Observations of a successive stellar occultation by Charon and graze by Pluto in 2011: Multiwavelength SpeX and MORIS data from the IRTF

Accepted Manuscript Observations of a successive stellar occultation by Charon and graze by Pluto in 2011: multiwavelength SpeX and MORIS data from the IRTF A.A.S. Gulbis, J.P. Emery, M.J. Person, A.S. Bosh, C.A. Zuluaga, J.M. Pasachoff, B.A. Babcock PII: DOI: Reference:

S0019-1035(14)00267-X http://dx.doi.org/10.1016/j.icarus.2014.05.014 YICAR 11096

To appear in:

Icarus

Received Date: Revised Date: Accepted Date:

20 December 2013 5 May 2014 6 May 2014

Please cite this article as: Gulbis, A.A.S., Emery, J.P., Person, M.J., Bosh, A.S., Zuluaga, C.A., Pasachoff, J.M., Babcock, B.A., Observations of a successive stellar occultation by Charon and graze by Pluto in 2011: multiwavelength SpeX and MORIS data from the IRTF, Icarus (2014), doi: http://dx.doi.org/10.1016/j.icarus. 2014.05.014

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Observations of a successive stellar occultation by Charon and graze by Pluto in 2011: multiwavelength SpeX and MORIS data from the IRTF A.A.S. Gulbisa,b, J.P. Emeryc, M.J. Personb, A.S. Boshb, C.A. Zuluagab, J.M. Pasachoffd, and B.A. Babcockd a

The Southern African Large Telescope and South African Astronomical Observatory Observatory, Cape Town 0735 South Africa b

Department of Earth, Atmospheric, and Planetary Sciences

Massachusetts Institute of Technology, Cambridge, MA 02139, USA c

Department of Earth and Planetary Sciences

University of Tennessee, Knoxville, TN 37920, USA d

Department of Astronomy

Williams College, Williamstown, MA 01267, USA Submitted: 20 Dec 2013; Resubmitted: 04 April 2014; 05 May 2014 Manuscript pages: 41 Figures: 12 Tables: 2 Highlights: We present an analysis of a double stellar occultation observation, by Pluto and Charon. Multiwavelength data are consistent with haze in Pluto’s lower atmosphere in 2011. The best-fit, simple, haze model contains spherical, micron-sized tholins. Corresponding author: Amanda A. S. Gulbis SAAO P.O. Box 9 Observatory, 0735, South Africa [email protected] +27(0)21.460.6294

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Abstract Pluto’s lower atmosphere has been observed to evolve since the first definitive occultation detection in 1988. Possibilities for explaining the lower atmospheric structure include a steep thermal gradient and/or extinction, the latter of which can be characterized as a dependence between occultation flux and wavelength. On 2011 June 23, a 14.43 UCAC magnitude star (R=13.64) was occulted by Pluto as observed from multiple sites. Observations made at NASA’s 3-m Infrared Telescope Facility (IRTF) on Mauna Kea, Hawai’i, showed a full occultation of the star by Charon followed by an atmospheric graze by Pluto. Data were taken simultaneously in visible-wavelength images and low-resolution, near-infrared spectra. This dataset is unique in that (i) the double occultation allows astrometric measurements for Pluto and Charon as well as accurate calibration of the Pluto light curve, and (ii) the wavelength-resolved data serve as a test for atmospheric extinction. The graze reached a minimum normalized flux level of roughly 0.35, serving primarily as a probe of Pluto’s upper atmosphere (which is typically defined to be above half-light level in occultation light curves). However, the light curve is well fit by atmospheric models with a power-law thermal gradient, a clear upper atmosphere, and haze in the lower atmosphere. We find a negative dependence between flux and wavelength in the deepest part of Pluto’s atmosphere probed by the graze and in a spike during emersion. A simple extinction model for spherical, μm-sized tholins matches the observed spectral trends. While the atmospheric fits cannot rule out a clear atmosphere having a steep thermal gradient at the bottom, the flux-wavelength dependence and the feasibility of our particle-scattering fits suggest that Pluto’s lower atmosphere contained haze in 2011. These results provide an important link in monitoring Pluto’s dynamic atmosphere. Keywords: Occultations; Photometry; Pluto, atmosphere; Pluto, satellites; Spectroscopy.

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1. Introduction For more than two-and-a-half decades, stellar occultations have provided unique snapshots of the Pluto system and specifically of Pluto’s atmospheric evolution. The first detailed occultation observation, in 1988, revealed an isothermal upper atmosphere with a “kink” at half- light level, below which was a steeper slope in the light curve (Elliot et al., 1989). Fourteen years later, observations of another stellar occultation by Pluto showed that the atmospheric pressure at constant radius had approximately doubled, and a distinct change in light-curve slope was no longer obvious (Elliot et al., 2003a; Sicardy et al., 2003). Between observations in 2002 and 2006, there was little atmospheric change – the temperature, pressure, and half-light radius varied only marginally – and the shape of occultation light curve at equivalent radii evolved from flat-bottomed to a slightly bowl-shaped bottom (Elliot et al., 2007; Young et al., 2008). A grazing occultation in 2007 detected internal gravity waves, demonstrating that Pluto’s atmosphere is dynamically active and providing insight into the underlying causes for scintillations in all stellar occultations (Hubbard et al., 2009; Person et al., 2008). Between 2006 and 2010, occultation observations indicated that Pluto’s atmosphere did not change significantly (Person et al., 2010; Young et al., 2008). However, the “kink” returned in 2011, this time demarcating a shallower slope in the light curve in the lower atmosphere relative to the upper atmosphere (Olkin et al., 2013; Person et al., 2013). Different analyses of the occultation data can return slightly varying results: for example, Zalucha et al. (2011a; 2011b) found that between 1988 and 2002 Pluto’s atmospheric pressure increased, but not as significantly as a factor of two. Nonetheless, the comprehensive picture arising from the occultation data is (i) Pluto’s post-perihelion, bulk atmospheric expansion is consistent with volatile migration models (Hansen and Paige, 1996; Olkin et al., 2013; Young, 2013), (ii) other than the overall expansion, the upper atmosphere (above half-light level) has been stable, and (iii) the lower atmosphere has displayed conspicuous variations. A change in flux drop in an occultation light curve, such as those observed at the “kink” in 1988 and 2011, may be caused by refraction from a steep thermal gradient (e.g., Eshleman, 1989; Hubbard et al., 1990) and/or the onset of atmospheric extinction (e.g., Elliot & Young, 1992). Pluto’s upper atmosphere has been consistently measured at ~100K; therefore, there must be a thermal gradient to connect the atmosphere to the N2 surface ices measured at ~40K (e.g.Tryka et al., 1994). However, it is difficult for solely refractive models to reach zero flux levels or to match the lower-atmosphere shapes in the observed light curves. Some models containing a strong thermal inversion have successfully matched the 1988 occultation data; however, those are not based on physical atmospheres (e.g. Stansberry et al., 1994). Physically-based models have provided generalized matches to occultation data (Hubbard et al., 1990) or provided good matches but do not reach zero flux levels (Zalucha et al., 2011a). It has been suggested that a varying combination of extinction-causing haze and thermal gradients has existed in Pluto’s lower atmosphere over time (e.g. Elliot et al., 2007; Elliot et al., 2003b; Person et al., 2013; Young et al., 2008).

