Radio occultation measurements of Pluto•s neutral ... · PDF fileRadio occultation...

Icarus 290 (2017) 96–111

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Icarus

journal homepage: www.elsevier.com/locate/icarus

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 b 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

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

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 ref-

erenced 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 at-

mosphere, 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 inver-

sion 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 N 2 . 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 N 2 ice in SP,

the local time of the RO observation, and confinement within SP by the surrounding topography and

∗ 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.


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D.P. Hinson et al. / Icarus 290 (2017) 96–111 97

katabatic winds. We have also

exit. The best pressure referenc

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. Introduction

Pluto’s atmosphere was discovered in a stellar occultation ob-

erved from Earth in 1988 ( Hubbard et al., 1988; Elliot et al., 1989 ).

his technique has proved to be remarkably effective at Pluto,

nd numerous subsequent observations — several acquired as New

orizons was en route to Pluto — have revealed important charac-

eristics of its atmosphere. There has been a roughly threefold in-

rease in the total mass of the atmosphere between 1988 and 2015

Elliot et al., 2003; Sicardy et al., 2003; Dias-Oliveira et al., 2015;

lkin et al., 2015; Sicardy et al., 2016 ). Atmospheric waves have

een detected, most notably in the stellar occultation of March

007 ( Person et al., 2008; McCarthy et al., 2008; Hubbard et al.,

009 ). A consistent picture has emerged for the temperature struc-

ure at about 120 0–140 0 km radius ( Sicardy et al., 2003; Young

t al., 2008a; Dias-Oliveira et al., 2015; Bosh et al., 2015; Sicardy

t al., 2016 ). But the stellar occultations do not reach the surface,

eaving substantial uncertainties about the temperature structure

f the lower atmosphere, Pluto’s radius, and the pressure at the

urface ( Lellouch et al., 2009; 2015 ).

New Horizons was equipped to answer these questions through

adio occultation sounding of Pluto’s atmosphere ( Tyler et al.,

0 08; Young et al., 20 08b ). This type of observation has the same

hysical basis as a stellar occultation: both measure the response

f electromagnetic waves to the vertical gradient of refractive in-

ex in the occulting atmosphere. However, the sensitivity of the

adio and stellar observations differs for two reasons. First, the

ormer measures the atmospheric phase delay while the latter

easures the change in signal intensity from defocusing. Second,

he range to Pluto is ∼10 5 times smaller for the radio observa-

ion. For these reasons, stellar occultations are most accurate at

1290 km radius (the half light level in Pluto’s atmosphere),

hereas the radio occultation is most accurate below 1215 km ra-

ius, within 25 km of the surface. This allowed New Horizons to

btain the first profiles of Pluto’s atmosphere that extend all the

ay to the ground and the first direct measure of surface pressure

Gladstone et al., 2016 ).

Gladstone et al. (2016) derived preliminary radio occultation

rofiles by applying a provisional method of analysis to a sub-

et of the observations. This paper reports improved results ob-

ained through comprehensive analysis of the entire radio occulta-

ion data set. Through innovative use of multiple signals, we ex-

and the vertical range of the atmospheric profiles, resolve the

tructure of the cold boundary layer adjacent to the surface in

putnik Planitia, and derive more accurate solutions for the sur-

ace pressure. The instrumentation, operations, and methodology

re explained in far greater detail than was possible in the brief

nitial report. We also provide a more extensive discussion of the

esults and their significance.

This paper considers only the neutral atmosphere. Pluto’s iono-

phere will be the subject of a separate paper; it has eluded detec-

ion in the analysis to date.

The paper is organized as follows. Section 2 describes the im-

lementation of the experiment. Section 3 characterizes the ob-

erving geometry. Section 4 gives a detailed discussion of data

alibration. Section 5 reports measurements of Pluto’s radius.

ection 6 explains the procedure used to retrieve the atmospheric

rofiles. The results are interpreted and compared with stellar oc-

determined the surface pressure and the local radius at both entry and

e is the mean value: 11.5 ± 0.7 microbar at 1189.9 ± 0.2 km.

© 2017 Elsevier Inc. All rights reserved.

ultation measurements in Section 7 . The paper closes with a brief

ummary in Section 8 .

. Instrumentation and operations

This section describes the configuration and operation of the

round and spacecraft equipment as well as the characteristics of

he data recorded on the spacecraft.

.1. Ground equipment and operations

The radio occultation was performed with signals transmitted

imultaneously by four antennas of the NASA Deep Space Network

DSN), as summarized in Table 1 . The uplink array comprised two

ntennas at the Goldstone complex in California, with diameters

f 70 m and 34 m, and an identical pair at the Canberra com-

lex in Australia. Each antenna radiated 20 kW without modula-

ion at a frequency of ∼7.18 GHz, corresponding to a wavelength

f ∼4.17 cm. A single hydrogen maser served as the frequency

eference at each DSN complex. Its stability, as expressed by the

llan deviation ( Allan, 1966 ), is about 3 × 10 −14 at an integration

ime of 10 s. One 70-m antenna transmitted right circular polar-

zation (RCP) and the other transmitted left circular polarization

LCP), while each 34-m antenna transmitted the opposite polariza-

ion as the 70-m antenna at the same complex.

The timing of the flyby was constrained to ensure that Pluto

as more than 15 ° above the horizon at the DSN complexes in

oth California and Australia throughout the observation ( Guo and

arquhar, 2008 ), thereby avoiding reliance on a single complex and

mproving the chances of a successful observation.

.2. Spacecraft equipment and operations

The spacecraft telecommunications system comprises a 2.1-m

iameter high gain antenna (HGA) and two independent radio re-

eivers ( Fountain et al., 2008 ). Each receiver includes a special-

zed radio science signal processor (or REX for short) as well as an

ltra-stable oscillator (USO) that provides the frequency reference

equired for precise radio occultation measurements ( Tyler et al.,

008 ). The two REX signal processors and their respective USOs

re designated as units A and B. Table 2 lists characteristics of the

SOs.

The spacecraft remained in a non-spinning “three axis inertial”

tate with the HGA pointed toward Earth throughout the observa-

ion. The radio signals transmitted by the DSN were received by

he HGA and split into pairs with the same polarization. Each pair

f signals was processed independently, with the RCP signals go-

ng to REX-A (USO-A) and the LCP signals going to REX-B (USO-B).

ee Tyler et al. (2008) for further discussion of the design of the

EX signal processors and their interface with the telecommunica-

ions system. In summary, each DSN complex transmitted signals

o both REXs, so that each REX received signals from both com-

lexes. As we show in Section 6.1 , the availability of multiple sig-

als that cross-link the two DSN complexes with the two REX in-

truments not only improves the sensitivity of the measurements

ut also yields an empirical estimate for their accuracy.

Both REX signal processors include a narrow band channel used

or recording occultation data ( Tyler et al., 2008 ). Its operation can

e summarized as follows. REX-A uses USO-A as a local oscillator

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

Table 1

Configuration of the DSN antennas.

Location Antenna Diameter Polarization a Frequency offset b

(m) (Hz)

Goldstone, California DSS 14 70 LCP + 486

Goldstone, California DSS 24 34 RCP −110

Canberra, Australia DSS 43 70 RCP + 100

Canberra, Australia DSS 34 34 LCP + 276

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 REX-

A, 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 Frequency shift a Allan deviation b

(MHz) (parts per billion) at τ = 10 s

USO-A 30 −25 . 859 1.0 × 10 −13

USO-B 30 +27 . 866 1.5 × 10 −13

Notes: (a) The frequency shift accounts for aging of the USOs during the 10-

year journey to Pluto but excludes the contribution from relativistic time

dilation. (b) The Allan deviation was measured at the Johns Hopkins Uni-

versity Applied Physics Laboratory; τ is the integration time.

