Radio occultation measurements of Pluto’s neutral atmosphere with New Horizons

Icarus 290 (2017) 96–111

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Radio occultation measurements of Pluto’s neutral atmosphere with New Horizons D.P. Hinson a,b,∗, I.R. Linscott b, L.A. Young c, G.L. Tyler b, S.A. Stern c, R.A. Beyer a,d, M.K. Bird e,f, K. Ennico d, G.R. Gladstone g, C.B. Olkin c, M. Pätzold e, P.M. Schenk h, D.F. Strobel i, M.E. Summers j, H.A. Weaver k, W.W. Woods b , the New Horizons ATM Theme Team, the New Horizons Science Team a

Carl Sagan Center, SETI Institute, Mountain View, CA 94043, USA Department of Electrical Engineering, Stanford University, Stanford, CA 94305, USA c Southwest Research Institute, Boulder, CO 80302, USA d NASA Ames Research Center, Moffett Field, CA 94035, USA e Rheinisches Institut für Umweltforschung, Universität Köln, Cologne 50931, Germany f Argelander Institut für Astronomie, Universität Bonn, Bonn 53121, Germany g Southwest Research Institute, San Antonio, TX 78238, USA h Lunar and Planetary Institute, Houston, TX 77058, USA i The Johns Hopkins University, Baltimore, MD 21218, USA j George Mason University, Fairfax, VA 22030, USA k The Johns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, USA b

a r t i c l e

i n f o

Article history: Received 3 December 2016 Revised 15 February 2017 Accepted 28 February 2017 Available online 1 March 2017 Keywords: Pluto, atmosphere Atmospheres, structure Occultations Radio observations

∗

Corresponding author. E-mail address: [email protected] (D.P. Hinson).

http://dx.doi.org/10.1016/j.icarus.2017.02.031 0019-1035/© 2017 Elsevier Inc. All rights reserved.

a b s t r a c t On 14 July 2015 New Horizons performed a radio occultation (RO) that sounded Pluto’s atmosphere down to the surface. The sensitivity of the measurements was enhanced by a unique configuration of ground equipment and spacecraft instrumentation. Signals were transmitted simultaneously by four antennas of the NASA Deep Space Network, each radiating 20 kW at a wavelength of 4.2 cm. The polarization was right circular for one pair of signals and left circular for the other pair. New Horizons received the four signals and separated them by polarization for processing by two independent receivers, each referenced to a different ultra-stable oscillator. The two data streams were digitized, filtered, and stored on the spacecraft for later transmission to Earth. The results reported here are the first to utilize the complete set of observations. We calibrated each signal to remove effects not associated with Pluto’s atmosphere, including the limb diffraction pattern. We then applied a specialized method of analysis to retrieve profiles of number density, pressure, and temperature from the combined phase measurements. Occultation entry sounded the atmosphere at sunset at 193.5°E, 17.0°S — on the southeast margin of an ice-filled basin known informally as Sputnik Planitia (SP); occultation exit occurred at sunrise at 15.7°E, 15.1°N — near the center of the Charon-facing hemisphere. Above 1215 km radius (∼25 km altitude) there is no discernible difference between the measurements at entry and exit, and the RO profiles are consistent with results derived from ground-based stellar occultation measurements. At lower altitudes the RO measurements reveal horizontal variations in atmospheric structure that had not been observed previously, and they are the first to reach the ground. The entry profile has a strong temperature inversion that ends 3.5 km above the surface, and the temperature in the cold boundary layer beneath the inversion is nearly constant, 38.9 ± 2.1 K, and close to the saturation temperature of N2 . The exit profile has a much weaker inversion that extends all the way to the ground, where the air temperature is 51.6 ± 3.8 K. Three factors appear to be responsible for the presence of a cold boundary layer in the entry profile (Forget et al., 2017): a substantial diurnal cycle of sublimation and condensation of N2 ice in SP, the local time of the RO observation, and confinement within SP by the surrounding topography and

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katabatic winds. We have also determined the surface pressure and the local radius at both entry and exit. The best pressure reference is the mean value: 11.5 ± 0.7 microbar at 1189.9 ± 0.2 km. © 2017 Elsevier Inc. All rights reserved.

1. Introduction Pluto’s atmosphere was discovered in a stellar occultation observed from Earth in 1988 (Hubbard et al., 1988; Elliot et al., 1989). This technique has proved to be remarkably effective at Pluto, and numerous subsequent observations — several acquired as New Horizons was en route to Pluto — have revealed important characteristics of its atmosphere. There has been a roughly threefold increase in the total mass of the atmosphere between 1988 and 2015 (Elliot et al., 2003; Sicardy et al., 2003; Dias-Oliveira et al., 2015; Olkin et al., 2015; Sicardy et al., 2016). Atmospheric waves have been detected, most notably in the stellar occultation of March 2007 (Person et al., 2008; McCarthy et al., 2008; Hubbard et al., 2009). A consistent picture has emerged for the temperature structure at about 120 0–140 0 km radius (Sicardy et al., 2003; Young et al., 2008a; Dias-Oliveira et al., 2015; Bosh et al., 2015; Sicardy et al., 2016). But the stellar occultations do not reach the surface, leaving substantial uncertainties about the temperature structure of the lower atmosphere, Pluto’s radius, and the pressure at the surface (Lellouch et al., 2009; 2015). New Horizons was equipped to answer these questions through radio occultation sounding of Pluto’s atmosphere (Tyler et al., 20 08; Young et al., 20 08b). This type of observation has the same physical basis as a stellar occultation: both measure the response of electromagnetic waves to the vertical gradient of refractive index in the occulting atmosphere. However, the sensitivity of the radio and stellar observations differs for two reasons. First, the former measures the atmospheric phase delay while the latter measures the change in signal intensity from defocusing. Second, the range to Pluto is ∼105 times smaller for the radio observation. For these reasons, stellar occultations are most accurate at ∼1290 km radius (the half light level in Pluto’s atmosphere), whereas the radio occultation is most accurate below 1215 km radius, within 25 km of the surface. This allowed New Horizons to obtain the first profiles of Pluto’s atmosphere that extend all the way to the ground and the first direct measure of surface pressure (Gladstone et al., 2016). Gladstone et al. (2016) derived preliminary radio occultation profiles by applying a provisional method of analysis to a subset of the observations. This paper reports improved results obtained through comprehensive analysis of the entire radio occultation data set. Through innovative use of multiple signals, we expand the vertical range of the atmospheric profiles, resolve the structure of the cold boundary layer adjacent to the surface in Sputnik Planitia, and derive more accurate solutions for the surface pressure. The instrumentation, operations, and methodology are explained in far greater detail than was possible in the brief initial report. We also provide a more extensive discussion of the results and their significance. This paper considers only the neutral atmosphere. Pluto’s ionosphere will be the subject of a separate paper; it has eluded detection in the analysis to date. The paper is organized as follows. Section 2 describes the implementation of the experiment. Section 3 characterizes the observing geometry. Section 4 gives a detailed discussion of data calibration. Section 5 reports measurements of Pluto’s radius. Section 6 explains the procedure used to retrieve the atmospheric profiles. The results are interpreted and compared with stellar oc-

cultation measurements in Section 7. The paper closes with a brief summary in Section 8. 2. Instrumentation and operations This section describes the configuration and operation of the ground and spacecraft equipment as well as the characteristics of the data recorded on the spacecraft. 2.1. Ground equipment and operations The radio occultation was performed with signals transmitted simultaneously by four antennas of the NASA Deep Space Network (DSN), as summarized in Table 1. The uplink array comprised two antennas at the Goldstone complex in California, with diameters of 70 m and 34 m, and an identical pair at the Canberra complex in Australia. Each antenna radiated 20 kW without modulation at a frequency of ∼7.18 GHz, corresponding to a wavelength of ∼4.17 cm. A single hydrogen maser served as the frequency reference at each DSN complex. Its stability, as expressed by the Allan deviation (Allan, 1966), is about 3 × 10−14 at an integration time of 10 s. One 70-m antenna transmitted right circular polarization (RCP) and the other transmitted left circular polarization (LCP), while each 34-m antenna transmitted the opposite polarization as the 70-m antenna at the same complex. The timing of the flyby was constrained to ensure that Pluto was more than 15° above the horizon at the DSN complexes in both California and Australia throughout the observation (Guo and Farquhar, 2008), thereby avoiding reliance on a single complex and improving the chances of a successful observation. 2.2. Spacecraft equipment and operations The spacecraft telecommunications system comprises a 2.1-m diameter high gain antenna (HGA) and two independent radio receivers (Fountain et al., 2008). Each receiver includes a specialized radio science signal processor (or REX for short) as well as an ultra-stable oscillator (USO) that provides the frequency reference required for precise radio occultation measurements (Tyler et al., 2008). The two REX signal processors and their respective USOs are designated as units A and B. Table 2 lists characteristics of the USOs. The spacecraft remained in a non-spinning “three axis inertial” state with the HGA pointed toward Earth throughout the observation. The radio signals transmitted by the DSN were received by the HGA and split into pairs with the same polarization. Each pair of signals was processed independently, with the RCP signals going to REX-A (USO-A) and the LCP signals going to REX-B (USO-B). See Tyler et al. (2008) for further discussion of the design of the REX signal processors and their interface with the telecommunications system. In summary, each DSN complex transmitted signals to both REXs, so that each REX received signals from both complexes. As we show in Section 6.1, the availability of multiple signals that cross-link the two DSN complexes with the two REX instruments not only improves the sensitivity of the measurements but also yields an empirical estimate for their accuracy. Both REX signal processors include a narrow band channel used for recording occultation data (Tyler et al., 2008). Its operation can be summarized as follows. REX-A uses USO-A as a local oscillator

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D.P. Hinson et al. / Icarus 290 (2017) 96–111 Table 1 Configuration of the DSN antennas. Location

Antenna

Goldstone, California Goldstone, California Canberra, Australia Canberra, Australia

DSS DSS DSS DSS

Diameter (m)

Polarizationa

Frequency offsetb (Hz)

70 34 70 34

LCP RCP RCP LCP

+486 −110 +100 +276

14 24 43 34

Notes: (a) RCP and LCP denote right and left circular polarization, respectively. (b) The reference for the frequency offset of the transmitted signal is band center of REXA, one of two radio science signal processors onboard New Horizons, as discussed in Section 2.2. Table 2 Characteristics of the New Horizons USOs. Unit

Nominal frequency (MHz)

Frequency shifta (parts per billion)

Allan deviationb at τ = 10 s

30 30

−25.859 +27.866

1.0 × 10−13 1.5 × 10−13

USO-A USO-B

The polarization of the signals transmitted by the DSN is not perfectly circular, and the RCP and LCP receivers on the spacecraft are not perfectly isolated from one another, which caused each REX to receive a small fraction (< 1%) of the energy intended for the other REX. However, the offsets in Table 1 ensured that the four signals arrived at the spacecraft with distinctly different frequencies, so that they remained safely separated from one another.