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One method for discriminating between refraction and extinction effects is to observe a stellar occultation over a range of wavelengths. Atmospheric extinction exhibits a flux dependence with wavelength, thus light curves observed at different wavelengths should vary in shape if there is haze and not vary significantly over the relevant wavelengths if the atmosphere is dominated by a thermal gradient. This approach was employed in 2002, for a Pluto occultation observed simultaneously with a near-infrared (NIR) spectrograph and visible-wavelength camera from NASA’s IRTF (Infrared Telescope Facility). Those data indicated a slight increase in the minimum flux versus wavelength, which was interpreted as extinction by submicron-sized particles in the lower atmosphere (Elliot et al., 2003a). A Pluto occultation central flash was observed simultaneously in blue and red imaging in 2007: the light curves were very similar, and the results ruled out a haze-only atmosphere (indicating either a purely refractive atmosphere or a combination of haze and thermal gradient, Olkin et al., 2011). Following in the footsteps of the 2002 multiwavelength observations, we present simultaneous visible and NIR data from the IRTF of a star that was occulted by Charon and then grazed Pluto’s atmosphere in 2011. The observations and data analysis are presented in Section 2. We report the results in Section 3, including Charon’s chord length, the time and distance between the events, and an examination of the Pluto atmospheric graze. Particular attention is paid to analysis of the observed flux versus wavelength for the lowest parts of the atmosphere probed by the graze. A discussion and conclusions are provided in Section 4. 2. Data

2.1 Observations Pluto and Charon were predicted to occult the star 2UCAC24677089 (magnitude 14.43, 13.64, 11.0, 10.1, and 9.7 in UCAC, NOMAD R, and 2MASS J, H, and K, respectively) on 23 June 2011. Descriptions of the observations from all of our groups’ sites, along with full details of the prediction, are provided in Person et al. (2013). The successful observing sites for this event were Mauna Kea, Hawai’i; Windward and Leeward Community Colleges on Oahu, Hawai’i; the mobile Stratospheric Observatory for Infrared Astronomy (SOFIA); and the U.S. Naval Observatory’s Flagstaff station, Arizona.

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Figure 1. Occultation geometry for the IRTF chord at Pluto. Pluto's North pole (based on the angular momentum vector) is apparent at the lower right. The solid black line represents the observed path of the star, and the dotted and dot-dashed circles represent flux drops in the light curve of 2% and 50%, respectively.

The work described herein focuses on observations made at the 3-m IRTF on Mauna Kea, which comprise a unique dataset in both occultation geometry and type of data obtained. The impact parameters of the occultations from this station were 241 ± 4 km for Charon and 1138 ± 3 km for Pluto. The geometry of the grazing Pluto occultation is shown in Fig. 1. We were awarded a 5-hour observing window at the IRTF to observe this event, centered near the predicted Pluto midtime. The shadow velocity from the IRTF was 24.23 km/s and the event was observed simultaneously with MORIS (the MIT Optical Rapid Imaging System, Gulbis et al., 2011) and SpeX (Rayner et al., 1993). MORIS recorded visible-wavelength images while SpeX obtained low-resolution, NIR spectra. Sample images and spectra are shown in Fig. 2, and instrument and observation parameters are listed in Table 1.

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Figure 2. Examples of data. (left) MORIS image from the occultation data cube, a 0.3-s exposure with a clear filter, in which Pluto and the star appear merged. (middle) SpeX Guidedog image, a 10-s exposure in the J filter, prior to the occultation when Pluto and the star were well separated. This field was rotated such that the slit used for spectroscopy aligned vertically with the labeled comparison star. (right) SpeX spectra from the occultation data cube, a 0.75-s exposure. The top spectrum is the comparison star and the bottom is the combined signal from Pluto, its moons, and the occultation star outside of the occultations.

Table 1. 23 June 2011 occultation observation parameters from the IRTF.

Instrument MORIS

Field of view (arcmin); plate scale (arcsec/pixel) 1×1; 0.114

Effective wavelength (μm) 0.74

Cadence (Hz) 3.33

Instrument settings

Dead time (s) 0.002

clear filter; 1 MHz conventional; 2.4× gain

Signalto-noise ratioa 125

0.9-μm dichroic; 1.6” ×60” slit; SpeX

1×1; 0.15

0.99–2.57b

~0.67c

~0.74c

4 SlowCnt; 1 NDR; R ~ 50

a

Per Pluto scale height of 60 km.

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80

7 b

Over 474 separate channels.

c

These values represent the mean dead time for all exposures in the SpeX occultation dataset. The integration time was 0.75 s, and the dead time varied between 0.71 and 1.5 s.