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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 re-

lated as follows:

f lo = f uso × 1158703 / 4840 , (1)

and

f b = f hga − f lo . (2)

Here f uso is the frequency of the USO (including a correction for

in-flight aging as specified in Table 2 ), f lo is the frequency of the

local oscillator, f hga is the frequency of the signal arriving at the

HGA, and f b is the frequency of the “baseband” signal. Both f hga

and f lo have values of about 7.18 GHz, f uso is about 30 MHz, and

the magnitude of f b 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 ( f hga = f lo and f b = 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” compo-

nent 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 s b ( 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 f hga and re-

mained at a nearly fixed frequency f b 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 up-

link arrived with an offset of about +100 Hz from band center of

the anti-aliasing filter, while the 34-m uplink arrived with an off-

set of about -110 Hz. Owing to normal aging of the USOs during

their 10-year journey to Pluto, f lo for REX-B exceeded f lo for REX-A

by 386 Hz at the time of the flyby.

The polarization of the signals transmitted by the DSN is not

erfectly circular, and the RCP and LCP receivers on the spacecraft

re not perfectly isolated from one another, which caused each REX

o receive a small fraction ( < 1%) of the energy intended for the

ther REX. However, the offsets in Table 1 ensured that the four

ignals arrived at the spacecraft with distinctly different frequen-

ies, so that they remained safely separated from one another.

. Geometry

The occultation of New Horizons by Pluto was nearly diametric

s viewed from Earth. The measurements at entry sounded the at-

osphere near the center of the anti-Charon hemisphere, on the

outheast margin of a region known informally as Sputnik Plani-

ia (SP), as shown in Fig. 1 . The measurements at exit sounded the

tmosphere near the center of the Charon-facing hemisphere.

Table 3 summarizes the event timing, the local conditions at

ntry and exit, and the geometry of the observations. The Earth-

o-spacecraft distance was 31.9 AU and the spacecraft was receding

rom Earth at a rate of ∼18 km s −1 .

The signals from the four DSN antennas traveled along differ-

nt paths to New Horizons. For example, the paths from the two

0-m antennas were separated by about 10 4 km at Earth, corre-

ponding to the distance between the DSN complexes in California

nd Australia, but had converged to within 120 m as they traversed

luto’s atmosphere. The ray path separation within the atmosphere

s less than 1% of the pressure scale height (see Section 6 ), too

mall to cause appreciable differences among the four sets of mea-

urements.

The observation was performed near solar opposition, so as to

inimize interference from plasma in the solar wind. The angle

etween the Sun and Pluto as viewed from Earth was 172 °. At the

avelength of these measurements the solar wind is almost cer-

ainly undetectable in this geometry ( Asmar et al., 2005 ).

. Data reduction on the ground

By February 2016 all REX data from the Pluto occultation had

een delivered to Earth via spacecraft telemetry. This section de-

cribes the method used for frequency calibration and explains

ow diffraction effects are removed from the data. These two steps

f analysis were applied separately to each of the four radio signals

eceived by New Horizons. Readers not interested in a detailed dis-

ussion of these topics can proceed to Section 5 .

.1. Frequency calibration

We used a digital filter to reduce the bandwidth of the REX data

y a factor of 16, to ∼76 Hz, aligning the filter so that the signal

f interest is at the center of the pass band. The filter completely

liminates the other three signals received by the spacecraft, which

ie well outside the pass band. With this reduction in bandwidth

he sample spacing increases proportionately, from 0.8192 ms to

3.1072 ms.


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.

Entry Exit

Time at surface a (UTC) 2015-07-14T12:45:15.4 2015-07-14T12:56:29.0

Location on surface b 193.5 °E, 17.0 °S 15.7 °E, 15.1 °N

Local true solar time c ,

h

16.52 (sunset) 4.70 (sunrise)

Solar zenith angle 90.2 ° 89.8 °Spacecraft-to-limb

distance d D , km

48,865 57,833

Fresnel scale e F , km 1.43 1.55

Ray path azimuth f 145 ° 216 °Radial speed of ray

path g , km s −1

−3 . 53 +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.

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Fig. 2. Examples of REX measurements. Panels A and B show the power and fre-

quency, 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 trans-

mitted 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 in-

tervals 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.

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After isolating each uplink signal, we derived provisional esti-

ates for signal power and frequency through spectral analysis.

hese are used only to characterize the original data but not for

etrieving atmospheric profiles. Fig. 2 gives an overview of the re-

ults. The occultation of the spacecraft by the solid body lasted

74 s ( Table 3 ), as reflected by the precipitous drop in power in

ig. 2 A. The thermal noise floor during this 674-s interval is ∼10 5

imes smaller than the power in the signal received from DSS 14

t the integration time used here (0.42 s).

Fig. 2 B and C show measurements of the frequency f b , which

xhibit several notable features. The signal transmitted by each

SN antenna has a frequency that varies linearly with time. The

amp rate is adjusted at intervals of a few hundred seconds to

ompensate for the Doppler shift caused by Earth’s rotation, ensur-

ng that f b remains nearly constant. Each change in ramp rate pro-

uces a cusp in f b , and the time variation of f b in the arcs between

he cusps is nearly quadratic. In addition, f b decreases gradually by

2 Hz over the 40 0 0-s span of the observations, a consequence

f uncertainties in the prediction of the spacecraft trajectory that

as used to generate the uplink tuning profiles. Finally, the loca-

ion of the surface is marked by a conspicuous diffraction pattern

see Section 4.2 ), including prominent diffraction “tails” in the fre-

uency measurements that extend into the geometric shadow of

he solid body. This results in a negative Doppler shift at entry and

positive Doppler shift at exit, with Doppler rates of −6 Hz s −1

nd −5 Hz s −1 at entry and exit, respectively. The effect of Pluto’s

tmosphere is barely discernible on the scale of Fig. 2 B and C, and

t is partially obscured by ramp rate changes that occurred near

oth entry ( Fig. 2 C) and exit ( Fig. 2 B).

Effects not associated with Pluto’s atmosphere must be re-

oved from the data. The procedure begins with a formula for the

elativistic Doppler effect ( Schinder et al., 2015 ):

f r / f t =

(1 − ˆ n · v̄ s /c

1 − ˆ n · v̄ d /c

)(1 + 2 U d /c 2 − v 2 d /c 2

1 + 2 U s /c 2 − v 2 s /c 2

)1 / 2

. (3)

ere, f t is the frequency of the signal transmitted by the DSN an-

enna (as observed in its rest frame), f r is the frequency of the sig-

al received by the spacecraft HGA (as observed in its rest frame),

¯ d is the velocity of the DSN antenna, v̄ s is the velocity of the

pacecraft, U d is the gravitational potential of the DSN antenna, U s

s the gravitational potential of the spacecraft, and c is the speed of

ight. We use Solar System barycentric coordinates. The unit vector

ˆ points from the position of the DSN antenna at the time a pho-


U

Fig. 3. Examples of partially calibrated REX data, as obtained through the proce-

dure described in Eqs. (3) , (5) and (7) . The signals shown here were (A) transmit-

ted 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 fre-

quency 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.)

Table 4

Allan deviation of the calibrated REX data at τ = 5 s.

DSN Antenna REX/USO unit Entry baseline Exit baseline

DSS 14 B 1.5 × 10 −13 1.6 × 10 −13

DSS 24 A 2.5 × 10 −13 2.4 × 10 −13

DSS 43 A 2.7 × 10 −13 2.5 × 10 −13

DSS 34 B 2.5 × 10 −13 2.2 × 10 −13

e

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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, f t , v̄ d , and U d are evaluated at the DSN transmit time,

whereas f r , v̄ s , and U s are evaluated at the spacecraft receive time.

The gravitational potential is expressed as

= −GM S /R S − GM E /R E − GM P /R P , (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 f t , ˆ n , v̄ d , v̄ s , U d , and U s , and for

the steady increase in the one-way light time from the DSN an-

tenna 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, ac-

counts 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 v 2 / c 2 account for relativis-

tic time dilation. The change in frequency from the gravitational ef-

fect 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 f r as the deterministic component of f hga . The cor-

responding deterministic phase φr is defined as

φr (t) = 2 π

∫ t

t re f

(f r (t ′ ) − f lo

)dt ′ , (5)

where t is time and t ref 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 a b ( t ) and phase φb ( t ) with each

complex sample s b ( t ) of REX data:

s b (t) = a b (t) · exp [ iφb (t)] , (6)

where i ≡ (−1) 1 / 2 . Each sample of a b and φb includes contribu-

tions 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 s c 1 ( t ) by mixing s b ( t ) with the deterministic phase φr ( t ):

s c1 (t) = s b (t) · exp [ −iφr (t)] = a b (t) · exp [ iφb (t) − iφr (t)] . (7)

This procedure removes the arcs and cusps from the frequency

measurements in Fig. 2 B and C along with other variations in fre-

quency not associated with Pluto and its atmosphere.