Notes: (a) The frequency shift accounts for aging of the USOs during the 10year journey to Pluto but excludes the contribution from relativistic time dilation. (b) The Allan deviation was measured at the Johns Hopkins University Applied Physics Laboratory; τ is the integration time.

3. Geometry

to reduce the frequency of the RCP signals to the audio frequency range. REX-B processes the LCP signals in the same manner, using USO-B as the frequency reference. The various frequencies are related as follows:

flo = fuso × 1158703/4840 ,

(1)

and

fb = fhga − flo .

(2)

Here fuso is the frequency of the USO (including a correction for in-flight aging as specified in Table 2), flo is the frequency of the local oscillator, fhga is the frequency of the signal arriving at the HGA, and fb is the frequency of the “baseband” signal. Both fhga and flo have values of about 7.18 GHz, fuso is about 30 MHz, and the magnitude of fb is about 100 Hz. An anti-aliasing filter with a bandwidth of ∼1 kHz is then applied to the baseband signal. The filter is aligned so that a signal arriving at the spacecraft with the same frequency as the local oscillator ( fhga = flo and fb = 0) would appear in the center of the REX pass band. Finally, both REX-A and REX-B sampled the output from their respective anti-aliasing filters with a uniform sample spacing of 0.8192 ms. Each sample comprises a 16-bit “in phase” component and a 16-bit “quadrature” component, which are equivalent to the real and imaginary parts of a complex signal (denoted in Section 4.1 as sb (t), where t is time). Data samples were recorded without interruption for a span of ∼40 0 0 s — extending to a radius of ∼70 0 0 km on both sides of Pluto — and stored on the spacecraft for later transmission to Earth. The frequency of each signal transmitted by the DSN was tuned continuously to compensate for relativistic time dilation and for the classical Doppler shifts arising from relative motion of the transmitting and receiving antennas. Each signal therefore arrived at the spacecraft with a nearly constant sky frequency fhga and remained at a nearly fixed frequency fb within the pass band of the anti-aliasing filter. A constant frequency offset was applied to each uplink signal to avoid interference among the four signals received by the spacecraft (see Table 1). For each polarization, the 70-m uplink arrived with an offset of about +100 Hz from band center of the anti-aliasing filter, while the 34-m uplink arrived with an offset of about -110 Hz. Owing to normal aging of the USOs during their 10-year journey to Pluto, flo for REX-B exceeded flo for REX-A by 386 Hz at the time of the flyby.

The occultation of New Horizons by Pluto was nearly diametric as viewed from Earth. The measurements at entry sounded the atmosphere near the center of the anti-Charon hemisphere, on the southeast margin of a region known informally as Sputnik Planitia (SP), as shown in Fig. 1. The measurements at exit sounded the atmosphere near the center of the Charon-facing hemisphere. Table 3 summarizes the event timing, the local conditions at entry and exit, and the geometry of the observations. The Earthto-spacecraft distance was 31.9 AU and the spacecraft was receding from Earth at a rate of ∼18 km s−1 . The signals from the four DSN antennas traveled along different paths to New Horizons. For example, the paths from the two 70-m antennas were separated by about 104 km at Earth, corresponding to the distance between the DSN complexes in California and Australia, but had converged to within 120 m as they traversed Pluto’s atmosphere. The ray path separation within the atmosphere is less than 1% of the pressure scale height (see Section 6), too small to cause appreciable differences among the four sets of measurements. The observation was performed near solar opposition, so as to minimize interference from plasma in the solar wind. The angle between the Sun and Pluto as viewed from Earth was 172°. At the wavelength of these measurements the solar wind is almost certainly undetectable in this geometry (Asmar et al., 2005). 4. Data reduction on the ground By February 2016 all REX data from the Pluto occultation had been delivered to Earth via spacecraft telemetry. This section describes the method used for frequency calibration and explains how diffraction effects are removed from the data. These two steps of analysis were applied separately to each of the four radio signals received by New Horizons. Readers not interested in a detailed discussion of these topics can proceed to Section 5. 4.1. Frequency calibration We used a digital filter to reduce the bandwidth of the REX data by a factor of 16, to ∼76 Hz, aligning the filter so that the signal of interest is at the center of the pass band. The filter completely eliminates the other three signals received by the spacecraft, which lie well outside the pass band. With this reduction in bandwidth the sample spacing increases proportionately, from 0.8192 ms to 13.1072 ms.

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Fig. 1. Cylindrical mosaic of Pluto (Stern et al., 2015; Moore et al., 2016) assembled from observations by the Long-Range Reconnaissance Imager (Cheng et al., 2008) and the Multispectral Visible Imaging Camera (Reuter et al., 2008). The locations of occultation entry and exit are indicated, along with the region known informally as Sputnik Planitia (SP).

Table 3 Pluto occultation event timing, conditions, and geometry.

Time at surfacea (UTC) Location on surfaceb Local true solar timec , h Solar zenith angle Spacecraft-to-limb distanced D, km Fresnel scalee F, km Ray path azimuthf Radial speed of ray pathg , km s−1

Entry

Exit

2015-07-14T12:45:15.4 193.5°E, 17.0°S 16.52 (sunset)

2015-07-14T12:56:29.0 15.7°E, 15.1°N 4.70 (sunrise)

90.2° 48,865

89.8° 57,833

1.43 145° −3.53

1.55 216° +3.53

Notes: (a) The beginning and end of the occultation by the solid body as observed on the spacecraft. (b) We adopt the IAU “small body” convention, where the north pole is defined by positive angular momentum. The sub-solar latitude was 51.6°N at the time of the flyby. (c) One “hour” corresponds to 15° of rotation on Pluto. (d) Measured at the time when the ray path grazed the surface. (e) The Fresnel scale is the geometric mean of the spacecraft-to-limb distance and the wavelength. (f) The ray path azimuth is the direction to New Horizons at the time and location at which the ray path grazed Pluto’s surface; local north is 0° and east is 90°. (g) The rate of change of the distance between the ray path and Pluto’s center of mass.

After isolating each uplink signal, we derived provisional estimates for signal power and frequency through spectral analysis. These are used only to characterize the original data but not for retrieving atmospheric profiles. Fig. 2 gives an overview of the results. The occultation of the spacecraft by the solid body lasted 674 s (Table 3), as reflected by the precipitous drop in power in Fig. 2A. The thermal noise floor during this 674-s interval is ∼105 times smaller than the power in the signal received from DSS 14 at the integration time used here (0.42 s). Fig. 2B and C show measurements of the frequency fb , which exhibit several notable features. The signal transmitted by each DSN antenna has a frequency that varies linearly with time. The ramp rate is adjusted at intervals of a few hundred seconds to compensate for the Doppler shift caused by Earth’s rotation, ensuring that fb remains nearly constant. Each change in ramp rate produces a cusp in fb , and the time variation of fb in the arcs between the cusps is nearly quadratic. In addition, fb decreases gradually by ∼2 Hz over the 40 0 0-s span of the observations, a consequence of uncertainties in the prediction of the spacecraft trajectory that was used to generate the uplink tuning profiles. Finally, the location of the surface is marked by a conspicuous diffraction pattern (see Section 4.2), including prominent diffraction “tails” in the frequency measurements that extend into the geometric shadow of the solid body. This results in a negative Doppler shift at entry and a positive Doppler shift at exit, with Doppler rates of −6 Hz s−1 and −5 Hz s−1 at entry and exit, respectively. The effect of Pluto’s atmosphere is barely discernible on the scale of Fig. 2B and C, and

Fig. 2. Examples of REX measurements. Panels A and B show the power and frequency, respectively, of the signal transmitted by DSS 14 (the 70-m antenna at Goldstone) and received by REX-B. Panel C shows the frequency of the signal transmitted by DSS 43 (the 70-m antenna at Canberra) and received by REX-A. Time is measured relative to the midpoint of the occultation as observed on the spacecraft (12:50:52 UTC). Power is measured relative to its average value in the baseline intervals before and after the occultation by the solid body. The frequency reference in (B) and (C) is the intended aimpoint of the respective uplink signals (including the frequency offset in Table 1). The time resolution is 0.42 s. In order to improve the performance of flight software in the event of an untimely computer anomaly, REX-B was intentionally powered on ∼300 s later than REX-A.

it is partially obscured by ramp rate changes that occurred near both entry (Fig. 2C) and exit (Fig. 2B). Effects not associated with Pluto’s atmosphere must be removed from the data. The procedure begins with a formula for the relativistic Doppler effect (Schinder et al., 2015):

f r / ft =

 1 − nˆ · v¯ /c  1 + 2U /c2 − v2 /c2 1/2 d s d . 1 − nˆ · v¯ d /c 1 + 2Us /c2 − v2s /c2

(3)

Here, ft is the frequency of the signal transmitted by the DSN antenna (as observed in its rest frame), fr is the frequency of the signal received by the spacecraft HGA (as observed in its rest frame), v¯ d is the velocity of the DSN antenna, v¯ s is the velocity of the spacecraft, Ud is the gravitational potential of the DSN antenna, Us is the gravitational potential of the spacecraft, and c is the speed of light. We use Solar System barycentric coordinates. The unit vector nˆ points from the position of the DSN antenna at the time a pho-