The MORIS occultation data consist of an 18000-frame datacube. Each frame was triggered by the GPS starting at 10:45:00 UT. The SpeX occultation data consist of 2000 frames started within a few seconds of 11:00 UT. SpeX was rotated to an angle such that both Pluto and a comparison star were in the slit during the occultation. Calibration images were taken with the occulted star and Pluto well separated (MORIS) and of the star or Pluto in the slit (SpeX). The seeing was subarcsec, and Charon was resolved in the longer, calibration images on MORIS. 2.2 Data Analysis Aperture photometry was performed on each frame of the MORIS occultation data to extract the signal from (i) the combination of Pluto+Charon+occultation star and (ii) two comparison stars. The data were bias subtracted and flatfielded. Note that the observing time did not include twilight, so flatfields taken four nights later were employed. The SpeX+MORIS instrument was scheduled on the telescope from the time of the occultation through the flatfield observations. A square aperture of 35 pixels per side was used for the comparison stars. A variable aperture size was used for the combined Pluto+Charon+star signal: the aperture decreased from 45 to 35 pixels as Pluto moved closer to the star. The full width at half maximum of the stars was approximately 7 pixels (0.8 arcsec), and the 35-pixel aperture was selected because it returned the highest signal-to-noise ratio light curve. The average of two, 20×20-pixel sky boxes was used for background subtraction. The signal was then calibrated by dividing Pluto+Charon+star by the average of the comparison stars. The resulting light curve clearly showed a complete occultation by Charon followed by an occultation graze by Pluto’s atmosphere. Next, the light curve was normalized by setting the signal of Pluto+Charon+star between the occultations to 1 and the signal of Pluto+Charon (when Charon was occulting the star) to 0. The Charon occultation allows extremely accurate calibration of the Pluto occultation, since it provides a measure of the occulted versus unocculted flux difference at essentially the same airmass. We also carried out the standard calibration method, point-spread function fitting analyses of data taken before and after the event when the objects were well separated. The results were consistent, with a measured background fraction (Pluto+Charon/Pluto+Charon+star) of 0.51 ± 0.02. Signal from the occulted star and a comparison star were obtained from the SpeX data by making and applying a flatfield and a bad pixel mask, applying a linearity correction, straightening the spectral smile, subtracting background flux, and then extracting the spectra in terms of counts per column. The occultation star data were normalized by first dividing by the average from the comparison star, then subtracting the Pluto+Charon flux as observed when the star was occulted by Charon, and then dividing by the mean value of Pluto+Charon+the star as observed in between occultations. Although the spectral data

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consist of 474 wavelength channels, we selected only channels 10 through 453 (1.02–2.50 μm) in order to have the wavelength coverage be as broad as possible while excluding noisy channels. The resulting light curves form MORIS and SpeX are shown in Fig. 3. 3. Results

To analyze the Charon occultation, we employ a model for light diffraction by an edge that is integrated over time. The model is based on the Fresnel-diffracted intensity on a screen, given by Hecht & Zajac (1974), and follows the same technique as Gulbis et al. (2006). The fitted midtime for the Charon occultation is 11:12:42.28 UT (± 0.01 s). The duration ia 45.73 ± 0.01 s, corresponding to a chord length on Charon of 1108.04 ± 0.24 km. The midtime of the Pluto graze

Figure 3. Calibrated IRTF light curves of the occultations by Charon and Pluto. The data follow the observational parameters listed in Table 1 for (top) visible-wavelength images from MORIS and (bottom) low-resolution, NIR spectra from SpeX summed over the analyzed wavelength range.

is 11:23:03.07 UT (± 0.10 s). The time between the centers of each occultation is thus 620.79 ± 0.10 s, corresponding to a center-to-center distance of 15041.7 ± 2.4 km. The graze reached as deep as 1259 km from Pluto’s center at a minimum normalized flux level of 0.31. BEING REVIEWED BY ICARUS – PLEASE DO NOT DISTRIBUTE

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3.1 Light-curve features and spectral trends The MORIS data constitute a light curve at one passband (~0.7 μm) while the SpeX data can be considered at full resolution or binned over different spectral ranges within the reduced dataset of 443 wavelength channels. Figure 4 shows expanded views of the occultation light curves, with the SpeX data summed over all wavelengths and binned into standard J, H, and K bandpasses. The wavelength ranges for these bandpasses are 1.164–1.326 μm, 1.483–1.779 μm, and 2.027–2.363

Figure 4. Expanded, multicolor views of the occultation light curves for Charon and Pluto. The data shown in Fig. 3 are overplotted on the bottom to allow direct comparison between visible and NIR wavelengths. Offset above, the SpeX data have been summed into standard NIR filter bandpasses: J is 1.164–1.326 μm, H is 1.483–1.779 μm, and K is 2.027–2.363 μm. Flux variations specifically identified in the text have been labeled A through G.

μm for J, H, and K, respectively. For Charon, there is no difference in the occulted flux level as a function of observational wavelength. It is difficult to calculate direct residuals between MORIS and SpeX data because the data were taken at different cadences. During the Charon occultation, the mean occulted flux is 10–5 for MORIS and 10–3 for all-wavelength SpeX, with standard deviations an order of magnitude larger. The means of the differences between J, H, and K at the bottom of the Charon light curve have a maximum of 2×10–3 flux, again with the standard deviation being an order of magnitude larger. Any variations of occulted flux with wavelength are thus below the noise for the Charon event. The Pluto graze is much more interesting, displaying multiple bumps and spikes that are due to density variations in Pluto’s atmosphere (e.g., Elliot and Veverka, 1976; French and Gierasch, 1974). There are many notable features in the light curve. Excluding the two broad bumps at the lowest light levels, flux variations more than 3 sigma from a smooth light curve appear in the MORIS data between 1347– 1352, 1355–1365, 1401–1414, and 1419 seconds from 11:00 UT (these features are labeled in Fig. 4 as A, B, C, and D, respectively). For reference, these times correspond to distance from the shadow center of approximately 1435–1365 and 1326–1220 km on ingress and 1219–1363 and 1433 km on egress. The

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corresponding distances from Pluto’s center are approximately 1445–1385 km and 1356–1292 km on ingress and 1292–1384 km and 1443 km on egress. Note that the conversion between time and distance in the shadow (typically the variable ρ) assumes a best-fit midtime of 1383.07 s and closest approach in the shadow of 1138.38 km, and between time and distance from Pluto’s center (typically the variable r) additionally assumes atmospheric parameters listed in Table 2 from a fit to all light curves for this event for an atmosphere with haze (Person et al., 2013).