Fig. 3 shows two examples of the results from Eq. (7) . The fre-

quency of the partially calibrated signal s c 1 ( 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 ve-

locity, with smaller contributions ( < 10 mHz) from USO drift and

from variations in the phase bias introduced by Earth’s neutral at-

mosphere 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 fre-

quency through spectral analysis of s c 1 , as shown in Fig. 3 . We then

fit a 4th-order polynomial f cal ( t ) to the frequency measurements,

excluding observations close to Pluto where the effects of the neu-

tral atmosphere and diffraction from the surface are appreciable.

(A total of 774 s of data centered on the midpoint of the occul-

tation were excluded from the fit.) We integrated f cal ( t ), as in Eq.

(5) , to obtain the corresponding empirical phase correction φcal ( t ).

Finally, we mixed s c 1 ( t ) with φcal ( t ), as in Eq. (7) , to derive a more

precisely calibrated signal s ( t ).
c 2
Table 4 lists the Allan deviation at an integration time of 5 s for

ach fully calibrated uplink signal s c 2 ( t ). By this metric the most

table signal is the one from DSS 14 to REX-B, but in all cases

he performance is sufficient for accurate measurements of Pluto’s

eutral atmosphere.

.2. Removal of diffraction effects

We used an established procedure to remove diffraction effects

rom the data. This section describes the method and illustrates its

erformance at Pluto.

Figs. 4 and 5 show profiles of amplitude a c 2 and phase φc 2 , re-

pectively, which were obtained directly from the real and imagi-

ary parts of each complex data sample s c 2 , as in Eq. (6) . The alti-

ude scale in these figures corresponds to the distance between the

ay path and the limb of Pluto at each discrete time step; the lo-

ation of the limb is determined from the data as explained below.

t a sample spacing of 13.1 ms, the change in altitude between

uccessive samples is 46.3 m.

The amplitude measurements in Fig. 4 contain a conspicuous

iffraction pattern. It consists of numerous oscillations, or diffrac-

ion fringes, that generally increase in magnitude with decreasing

ltitude above the surface, along with a diffraction tail that extends

nto the geometric shadow of Pluto. Note that the spacecraft-to-

luto distance, about 50,0 0 0 km, was too small for refractive de-

ocusing in the atmosphere to have an appreciable effect on the

bserved amplitude. The impact of defocusing is ∼10 5 smaller in

hese observations than in stellar occultations observed from Earth

t a distance of about 30 AU.


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 ampli-

tude has been normalized by its average value at altitudes of 10–60 km. The sam-

ple 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.)

i

s

s

r

f

f

t

t

w

a

P

a

d

i

d

t

i

t

i

s

a

t

m

n

d

m

a

t

∼

s

t

f

r

c

w

a

A

p

∼

t

t

r

∼

s

P

P

s

c

s

i

n

s

i

t

i

a

c

i

t

t

p

t

n

f

a

t

1

a

l

f

t

We removed the diffraction effects from the REX data by apply-

ng an inverse Fresnel filter ( Marouf et al., 1986 ) to the complex

amples s c 2 ( t ). This technique was first developed to improve the

patial resolution in radio occultation measurements of planetary

ings ( Marouf et al., 1986; Gresh et al., 1989 ). It was later adapted

or use in atmospheric occultations, where it can remove the ef-

ects of diffraction from the surface ( Tyler et al., 1989 ), enhance

he vertical resolution in retrieved profiles of atmospheric struc-

ure ( Karayel and Hinson, 1997 ), and disentangle effects associated

ith multipath propagation ( Hinson et al., 1997; 1998 ). Here we

re concerned only with surface diffraction and vertical resolution;

luto’s atmosphere is too tenuous to cause multipath propagation

t the small spacecraft-to-limb distance of the REX observation.

The Fresnel filter is based on a Huygens–Fresnel formulation for

iffraction of electromagnetic waves ( Born and Wolf, 1999 ). Our

mplementation of the filter accounts for the steady increase in

istance from New Horizons to Pluto during the observation and

he resultant increase in the Fresnel scale F ≡ ( λD ) 1/2 , where λs the wavelength and D is the distance along the ray path be-

ween New Horizons and the point nearest Pluto. For example, F

ncreased from 1.43 km to 1.55 km during the interval when the

pacecraft was occulted by the solid body ( Table 3 ). The filter also

ccounts for the transverse curvature of Pluto’s limb (in the direc-

ion perpendicular to the ray path), but we assume circular sym-

etry so that variations in surface radius along the limb are ig-

ored.

The theoretical foundation for the Fresnel filter is described in

etail by Marouf et al. (1986) and will not be repeated here. It is

ore informative to illustrate its performance empirically. Fig. 4 A

nd B show the diffraction-corrected amplitude profiles at en-

ry and exit, respectively, for a filter with a vertical resolution of

600 m. (The diffraction-corrected phase measurements are

hown in Figs. 5, 8 , and 9 .) The Fresnel filter removes the diffrac-

ion fringes and produces a sharper drop in amplitude at the sur-

ace, providing a more precise indication of its location.

We used the diffraction-corrected amplitude measurements to

egister the REX data with respect to Pluto’s surface. (We defer dis-

ussion of Pluto’s radius to Section 5 .) The limb of Pluto is aligned

ith the location where the amplitude has decreased by 50% ( Born

nd Wolf, 1999 ), equivalent to a 75% reduction in signal power.

ltitude is measured from this reference level in all results re-

orted here. We estimate the 1-sigma uncertainty in altitude to be

200 m, commensurate with the decrease in normalized ampli-

ude from 0.75 to 0.25 within a radial span of ∼400 m. Note that

he Fresnel filter compensates for the small deflection caused by

efractive bending in Pluto’s atmosphere, but its peak value is only

30 m, smaller than the sample spacing and not discernible on the

cale of Fig. 4 .

Fig. 5 illustrates similar aspects of the phase measurements.

rior to removal of diffraction effects, the phase shift caused by

luto’s neutral atmosphere is modulated by diffraction from the

urface, producing an extensive pattern of diffraction fringes. Their

ontribution to the net phase is substantial, particularly near the

urface, where the peak phase shift from the neutral atmosphere

s only ∼5 times larger than the magnitude of the strongest fringe.

Fig. 5 demonstrates the capacity of the Fresnel filter to elimi-

ate the fringes while preserving the effect of Pluto’s neutral atmo-

phere. It performs as expected with one minor exception — there

s a peculiar inflection in the diffraction-corrected phase profile in

he lowest 500 m above the surface. This artifact, which appears

n the phase profiles derived from all four uplink signals, may be

ssociated with the spatial resolution of the Fresnel filter and the

oncomitant, rapid decrease in the diffraction-corrected amplitude

n the same altitude interval ( Fig. 4 A). As we show in Section 6.1 ,

he magnitude of this phase inflection is smaller than the uncer-

ainty of the measurements.

We now take a closer look at the diffraction pattern in the

hase data, which can be isolated by computing the difference be-

ween the profiles in Fig. 5 . This step removes the effect of Pluto’s

eutral atmosphere. Fig. 6 shows the resulting profiles of phase

ringes for the signals from the two 70-m antennas at both entry

nd exit. Note that the observed phase shift from diffraction goes

o zero at the surface in accordance with theory ( Born and Wolf,

999 ). Judging by the results in Figs. 4 , 5 and 6 , the Fresnel filter

ppears to perform well at Pluto.

The arrows in Fig. 6 denote altitudes where phase fringes are

argely absent from the observations at entry. (The amplitude

ringes in Fig. 4 A exhibit the same behavior.) The altitude where

his feature appears is somewhat different in the profiles from


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.

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 mea-

surements (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.

t

h

u

m

a

e

v

e

d

t

m

c

c

—

p

1

R

a

u

P

6

P

fi

a

a

l

6

b

c

a

s

t

o

φ

H

φ

i

a

t

a

m

φ

s

f

s

n

s

b

c

c

φ

DSS 14 and DSS 43, but its presence in both signals points to Pluto

as the source. We suspect that local variations in surface topogra-

phy are producing an interference pattern within the diffracted sig-

nal, 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 interpreta-

tion, 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. 4 A and 5 , respectively.

