.9 . . 0.8 . - 0.7 Palomar 0.6 100 900 1000 1100 1200 Seconds after 2002 08 21 0630 00 19

Table 2. Summary of 94% light times used in atmospheric figure fits from P131.1 occultation. Station 94% light time (Immersion) 94% light time (Emersion) (21 Aug. 2002 UT) (21 Aug. 2002 UT) Lowell 06:46:01.3 8.1 06:46:01.3 8.1 Lick 06:42:40.5 4.9 06:48:57.0 4.9 UH 2.2m 06:47:21.6 1.0 06:53:46.1 1.0 Palomar 06:44:51.2 21.8 06:47:29.5 21.5 Haleakala Not observed 06:53:32.8 1.5

Fig. 2. Immersion and emersion points of P131.1 occultation plotted in (f g) coordinates with best-fit circle (fit 3 in Table 3). Note that the fit is overreaching three points in the Southeast corner. Also note that the Lowell point was given zero weight, but is shown here for reference. Error bars are shown for all points except Lowell, whose projected error, by definition, must be zero.

UH 2.2m

Maui 1000Li

500

W0 0 Palomar g-gO (km) --500wel UH 2.2m -1000. oar Lick -1500 -1000-500 0 .500 1000 S f-fE (km) 20

Table 3. Summary of fits to Pluto's atmospheric figure from P131.1 occultation. "Type" refers to the shape fit and the weights used. JO and gO are the figure's center in (f; g) space. Mean radius is simply the radius for the circular case; for the elliptical case it is given by 4 (ab) where a and b are the semi-major and semi-minor axes, respectively. E is the ellipticity where E = 1 - b/a. "PA" is the position angle of the ellipse, defined here as the angle between the ellipse major axis and the f axis . "DoF" is the number or degrees of freedom in the fit and" Red X2" is the reduced chi-squared. Fit Type fO g0 Mean SM-axis E PA DoF Red 94% X2 light rad (km) 1 Circ, no 7318.9 9804.39 1412.65 - -- 5 3.35 weight 2 Circ, S/N 7323.76 9815.22 1400.55 - -- 5 1.40 weights 3 Circ, time 7353.75 9798.78 1413.88 - -- 4 0.87 err weights 4 Circ, 7353.75 9798.78 1413.88 4 4.26 adjusted weights 5 Ell., no 7371.03 9777.81 1385.08 1442.92 0.07 66.3 3 0.11 weight 8 8 6 Ell., S/N 7365.77 9787.06 1386.89 1434.75 0.06 64.6 3 0.23 weights 6 5 7 Ell., time 7369.56 9777.12 1385.8 1441.58 0.07 68.4 2 0.076 err 6 8 weights 8 Ell., 7369.56 9777.12 1385.8 1441.58 0.07 68.4 2 0.37 adjusted 6 8 weights 77 Massachusetts Avenue Cambridge, MA 02139 MITLibraries http://libraries.mit.edu/ask

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Figure 4. 94% light times with error bars, as determined with 6 different lightcurves obtained on Mauna Kea, plotted with a line representing their weighted mean. Note that the weighted mean seems to approximate the points better than the error bars would suggest. The reduced y2 values for the fit of the mean to these data are 0.17 and 0.29, respectively, from immersion and emersion.

Mauna Kea immersion 94% light times 1048 - -4

1046

1044 seconds after 06 30 00 UT 1042 - _ _ _ -I_ 1040

1038

UH2.2m UH 0.6m IRTF1 IRTF2 IRTF3 IRTF4

Mauna Kea emersion 94% light times 1430

1420 1426 1 1 1424 se co nds after 06 30 00 UT 1422

1420

1418

1416 UH2.2m UH 0.6m IRTF1 IRTF2 IRTF3 IRTF4 Table 4 Observing summary from 1988 occultation of P8 by Pluto *

Site name Latitude Longitude (East) Altitude (m) Aperture (m) Passband S/N Type UTC at 23.6% Level