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ton was transmitted to the position of the spacecraft at the time the same photon was received; the two times differ by ∼4.4 h. Similarly, ft , v¯ d , and Ud are evaluated at the DSN transmit time, whereas fr , v¯ s , and Us are evaluated at the spacecraft receive time. The gravitational potential is expressed as

U = −GMS /RS − GME /RE − GMP /RP ,

(4)

where GM is the standard gravitational parameter; the subscripts denote Sun (S), Earth (E), and Pluto (P); and R is the distance from the position of interest (either the spacecraft or the DSN antenna) to the center of mass of each body. In applying Eqs. (3) and (4) we account for the time variations in ft , nˆ , v¯ d , v¯ s , Ud , and Us , and for the steady increase in the one-way light time from the DSN antenna to the receding spacecraft. Eq. (3) predicts the time-varying frequency of the signal that would be received by the spacecraft if Pluto were a point mass with no atmosphere. The leading factor, in parentheses, accounts for the classical Doppler shift caused by relative motion of the transmitter and receiver, which changed the frequency by ∼430 kHz. The factors containing U and v2 /c2 account for relativistic time dilation. The change in frequency from the gravitational effect of the Sun was ∼70 Hz, much larger than the frequency shifts caused by the gravity fields of Earth (∼5 Hz) and Pluto (∼1 mHz). We will refer to fr as the deterministic component of fhga . The corresponding deterministic phase φ r is defined as

φr (t ) = 2 π



t

tre f





fr (t  ) − flo dt  ,

(5)

where t is time and tref is an arbitrary reference value. The calculation in Eq. (3) requires a precise reconstruction of the position and velocity of the spacecraft. We used the so-called “OD122” version of the trajectory solution derived by the New Horizons Navigation Team from a combination of Doppler tracking data and images acquired by New Horizons. We can associate an amplitude ab (t) and phase φ b (t) with each complex sample sb (t) of REX data:

sb (t ) = ab (t ) · exp[iφb (t )] ,

(6)

where i ≡ Each sample of ab and φ b includes contributions from the uplink signal as well as thermal noise, but the signal dominates even at a bandwidth of 76 Hz. We obtain a calibrated signal sc1 (t) by mixing sb (t) with the deterministic phase φ r (t):

(−1 )1/2 .

sc1 (t ) = sb (t ) · exp[−iφr (t )] = ab (t ) · exp[iφb (t ) − iφr (t )] .

Fig. 3. Examples of partially calibrated REX data, as obtained through the procedure described in Eqs. (3), (5) and (7). The signals shown here were (A) transmitted by DSS 24 (Goldstone) and received by REX-A and (B) transmitted by DSS 34 (Canberra) and received by REX-B. We fit 4th-order polynomials (blue) to the frequency measurements (gray), excluding data from a 774-s window centered on the midpoint of the occultation, as discussed in the text. See the caption to Fig. 2 for further comments. This figure shows only the data used in the fit. Figs. 5, 8, and 9 provide a detailed look at the effect of Pluto’s atmosphere. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

(7)

This procedure removes the arcs and cusps from the frequency measurements in Fig. 2B and C along with other variations in frequency not associated with Pluto and its atmosphere. Fig. 3 shows two examples of the results from Eq. (7). The frequency of the partially calibrated signal sc1 (t) decreases steadily by ∼100 mHz over the 40 0 0-s time span of the measurements. This drift in frequency arises primarily from a small discrepancy between the trajectory reconstruction and the true spacecraft velocity, with smaller contributions (< 10 mHz) from USO drift and from variations in the phase bias introduced by Earth’s neutral atmosphere and ionosphere. A second step of calibration, analogous to the one in Eq. (7), is required to compensate for these effects. It was performed as follows. First, we extracted a time history of frequency through spectral analysis of sc1 , as shown in Fig. 3. We then fit a 4th-order polynomial fcal (t) to the frequency measurements, excluding observations close to Pluto where the effects of the neutral atmosphere and diffraction from the surface are appreciable. (A total of 774 s of data centered on the midpoint of the occultation were excluded from the fit.) We integrated fcal (t), as in Eq. (5), to obtain the corresponding empirical phase correction φ cal (t). Finally, we mixed sc1 (t) with φ cal (t), as in Eq. (7), to derive a more precisely calibrated signal sc2 (t).

Table 4 Allan deviation of the calibrated REX data at τ = 5 s. DSN Antenna DSS DSS DSS DSS

14 24 43 34

REX/USO unit B A A B

Entry baseline 1.5 2.5 2.7 2.5

× × × ×

10−13 10−13 10−13 10−13

Exit baseline 1.6 2.4 2.5 2.2

× × × ×

10−13 10−13 10−13 10−13

Table 4 lists the Allan deviation at an integration time of 5 s for each fully calibrated uplink signal sc2 (t). By this metric the most stable signal is the one from DSS 14 to REX-B, but in all cases the performance is sufficient for accurate measurements of Pluto’s neutral atmosphere. 4.2. Removal of diffraction effects We used an established procedure to remove diffraction effects from the data. This section describes the method and illustrates its performance at Pluto. Figs. 4 and 5 show profiles of amplitude ac2 and phase φ c2 , respectively, which were obtained directly from the real and imaginary parts of each complex data sample sc2 , as in Eq. (6). The altitude scale in these figures corresponds to the distance between the ray path and the limb of Pluto at each discrete time step; the location of the limb is determined from the data as explained below. At a sample spacing of 13.1 ms, the change in altitude between successive samples is 46.3 m. The amplitude measurements in Fig. 4 contain a conspicuous diffraction pattern. It consists of numerous oscillations, or diffraction fringes, that generally increase in magnitude with decreasing altitude above the surface, along with a diffraction tail that extends into the geometric shadow of Pluto. Note that the spacecraft-toPluto distance, about 50,0 0 0 km, was too small for refractive defocusing in the atmosphere to have an appreciable effect on the observed amplitude. The impact of defocusing is ∼105 smaller in these observations than in stellar occultations observed from Earth at a distance of about 30 AU.

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Fig. 4. Amplitude measurements at (A) entry and (B) exit for the uplink signal from DSS 14 to REX-B. The pair of profiles in each panel shows results before (blue) and after (black) removal of diffraction effects caused by the surface of Pluto. The amplitude has been normalized by its average value at altitudes of 10–60 km. The sample spacing is 46.3 m. Pluto’s limb coincides with the location where the amplitude has dropped by 50%, as denoted by the symbol. This location is the reference for the altitude scale. Local variations in surface topography may be responsible for the asymmetry between the diffraction tails at entry and exit; see Fig. 6 for further discussion. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 5. Phase measurements near Pluto’s surface at occultation entry for the uplink signal from DSS 14 to REX-B. The pair of profiles shows results before (blue) and after (black) removal of diffraction effects from Pluto’s surface. The sample spacing is 46.3 m. We adopt a sign convention, implicit in Section 4.1, where the phase shift from the neutral atmosphere is negative. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

We removed the diffraction effects from the REX data by applying an inverse Fresnel filter (Marouf et al., 1986) to the complex samples sc2 (t). This technique was first developed to improve the spatial resolution in radio occultation measurements of planetary rings (Marouf et al., 1986; Gresh et al., 1989). It was later adapted for use in atmospheric occultations, where it can remove the effects of diffraction from the surface (Tyler et al., 1989), enhance the vertical resolution in retrieved profiles of atmospheric structure (Karayel and Hinson, 1997), and disentangle effects associated with multipath propagation (Hinson et al., 1997; 1998). Here we are concerned only with surface diffraction and vertical resolution; Pluto’s atmosphere is too tenuous to cause multipath propagation at the small spacecraft-to-limb distance of the REX observation.

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The Fresnel filter is based on a Huygens–Fresnel formulation for diffraction of electromagnetic waves (Born and Wolf, 1999). Our implementation of the filter accounts for the steady increase in distance from New Horizons to Pluto during the observation and the resultant increase in the Fresnel scale F ≡ (λD)1/2 , where λ is the wavelength and D is the distance along the ray path between New Horizons and the point nearest Pluto. For example, F increased from 1.43 km to 1.55 km during the interval when the spacecraft was occulted by the solid body (Table 3). The filter also accounts for the transverse curvature of Pluto’s limb (in the direction perpendicular to the ray path), but we assume circular symmetry so that variations in surface radius along the limb are ignored. The theoretical foundation for the Fresnel filter is described in detail by Marouf et al. (1986) and will not be repeated here. It is more informative to illustrate its performance empirically. Fig. 4A and B show the diffraction-corrected amplitude profiles at entry and exit, respectively, for a filter with a vertical resolution of ∼600 m. (The diffraction-corrected phase measurements are shown in Figs. 5, 8, and 9.) The Fresnel filter removes the diffraction fringes and produces a sharper drop in amplitude at the surface, providing a more precise indication of its location. We used the diffraction-corrected amplitude measurements to register the REX data with respect to Pluto’s surface. (We defer discussion of Pluto’s radius to Section 5.) The limb of Pluto is aligned with the location where the amplitude has decreased by 50% (Born and Wolf, 1999), equivalent to a 75% reduction in signal power. Altitude is measured from this reference level in all results reported here. We estimate the 1-sigma uncertainty in altitude to be ∼200 m, commensurate with the decrease in normalized amplitude from 0.75 to 0.25 within a radial span of ∼400 m. Note that the Fresnel filter compensates for the small deflection caused by refractive bending in Pluto’s atmosphere, but its peak value is only ∼30 m, smaller than the sample spacing and not discernible on the scale of Fig. 4. Fig. 5 illustrates similar aspects of the phase measurements. Prior to removal of diffraction effects, the phase shift caused by Pluto’s neutral atmosphere is modulated by diffraction from the surface, producing an extensive pattern of diffraction fringes. Their contribution to the net phase is substantial, particularly near the surface, where the peak phase shift from the neutral atmosphere is only ∼5 times larger than the magnitude of the strongest fringe. Fig. 5 demonstrates the capacity of the Fresnel filter to eliminate the fringes while preserving the effect of Pluto’s neutral atmosphere. It performs as expected with one minor exception — there is a peculiar inflection in the diffraction-corrected phase profile in the lowest 500 m above the surface. This artifact, which appears in the phase profiles derived from all four uplink signals, may be associated with the spatial resolution of the Fresnel filter and the concomitant, rapid decrease in the diffraction-corrected amplitude in the same altitude interval (Fig. 4A). As we show in Section 6.1, the magnitude of this phase inflection is smaller than the uncertainty of the measurements. We now take a closer look at the diffraction pattern in the phase data, which can be isolated by computing the difference between the profiles in Fig. 5. This step removes the effect of Pluto’s neutral atmosphere. Fig. 6 shows the resulting profiles of phase fringes for the signals from the two 70-m antennas at both entry and exit. Note that the observed phase shift from diffraction goes to zero at the surface in accordance with theory (Born and Wolf, 1999). Judging by the results in Figs. 4, 5 and 6, the Fresnel filter appears to perform well at Pluto. The arrows in Fig. 6 denote altitudes where phase fringes are largely absent from the observations at entry. (The amplitude fringes in Fig. 4A exhibit the same behavior.) The altitude where this feature appears is somewhat different in the profiles from

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Fig. 6. Diffraction fringes in the phase measurements as obtained by differencing pairs of profiles such as the ones in Fig. 5. Results are shown at both entry (left pair) and exit (right pair) for the uplinks from DSS 14 to REX-B and from DSS 43 to REX-A. Three of the profiles have been shifted by an integer multiple of 0.5 rad for clarity. The Fresnel scale, which is smaller at entry than at exit (Table 3), determines the spatial scale of the fringes. Arrows denote altitudes where the phase fringes are subdued.