5. Pluto’s radius

As noted in the preceding section, the diffraction-corrected am-

plitude measurements yield estimates for Pluto’s radius. The re-

sults 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 space-

craft 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 con-

tributes only ∼14 m of uncertainty to the length of the occultation

chord across Pluto.

The uncertainty in radius reflects the possible presence of a sys-

ematic bias in spacecraft position. For the geometry considered

ere — only 33 km from diametric — this sort of error causes an

nderestimate of the radius on one side of Pluto and an overesti-

ate of nearly equal magnitude on the other side. For this reason

bias in spacecraft position of 2.5 km (0.7 sigma), when prop-

rly aligned, would bring the radii at entry and exit to the same

alue. The REX results therefore imply that the radius is larger at

xit than at entry with a probability of 76% (for a standard normal

istribution).

The dominant contribution to the uncertainties in radius at en-

ry and exit can be removed through averaging, which yields a

ean radius of 1189.9 ± 0.2 km. This reduces the impact of un-

ertainty in spacecraft position to 0.1 km — smaller than the un-

ertainty in locating the surface in the amplitude measurements

and provides a better reference for characterizing atmospheric

ressure, as discussed in Section 7.3 .

The REX results are consistent with the global average radius of

188.3 ± 1.6 km (2 sigma) derived from observations by the Long-

ange Reconnaissance Imager ( Nimmo et al., 2017 ). The difference

t exit is relatively large, 4.1 km, but still within the measurement

ncertainties and the large range of topographic relief observed on

luto ( Stern et al., 2015; Moore et al., 2016 ).

. Profiles of the neutral atmosphere

In Section 4 we calibrated the phase data to isolate the effect of

luto’s neutral atmosphere. We now use the results to derive pro-

les of atmospheric structure. This section focuses on the retrieval

lgorithm and the effect of measurement noise. The REX profiles

re interpreted and compared with results from Earth-based stel-

ar occultation measurements in Section 7 .

.1. Phase profiles

The long baselines that preceded and followed the occultation

y Pluto, each with a duration of ∼1500 s, were required for pre-

ise calibration ( Section 4.1 ). However, the effect of Pluto’s neutral

tmosphere is significant only at altitudes below ∼100 km, corre-

ponding to a time span of 28 s, and we now focus on data from

hat interval.

We characterized the structure of Pluto’s neutral atmosphere at

ccultation entry by averaging all available phase data:

a v e (r) =

φ14 (r) + φ24 (r) + φ34 (r) + φ43 (r)

4

. (8)

ere, r is radius, φave is the average phase, and φ14 , φ24 , φ34 , and

43 are the diffraction-corrected phase profiles derived from the

ndividual signals, as in Fig. 5 , with subscripts denoting the source

ntenna at the DSN. The results appear in Fig. 8 . We have omitted

he phase measurements in the lowest 500 m above the surface to

void the artifact discussed in connection with Fig. 5 .

An unknown constant bias is inherent to the type of phase

easurement considered here. We solved for φbias , the bias in

ave ( r ), by fitting a model to the data, as explained later in this

ection in connection with Eq. (12) . This bias has been removed

rom the phase measurements in Fig. 8 (and Fig. 9 below). As we

how in Section 6.2 , φbias has no effect on the retrieved profiles of

umber density, pressure, and temperature.

The phase measurements are affected by noise from several

ources, which can be characterized by computing the difference

etween appropriate pairs of signals. For example, the following

ombination isolates the noise caused by equipment on the space-

raft φsc ( r ):

sc (r) =

[ φ14 (r) − φ24 (r)] + [ φ34 (r) − φ43 (r)] . (9)

4


Fig. 8. Diffraction-corrected phase measurements at entry, showing the phase shift

caused by Pluto’s neutral atmosphere. The black curve shows φa v e (r) − φbias , the av-

erage 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 φave , 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.)

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 explana-

tion. 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.

E

i

e

a

t

D

n

c

f

p

t

d

f

t

φ

E

o

s

t

s

a

c

l

σ

T

F

t

s

i

P

t

σ

b

(

t

a

d

t

s

t

w

s

φ

H

e

p

c

fi

s

p

(

i

l

W

0

o

p

p

a

m

t

|a

A

ach term in brackets is the difference between signals that orig-

nated from the same DSN complex but were received by differ-

nt REXs. This combination removes the effect of Pluto’s neutral

tmosphere and also largely eliminates the “telluric” contribution

o the noise. The latter comprises not only noise associated with

SN equipment but also any variations in phase caused by Earth’s

eutral atmosphere and ionosphere within this 28-s interval. (The

ancellation of the atmospheric and ionospheric effects is imper-

ect owing to the separation of the ground antennas, 9.6 km for the

air in California and 0.4 km for the pair in Australia.) Fig. 8 shows

he resulting profile of φsc ( r ) (orange curve), which has a standard

eviation σ sc of 0.047 rad. The largest contribution probably comes

rom the spacecraft USOs.

Conversely, the following combination of phase data isolates the

elluric noise φtel ( r ):

tel (r) =

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

4

. (10)

ach term in brackets is now the difference between signals that

riginated from different DSN complexes but were received by the

ame REX. This combination removes the effects of Pluto’s neu-

ral atmosphere as well as noise introduced by equipment on the

pacecraft. The resulting profile of φtel ( r ) (blue curve) in Fig. 8 has

standard deviation σ tel of 0.018 rad.

Finally, we obtained an estimate for the net phase noise σφ by

ombining the contributions from spacecraft equipment and tel-

uric effects:

φ = (σ 2 sc + σ 2

tel ) 1 / 2 . (11)

he value of σφ at entry is 0.050 rad, as shown by gray shading in

ig. 8 . This is 25 times smaller than the phase shift at the base of

he profile. As the differences among the four signals are relatively

mall within this segment of data, we decided to use equal weights

n computing φave in Eq. (8) .

We used the same procedure to characterize the structure of

luto’s atmosphere and the measurement uncertainty at occulta-

ion exit. Fig. 9 shows the results. In this case σ sc is 0.024 rad,

tel is 0.020 rad, and σφ is 0.031 rad. The phase shift at the

ase 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

he difference in radius at the two locations.

The measurements in Figs. 8 and 9 are essentially the same

bove a radius of ∼1215 km, where the standard deviation of the

ifference between the entry and exit profiles is 0.018 rad, smaller

han σφ at both entry and exit. In characterizing the atmospheric

tructure in this region (henceforth the upper atmosphere) we

herefore averaged the profiles of φave ( r ) from the two locations,

hich reduces the noise and yields more reliable results.

It is instructive to compare the phase measurements with a

imple, two-parameter model for the upper atmosphere:

f it (r) = φo × exp [ −(r − 1187 . 4) /H φ] . (12)

ere, H φ is the scale height and φo is the phase shift at a refer-

nce radius of 1187.4 km (the surface at entry). We averaged the

hase profiles from entry and exit, weighting each by the recipro-

al of its variance σ 2 φ

( Brandt, 1989 ), and then tuned the model to

t the combined observations at 1215–1277 km radius. (The rea-

ons for choosing this radius interval are explained below.) This

rocedure yields least-squares solutions for H φ (61 ± 4 km), φo

−0 . 71 ± 0 . 04 rad), and a third parameter φbias , the constant bias

nherent to measurements of φave ( r ), as mentioned previously fol-

owing Eq. (8) .

The dashed black line in Figs. 8 and 9 shows the best-fit model.

ithin the fitting interval the standard deviation of φa v e − φ f it is

.016 rad at entry and 0.013 rad at exit, well within our estimates

f σφ . Hence, the model is an accurate representation of both

hase profiles at 1215–1277 km radius. Conversely, the measured

hase profiles diverge significantly from the model, and from one

nother, in the lower atmosphere. We examine these differences

ore closely in the next section.