Charters Towers -20*00'31".30 +9"45m13s.75 285 0.36 EMI 9789B 22.8 I 10 40 43.84 0.88 No filter E 10 42 10.41 1.57 KAO immersion -20 25 06.00 -11 2240.80 12500 0.9 Texas Instr. 74 I 10 36 35.55 0.15 CCD No filter KAO emersion -20 1648.00 -11 22 59.20 E 10 38 18.19 0.15

Toowoomba -27 47 58.00 +1007 26.13 678 0.36 Silicon Pin 6.1 I 10 39 44.57 0.6 Photo Diode E 10 41 56.50 0.5 No filter Mt. Tamborine -27 58 20.69 +10 12 51.18 530 0.32 B 3.8 I 10 39 42.8 0.5 E 10 41 52.1 1.4 Auckland -36 5428.00 +11 39 06.53 80 0.50 EMI 9502 9.6 I 10 38 1.00 No filter E 1040 5.69 Black Birch -41 44 55.85 +11 35 12.87 1396 0.41 EMI 9813B 18.7 I 10 38 29.21 0.9 No filter - - Hobart -42 50 57.30 +949 43.54 310 1.0 EMI 9585A No 14.5 I 10 40 31.49 1.4 filter E 10 41 29.76 2.5 Mt. John -43 59 14.70 +11 21 51.59 1029 0.61 V 21.7 - 10 39 19.62 0.78 0.61 V 1.0 V

*This table is identical to Table I in Millis et al., except that the Mt. Tamborine emersion point is correctly stated as 10:41:52.1, rather than 10:40:52.1 24

Table 5. Summary of Fits to P8 Occultation datasets

All fits included only points with S/N>10. PA here is defined as angle (in degrees) between ellipse major axis andf axis Fi Type fO gO Mean SM- e PA Red DoF t rad axis x2 1 Circ -21733. -6185.5 1273.1 - -- 8.76 5 Equal 4 5 4 2 Circ -21736. -6179.8 1277.3 1.77 4 Time Err 9 4 5 3 Ell -21734. -6191.6 1278.6 1296.1 0.02 5.22 9.39 3

_Equal 3 7 6 7 7 4 Ell -21734. -6203.4 1287.8 1351.1 0.09 0.9 0.58 2 Time Err 8 1 7 1 5 Ell, plus -21764. -6147.7 1257.9 1216.5 0.06 76.5 6.68 4 Toowoomb 6 3 8 7 5 a Time Err

6 Ell, plus Mt. -21726. -6150.2 1260.5 1179.1 0.12 94.2 12.1 4 Tamborine 7 8 2 7 4 4 Time Err 25

Figure 5. Best fit figures to the P8 1998 occultation by Pluto. All points are plotted in the (f g) plane and represent the point of 76.4% light. The ellipse axes and Pluto's rotation axis are labeled. Error bars are shown, but are generally too small to distinguish from the points themselves. a) shows the best fit circle to all points with S/N > 10. b) shows the best fit ellipse with fitted points and c) shows this same ellipse with ALL points, even those not used in fit. a)

Charters Towers 1000 Charters Towers KAO

500

W 0 g-gO (km)

-500

-1000 Black Birch Hobart Hobart -1000 -500 0 500 1000 S NOD (km)

b) c)

.Charters Towers ,Charters Towers 1000 1000 KAO Charters To ers KA 500 500 Toowoomba rotation axis: * Mt; Tamborine r ion axis 0 - Ilipsa axis ~- -~ ellipse g-go (km) g-go (km axis -500 -500 Auckland -1000 Black Birch, Mt. John -1000 Black 8irch- HLol-obart HhHart -2 000 -1000 0 1000 2000 -2 000 -1000 0 1000 2000 S S 1-10(kin0 1-10 (km) 26

Table 6. Comparison of best elliptical fits from 1988 and 2002. Position angles are measured from the f axis and are in degrees. Occultation PA of ellipse PA of rotation axis difference ellipticity P131.1 (2002) 68.48 18.69 49.79 0.076 P8 (1988) 0.90 9.28 8.38 0.09 27

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