The uncertainty in radius reflects the possible presence of a systematic bias in spacecraft position. For the geometry considered here — only 33 km from diametric — this sort of error causes an underestimate of the radius on one side of Pluto and an overestimate of nearly equal magnitude on the other side. For this reason a bias in spacecraft position of 2.5 km (0.7 sigma), when properly aligned, would bring the radii at entry and exit to the same value. The REX results therefore imply that the radius is larger at exit than at entry with a probability of 76% (for a standard normal distribution). The dominant contribution to the uncertainties in radius at entry and exit can be removed through averaging, which yields a mean radius of 1189.9 ± 0.2 km. This reduces the impact of uncertainty in spacecraft position to 0.1 km — smaller than the uncertainty in locating the surface in the amplitude measurements — and provides a better reference for characterizing atmospheric pressure, as discussed in Section 7.3. The REX results are consistent with the global average radius of 1188.3 ± 1.6 km (2 sigma) derived from observations by the LongRange Reconnaissance Imager (Nimmo et al., 2017). The difference at exit is relatively large, 4.1 km, but still within the measurement uncertainties and the large range of topographic relief observed on Pluto (Stern et al., 2015; Moore et al., 2016). 6. Profiles of the neutral atmosphere In Section 4 we calibrated the phase data to isolate the effect of Pluto’s neutral atmosphere. We now use the results to derive profiles of atmospheric structure. This section focuses on the retrieval algorithm and the effect of measurement noise. The REX profiles are interpreted and compared with results from Earth-based stellar occultation measurements in Section 7.

Fig. 7. Comparison of measured diffraction fringes with model predictions. The middle profile shows phase measurements at occultation entry on the uplink from DSS 43 (as in Fig. 6). One model (left) shows the phase oscillations produced by Fresnel diffraction from a straight edge (Born and Wolf, 1999). The other model (right) shows the interference pattern that results from superposition of two such edge diffraction patterns, one shifted vertically by 240 m relative to the other. The second model contains a null in the phase fringes similar to the one in the measurements (arrows) and is better aligned with the measured fringes at altitudes above the null (dashed line). The model profiles are offset by ± 0.25 rad for clarity.

DSS 14 and DSS 43, but its presence in both signals points to Pluto as the source. We suspect that local variations in surface topography are producing an interference pattern within the diffracted signal, and that the transverse separation of the two ray paths results in a small shift in the altitude where cancellation occurs. We used a simple model to demonstrate the plausibility of this interpretation, as shown in Fig. 7. Regardless of its origin, the Fresnel filter removes the modulated profile of fringes from both the phase and amplitude measurements, as shown in Figs. 4A and 5, respectively.

5. Pluto’s radius As noted in the preceding section, the diffraction-corrected amplitude measurements yield estimates for Pluto’s radius. The results obtained from each of the four signals received by REX agree to within ∼30 m at both entry and exit; the average values are 1187.4 ± 3.6 km at entry and 1192.4 ± 3.6 km at exit. The error bars (1 sigma) were derived from the formal uncertainty in spacecraft position associated with the OD122 trajectory reconstruction, which is the dominant error source. The uncertainty in spacecraft velocity has a negligible effect on the radius estimates — it contributes only ∼14 m of uncertainty to the length of the occultation chord across Pluto.

6.1. Phase profiles The long baselines that preceded and followed the occultation by Pluto, each with a duration of ∼1500 s, were required for precise calibration (Section 4.1). However, the effect of Pluto’s neutral atmosphere is significant only at altitudes below ∼100 km, corresponding to a time span of 28 s, and we now focus on data from that interval. We characterized the structure of Pluto’s neutral atmosphere at occultation entry by averaging all available phase data:

φa v e ( r ) =

φ14 (r ) + φ24 (r ) + φ34 (r ) + φ43 (r ) 4

.

(8)

Here, r is radius, φ ave is the average phase, and φ 14 , φ 24 , φ 34 , and φ 43 are the diffraction-corrected phase profiles derived from the individual signals, as in Fig. 5, with subscripts denoting the source antenna at the DSN. The results appear in Fig. 8. We have omitted the phase measurements in the lowest 500 m above the surface to avoid the artifact discussed in connection with Fig. 5. An unknown constant bias is inherent to the type of phase measurement considered here. We solved for φ bias , the bias in φ ave (r), by fitting a model to the data, as explained later in this section in connection with Eq. (12). This bias has been removed from the phase measurements in Fig. 8 (and Fig. 9 below). As we show in Section 6.2, φ bias has no effect on the retrieved profiles of number density, pressure, and temperature. The phase measurements are affected by noise from several sources, which can be characterized by computing the difference between appropriate pairs of signals. For example, the following combination isolates the noise caused by equipment on the spacecraft φ sc (r):

φsc (r ) =

[φ14 (r ) − φ24 (r )] + [φ34 (r ) − φ43 (r )] . 4

(9)

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pair in California and 0.4 km for the pair in Australia.) Fig. 8 shows the resulting profile of φ sc (r) (orange curve), which has a standard deviation σ sc of 0.047 rad. The largest contribution probably comes from the spacecraft USOs. Conversely, the following combination of phase data isolates the telluric noise φ tel (r):

φtel (r ) =

[φ14 (r ) − φ34 (r )] + [φ24 (r ) − φ43 (r )] . 4

(10)

Each term in brackets is now the difference between signals that originated from different DSN complexes but were received by the same REX. This combination removes the effects of Pluto’s neutral atmosphere as well as noise introduced by equipment on the spacecraft. The resulting profile of φ tel (r) (blue curve) in Fig. 8 has a standard deviation σ tel of 0.018 rad. Finally, we obtained an estimate for the net phase noise σ φ by combining the contributions from spacecraft equipment and telluric effects: 2 1/2 σφ = (σsc2 + σtel ) .

Fig. 8. Diffraction-corrected phase measurements at entry, showing the phase shift caused by Pluto’s neutral atmosphere. The black curve shows φave (r ) − φbias , the average phase profile with the bias removed. The orange curve shows noise associated with equipment on the spacecraft, as defined in Eq. (9). The blue curve shows noise from telluric effects, as defined in Eq. (10). The gray shading indicates the standard deviation of φ ave , as derived from Eq. (11). The dashed black line is an atmospheric model, defined in Eq. (12), which was tuned to fit the measurements at 1215–1277 km radius. The radius scale begins at the surface (1187.4 km); the vertical range is 100 km. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

(11)

The value of σ φ at entry is 0.050 rad, as shown by gray shading in Fig. 8. This is 25 times smaller than the phase shift at the base of the profile. As the differences among the four signals are relatively small within this segment of data, we decided to use equal weights in computing φ ave in Eq. (8). We used the same procedure to characterize the structure of Pluto’s atmosphere and the measurement uncertainty at occultation exit. Fig. 9 shows the results. In this case σ sc is 0.024 rad, σ tel is 0.020 rad, and σ φ is 0.031 rad. The phase shift at the base of the profile (500 m above the surface) is smaller at exit (−0.91 ± 0.03 rad) than entry (−1.27 ± 0.05 rad), a consequence of the difference in radius at the two locations. The measurements in Figs. 8 and 9 are essentially the same above a radius of ∼1215 km, where the standard deviation of the difference between the entry and exit profiles is 0.018 rad, smaller than σ φ at both entry and exit. In characterizing the atmospheric structure in this region (henceforth the upper atmosphere) we therefore averaged the profiles of φ ave (r) from the two locations, which reduces the noise and yields more reliable results. It is instructive to compare the phase measurements with a simple, two-parameter model for the upper atmosphere:

φ f it (r ) = φo × exp[−(r − 1187.4 )/Hφ ] .

(12)

Here, Hφ is the scale height and φ o is the phase shift at a reference radius of 1187.4 km (the surface at entry). We averaged the phase profiles from entry and exit, weighting each by the reciprocal of its variance σφ2 (Brandt, 1989), and then tuned the model to

Fig. 9. Diffraction-corrected phase measurements at exit, showing the phase shift caused by Pluto’s neutral atmosphere. See the caption to Fig. 8 for further explanation. The radius scale begins at the surface (1192.4 km); the vertical range is 100 km. As in Fig. 8, we have omitted phase measurements in the lowest 500 m above the surface.