We imposed two constraints in selecting the interval for fitting

he model to the measurements. The first requirement is that

φa v e | > 3 σφ (13)

t both entry and exit, which determines the upper boundary.

bove 1277 km the data are noisy and provide little additional in-


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%.

w

i

u

o

t

p

c

(

s

p

t

t

i

δ

i

i

g

s

p

g

i

(

t

e

e

fl

e

a

t

e

g

r

δ

W

t

t

n

formation. The second requirement is that ∣∣φa v e − φ f it

∣∣ < σφ (14)

at both entry and exit, which determines the lower boundary. Be-

low 1215 km the simple model is inconsistent with the observa-

tions.

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 αbetween the incoming and outgoing segments of the path. In re-

sponse to this deflection the physical length of the path between

Pluto and New Horizons increases by an amount

δ ≈ α2 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 rep-

resent 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 at-

mosphere ( 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

2 π2

∫ ∞

r

dφ(r ′ ) dr ′

dr ′ √

r ′ 2 − r 2 . (16)

As the integrand involves only the radial derivative d φ( r )/ dr , a con-

stant 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 N 2 , which has a

refractive volume κ of 1 . 095 × 10 −29 m

3 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 be-

low.

6.2.2. Occultation entry

We used a composite representation of d φ( r )/ dr to evaluate the

integral in Eq. (16) . This approach is designed to reduce the uncer-

tainties in the retrieved profiles at altitudes below ∼25 km, con-

sistent with the primary objectives of the radio occultation.

For r < 1210 km, d φ/ dr was derived directly from the mea-

surements in Fig. 8 . We divided the data into non-overlapping al-

titude intervals and computed the derivative from a least-squares

linear fit to φave ( r ) within each interval. The sample spacing is con-

strained 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).

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

dφ

dr = −φ f it (r)

H φ, (18)

hich improves the accuracy of the atmospheric profiles by reduc-

ng the effect of stochastic phase noise. We extrapolated the model

pward to 1450 km ( ∼260 km altitude) and truncated integration

f Eq. (16) at this radius. The sample spacing is 5 km throughout

his radial range. In Section 7.1 we assess the validity of this ap-

roach through comparisons with results derived from stellar oc-

ultations.

Fig. 10 shows the profile of number density derived from Eqs.

16) and (17) at occultation entry. The density in the upper atmo-

phere increases gradually from ∼9 × 10 19 m

−3 at the top of the

rofile to ∼5 × 10 20 m

−3 at 1205 km radius. Closer to the surface

he vertical gradient of density is much stronger, as reflected by

he threefold change in density in the layer at 1191–1199 km.

There are two sources of uncertainty in the density profile; one

s stochastic and the other is computational. The stochastic error

n s is a consequence of spacecraft and telluric noise, as discussed

n Section 6.1 . We characterized the standard deviation of δn s and

ts variation with radius through the following procedure. First, we

enerated a set of phase noise profiles by applying Eq. (8) to mea-

urements from 50 non-overlapping intervals in the baselines that

receded and followed the occultation by Pluto. We then propa-

ated each realization of noise through the full retrieval algorithm,

ncluding the solution for φfit ( r ), to determine its effect on n ( r ).

We increased the sample size by performing additional calcula-

ions using simulated phase noise with the same statistical prop-

rties as the measurements.) The simulated retrievals include the

ffect of the Fresnel filter, which changes the statistics of the noise

uctuations on scales comparable to the Fresnel scale ( Marouf

t al., 1986 ). Our error analysis indicates that the standard devi-

tion of δn s increases from 1.5 × 10 19 m

−3 at the top of the profile

o 3.5 × 10 19 m

−3 at the bottom. These correspond to fractional

rrors in n ( r ) of 16% and 1.5%, respectively.

The computational error δn c arises from ending numerical inte-

ration of Eq. (16) at a finite radius r t . From Eqs. (16) and (17) , the

esulting error is

n c (r) =

λ

2 κ π2

∫ ∞

r t

dφ(r ′ ) dr ′

dr ′ √

r ′ 2 − r 2 <

λ

2 κ π2

| φ(r t ) | √

r 2 t − r 2 . (19)

e set r t to 1450 km, as noted above, which reduces δn c ( r ) to less

han 3 × 10 18 m

−3 throughout the radial range in Fig. 10 , ensuring

hat δn c is considerably smaller than δn s . The net uncertainty in

( r ) from these two sources is shown by shading in Fig. 10 .


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

r

w

p

t

1

t

d

6

a

H

t

a

(

l

n

a

t

T

i

T

I

r

c

2

t

o

F

t

d

b

t

a

(

p

a

o

E

0

T

i

c

a

F

a

a

r

p

p

r

t

u

d

C

i

s

i

T

t

F

a

o

o

s

o

b

c

∼

t

7

l

c

7

w

2

F

t

t

(

s

a

b

c

t

t

t

T

k

t

v

h

.2.3. Occultation exit

We used the same approach, with two minor variations, to de-

ive a number density profile at occultation exit. In this case φfit

as used to compute d φ/ dr for r > 1220 km. Moreover, the sam-

le spacing in the lower part of the profiles is not the same, owing

o differences in the atmospheric structure at entry and exit.

By design, the profiles at entry and exit are identical for r >

220 km. Fig. 11 compares the results over the radial range where

hey differ. The offset between the profiles exceeds the standard

eviation of the measurements for r < 1205 km.

.3. Profiles of pressure and temperature

A profile of pressure versus radius p ( r ) is derived from n ( r ) by

ssuming hydrostatic balance and integrating vertically:

p(r) = n b k T b + m

∫ r b

r

n (r ′ ) GM P

r ′ 2 dr ′ . (20)

ere, k is the Boltzmann constant, and GM P (the standard gravita-

ional parameter of Pluto) is 869.6 km

3 s −2 ( Stern et al., 2015 ). For

pure N 2 atmosphere the molecular mass m is 4 . 652 × 10 −26 kg.

The effect of minor constituents on the value of m is discussed be-

ow.) The pressure profile extends upward to a radius r b , where the

umber density n b is known but the temperature T b is required as

boundary condition. The ideal gas law has been used to express

he first term on the right-hand side of Eq. (20) in terms of n b and

b rather than the pressure p b at the upper boundary.

The temperature profile T ( r ) follows from n ( r ), p ( r ), and the

deal gas law:

(r) =

n b T b n (r)

+

m

n (r) k

∫ r b

r

n (r ′ ) GM P

r ′ 2 dr ′ . (21)

n evaluating Eqs. (20) and (21) , we set T b to 95.5 K at a radius

b of 1302.4 km, as determined from analysis of recent stellar oc-

ultation measurements ( Dias-Oliveira et al., 2015; Sicardy et al.,

016 ).

We used the van der Waals equation to check the validity of

he ideal gas law. Temperatures obtained from the two equations

f state agree to within 10 −4 K throughout Pluto’s atmosphere.

The REX profiles of temperature versus pressure appear in

ig. 12 . The complete atmospheric profiles — n, p , and T versus al-

itude and radius — are listed in Tables 5 and 6 . Section 7 gives a

etailed discussion of the results and their significance.

The accuracy of the pressure and temperature profiles is limited

y stochastic phase noise and by uncertainty in T b . The stochas-

ic errors in p ( r ) and T ( r ) were characterized in the same manner

s for n ( r ), except that the simulated retrievals now include Eqs.

20) and (21) . In assessing the impact of the boundary condition on

( r ) and T ( r ) we assumed that the standard deviation of T b is 7 K,

very conservative estimate based on results from recent stellar

ccultation measurements ( Dias-Oliveira et al., 2015 , Fig. 10). From

q. (20) the error in p ( r ) associated with the uncertainty in T b is

.09 microbar, independent of radius. The corresponding error in

( r ) is inversely proportional to n ( r ), as shown in Eq. (21) , so that

t decreases from 7 K at the top of the profiles to 1.5 K at 6 mi-

robar and less than 1 K at the base of the profiles (0.3 K at entry

nd 0.5 K at exit).

The net uncertainties in n, p , and T are listed in Tables 5 and 6 .

or example, the standard deviations of p and T are 0.69 microbar

nd 2.1 K at the base of the entry profile. The corresponding values

t exit are 0.66 microbar and 3.7 K.