Table 2. Parameters for model-atmosphere fits. Clear-model atmosphere Parametera

All data,

IRTF data only

All data,

IRTF data only

from Person et al. (2013)c

from Person et al. (2013; flux > 0.6)b Half-light radius, rh (km)

Model atmosphere with haze

1288.4

1288.4

1289.5

1289.5

1383.06±0.17

1383.06±0.11

1383.07±0.11

1383.07±0.10

Energy-binding ratio, λh

14.0

20.8±0.4

18.9

17.1±0.5

Thermal-gradient parameter, b

–2.7

0.6±0.6

0.2

–1.3±0.4

Haze-onset radius, r1 (km)

-

-

1245.3

1280.7±2.6

Haze scale height, Hτ1 (km)

-

-

18.7

52.0±22.1

Haze unit optical depth, r2 (km)

-

-

1197.8

1136.2±39.9

Residuals: occultationd

–2.3×10-2

–8.1×10-3

–3.5×10-4

–3.0×10-4

Residuals: unocculted fluxd

6.6×10-3

5.7×10-3

4.8×10-3

–1.8×10-4

Midtime (s from 11:00 UT)

a

Detailed descriptions of these parameters are found in Elliot and Young (1992).

b

Values from the “Free Atmosphere” model listed in Table 7 of Person et al. (2013), for a clear atmosphere with freely-varying parameters.

c

Values from the “Haze-free Atmosphere” model listed in Table 7 of Person et al. (2013), for an atmosphere containing haze with freely-varying parameters. d

Mean residuals for the data minus the model, where the model is fit to the data shown in Fig. 9. Here, the occultation is considered to be from 1312.05–1453.95 s and the unocculted flux (provided for comparison) is 1255.05–1311.75 and 1454.25–1509.75 s. For reference, the standard deviation in the baseline data is 0.02.

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To test for symmetry, the MORIS Pluto occultation data are overplotted with the time axis reversed in Fig. 5. The most obvious fluctuations are apparent in both ingress and egress between ~1290–1360 km in distance from Pluto's center. The spikes are more pronounced and at slightly higher altitudes during ingress; however, the ingress and egress light curves in this range show similar upward and downward trends at the same distances from Pluto. The bump at the bottom of the curve is asymmetric by approximately 4 km in the shadow or 2 km in distance from Pluto’s center. While this feature looks extended relative to the other spikes during ingress and egress in the light curves, it spans only ~5 km vertically in the atmosphere (down to the minimum flux reached at 1259 km; it possibly extends lower, but that region was not probed). The geometry is such that at the lowest flux levels the star is moving nearly tangential to Pluto’s limb; therefore,

Figure 5. A test for symmetry. The MORIS Pluto graze is plotted with increasing time and overplotted in reversed time (top) with an expanded view of the lowest flux regions plotted versus calculated distance from Pluto’s center (bottom). The largest amplitude spikes are apparent between ~1220– 1330 km in the shadow, corresponding to ~1290–1360 km from Pluto's center.

the altitude probed in the atmosphere varies more quickly as a function of time farther away from closest approach (c.f. Fig. 1 and the lower plot in Fig. 5). Next we consider how the Pluto graze varies with observed wavelength. In the broadband light curves shown in Fig. 4, the NIR data have higher flux than the visible data in a spike at the start of ingress BEING REVIEWED BY ICARUS – PLEASE DO NOT DISTRIBUTE

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(at 1345 s or ~1472 km from Pluto center, labeled as F) and during egress in the bumps at the bottom, as well as in a spike feature at 1397 s (~1278 km from Pluto center, labeled as E). The most prominent visible-wavelength spikes are matched by NIR spikes on ingress but are ~10 km higher than the most obvious NIR spike on egress. Light curves of the three NIR broadband colors are similar, excluding the egress spike and in a J-only spike at 1425 s (~1530 km from Pluto’s center, labeled as G in Fig. 4). In order to investigate the wavelength dependence of these features, we employ the SpeX data at full wavelength resolution. Excluding the MORIS data at this stage prevents any effects from differences in the instruments or data reduction techniques. In Fig. 6, the J–K color index (2.5 times the log of the ratio of the weighted average in the K band to the weighted average in the J band) and the slope over the SpeX spectral range are plotted as functions of time for the Pluto graze. The slope is determined from a linear fit to flux versus wavelength in each time bin. The SpeX K light curve is provided for reference, so that light curve features can be easily correlated with spectral trends. In the broadband colors, there is an average inverse correlation between flux and wavelength throughout the deepest part of the occultation and most obviously in the spike feature during emersion. This trend persists when broadband data are binned up to 20 points (~723 km in the shadow). Notably, Fig. 6 demonstrates that the emersion spike is a Pluto atmospheric effect.

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Figure 6. Investigation of color variations in SpeX Pluto light curve features. (top) The J-K color index and (bottom) the linear-fit spectral slope are plotted as functions of time. The K-band light curve is displayed for comparison of spectral trends with light curve features. The broadband data are shown at full time resolution and binned in time by up to 20 data points to assess the robustness of the color trends. An average inverse correlation between flux and observed wavelength is apparent throughout the deepest portion of the graze, and there is a strong inverse color trend during the emersion spike.

A similar-looking spike seen in the baseline of the light curve at ~1345 s in Fig. 4 (labeled F) does not stand out in Fig. 6 and thus could be due to noise or a different type of atmospheric effect. To investigate the color trends in more detail, the flux versus wavelength was extracted for the deepest portion of the graze (defined to be normalized flux <0.4, which spans 1369–1391 s) and in the emersion spike from 1393–1399 s (the region labeled as E in Fig. 4). In Fig. 7, the flux from those regions is compared to the flux versus wavelength for unocculted data spanning similar time ranges. As a firstorder test for a correlation between flux and wavelength, we carry out least-squares linear fits to the data shown in Fig. 7. A linear fit is chosen following Elliot et al. (2003a), and because it is the dominant shape for large portions of the expected extinction as a function of wavelength for particles suspended in an atmosphere (see Section 3.4 for more details on particle scattering). Linear fits to the extracted regions, weighted according to the error bars on each data point, return slopes of –0.011±0.003 flux per μm in the bottom of the light curve and –0.030±0.006 flux per μm in the emersion spike. Because the baselines do not show any spectral

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Figure 7. SpeX data as a function of wavelength for (top) the deepest part of the atmosphere probed by the light curve (defined as <0.4 flux, spanning 1369–1391 s) and (bottom) the spike feature during emersion (spanning 1393–1399 s, labeled E in Fig. 4). The baseline is an average of the same number of data points as the compared region, well outside of the occultations. The baseline has no spectral slope, while the bottom of the light curve and the emersion feature show slight inverse correlations between flux and wavelength. The gaps are wavelengths where data are excluded, due to noise from terrestrial atmospheric absorption.