Each term in brackets is the difference between signals that originated from the same DSN complex but were received by different REXs. This combination removes the effect of Pluto’s neutral atmosphere and also largely eliminates the “telluric” contribution to the noise. The latter comprises not only noise associated with DSN equipment but also any variations in phase caused by Earth’s neutral atmosphere and ionosphere within this 28-s interval. (The cancellation of the atmospheric and ionospheric effects is imperfect owing to the separation of the ground antennas, 9.6 km for the

fit the combined observations at 1215–1277 km radius. (The reasons for choosing this radius interval are explained below.) This procedure yields least-squares solutions for Hφ (61 ± 4 km), φ o (−0.71 ± 0.04 rad), and a third parameter φ bias , the constant bias inherent to measurements of φ ave (r), as mentioned previously following Eq. (8). The dashed black line in Figs. 8 and 9 shows the best-fit model. Within the fitting interval the standard deviation of φave − φ f it is 0.016 rad at entry and 0.013 rad at exit, well within our estimates of σ φ . Hence, the model is an accurate representation of both phase profiles at 1215–1277 km radius. Conversely, the measured phase profiles diverge significantly from the model, and from one another, in the lower atmosphere. We examine these differences more closely in the next section. We imposed two constraints in selecting the interval for fitting the model to the measurements. The first requirement is that

|φave | > 3 σφ

(13)

at both entry and exit, which determines the upper boundary. Above 1277 km the data are noisy and provide little additional in-

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formation. The second requirement is that

  φave − φ f it  < σφ

(14)

at both entry and exit, which determines the lower boundary. Below 1215 km the simple model is inconsistent with the observations. 6.2. Profiles of refractivity and number density We retrieved profiles of refractivity and number density from the phase profiles in Figs. 8 and 9. This section describes the methodology, its application to Pluto, and the results at entry and exit. 6.2.1. Prodecure A radio signal traveling from Earth to New Horizons follows a straight line except where it intersects Pluto’s atmosphere. Within the atmosphere the path bends slightly in response to the radial gradient of refractive index, causing a deflection by an angle α between the incoming and outgoing segments of the path. In response to this deflection the physical length of the path between Pluto and New Horizons increases by an amount

δ ≈ α 2 D/2 .

(15)

However, α < 1 μrad, so that δ < 25 μm. This corresponds to a change in the phase of the radio signal of less than 0.004 rad, much smaller than the measurement noise. We can therefore represent the entire propagation path as a straight line. (Actually, the Fresnel filter removes the indirect phase shift associated with this deflection, leaving only the direct phase shift caused by Pluto’s atmosphere (Karayel and Hinson, 1997), but the preceding discussion gives a simpler justification for the straight-line approximation.) With this approximation the refractive index of the atmosphere μ(r) and its refractivity ν (r) are related to the phase of the radio signal φ (r) by the following Abel transform (Bracewell, 1986):

ν (r ) ≡ μ (r ) − 1 =

λ 2π 2



∞ r

d φ (r  ) dr  . √ dr  r 2 − r 2

(16)

As the integrand involves only the radial derivative dφ (r)/dr, a constant phase bias has no effect on ν (r). Eq. (16) is valid when there are no significant deviations from local spherical symmetry, so that ν depends only on r in the vicinity of the observations. As in recent analyses of stellar occultation data (Dias-Oliveira et al., 2015; Sicardy et al., 2016), we ignore the effects of minor constituents and assume a composition of pure N2 , which has a refractive volume κ of 1.095 × 10−29 m3 at the wavelength used here (Essen and Froome, 1951; Orcutt and Cole, 1967; Achtermann et al., 1991). With this assumption the number density n(r) can be obtained from ν (r):

n(r ) = ν (r )/κ .

(17)

The effect of minor constituents on the value of κ is discussed below. 6.2.2. Occultation entry We used a composite representation of dφ (r)/dr to evaluate the integral in Eq. (16). This approach is designed to reduce the uncertainties in the retrieved profiles at altitudes below ∼25 km, consistent with the primary objectives of the radio occultation. For r < 1210 km, dφ /dr was derived directly from the measurements in Fig. 8. We divided the data into non-overlapping altitude intervals and computed the derivative from a least-squares linear fit to φ ave (r) within each interval. The sample spacing is constrained by the sensitivity of the measurements; it increases from 1 km near the surface to 4 km as r approaches 1210 km (∼20 km above the surface).

Fig. 10. Number density versus radius at occultation entry. The profile extends from 1188.4 km (1 km above the local surface) to 1302.4 km, with a sample spacing that increases from 1 km at the bottom of the profile to 5 km at the top. Gray shading denotes the standard deviation. The profile is most accurate near the surface, where the uncertainty is 1.5%.

For r > 1210 km, dφ /dr was derived entirely from φ fit (r):

φ f it (r ) dφ =− , dr Hφ

(18)

which improves the accuracy of the atmospheric profiles by reducing the effect of stochastic phase noise. We extrapolated the model upward to 1450 km (∼260 km altitude) and truncated integration of Eq. (16) at this radius. The sample spacing is 5 km throughout this radial range. In Section 7.1 we assess the validity of this approach through comparisons with results derived from stellar occultations. Fig. 10 shows the profile of number density derived from Eqs. (16) and (17) at occultation entry. The density in the upper atmosphere increases gradually from ∼9 × 1019 m−3 at the top of the profile to ∼5 × 1020 m−3 at 1205 km radius. Closer to the surface the vertical gradient of density is much stronger, as reflected by the threefold change in density in the layer at 1191–1199 km. There are two sources of uncertainty in the density profile; one is stochastic and the other is computational. The stochastic error δ ns is a consequence of spacecraft and telluric noise, as discussed in Section 6.1. We characterized the standard deviation of δ ns and its variation with radius through the following procedure. First, we generated a set of phase noise profiles by applying Eq. (8) to measurements from 50 non-overlapping intervals in the baselines that preceded and followed the occultation by Pluto. We then propagated each realization of noise through the full retrieval algorithm, including the solution for φ fit (r), to determine its effect on n(r). (We increased the sample size by performing additional calculations using simulated phase noise with the same statistical properties as the measurements.) The simulated retrievals include the effect of the Fresnel filter, which changes the statistics of the noise fluctuations on scales comparable to the Fresnel scale (Marouf et al., 1986). Our error analysis indicates that the standard deviation of δ ns increases from 1.5 × 1019 m−3 at the top of the profile to 3.5 × 1019 m−3 at the bottom. These correspond to fractional errors in n(r) of 16% and 1.5%, respectively. The computational error δ nc arises from ending numerical integration of Eq. (16) at a finite radius rt . From Eqs. (16) and (17), the resulting error is

δ nc ( r ) =

λ 2 κ π2



∞ rt

d φ (r  ) dr  λ < √  dr 2 κ π2 r 2 − r 2

|φ (r )|  t . rt2 − r 2

(19)

We set rt to 1450 km, as noted above, which reduces δ nc (r) to less than 3 × 1018 m−3 throughout the radial range in Fig. 10, ensuring that δ nc is considerably smaller than δ ns . The net uncertainty in n(r) from these two sources is shown by shading in Fig. 10.

D.P. Hinson et al. / Icarus 290 (2017) 96–111

Fig. 11. Number density versus radius at entry (circles) and exit (triangles). Gray shading denotes the standard deviation. The base of each profile is 1 km above the local surface.

6.2.3. Occultation exit We used the same approach, with two minor variations, to derive a number density profile at occultation exit. In this case φ fit was used to compute dφ /dr for r > 1220 km. Moreover, the sample spacing in the lower part of the profiles is not the same, owing to differences in the atmospheric structure at entry and exit. By design, the profiles at entry and exit are identical for r > 1220 km. Fig. 11 compares the results over the radial range where they differ. The offset between the profiles exceeds the standard deviation of the measurements for r < 1205 km. 6.3. Profiles of pressure and temperature A profile of pressure versus radius p(r) is derived from n(r) by assuming hydrostatic balance and integrating vertically:

p(r ) = nb k Tb + m



rb r

n (r  )

GMP  dr . r 2

(20)

Here, k is the Boltzmann constant, and GMP (the standard gravitational parameter of Pluto) is 869.6 km3 s−2 (Stern et al., 2015). For a pure N2 atmosphere the molecular mass m is 4.652 × 10−26 kg. (The effect of minor constituents on the value of m is discussed below.) The pressure profile extends upward to a radius rb , where the number density nb is known but the temperature Tb is required as a boundary condition. The ideal gas law has been used to express the first term on the right-hand side of Eq. (20) in terms of nb and Tb rather than the pressure pb at the upper boundary. The temperature profile T(r) follows from n(r), p(r), and the ideal gas law:

T (r ) =

nb Tb m + n (r ) n (r ) k



rb r

n (r  )

GMP  dr . r 2

(21)

In evaluating Eqs. (20) and (21), we set Tb to 95.5 K at a radius rb of 1302.4 km, as determined from analysis of recent stellar occultation measurements (Dias-Oliveira et al., 2015; Sicardy et al., 2016). We used the van der Waals equation to check the validity of the ideal gas law. Temperatures obtained from the two equations of state agree to within 10−4 K throughout Pluto’s atmosphere. The REX profiles of temperature versus pressure appear in Fig. 12. The complete atmospheric profiles — n, p, and T versus altitude and radius — are listed in Tables 5 and 6. Section 7 gives a detailed discussion of the results and their significance. The accuracy of the pressure and temperature profiles is limited by stochastic phase noise and by uncertainty in Tb . The stochastic errors in p(r) and T(r) were characterized in the same manner as for n(r), except that the simulated retrievals now include Eqs. (20) and (21). In assessing the impact of the boundary condition on p(r) and T(r) we assumed that the standard deviation of Tb is 7 K, a very conservative estimate based on results from recent stellar