Fig. 13 shows the fractional errors in n, p , and T at entry. The

esults at exit (not shown) are essentially the same. For both n and

the dominant source of uncertainty is stochastic phase noise. The

rimary source of uncertainty in T is stochastic phase noise for

< 1265 km and uncertainty in T b for r > 1265 km. The frac-

ional error in T is ∼6% throughout the radial range of Fig. 13 . The

ncertainties in n and p exceed 16% at the top of the profile but

ecrease to 1.5% and 5.7%, respectively, at the bottom.

The most important minor constituent in Pluto’s atmosphere is

H 4 , with an abundance of ∼0.5% ( Lellouch et al., 2009; 2015 ), but

t has little impact on either κ or m . When the composition is as-

umed to be 99.5% N 2 and 0.5% CH 4 , κ increases by 0.24% from

ts value in a pure N 2 atmosphere, whereas m decreases by 0.21%.

he resulting changes in n ( r ), p ( r ), and T ( r ) are much smaller than

he other sources of uncertainty throughout the vertical range of

ig. 13 . Likewise, Pluto’s atmospheric haze ( Gladstone et al., 2016 )

nd trace constituents such as CO have no appreciable effect on κr m .

The horizontal resolution of the measurements along the line

f sight from Earth to New Horizons is constrained by the limb-

ounding geometry. A radio signal traverses an atmospheric layer

f depth d in a distance L ≈ 2 √

2 r d , where r is the radius at the

ase of the layer. For example, when d is 3.5 km, the depth of the

old 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

he ray path is given in Table 3 .

. Discussion

This section addresses four topics: the upper atmosphere, the

ower atmosphere, conditions at the surface, and the origin of the

old boundary layer in the REX entry profile.

.1. The upper atmosphere ( r > 1215 km)

The amplitude of atmospheric waves on Pluto is less than 1 K

ithin the vertical range of the REX profiles in Fig. 12 ( Young et al.,

0 08a; Person et al., 20 08; McCarthy et al., 20 08; Toigo et al., 2010;

rench et al., 2015; Gladstone et al., 2016; Forget et al., 2017 ). De-

ection of such waves is beyond the capabilities of REX.

Above 1215 km radius ( p < 6 microbar), the temperature struc-

ure is controlled by the radiative properties of CH 4 and CO

Zalucha et al., 2011 ); haze particles may also be a significant

ource of local radiative heating. Apart from weak modulation by

tmospheric waves, the atmosphere in this region is expected to

e horizontally uniform for two reasons. First, the radiative time

onstant is ∼700 Pluto days ( Strobel et al., 1996 ), so that diurnal

emperature variations are small ( Gladstone et al., 2016 ). In addi-

ion, the ratio of the Rossby radius to Pluto’s radius is much larger

han the corresponding ratio on planets such as Earth and Mars.

hat makes it easier to convert atmospheric potential energy into

inetic energy ( Gill, 1982 ), which tends to eliminate any horizontal

emperature gradients, including those that would otherwise de-

elop at the winter pole. Recent stellar occultation measurements

ave confirmed these expectations, showing that any horizontal


Table 5

REX profile at occultation entry.

Altitude Radius n σ n p σ p T σ T

(km) (km) (10 19 m

−3 ) (10 19 m

−3 ) (microbar) (microbar) (K) (K)

115 .0 1302 .4 8 .96 1 .47 1 .182 0 .209 95 .50 7 .00

110 .0 1297 .4 9 .77 1 .53 1 .294 0 .225 95 .89 6 .45

105 .0 1292 .4 10 .65 1 .58 1 .417 0 .242 96 .34 6 .00

100 .0 1287 .4 11 .61 1 .63 1 .552 0 .261 96 .83 5 .65

95 .0 1282 .4 12 .65 1 .68 1 .701 0 .279 97 .37 5 .40

90 .0 1277 .4 13 .79 1 .73 1 .864 0 .299 97 .95 5 .23

85 .0 1272 .4 15 .02 1 .78 2 .043 0 .320 98 .56 5 .13

80 .0 1267 .4 16 .35 1 .82 2 .240 0 .341 99 .20 5 .10

75 .0 1262 .4 17 .81 1 .85 2 .456 0 .363 99 .88 5 .11

70 .0 1257 .4 19 .39 1 .88 2 .693 0 .386 100 .56 5 .17

65 .0 1252 .4 21 .12 1 .90 2 .953 0 .409 101 .28 5 .25

60 .0 1247 .4 22 .99 1 .91 3 .238 0 .434 102 .02 5 .36

55 .0 1242 .4 25 .02 1 .91 3 .551 0 .458 102 .79 5 .49

50 .0 1237 .4 27 .24 1 .89 3 .895 0 .482 103 .57 5 .63

45 .0 1232 .4 29 .65 1 .86 4 .272 0 .506 104 .37 5 .77

40 .0 1227 .4 32 .27 1 .81 4 .686 0 .530 105 .19 5 .92

35 .0 1222 .4 35 .11 1 .74 5 .140 0 .554 106 .02 6 .07

30 .0 1217 .4 38 .21 1 .64 5 .638 0 .576 106 .87 6 .23

25 .0 1212 .4 41 .82 1 .55 6 .186 0 .597 107 .14 6 .37

20 .0 1207 .4 46 .56 1 .59 6 .796 0 .618 105 .72 6 .34

16 .0 1203 .4 51 .86 1 .65 7 .344 0 .633 102 .57 6 .24

12 .0 1199 .4 60 .93 1 .91 7 .976 0 .649 94 .81 5 .91

9 .0 1196 .4 78 .94 2 .23 8 .567 0 .660 78 .61 4 .98

7 .0 1194 .4 110 .62 2 .55 9 .104 0 .667 59 .61 3 .80

5 .3 1192 .7 151 .62 3 .15 9 .737 0 .674 46 .51 2 .92

4 .0 1191 .4 180 .48 3 .47 10 .351 0 .679 41 .54 2 .51

3 .0 1190 .4 202 .28 3 .40 10 .897 0 .683 39 .02 2 .25

2 .0 1189 .4 215 .70 3 .37 11 .493 0 .687 38 .59 2 .13

1 .0 1188 .4 224 .69 3 .46 12 .123 0 .691 39 .08 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 Radius n σ n p σ p T σ T

(km) (km) (10 19 m

−3 ) (10 19 m

−3 ) (microbar) (microbar) (K) (K)

110 .0 1302 .4 8 .96 1 .47 1 .182 0 .209 95 .50 7 .00

105 .0 1297 .4 9 .77 1 .53 1 .294 0 .225 95 .89 6 .45

100 .0 1292 .4 10 .65 1 .58 1 .417 0 .242 96 .34 6 .00

95 .0 1287 .4 11 .61 1 .63 1 .552 0 .261 96 .83 5 .65

90 .0 1282 .4 12 .65 1 .68 1 .701 0 .279 97 .37 5 .40

85 .0 1277 .4 13 .79 1 .73 1 .864 0 .299 97 .95 5 .23

80 .0 1272 .4 15 .02 1 .78 2 .043 0 .320 98 .56 5 .13

75 .0 1267 .4 16 .35 1 .82 2 .240 0 .341 99 .20 5 .10

70 .0 1262 .4 17 .81 1 .85 2 .456 0 .363 99 .88 5 .11

65 .0 1257 .4 19 .39 1 .88 2 .693 0 .386 100 .56 5 .17

60 .0 1252 .4 21 .12 1 .90 2 .953 0 .409 101 .28 5 .25

55 .0 1247 .4 22 .99 1 .91 3 .238 0 .434 102 .02 5 .36

50 .0 1242 .4 25 .02 1 .91 3 .551 0 .458 102 .79 5 .49

45 .0 1237 .4 27 .24 1 .89 3 .895 0 .482 103 .57 5 .63

40 .0 1232 .4 29 .65 1 .86 4 .272 0 .506 104 .37 5 .77

35 .0 1227 .4 32 .27 1 .81 4 .686 0 .530 105 .19 5 .92

30 .0 1222 .4 35 .11 1 .74 5 .140 0 .554 106 .02 6 .07

25 .0 1217 .4 38 .49 1 .65 5 .640 0 .576 106 .12 6 .23

20 .0 1212 .4 43 .11 1 .62 6 .199 0 .597 104 .15 6 .36

16 .0 1208 .4 48 .30 1 .65 6 .703 0 .613 100 .51 6 .34

12 .0 1204 .4 56 .76 1 .73 7 .287 0 .628 92 .98 6 .00

9 .0 1201 .4 65 .64 1 .79 7 .800 0 .638 86 .07 5 .59

7 .0 1199 .4 73 .48 1 .86 8 .191 0 .644 80 .73 5 .25

5 .0 1197 .4 84 .20 2 .03 8 .635 0 .650 74 .28 4 .85

3 .0 1195 .4 99 .72 2 .30 9 .154 0 .657 66 .49 4 .31

1 .0 1193 .4 124 .37 3 .01 9 .789 0 .662 57 .01 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.