trend (having linear-fit slopes of 0.005±0.005 and 0.002±0.003), we are confident that the effect must come from Pluto’s atmosphere. Figure 8 shows the SpeX data points and error bars plotted along with the least-squares linear fits. For the deepest portion of the graze, the flux versus wavelength trend is subtle and is not visually striking. As a measure of the strength of the dependence, we compute the linear correlation coefficient (Pearson’s r value, following Press et al., 2007). The resulting Pearson’s r value of –0.1 indicates a weak, negative correlation between flux and wavelength. A better test for

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Figure 8. SpeX data and errors from (top) the deepest part of the atmosphere probed by the light curve (defined as <0.4 flux, spanning 1369–1391 s) and (bottom) the spike feature during emersion (spanning 1393–1399 s, labeled E in Fig. 4), with the best-fit lines plotted in black to demonstrate the inverse color trends (–0.011 and –0.030 flux per μm, respectively). For clarity, the data are binned by three. A dashed gray line at the mean of each dataset is provided for reference, representing no correlation between flux and wavelength. Although the negative spectral trend is not obvious in the top plot, statistical tests demonstrate that it is a better match to the data than the flat line.

determining whether the linear fit is appropriate is a Bayesian analysis of model suitability (Sivia and Skilling, 2006). We consider the null hypothesis, the probability of the data given no trend between flux and wavelength (with flux fixed at the mean of the dataset), versus the probability of the data given the least-squares linear fit with the best-fit slope as a parameter (assuming a Gaussian probability distribution for the errors on the linear fit). The calculation presented in Appendix A returns a Bayes Factor of 0.02 for the flux at the bottom of the light curve, which is considered to be strong evidence against the null hypothesis and for the best-fit negative trend between flux and wavelength.

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3.2 Model-atmosphere fits Pluto’s upper atmosphere has consistently had the same global thermal structure; therefore, atmospheric fits to multi-chord occultation datasets typically combine the data using only flux levels greater than 0.4–0.5. Here we consider how well the IRTF MORIS data are matched by atmospheric fits to the full multi-chord dataset for this event, as derived by Person et al. (2013), and by fits solely to data from the IRTF light curve. We opt to use the MORIS data because they are higher signal-to-noise ratio than SpeX. Our atmospheric models follow the methodology of Elliot & Young (1992) and contain a number of assumptions, including that the atmosphere is in hydrostatic equilibrium, the molecular weight is constant with height, and that the temperature profile follows a power law. Notably, the power-law thermal structure represents an empirical atmosphere that does not match temperature profiles based on physical models (such as Strobel et al. 1996) and thus may not be an accurate description of the region of Pluto’s atmosphere probed by this occultation. We consider two-limb models, with and without atmospheric haze. The fit parameters are listed in Table 2, where all fits also include variables for full scale and slope and

Figure 9. Atmospheric model fits for the Pluto graze. The displayed models are best fits to (left) all chords from the 2011 event derived in Person et al. (2013) and (right) only the IRTF MORIS data (which are shown as data points in both plots). The model parameters are listed in Table 2, and clear models are plotted in gray while the black lines represent models with an atmospheric haze. The residuals of data minus the models are displayed below the curves, along with reference lines representing the number of standard deviations away from the mean.

have assumed values for closest approach in the shadow of 1138.38 km, a shadow velocity of 24.23 km/s, and a time step of 0.3 s. The half-light radii for the IRTF-only fits are fixed at the values from the results for the full dataset (since it is a single grazing chord, fits for the half-light radius diverge when using only the IRTF data). As shown in Table 2 and Fig. 9, the model fits to the IRTF data alone return lower residuals than fits to data from all chords for the event. This is expected, since the IRTF-only fits are optimized to that data. Notably, the fits with atmospheric haze provide better fits than those without.

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A third type of model has been proposed to match Pluto occultation data, that of a strong thermal inversion layer in the lower atmosphere (Eshleman, 1989; Stansberry et al., 1994). We considered a simplified version of this scenario by fitting our clear model to the data above half-light level, then fitting the same model with free thermal parameters to the data below half light. The small amount of data at lower fluxes makes this hybridized modeling a challenge, and the resulting least-squares, best-fit error bars on the thermal-gradient parameter in the lower atmosphere were significantly larger than the value itself. Furthermore, this model is discontinuous at the joint and is not based on a physical atmosphere. We thus refrain from considering it further here. It is possible that more computationally intensive, physically-based, clear-atmosphere models, such as those by Hubbard (1990) and Zalucha et al. (2011a; 2013), could provide better matches to the data. 3.3 Light curve inversion In Fig. 10 we present the temperature profile resulting from the inversion (Elliot et al., 2003b) of the emersion portion of the MORIS light curve. The immersion results are similar. The inversion process itself assumes that no light is lost to extinction, such as scattering by particulate haze, so this temperature profile is incompatible with any haze models. The best-fit atmospheric models with haze have clear atmospheres down to either 1281 or 1245 km; therefore, the majority of the graze is expected to be clear and the inversion data are nullified at these lowest levels if haze exists. Note that the upper region of the inversion (above 1475 km) is distorted due to the boundary conditions needed to start the process. In this case, the boundary condition was set at the model fit to the global atmospheric solution from the 2011 event (the first data column in Table 2), which is dominated by the SOFIA light curves. The first several inversion shells compensate by dragging this average solution over to the individual IRTF fit. A smooth thermal gradient with slope –0.23 ± 0.05 K/km then dominates, which is consistent with those observed in 2011 and 2013 (Bosh et al., 2014; Person et al., 2013). In this case, the profile does not reach the turnaround point in the other light curves, where the ~100K maximum temperature starts decreasing toward the surface temperature of ~40K. This plot aligns nicely with the inversion of the 2013 SOFIA data shown in Fig. 10 of Person et al. (2013), where that plot reaches a maximum distance

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Figure 10: Inversion of the 2011 MORIS light curve during emersion. The recovered temperature is plotted versus radius from Pluto's center. Note the smooth thermal gradient of –0.23 K/km that dominates the profile. The upper portion of the inversion (above roughly 1475 km) is primarily due to the effects of the imposed boundary condition. Although the inversion is invalid if there is atmospheric extinction, the best-fit model atmosphere has haze starting below the altitudes shown in this plot, at 1281 km.