105

occultation measurements (Dias-Oliveira et al., 2015, Fig. 10). From Eq. (20) the error in p(r) associated with the uncertainty in Tb is 0.09 microbar, independent of radius. The corresponding error in T(r) is inversely proportional to n(r), as shown in Eq. (21), so that it decreases from 7 K at the top of the profiles to 1.5 K at 6 microbar and less than 1 K at the base of the profiles (0.3 K at entry and 0.5 K at exit). The net uncertainties in n, p, and T are listed in Tables 5 and 6. For example, the standard deviations of p and T are 0.69 microbar and 2.1 K at the base of the entry profile. The corresponding values at exit are 0.66 microbar and 3.7 K. Fig. 13 shows the fractional errors in n, p, and T at entry. The results at exit (not shown) are essentially the same. For both n and p the dominant source of uncertainty is stochastic phase noise. The primary source of uncertainty in T is stochastic phase noise for r < 1265 km and uncertainty in Tb for r > 1265 km. The fractional error in T is ∼6% throughout the radial range of Fig. 13. The uncertainties in n and p exceed 16% at the top of the profile but decrease to 1.5% and 5.7%, respectively, at the bottom. The most important minor constituent in Pluto’s atmosphere is CH4 , with an abundance of ∼0.5% (Lellouch et al., 2009; 2015), but it has little impact on either κ or m. When the composition is assumed to be 99.5% N2 and 0.5% CH4 , κ increases by 0.24% from its value in a pure N2 atmosphere, whereas m decreases by 0.21%. The resulting changes in n(r), p(r), and T(r) are much smaller than the other sources of uncertainty throughout the vertical range of Fig. 13. Likewise, Pluto’s atmospheric haze (Gladstone et al., 2016) and trace constituents such as CO have no appreciable effect on κ or m. The horizontal resolution of the measurements along the line of sight from Earth to New Horizons is constrained by the limbsounding geometry. A radio signal √ traverses an atmospheric layer of depth d in a distance L ≈ 2 2 r d, where r is the radius at the base of the layer. For example, when d is 3.5 km, the depth of the cold layer at the base of the entry profile (see Section 7.2), L is ∼180 km, equivalent to a 9° arc of a great circle. The azimuth of the ray path is given in Table 3. 7. Discussion This section addresses four topics: the upper atmosphere, the lower atmosphere, conditions at the surface, and the origin of the cold boundary layer in the REX entry profile. 7.1. The upper atmosphere (r > 1215 km) The amplitude of atmospheric waves on Pluto is less than 1 K within the vertical range of the REX profiles in Fig. 12 (Young et al., 20 08a; Person et al., 20 08; McCarthy et al., 20 08; Toigo et al., 2010; French et al., 2015; Gladstone et al., 2016; Forget et al., 2017). Detection of such waves is beyond the capabilities of REX. Above 1215 km radius (p < 6 microbar), the temperature structure is controlled by the radiative properties of CH4 and CO (Zalucha et al., 2011); haze particles may also be a significant source of local radiative heating. Apart from weak modulation by atmospheric waves, the atmosphere in this region is expected to be horizontally uniform for two reasons. First, the radiative time constant is ∼700 Pluto days (Strobel et al., 1996), so that diurnal temperature variations are small (Gladstone et al., 2016). In addition, the ratio of the Rossby radius to Pluto’s radius is much larger than the corresponding ratio on planets such as Earth and Mars. That makes it easier to convert atmospheric potential energy into kinetic energy (Gill, 1982), which tends to eliminate any horizontal temperature gradients, including those that would otherwise develop at the winter pole. Recent stellar occultation measurements have confirmed these expectations, showing that any horizontal

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Table 5 REX profile at occultation entry. Altitude (km)

Radius (km)

n (1019 m−3 )

σn

(1019 m−3 )

p (microbar)

(microbar)

σp

T (K)

(K)

σT

115.0 110.0 105.0 100.0 95.0 90.0 85.0 80.0 75.0 70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0 30.0 25.0 20.0 16.0 12.0 9.0 7.0 5.3 4.0 3.0 2.0 1.0

1302.4 1297.4 1292.4 1287.4 1282.4 1277.4 1272.4 1267.4 1262.4 1257.4 1252.4 1247.4 1242.4 1237.4 1232.4 1227.4 1222.4 1217.4 1212.4 1207.4 1203.4 1199.4 1196.4 1194.4 1192.7 1191.4 1190.4 1189.4 1188.4

8.96 9.77 10.65 11.61 12.65 13.79 15.02 16.35 17.81 19.39 21.12 22.99 25.02 27.24 29.65 32.27 35.11 38.21 41.82 46.56 51.86 60.93 78.94 110.62 151.62 180.48 202.28 215.70 224.69

1.47 1.53 1.58 1.63 1.68 1.73 1.78 1.82 1.85 1.88 1.90 1.91 1.91 1.89 1.86 1.81 1.74 1.64 1.55 1.59 1.65 1.91 2.23 2.55 3.15 3.47 3.40 3.37 3.46

1.182 1.294 1.417 1.552 1.701 1.864 2.043 2.240 2.456 2.693 2.953 3.238 3.551 3.895 4.272 4.686 5.140 5.638 6.186 6.796 7.344 7.976 8.567 9.104 9.737 10.351 10.897 11.493 12.123

0.209 0.225 0.242 0.261 0.279 0.299 0.320 0.341 0.363 0.386 0.409 0.434 0.458 0.482 0.506 0.530 0.554 0.576 0.597 0.618 0.633 0.649 0.660 0.667 0.674 0.679 0.683 0.687 0.691

95.50 95.89 96.34 96.83 97.37 97.95 98.56 99.20 99.88 100.56 101.28 102.02 102.79 103.57 104.37 105.19 106.02 106.87 107.14 105.72 102.57 94.81 78.61 59.61 46.51 41.54 39.02 38.59 39.08

7.00 6.45 6.00 5.65 5.40 5.23 5.13 5.10 5.11 5.17 5.25 5.36 5.49 5.63 5.77 5.92 6.07 6.23 6.37 6.34 6.24 5.91 4.98 3.80 2.92 2.51 2.25 2.13 2.06

Notes: The symbols σ n , σ p , and σ T denote the standard deviations of n, p, and T, respectively. The stochastic phase noise and the resulting uncertainties in n, p, and T are correlated over vertical scales of roughly 50 km.

Table 6 REX profile at occultation exit. Altitude (km)

Radius (km)

n (1019 m−3 )

σn

(1019 m−3 )

p (microbar)

(microbar)

σp

T (K)

(K)

σT

110.0 105.0 100.0 95.0 90.0 85.0 80.0 75.0 70.0 65.0 60.0 55.0 50.0 45.0 40.0 35.0 30.0 25.0 20.0 16.0 12.0 9.0 7.0 5.0 3.0 1.0

1302.4 1297.4 1292.4 1287.4 1282.4 1277.4 1272.4 1267.4 1262.4 1257.4 1252.4 1247.4 1242.4 1237.4 1232.4 1227.4 1222.4 1217.4 1212.4 1208.4 1204.4 1201.4 1199.4 1197.4 1195.4 1193.4

8.96 9.77 10.65 11.61 12.65 13.79 15.02 16.35 17.81 19.39 21.12 22.99 25.02 27.24 29.65 32.27 35.11 38.49 43.11 48.30 56.76 65.64 73.48 84.20 99.72 124.37

1.47 1.53 1.58 1.63 1.68 1.73 1.78 1.82 1.85 1.88 1.90 1.91 1.91 1.89 1.86 1.81 1.74 1.65 1.62 1.65 1.73 1.79 1.86 2.03 2.30 3.01

1.182 1.294 1.417 1.552 1.701 1.864 2.043 2.240 2.456 2.693 2.953 3.238 3.551 3.895 4.272 4.686 5.140 5.640 6.199 6.703 7.287 7.800 8.191 8.635 9.154 9.789

0.209 0.225 0.242 0.261 0.279 0.299 0.320 0.341 0.363 0.386 0.409 0.434 0.458 0.482 0.506 0.530 0.554 0.576 0.597 0.613 0.628 0.638 0.644 0.650 0.657 0.662

95.50 95.89 96.34 96.83 97.37 97.95 98.56 99.20 99.88 100.56 101.28 102.02 102.79 103.57 104.37 105.19 106.02 106.12 104.15 100.51 92.98 86.07 80.73 74.28 66.49 57.01

7.00 6.45 6.00 5.65 5.40 5.23 5.13 5.10 5.11 5.17 5.25 5.36 5.49 5.63 5.77 5.92 6.07 6.23 6.36 6.34 6.00 5.59 5.25 4.85 4.31 3.70

Notes: The symbols σ n , σ p , and σ T denote the standard deviations of n, p, and T, respectively. The stochastic phase noise and the resulting uncertainties in n, p, and T are correlated over vertical scales of roughly 50 km.

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Fig. 12. Profiles of temperature versus pressure retrieved from REX measurements at (A) entry and (B) exit. Gray shading denotes the standard deviation of temperature, which includes the uncertainty in the boundary condition Tb at the top of the profile. The base of each profile is 1 km above the local surface. The blue line is the saturation temperature of N2 (Fray and Schmitt, 2009). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 13. Fractional errors in number density (n), pressure (p), and temperature (T) at occultation entry.

variations in temperature are no larger than a few kelvin at 1220– 1400 km radius (Dias-Oliveira et al., 2015, Fig. 10). This explains the close agreement between the REX phase profiles at entry and exit for r > 1215 km, despite the differences in location and local time. Sicardy et al. (2016) derived a pressure of 6.94 ± 0.5 microbar at 1215 km from multi-chord observations of a stellar occultation on 29 June 2015, only 15 days before the REX measurements. This differs from the corresponding REX result, 5.91 ± 0.6 microbar, by only 1.0 microbar or ∼2 sigma. Hence, any bias between the two types of observation is probably no larger than ∼0.5 microbar. Fig. 14 compares the temperature structure at REX entry with the best-fit model derived by Sicardy et al. (2016) from the contemporaneous stellar occultation measurements. Both profiles have a temperature maximum near 1215 km, and the temperature decreases steadily with increasing radius between 1215 km and the top of the REX profile. The two profiles differ by less than 1 sigma throughout this interval. The mean temperature gradient at 1220– 1300 km is −0.14 K km−1 in the REX profile as compared with −0.17 K km−1 in the stellar occultation profile. More generally, the REX solutions for the peak temperature (107 ± 6 K), the radius of the peak (1215 km), and the temperature gradient above the peak are also consistent with results from other stellar occultations (Young et al., 2008a; Dias-Oliveira et al., 2015; Bosh et al., 2015). We discuss the atmospheric structure below 1215 km in the next section. The preceding discussion further validates the phase model in Eq. (12), which not only provides a good fit to the REX measurements at 1215–1277 km, as shown in Figs. 8 and 9, but also captures basic characteristics of Pluto’s atmosphere that had been determined previously from stellar occultations.