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 T b 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 N 2 ( 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.

v

1

t

e

t

a

o

d

o

t

t

t

a

c

t

t

1

−

R

o

p

(

W

s

E

m

t

t

Fig. 14. Comparison of the temperature structure at REX entry with a model de-

rived 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 T b .

(For interpretation of the references to colour in this figure legend, the reader is

referred to the web version of this article.)

7

—

l

m

r

t

m

c

t

c

t

w

a

n

r

i

t

ariations in temperature are no larger than a few kelvin at 1220–

400 km radius ( Dias-Oliveira et al., 2015 , Fig. 10). This explains

he close agreement between the REX phase profiles at entry and

xit for r > 1215 km, despite the differences in location and local

ime.

Sicardy et al. (2016) derived a pressure of 6.94 ± 0.5 microbar

t 1215 km from multi-chord observations of a stellar occultation

n 29 June 2015, only 15 days before the REX measurements. This

iffers from the corresponding REX result, 5.91 ± 0.6 microbar, by

nly 1.0 microbar or ∼2 sigma. Hence, any bias between the two

ypes of observation is probably no larger than ∼0.5 microbar.

Fig. 14 compares the temperature structure at REX entry with

he best-fit model derived by Sicardy et al. (2016) from the con-

emporaneous stellar occultation measurements. Both profiles have

temperature maximum near 1215 km, and the temperature de-

reases steadily with increasing radius between 1215 km and the

op of the REX profile. The two profiles differ by less than 1 sigma

hroughout this interval. The mean temperature gradient at 1220–

300 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

EX solutions for the peak temperature (107 ± 6 K), the radius

f the peak (1215 km), and the temperature gradient above the

eak are also consistent with results from other stellar occultations

Young et al., 2008a; Dias-Oliveira et al., 2015; Bosh et al., 2015 ).

e discuss the atmospheric structure below 1215 km in the next

ection.

The preceding discussion further validates the phase model in

q. (12) , which not only provides a good fit to the REX measure-

ents at 1215–1277 km, as shown in Figs. 8 and 9 , but also cap-

ures basic characteristics of Pluto’s atmosphere that had been de-

ermined previously from stellar occultations.

.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

ower atmosphere and its horizontal variations. These improve-

ents are a consequence of basic differences between stellar and

adio occultation measurements. The lower atmosphere is where

he REX profiles are most reliable, as shown in Fig. 13 , whereas at-

ospheric defocusing greatly reduces the sensitivity of stellar oc-

ultation measurements in this region. (Defocusing is negligible in

he REX observations, as discussed in Section 4.2 .) In the stellar oc-

ultations strong defocusing also causes the motion of the ray path

o become nearly horizontal (e.g., Dias-Oliveira et al., 2015 , Fig. 2),

hich conflates the effects of vertical and horizontal variations in

tmospheric structure, while the motion of the ray path remains

early vertical throughout the REX observation.

Fig. 15 compares the temperature profiles from Fig. 12 over the

adial range where they differ. The REX entry profile has a strong

nversion that ends ∼3.5 km above the surface, and the tempera-

ure at lower altitudes is nearly constant and close to saturation. In


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 N 2 ( 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.)

t

d

r

s

t

n

o

Y

F

s

s

c

fi

e

e

A

a

b

f

w

P

d

P

s

i

d

7

a

s

i

c

t

a

f

a

f

e

t

e

c

c

a

a

the cold boundary layer beneath the inversion the average temper-

ature is 38.9 ± 2.1 K. The temperature structure in the exit profile

is significantly different — the inversion is much weaker and it ex-

tends 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 strati-

fication.

Heat conduction transports thermal energy away from the tem-

perature maximum at ∼1215 km radius. The heat flux F c depends

on both the temperature and its vertical gradient:

F c = −A T d T /d r , (22)

where F c > 0 for an upward heat flux and A is 9 . 37 × 10 −5 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

he inversion ( Fig. 16 ). At exit the downward heat flux is delivered

irectly to the surface, where it is emitted to space as black-body

adiation (along with the far larger energy flux from sunlight ab-

orbed at the surface). At entry the downward heat flux warms

he cold boundary layer, but its contribution to the energy balance

ear the surface is relatively small ( Section 7.4 ).

The temperature inversion in the lower atmosphere has been

bserved repeatedly in stellar occultations ( Sicardy et al., 2003;

oung et al., 2008a; Dias-Oliveira et al., 2015; Sicardy et al., 2016 ).

ig. 14 compares the inversions in the contemporaneous radio and

tellar occultation measurements. Both profiles have essentially the

ame vertical gradient in the interval where the temperature in-

reases from 80 K to 100 K, but the inversion in the REX entry pro-

le appears at a different radius than the one reported by Sicardy

t al. (2016) . This discrepancy is probably too large to be attributed

ntirely to the uncertainty in REX radius for the following reason.

downward shift in radius by 5 km at REX entry, which would

lign the inversions in Fig. 14 , would also require an upward shift

y 5 km at REX exit, as explained in Section 5 . The REX solutions

or Pluto’s radius at entry and exit would then differ by 15 km,

hich seems excessive when compared with other observations of

luto’s topography ( Nimmo et al., 2017 , Fig. 3). Alternatively, the

iscrepancy could arise from uncertainty in the contributions of

luto and Charon to the stellar occultation light curve. This error

ource increases the uncertainty in radius within the temperature

nversion, where the stellar flux is greatly reduced by atmospheric

efocusing ( Dias-Oliveira et al., 2015 , Fig. 9).

.3. Conditions at the surface

The lowest sample in both the entry and exit profiles is 1 km

bove the ground. Downward extrapolation yields a surface pres-

ure of 12.8 ± 0.7 microbar at REX entry, where the temperature

n the cold boundary layer is 38.9 ± 2.1 K. These conditions are

ompatible with a surface composed of N 2 ice, which would have a

emperature of 37.1 K to maintain vapor pressure equilibrium ( Fray

nd Schmitt, 2009 ). At exit, downward extrapolation yields a sur-

ace pressure of 10.2 ± 0.7 microbar and a much warmer temper-

ture adjacent to the surface, 51.6 ± 3.8 K, suggesting that the sur-

ace in the vicinity of the exit observation is devoid of N 2 ice. (We

xtrapolated the temperature with a quadratic polynomial fitted to

he bottom three samples of the exit profile in Fig. 15 B.)

Below ∼1215 km, the atmospheric structure is strongly influ-

nced by Pluto’s surface, resulting in a temperature inversion that

onnects the relatively warm upper atmosphere with the much

older surface. The difference in the surface temperature at entry

nd exit leads to a stronger inversion where the surface is colder,

t REX entry, as shown in Fig. 15 . The temperature gradient within


t

p

s

a

c

(

p

s

±

d

n

e

a

a

m

c

(

2

t

(

z

(

1

t

l

7

a

p

e

i

i

m

n

d

T

c

a

l

c

s

l

a

p

c

c

fi

n

e

w

s

c

w

t

u

c

t

m

S

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.)

c

s

w

l

l

t

g

u

r

p

t

c

S

e

r

t

e

A

m

c

t

t

n

o

a

p

e

m

he inversion is also influenced by surface elevation and by the

resence of a cold boundary layer at REX entry.

REX has obtained the first direct measurements of surface pres-

ure on Pluto. There is a significant difference between the results

t entry (12.8 ± 0.7 microbar) and exit (10.2 ± 0.7 microbar), a

onsequence 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 tem-

eratures 1 km above the surface at entry and exit.) The best pres-

ure 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 re-

uces the uncertainty in radius, as discussed in Section 5 , it does

ot change the uncertainty in pressure. The profiles at entry and

xit are constrained to be the same above 1220 km, and this causes

strong correlation between the uncertainties in surface pressure

t the two locations.