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of ~1290 km from Pluto’s center and this one begins at ~1310 km. Upon cursory examination, the number densities derived from this inversion do not exhibit the obvious wave signature seen in other high-altitude inversion curves (Elliot et al., 2003b; McCarthy et al., 2008; Person et al., 2008). The density analysis is particularly sensitive to the boundary conditions, and we reserve detailed investigation of atmospheric profiles for future work. 3.4 Particle-scattering model Although the atmospheric model fits cannot rule out a clear atmosphere, there is a definitive (although slight) correlation between flux and wavelength at the lowest part of the light curve. We proceed by considering our best-fit haze model. This haze model is simply based on the amount of extinction as a function of optical depth and is not meant to provide details of the nature of the haze. To better characterize a possible atmospheric haze, we consider a particle extinction model to match the spectral slope at the bottom of the light curve and in the emersion feature in the SpeX data. The extinction of starlight by haze depends on particle composition, size, shape, and number density. We opt to investigate extinction by dark, organic tholins as detected on Pluto’s surface (e.g., Grundy and Buie, 2002; Olkin et al., 2007) and as used in the flux versus wavelength analysis for Pluto occultation data in 2002 (Elliot et al., 2003a). The indices of refraction for tholins are determined by interpolating between the visible and NIR values given in Khare et al. (1984): across the SpeX wavelengths, the real component ranges from 1.650 to 1.615 and the imaginary from 4×10–4 to 1.7×10–3. We employ rigorous Mie scattering theory for a collection of spherical particles to derive the efficiency factor for extinction, Qext, which is defined to be the sum of the efficiency factors for scattering and absorption (van de Hulst, 1981). We allow for a particle-size distribution such that the number density of particle radius a follows a power-law model:

⎛ a ⎞q n(a) = n 0 ⎜ 0 ⎟ , ⎝a⎠

(1)

where a0 and n0 are a reference particle radius and number density, and q represents the number density power. This power law form is a reasonable assumption given that it matches the size distribution for small atmospheric aerosols (e.g. Cours et al., 2011; Welander, 1959), the ejecta from impacts (e.g. Hartmann, 1969; Shuvalov and Dypvik, 2013), Saturn’s ring particles (e.g. Kempf et al., 2008; Marouf et al., 1983), and icy geysers on Enceladus (e.g. Schmidt et al., 2008). Considering the simplest case, where the transmission of flux is determined by extinction along the line of sight, the normalized intensity as a result of the haze can be written as

I = exp(–τ ),

τ=

w here

⎛a ⎞ n(a0 )⎜ 0 ⎟ πa 2Qext da, ⎝a⎠ a min

a max

∫

q

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(2)

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and the extinction parameters are encapsulated in the optical depth term, τ. Assuming a reference particle radius halfway between the maximum and minimum (amax and amin), Eqn. 2 can be fit to the fluxversus-wavelength data (shown in Figs. 7 and 8), with four parameters: minimum and maximum particle size, number density slope, and reference particle density. The flux-versus-wavelength data are binned by two for fitting to reduce the computational time. This binning has a negligible effect on the overall structure and spectral trends. As shown in Fig. 11, the spectral trend at the deepest part of the atmosphere probed by the occultation is well matched by our simple extinction model for spherical tholin particles between 2.34 ± 0.12 and 3.92 ± 0.14 μm in radius, with a number density power of q =1.08 ± 0.98 and reference number density of 9.3 (±1.1)×109 cm–3. The emersion spike is best fit by a distribution that includes smaller particles, from 0.99 ± 0.11 to 2.43 ± 0.11 μm in radius with power q = 1.32 ± 0.53 and reference number density 26.5 (±0.3)×109 cm–3. 4. Discussion and Conclusions

The primary value of this dataset lies in the wavelength resolution of the Pluto occultation graze. Our analysis focuses on that aspect; however, we begin by noting the other results that can be employed for future analyses. First, the rare double-occultation geometry of this event allows refinement of Pluto and Charon’s ephemerides (e.g., Sicardy et al., 2011). An analysis of Charon’s shape and size is in preparation, from the data presented here combined with data from our two other successful sites (Zuluaga et al., 2011).

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Figure 11. Best fits from particle-scattering models. Points are the SpeX light curve data for (top) the deepest part of Pluto’s atmosphere probed (flux < 0.4, spanning 1369–1391 s) and (bottom) the spike feature during emersion (spanning 1393–1399 s, labeled E in Fig. 4). The data are the same as that shown in Fig. 7, only binned by 2 and including errors bars. The lines are least-squares, best-fit models from Eqn. 2. The particles are spherical tholins, 2.3–3.9 μm in radius for the bottom of the light curve and 1.0–2.4 μm for the emersion feature.

Second, we plan to further investigate individual spikes and fluctuations in the light curves. The observed spikes are higher in the atmosphere than spikes analyzed for previous Pluto occultations (e.g., Pasachoff et al., 2005; Young et al., 2008), except for the 2007 graze. Figure 12 shows the data compared to that from 2007, which contain features identified as gravity waves with possibly some contribution from Rossby waves (Hubbard et al., 2009; Person et al., 2008). As shown in Fig. 1, the 2011 graze occurred in an approximate W-E trajectory in Pluto’s atmosphere, probing only a small variation in Pluto atmospheric latitudes. Large variations between ingress and egress would not necessarily be expected, since Pluto atmospheric general circulation models have fairly consistent pressures at similar latitudes (Zalucha and Gulbis, 2012; Zalucha and Michaels, 2013). This geometry is unlike the 2007 event, which grazed the opposite limb of Pluto and at which time the pole was rotated more toward the edge – and less face-on – than in 2011 (see Figure 3 from Person et al., 2008). The 2007 event thus probed along more of a S-N trajectory through Pluto’s atmosphere. The cursory light curve inversion carried out in this work BEING REVIEWED BY ICARUS – PLEASE DO NOT DISTRIBUTE

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indicated some fluctuations in mass density relative to an isothermal profile, but the analysis is highly dependent on boundary conditions and requires finesse due to the grazing nature of the occultation. It will be worthwhile to carry out a more careful analysis of the temperature and density as possible indicators of waves, especially with respect to the parameters of the waves observed in 2007. The lack of obvious wave features in the 2011 dataset could be due to the occultation geometry occurring over a relatively quiescent portion of the atmosphere, or the global wave pattern may be highly variable in time, either seasonally or diurnally. In addition, models