Fig. 14. Comparison of the temperature structure at REX entry with a model derived from contemporaneous stellar occultation measurements (Sicardy et al., 2016). The REX result is shown by the black line, with gray shading to indicate the 1-sigma uncertainty. The stellar occultation model (red line) extends downward to 1191 km, the deepest level accessible in this event, but it does not reach the surface. As noted in Section 6.3, the profiles match at 1302.4 km because of the value assigned to Tb . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

7.2. The lower atmosphere (r < 1215 km) The REX atmospheric profiles — the first to reach the surface — provide unique insight into the temperature structure of the lower atmosphere and its horizontal variations. These improvements are a consequence of basic differences between stellar and radio occultation measurements. The lower atmosphere is where the REX profiles are most reliable, as shown in Fig. 13, whereas atmospheric defocusing greatly reduces the sensitivity of stellar occultation measurements in this region. (Defocusing is negligible in the REX observations, as discussed in Section 4.2.) In the stellar occultations strong defocusing also causes the motion of the ray path to become nearly horizontal (e.g., Dias-Oliveira et al., 2015, Fig. 2), which conflates the effects of vertical and horizontal variations in atmospheric structure, while the motion of the ray path remains nearly vertical throughout the REX observation. Fig. 15 compares the temperature profiles from Fig. 12 over the radial range where they differ. The REX entry profile has a strong inversion that ends ∼3.5 km above the surface, and the temperature at lower altitudes is nearly constant and close to saturation. In

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Fig. 15. REX profiles of temperature versus (A) radius and (B) local altitude. In both panels the orange line is the entry profile, the blue line is the exit profile, and the black line is the saturation temperature of N2 (Fray and Schmitt, 2009) corresponding to the pressure profile at entry. The base of each profile in (A) is 1 km above the local surface. The profiles are plotted versus altitude in (B) to emphasize the difference in conditions near the ground. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 16. The temperature gradient dT/dr in the REX profiles at entry (orange) and exit (blue). The black line is the dry adiabat. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

the cold boundary layer beneath the inversion the average temperature is 38.9 ± 2.1 K. The temperature structure in the exit profile is significantly different — the inversion is much weaker and it extends to the surface with no sign of a boundary layer. At exit the temperature 1 km above the surface is 57.0 ± 3.7 K, ∼18 K warmer than at entry. Fig. 16 compares the REX profiles of dT/dr at entry and exit. The temperature inversion is significantly stronger at entry, where the peak gradient is +9.5 ± 1.2 K km−1 at a pressure of 9 microbar (1195 km). The temperature gradient at the same pressure in the exit profile is only +3.9 ± 1.0 K km−1 , a difference of more than 4 sigma. At the base of the entry profile in Fig. 16, within the cold boundary layer, the measured temperature gradient is −0.5 ± 0.7 K km−1 at 11.8 microbar. This is close to the dry adiabatic temperature gradient of −0.6 K km−1 but also consistent with an isothermal atmosphere. Hence, the uncertainty in dT/dr is slightly too large to distinguish between neutral stability and stable stratification. Heat conduction transports thermal energy away from the temperature maximum at ∼1215 km radius. The heat flux Fc depends on both the temperature and its vertical gradient:

Fc = −A T dT /dr ,

(22) 9.37 × 10−5

where Fc > 0 for an upward heat flux and A is W m−1 K−2 (Touloukian et al., 1970). For the profiles in Tables 5 and 6, the average heat flux in the upper atmosphere at 1220–1300 km radius is +1.3 × 10−6 W m−2 at both entry and exit. The downward heat flux in the lower atmosphere has a peak value of −6.2 × 10−5 W m−2 at entry but only −2.7 × 10−5 W m−2 at exit, reflecting the difference between the temperature gradients within

the inversion (Fig. 16). At exit the downward heat flux is delivered directly to the surface, where it is emitted to space as black-body radiation (along with the far larger energy flux from sunlight absorbed at the surface). At entry the downward heat flux warms the cold boundary layer, but its contribution to the energy balance near the surface is relatively small (Section 7.4). The temperature inversion in the lower atmosphere has been observed repeatedly in stellar occultations (Sicardy et al., 2003; Young et al., 2008a; Dias-Oliveira et al., 2015; Sicardy et al., 2016). Fig. 14 compares the inversions in the contemporaneous radio and stellar occultation measurements. Both profiles have essentially the same vertical gradient in the interval where the temperature increases from 80 K to 100 K, but the inversion in the REX entry profile appears at a different radius than the one reported by Sicardy et al. (2016). This discrepancy is probably too large to be attributed entirely to the uncertainty in REX radius for the following reason. A downward shift in radius by 5 km at REX entry, which would align the inversions in Fig. 14, would also require an upward shift by 5 km at REX exit, as explained in Section 5. The REX solutions for Pluto’s radius at entry and exit would then differ by 15 km, which seems excessive when compared with other observations of Pluto’s topography (Nimmo et al., 2017, Fig. 3). Alternatively, the discrepancy could arise from uncertainty in the contributions of Pluto and Charon to the stellar occultation light curve. This error source increases the uncertainty in radius within the temperature inversion, where the stellar flux is greatly reduced by atmospheric defocusing (Dias-Oliveira et al., 2015, Fig. 9). 7.3. Conditions at the surface The lowest sample in both the entry and exit profiles is 1 km above the ground. Downward extrapolation yields a surface pressure of 12.8 ± 0.7 microbar at REX entry, where the temperature in the cold boundary layer is 38.9 ± 2.1 K. These conditions are compatible with a surface composed of N2 ice, which would have a temperature of 37.1 K to maintain vapor pressure equilibrium (Fray and Schmitt, 2009). At exit, downward extrapolation yields a surface pressure of 10.2 ± 0.7 microbar and a much warmer temperature adjacent to the surface, 51.6 ± 3.8 K, suggesting that the surface in the vicinity of the exit observation is devoid of N2 ice. (We extrapolated the temperature with a quadratic polynomial fitted to the bottom three samples of the exit profile in Fig. 15B.) Below ∼1215 km, the atmospheric structure is strongly influenced by Pluto’s surface, resulting in a temperature inversion that connects the relatively warm upper atmosphere with the much colder surface. The difference in the surface temperature at entry and exit leads to a stronger inversion where the surface is colder, at REX entry, as shown in Fig. 15. The temperature gradient within

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the inversion is also influenced by surface elevation and by the presence of a cold boundary layer at REX entry. REX has obtained the first direct measurements of surface pressure on Pluto. There is a significant difference between the results at entry (12.8 ± 0.7 microbar) and exit (10.2 ± 0.7 microbar), a consequence of the 5 km difference in radius at the two locations. (The pressure scale height is 23 km at 48 K, the mean of the temperatures 1 km above the surface at entry and exit.) The best pressure reference is the average of the results at entry and exit: 11.5 ± 0.7 microbar at 1189.9 ± 0.2 km. Although averaging greatly reduces the uncertainty in radius, as discussed in Section 5, it does not change the uncertainty in pressure. The profiles at entry and exit are constrained to be the same above 1220 km, and this causes a strong correlation between the uncertainties in surface pressure at the two locations. Previous estimates of surface pressure relied on an atmospheric model to bridge the gap between the bottom of a stellar occultation profile and the surface. For example, Lellouch et al. (2009) constrained the allowable range of surface pressure to 6.5– 24 microbar, but the accuracy was limited by large uncertainties in Pluto’s radius and the structure of the lower atmosphere. (See Lellouch et al. (2015) for further discussion.) After New Horizons had determined the radius (Stern et al., 2015), Sicardy et al. (2016) were able to reduce the range to 11.9–13.7 microbar (at 1187 km). The REX measurements have further improved the solution for surface pressure by determining both the structure of the lower atmosphere and the local radius of Pluto. 7.4. The cold boundary layer The REX entry profile is on the southeast margin of SP (Fig. 1), an enormous topographic basin that contains kilometer-deep deposits of N2 ice (Grundy et al., 2016; McKinnon et al., 2016). The elevation of its smooth bright surface, which covers ∼5% of Pluto, is 2–3 km below the surrounding terrain (Moore et al., 2016; McKinnon et al., 2016), as shown in Fig. 17. By performing numerical simulations with a Pluto Global Climate Model (GCM) Forget et al. (2017) have shown that the diurnal cycle of N2 sublimation and condensation within SP can produce a cold boundary layer like the one in the REX entry profile. Their main conclusions can be summarized as follows. A significant amount of N2 is cycled diurnally between the surface and the atmosphere, with sublimation occurring when the icy surface is illuminated by sunlight and condensation occurring at night. The local time on Pluto at REX entry was near sunset, at the end of the sublimation phase of this diurnal cycle, when the cold boundary layer has reached its maximum depth (1.5 km in the simulation as compared with 3.5 km in the observation). Surface topography plays a crucial role in the formation of the boundary layer — the cold dense air released by daytime sublimation in SP is partially confined by the surrounding elevated terrain. This physical confinement is reinforced by steady katabatic winds flowing into SP. In the GCM simulations the cold boundary layer is most prominent around sunset, at the end of daytime sublimation (Forget et al., 2017). Nighttime condensation causes it to vanish by sunrise, when it is superseded by a temperature inversion that reaches the surface. This dependence on local time by itself is sufficient to account for the absence of a cold boundary layer at occultation exit, where REX sounded the atmosphere at sunrise near the center of the Charon-facing hemisphere (Table 3). The conditions at REX entry differ in two respects from those used in the GCM simulation of the N2 condensation-sublimation cycle. First, the topography of the SP basin is more complex than the representation used in the model, which consists of a 3800m-deep circular crater extending from the equator to about 45°N. Second, to compensate for this simplified topography, the diurnal