Previous estimates of surface pressure relied on an atmospheric

odel to bridge the gap between the bottom of a stellar oc-

ultation profile and the surface. For example, Lellouch et al.

2009) constrained the allowable range of surface pressure to 6.5–

4 microbar, but the accuracy was limited by large uncertain-

ies in Pluto’s radius and the structure of the lower atmosphere.

See Lellouch et al. (2015) for further discussion.) After New Hori-

ons 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

187 km). The REX measurements have further improved the solu-

ion for surface pressure by determining both the structure of the

ower atmosphere and the local radius of Pluto.

.4. The cold boundary layer

The REX entry profile is on the southeast margin of SP ( Fig. 1 ),

n enormous topographic basin that contains kilometer-deep de-

osits of N 2 ice ( Grundy et al., 2016; McKinnon et al., 2016 ). The

levation of its smooth bright surface, which covers ∼5% of Pluto,

s 2–3 km below the surrounding terrain ( Moore et al., 2016; McK-

nnon et al., 2016 ), as shown in Fig. 17 .

By performing numerical simulations with a Pluto Global Cli-

ate Model (GCM) Forget et al. (2017) have shown that the diur-

al cycle of N 2 sublimation and condensation within SP can pro-

uce a cold boundary layer like the one in the REX entry profile.

heir main conclusions can be summarized as follows. A signifi-

ant amount of N 2 is cycled diurnally between the surface and the

tmosphere, with sublimation occurring when the icy surface is il-

uminated by sunlight and condensation occurring at night. The lo-

al time on Pluto at REX entry was near sunset, at the end of the

ublimation phase of this diurnal cycle, when the cold boundary

ayer has reached its maximum depth (1.5 km in the simulation

s compared with 3.5 km in the observation). Surface topography

lays a crucial role in the formation of the boundary layer — the

old dense air released by daytime sublimation in SP is partially

onfined by the surrounding elevated terrain. This physical con-

nement is reinforced by steady katabatic winds flowing into SP.

In the GCM simulations the cold boundary layer is most promi-

ent around sunset, at the end of daytime sublimation ( Forget

t al., 2017 ). Nighttime condensation causes it to vanish by sunrise,

hen it is superseded by a temperature inversion that reaches the

urface. This dependence on local time by itself is sufficient to ac-

ount for the absence of a cold boundary layer at occultation exit,

here REX sounded the atmosphere at sunrise near the center of

he Charon-facing hemisphere ( Table 3 ).

The conditions at REX entry differ in two respects from those

sed in the GCM simulation of the N 2 condensation-sublimation

ycle. First, the topography of the SP basin is more complex than

he representation used in the model, which consists of a 3800-

-deep circular crater extending from the equator to about 45 °N.

econd, to compensate for this simplified topography, the diurnal

ycle within the SP basin was analyzed at 7.5 °N, much closer to the

ub-solar latitude than REX entry at 17.0 °S. (The sub-solar latitude

as 51.6 °N at the time of the REX observation.) We take a closer

ook at these two issues in the remainder of this section.

Fig. 17 puts the entry observation into context with SP and the

ocal topography of Pluto. The SP basin extends from about 50 °No 25 °S; its shape is circular in the north but narrower and elon-

ated toward the south. Occultation entry occurred near an irreg-

lar boundary between smooth, ice-rich surface to the west and

ougher, ice-free surface to the east ( Grundy et al., 2016 ). Most im-

ortant, the elevation at entry is low enough, −1 . 8 km, to expose

he local atmosphere to the diurnal cycle of N 2 sublimation and

ondensation within SP.

We examined the latitude dependence of the diurnal cycle in

P by applying a simple energy balance model to a surface cov-

red with N 2 ice. The surface absorbs sunlight and emits thermal

adiation, and the net radiation is balanced predominantly by la-

ent heating ( Young, 2012 ). We adopted an albedo of 0.67 and an

missivity of 0.85 for these calculations, as in Forget et al. (2017) .

t a given location in SP, energy is lost at night but gained during

ost of the day, when the elevation of the Sun is sufficient to over-

ome thermal emission. With the assumption that the net radia-

ion is balanced entirely by latent heating, it is simple to calculate

he rates of sublimation and condensation. For example, at 20 °N,

ear the center of SP, daytime sublimation releases +0 . 2 kg m

−2

f N 2 into the atmosphere and nighttime condensation reclaims

bout half of that amount, for a net sublimation of +0 . 1 kg m

−2

er Pluto day. For comparison, the cold boundary layer in the REX

ntry profile has a mass of ∼0.3 kg m

−2 .

At the time of the REX observation sunlight delivered 1.26 W

−2 to Pluto, far exceeding the thermal emission from N ice of
2


Table 7

Characteristics of Pluto and its atmosphere.

Entry Exit

Measurement location 193.5 °E, 17.0 °S 15.7 °E, 15.1 °N

Pluto’s radius, km 1187.4 ± 3.6 1192.4 ± 3.6

Surface pressure, microbar 12.8 ± 0.7 10.2 ± 0.7

Temperature near surface a , K 38.9 ± 2.1 51.6 ± 3.8

dT / dr near surface b , K km

−1 −0 . 5 ± 0 . 7 +4 . 7 ± 0 . 9

Maximum temperature, K 107 ± 6 (at 1215 km) 106 ± 6 (at 1220 km)

Combined

Reference pressure 11.5 ± 0.7 microbar at 1189.9 ± 0.2 km

Pressure at 1215 km 5.9 ± 0.6 microbar

dT / dr at 1220–1300 km −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.

e

t

a

v

m

m

s

2

o

h

(

A

S

s

f

n

e

t

c

V

S

A

S

i

P

t

R

g

t

t

g

a

H

R

A

B

B

B

B

C

D

E

F

F

F

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 N 2 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 subli-

mation 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 N 2 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 atmo-

sphere 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 re-

ceived by New Horizons, split into pairs, and processed by two in-

dependent 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 aver-

aged the resulting phase profiles ( Section 6.1 ). This approach im-

proves 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 appropri-

ate 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 pro-

files 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-

ry of a cold boundary layer above Sputnik Planitia, which is at-

ributed to the diurnal cycling of N 2 between the surface and the

tmosphere.

Table 7 lists the surface pressures at entry and exit; their mean

alue is the best pressure reference. Stated in another way, the

ass of the atmospheric column at occultation entry is ∼2.4 kg

−2 , as obtained by integrating the density profile in Fig. 10 . As-

uming a density of 1030 kg m

−3 for solid N 2 ( Trowbridge et al.,

016 ), this is equivalent to a layer of N 2 ice with a thickness of

nly 2.3 mm. For comparison, the reservoir of N 2 ice in SP would

ave a depth of order 100 m if distributed uniformly across Pluto

McKinnon et al., 2016 ).

cknowledgments

We are indebted to the New Horizons Project Team at the

outhwest Research Institute (SwRI) and the Johns Hopkins Univer-

ity Applied Physics Laboratory (APL) for shepherding the mission

rom proposal to Pluto and beyond; to the highly capable person-

el of the NASA Deep Space Network (DSN) for their flawless op-

ration of the ground equipment used in the REX measurements;

o Ann Harch (Cornell University) for detailed design of the space-

raft sequence that implemented the REX observations; to Michael

incent (SwRI) for management of REX Team activities; to Becca

epan (APL) for coordination of REX real-time operations; to Aseel

nabtawi, Kamal Oudrhiri, and Sami Asmar of the Radio Science

ystems Group at the Jet Propulsion Laboratory for real-time mon-

toring of the DSN equipment used in the REX observations; to Joe

eterson (SwRI) for maintaining the project archive of REX data on

he ground and for assistance with cruise phase debugging of the

EX data records; to Frédéric Pelletier of the New Horizons Navi-

ation Team (KinetX Aerospace) for providing the error analysis of

he trajectory reconstruction; to Bob Jensen (APL) for monitoring

he frequency drift of the USOs; and to Bruno Sicardy, François For-

et, and Tanguy Bertrand for informative discussions about Pluto’s

tmosphere. Funding for this work was provided by the NASA New

orizons Mission.

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