Figure 12. Light curves of Pluto atmospheric grazes. Data are shown from this work and in 2007 when gravity waves were detected using the Portable Occultation Eclipse and Transit System (POETS, Souza et al., 2006) on the 6.5-m Multiple Mirror Telescope (MMT). The data are plotted as functions of distance from the center of Pluto's shadow, which is a directly measured quantity that allows comparison between features in light curves from different epochs. The 2011 event probed significantly deeper into the atmosphere than the 2007 graze but shows similar fluctuations.

such as those developed to investigate the effect on light curves of atmospheric tides (driven by sublimation and freezing of surface nitrogen) should be fit to the data to help further our understanding of those processes (French et al., 2013; Togio et al., 2010). In this work, we have shown that the 2011 Pluto graze is well matched by atmospheric-model fits having a power-law thermal gradient, a clear upper atmosphere, and haze in the lower atmosphere. We note that the model fits do not rule out a clear atmosphere with a strong thermal gradient in the lower atmosphere. The best atmospheric fits to data from all sites for this event suggest that if a haze layer were present it would start at 1245 km from Pluto’s center (1096 km in the shadow, Person et al., 2013). Based on that model, the IRTF graze did not probe deeply enough in the atmosphere to detect such a haze, reaching 1259 km from Pluto’s center (1138 km in the shadow). However, we find that the best atmospheric-model fit to only the IRTF data has a haze starting at 1281 km. Although the atmospheric structure is expected to be the same around Pluto because the radiative time constants are long (e.g., Yelle and Elliot, 1997; Young et al., 2008), it is possible that a global haze, or a local haze-producing event, could reach slightly different altitudes at different locations on Pluto. Thus the IRTF data may have

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sampled a haze at higher altitudes than would be suggested from the global atmospheric fits, which were heavily weighted by the nearly-central SOFIA chords. The negative trend between flux and NIR wavelength seen at the deepest parts of the atmosphere probed by the light curve is slight but statistically significant. We find a feasible fit to the data using a simple extinction model for spherical tholin particles from 2.3–3.9 μm in radius. Pluto occultation data from 2002 showed a positive trend of flux versus SpeX NIR wavelengths, which was modeled as extinction by spherical, 0.2-μm tholin particles (Elliot et al., 2003a). It may seem strange that we are able to model the opposite trend using particles of the same general composition; however, both positive and negative spectral slopes occur in the models due to the oscillating nature of the extinction efficiency factor. Tholins were selected because they have been observed on multiple icy surfaces in the outer Solar System, including Pluto and its closest counterpart, Triton (e.g., Cruikshank and Dalle Ore, 2003; Grundy and Buie, 2002; McDonald et al., 1994). Any Pluto haze is not likely to be generated by photochemical processes, since those known to occur on Triton, Titan, Uranus, and Neptune are not capable of producing the amount of extinction or sharp boundaries observed in stellar occultations (Krasnopolsky and Cruikshank, 1999; Rannou and Durry, 2009; Stansberry et al., 1989). However, larger particles could be suspended in Pluto’s atmosphere through other means. Models for geyser eruptions on Triton include pressurized, subsurface nitrogen decompressing through fractures, which is likely to entrain dark particles from the surface into plumes (Soderblom et al., 1990). Also, particles < 5μm in diameter may be lofted through aeolian processes in Triton’s tenuous atmosphere (Sagan and Chyba, 1990). Grundy et al. (2002) found that nonvolatile species on Pluto are widely distributed in regions dominated by volatiles, which could be explained by nonvolatile redistribution through aeolian transport or geyser plumes. In fact, cryovolcanism has been proposed as a mechanism for surface renewal on Charon and other large Kuiper Belt objects (Cook et al., 2007). Strong zonal winds are expected on Pluto based on ellipticity in stellar occultation central flashes (e.g., Person et al., 2013) and atmospheric general circulation models (Zalucha and Gulbis, 2012; Zalucha and Michaels, 2013). Yet it is not evident that Pluto has surface winds, much less winds that could lift particles tens of kilometers. While the exact mechanism is currently unknown, μm -sized tholins are a plausible material and size for a dynamic, extinction-generating process on Pluto. Our best-fit extinction model does contain particles of larger sizes than those found in 2002. The 2002 analysis considered only models with single-sized particles rather than a particle size distribution. Also, the 2011 occultation could have different particle sizes because it occurred more closely in time or geometry to an extinction-generating event. A spike feature at emersion, roughly 1278 km from Pluto’s center, shows the most significant spectral trend in the 2011 dataset. The best-fit extinction model returns smaller particles than those found for the bottom of the light curve: 1.0 to 2.4 μm in radius. It makes intuitive sense that smaller particles could be lifted higher into the atmosphere than larger ones; however, that wouldn’t explain why deeper parts of the atmosphere are lacking in small particles. Perhaps the particles in this feature were entrained by an atmospheric wave. The dynamical timescale in Pluto's atmosphere is thought to be on the order of days (e.g. Young et al., 2008). Particles lofted into the atmosphere thus might be expected to have a global distribution, whereas this feature is asymmetric (no

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similar feature appears on immersion). Furthermore, the slopes of the best-fit size distributions for the bottom of the light curve and the emersion spike, q between one and two, are shallow compared to that expected from fragmentation processes at subsonic velocities, as seen on the Earth, Moon, asteroids, and in planetary rings (2.75 < q < 3.5, Cuzzi et al., 2009; Dohnanyi, 1969; Greenberg et al., 1977; Hartmann, 1969). It is worth stressing that the particle-scattering model results are unlikely to be unique, and merely serve to demonstrate one possible set of haze parameters that match the 2011 data. More advanced models could impact the results in that (i) aggregate particles would lower the flux level by having higher extinction efficiencies than spheres, (ii) other particle compositions would have different extinction efficiencies and thus different spectral trends throughout our observed wavelength range (other materials to consider would be N2, CH4, CO2, H2O, or a mixture of these, following e.g., Grundy and Buie, 2002; Grundy et al., 2013), and (iii) more complicated relationships between observed flux and optical depth could be considered (e.g., including multiple scattering and integration over incident light angles). In particular, an interpretation of the data with respect to physically-based thermal models (e.g. Strobel et al., 1996) would be valuable. The 1988 occultation launched a debate about whether a thermal gradient and/or haze in Pluto’s lower atmosphere could cause the observed light curve structure. The evolution of Pluto’s lower atmosphere since that time suggests that a thermal gradient is always present and that there is intermittent haze. It seems likely that some haze must have existed in 1988 in order for that light curve to reach zero flux. The multiwavelength occultation data from 2002 provided the most definitive detection of haze being present in Pluto’s atmosphere. Yet in 2006, the rounded light curves suggested that any haze had dissipated. Our results suggest that a haze was again present in 2011. The haze is possibly asymmetric, since atmospheric-model fits to all chords from the event return different haze parameters than fits to only the IRTF data, and the feature with the most significant spectral trend appears only during emersion. More advanced haze models could be investigated to better characterize the particles producing the observed spectral trends and to compare with parameters from possible Pluto cryovolcanic processes. We encourage future Pluto stellar occultation observations to be carried out across a wide wavelength range in order to be able to detect any haze and to better understand Pluto’s atmospheric evolution. Acknowledgments