Fig. 17. Topography of Sputnik Planitia and its surroundings. The elevation ranges from −3.0 to +1.5 km, as indicated by color shading. The zero reference is 1188.3 ± 1.6 km (Nimmo et al., 2017). The elevation at occultation entry (orange dot) is −1.8 km, corresponding to a radius of 1186.5 ± 1.6 km. This digital elevation model was constructed from stereo images acquired by New Horizons (Moore et al., 2016; McKinnon et al., 2016). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

cycle within the SP basin was analyzed at 7.5°N, much closer to the sub-solar latitude than REX entry at 17.0°S. (The sub-solar latitude was 51.6°N at the time of the REX observation.) We take a closer look at these two issues in the remainder of this section. Fig. 17 puts the entry observation into context with SP and the local topography of Pluto. The SP basin extends from about 50°N to 25°S; its shape is circular in the north but narrower and elongated toward the south. Occultation entry occurred near an irregular boundary between smooth, ice-rich surface to the west and rougher, ice-free surface to the east (Grundy et al., 2016). Most important, the elevation at entry is low enough, −1.8 km, to expose the local atmosphere to the diurnal cycle of N2 sublimation and condensation within SP. We examined the latitude dependence of the diurnal cycle in SP by applying a simple energy balance model to a surface covered with N2 ice. The surface absorbs sunlight and emits thermal radiation, and the net radiation is balanced predominantly by latent heating (Young, 2012). We adopted an albedo of 0.67 and an emissivity of 0.85 for these calculations, as in Forget et al. (2017). At a given location in SP, energy is lost at night but gained during most of the day, when the elevation of the Sun is sufficient to overcome thermal emission. With the assumption that the net radiation is balanced entirely by latent heating, it is simple to calculate the rates of sublimation and condensation. For example, at 20°N, near the center of SP, daytime sublimation releases +0.2 kg m−2 of N2 into the atmosphere and nighttime condensation reclaims about half of that amount, for a net sublimation of +0.1 kg m−2 per Pluto day. For comparison, the cold boundary layer in the REX entry profile has a mass of ∼0.3 kg m−2 . At the time of the REX observation sunlight delivered 1.26 W m−2 to Pluto, far exceeding the thermal emission from N2 ice of

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Table 7 Characteristics of Pluto and its atmosphere.

Measurement location Pluto’s radius, km Surface pressure, microbar Temperature near surfacea , K dT/dr near surfaceb , K km−1 Maximum temperature, K

Entry

Exit

193.5°E, 17.0°S 1187.4 ± 3.6 12.8 ± 0.7 38.9 ± 2.1 −0.5 ± 0.7 107 ± 6 (at 1215 km)

15.7°E, 15.1°N 1192.4 ± 3.6 10.2 ± 0.7 51.6 ± 3.8 +4.7 ± 0.9 106 ± 6 (at 1220 km)

Combined Reference pressure Pressure at 1215 km dT/dr at 1220–1300 km

11.5 ± 0.7 microbar at 1189.9 ± 0.2 km 5.9 ± 0.6 microbar −0.14 K km−1

Notes: (a) At entry this is the average temperature in the cold boundary layer (the lowest three samples in the profile); at exit this is the downward extrapolation of the profile to the surface. (b) Computed from the bottom pair of samples in each profile.

less than 0.1 W m−2 , so that sublimation occurs during part of the day throughout SP, even at the REX entry latitude in the southern hemisphere. However, daytime sublimation at 17°S releases less than +0.1 kg m−2 of N2 into the atmosphere. As this local source is not sufficient to fill the cold boundary layer in the REX entry profile, we suspect that horizontal transport is required to explain the observation. When averaged over a Pluto day there is net sublimation north of the equator (more than +0.3 kg m−2 at 45°N) and net condensation to the south. This drives southward atmospheric flow within the SP basin — guided by the surrounding highlands and katabatic winds — toward the REX entry latitude, as noted by Forget et al. (2017). Hence, southward transport of cold N2 may be responsible for the presence of the relatively deep boundary layer observed at the southeast margin of SP. 8. Conclusions Our main results are summarized in Table 7. The radio occultation measurements of Pluto’s tenuous atmosphere required a novel implementation (Section 2). Signals were transmitted from Earth by four antennas of the DSN, one pair in California and a second pair in Australia. The four signals were received by New Horizons, split into pairs, and processed by two independent REX instruments, each referenced to a different USO. After the complete data set had been received on the ground, we calibrated each signal separately (Section 4) and then averaged the resulting phase profiles (Section 6.1). This approach improves the sensitivity to Pluto’s atmosphere (Figs. 8 and 9). We also characterized the measurement noise and demonstrated the level of consistency among the four signals by differencing appropriate pairs of phase profiles. Measurements at entry and exit agree closely in the upper atmosphere (r > 1215 km) but differ markedly at lower altitudes. We determined the local radius of Pluto from measurements of signal amplitude (Fig. 4 and Section 5). Table 7 lists the results at entry and exit as well as the mean value. In a nearly diametric occultation we know the length of the chord across Pluto much better than the radius at either end, which accounts for the much smaller uncertainty in the average radius. The result at entry is consistent with the value at the same location derived from stereo images (Fig. 17). We retrieved a pair of atmospheric profiles — n, p, and T versus altitude and radius — on opposite sides of Pluto (Tables 5 and 6, Figs. 10, 11, 12). In the upper atmosphere (r > 1215 km) the profiles are consistent with results derived from Earth-based stellar occultation measurements. The REX profiles are the first to reach the surface, providing definitive measurements of the temperature structure in the lower atmosphere (Figs. 12, 15, and 16) and the pressure at the surface. The observations also led to the discov-

ery of a cold boundary layer above Sputnik Planitia, which is attributed to the diurnal cycling of N2 between the surface and the atmosphere. Table 7 lists the surface pressures at entry and exit; their mean value is the best pressure reference. Stated in another way, the mass of the atmospheric column at occultation entry is ∼2.4 kg m−2 , as obtained by integrating the density profile in Fig. 10. Assuming a density of 1030 kg m−3 for solid N2 (Trowbridge et al., 2016), this is equivalent to a layer of N2 ice with a thickness of only 2.3 mm. For comparison, the reservoir of N2 ice in SP would have a depth of order 100 m if distributed uniformly across Pluto (McKinnon et al., 2016). Acknowledgments We are indebted to the New Horizons Project Team at the Southwest Research Institute (SwRI) and the Johns Hopkins University Applied Physics Laboratory (APL) for shepherding the mission from proposal to Pluto and beyond; to the highly capable personnel of the NASA Deep Space Network (DSN) for their flawless operation of the ground equipment used in the REX measurements; to Ann Harch (Cornell University) for detailed design of the spacecraft sequence that implemented the REX observations; to Michael Vincent (SwRI) for management of REX Team activities; to Becca Sepan (APL) for coordination of REX real-time operations; to Aseel Anabtawi, Kamal Oudrhiri, and Sami Asmar of the Radio Science Systems Group at the Jet Propulsion Laboratory for real-time monitoring of the DSN equipment used in the REX observations; to Joe Peterson (SwRI) for maintaining the project archive of REX data on the ground and for assistance with cruise phase debugging of the REX data records; to Frédéric Pelletier of the New Horizons Navigation Team (KinetX Aerospace) for providing the error analysis of the trajectory reconstruction; to Bob Jensen (APL) for monitoring the frequency drift of the USOs; and to Bruno Sicardy, François Forget, and Tanguy Bertrand for informative discussions about Pluto’s atmosphere. Funding for this work was provided by the NASA New Horizons Mission. References Achtermann, H.J., Magnus, G., Bose, T.K., 1991. Refractivity virial coefficients of gaseous CH4, C2H4, C2H6, CO2, SF6, H2, N2, He, and Ar. J. Chem. Phys. 94, 5669–5684. doi:10.1063/1.460478. Allan, D.W., 1966. Statistics of atomic frequency standards. IEEE Proc. 54. doi:10. 1109/PROC.1966.4634. Asmar, S.W., Armstrong, J.W., Iess, L., Tortora, P., 2005. Spacecraft doppler tracking: noise budget and accuracy achievable in precision radio science observations. Radio Sci. 40, RS2001. doi:10.1029/2004RS003101. Born, M., Wolf, E., 1999. Principles of Optics. Cambridge University Press, Cambridge. Bosh, A.S., et al., 2015. The state of Pluto’s atmosphere in 2012–2013. Icarus 246, 237–246. doi:10.1016/j.icarus.2014.03.048. Bracewell, R.N., 1986. The Fourier Transform and its Applications. McGraw-Hill, New York. Brandt, S., 1989. Statistical and Computational Methods in Data Analysis. Amsterdam: North-Holland, 1976, 2nd rev. ed., 5th repr. 1989. Cheng, A.F., et al., 2008. Long-Range Reconnaissance Imager on New Horizons. Space Sci. Rev. 140, 189–215. doi:10.10 07/s11214-0 07- 9271- 6. 0709.4278. Dias-Oliveira, A., et al., 2015. Pluto’s atmosphere from stellar occultations in 2012 and 2013. Astrophys. J. 811, 53. doi:10.1088/0 0 04-637X/811/1/53. 1506.08173. Elliot, J.L., et al., 2003. The recent expansion of Pluto’s atmosphere. Nature 424, 165–168. Elliot, J.L., Dunham, E.W., Bosh, A.S., Slivan, S.M., Young, L.A., Wasserman, L.H., Millis, R.L., 1989. Pluto’s atmosphere. Icarus 77, 148–170. doi:10.1016/ 0 019-1035(89)90 014-6. Essen, L., Froome, K.D., 1951. The refractive indices and dielectric constants of air and its principal constituents at 24,0 0 0 Mc/s. Proc. Phys. Soc. B 64, 862–875. doi:10.1088/0370-1301/64/10/303. Forget, F., Bertrand, T., Vangvichith, M., Leconte, J., Millour, E., Lellouch, E., 2017. A post-New Horizons global climate model of Pluto including the N2 , CH4 and CO cycles. Icarus 287, 54–71. doi:10.1016/j.icarus.2016.11.038. Fountain, G.H., et al., 2008. The New Horizons spacecraft. Space Sci. Rev. 140, 23–47. doi:10.10 07/s11214-0 08-9374-8. 0709.4288. Fray, N., Schmitt, B., 2009. Sublimation of ices of astrophysical interest: a bibliographic review. Planet. Space Sci. 57, 2053–2080. doi:10.1016/j.pss.2009.09.011.

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