Thanks to John C. Kern II (Duquesne University) for consultation on the statistical analyses of the flux versus wavelength trend at the bottom of the Pluto light curve. Funding for this work was provided in part by the South African National Research Foundation (NRF) and NASA grants NNX12AJ29G (Williams College), NNX10AB27G (Massachusetts Institute of Technology), and NNX10AB23G (UT). AASG and JPE were visiting astronomers at the IRTF, which is operated by the University of Hawaii under Cooperative Agreement no. NNX-08AE38A with the National Aeronautics and Space Administration, Science Mission

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Directorate, Planetary Astronomy Program. Appendix A. Bayesian analysis of model suitability for a linear spectral trend in the deepest part of the Pluto occultation graze.

As a statistical test of whether the flux at the bottom of the Pluto light curve shows a linear trend with wavelength, we consider a Bayesian analysis of model suitability. The null hypothesis, M1, is that there is no slope to the flux-versus-wavelength data and the proposed model, M2, is that of a linear, leastsquares, best fit to the data. Assuming the priors are equally probable (in other words, there is no reason to favor either the null hypothesis or the model), the Bayes Factor, KB, is equivalent to the ratio of the posteriors:

KB =

( ) × prob( M ) = prob({data} M ) prob({data} M ) prob( M ) prob({data} M ) prob {data} M1

1

1

2

2

2

.

(A1)

Since our primary concern is whether or not there is a trend between flux and wavelength, we fix the linear model intercept and the model is dependent on only one parameter, slope m. We apply the simplifying assumption that the prior probability for the linear model is uniform and evenly distributed over a range of expected slopes within limits mmin and mmax, with m0 ± δm being the best-fit slope and error. Following Sivia & Skilling (2006), a reasonable fit for the slope parameter can be represented analytically by a Gaussian probability distribution function, and the probability as a function of the linear model can thus be written

(

) ∫ prob({data} M ,m)prob(m M )dm,

prob {data} M 2 =

(

)

prob m M 2 =

2

2

where

1 , for mmin ≤ m ≤ mmax . mmax − mmin

(A2) (A3)

Combining equations (A2) and (A3),

(

)

prob {data} M 2 =

1 mmax − mmin

m max

∫ prob({data} M ,m)dm = 2

δm 2π prob({data} M 2 ,m0 )

m min

mmax − mmin

.

(A4)

Combining equations (A1) and (A4), the Bayes Factor can be expressed as

KB =

(

prob {data} M1

(

)

prob {data} M 2 ,m0

)

×

mmax − mmin , δm 2π

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(A5)

26

where the right term represents the Ockham factor, which essentially acts to penalize the model for having an extra fitting parameter (Sivia and Skilling, 2006). We can compare the data to the null hypothesis and to the linear model by assuming Gaussian error distributions, such that the probability of xi (the flux at the ith data point) with error σxi is given by

(

)

prob x i f i (M),σxi =

1

σxi

⎡ x − f (M) 2 ⎤ (i i )⎥ , exp ⎢− 2σxi2 2π ⎢⎣ ⎥⎦

(A6)

where fi(M) is the modeled flux for that data point from model M. The probability for the dataset is the product of the probabilities over the total N data points (where the corresponding model data points, fi(M), are generated by the respective models): N

prob({x i=1 ...x i=N } M ) = ∏ i=1

1

σxi

⎡ x − f (M) 2 ⎤ ( i i ) ⎥. exp ⎢− 2σxi2 2π ⎢⎣ ⎥⎦

(A7)

For the null hypothesis of no slope, the flux is always equal to the average flux of the data, N

f i ( M1 ) = x i =

∑x i=1

N

i

.

(A8)

In the linear model, the intercept is fixed at the best-fit value, c, and the flux depends on λi, the wavelength at the ith data point (which we offset by 1 since the wavelength values start at 1 micron):

f i (M 2 ,m0 ) = m0 (λi −1) + c .

(A9)

Substituting equations (A7), (A8) & (A9) into equation (A5), we calculate the Bayes Factor as the following: 2⎤ ⎡ xi − xi ⎥ ⎢ ∏ σ 2π exp⎢− 2σ 2 ⎥ xi i=1 xi ⎣ ⎦ KB = ⎡ N x i − m0 (λi −1) + c 1 ∏ σ 2π exp⎢⎢− 2σxi2 i=1 xi ⎣ N

(

1

(

)

)

2

⎤ ⎥ ⎥ ⎦

×

mmax − mmin . δm 2π

(A10)

Given the least-squares, best-fit values of m0 = –0.011, δm = 0.003, and c =0.404, and assuming a reasonable range of slopes mmin = –0.0257 and mmax = 0.0 (which are roughly m0±4δm), the Bayes Factor for the flux at the bottom of the Pluto light curve is 0.022. A Bayes Factor between 0.01 and 0.1 is considered to be “strong evidence against” the null hypothesis and in favor of the compared model

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(Jeffreys, 1961) . Therefore, the flux versus wavelength data at the bottom of the Pluto light curve are better matched by a line with slope –0.011 ± 0.003 than a flat line.

References

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Observations of a successive stellar occultation by Charon and graze by Pluto in 2011 A.A.S. Gulbis, et al.

Highlights: We present an analysis of a double stellar occultation observation, by Pluto and Charon. Multiwavelength data are consistent with haze in PlutoÕs lower atmosphere in 2011. The best-fit, simple, haze model contains spherical, micron-sized tholins.

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