Icarus 329 (2019) 148–165

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The CH4 cycles on Pluto over seasonal and astronomical timescales
a,*

b

a

a

c

T

c

T. Bertrand , F. Forget , O.M. Umurhan , J.M. Moore , L.A. Young , S. Protopapa ,W.M. Grundyd, B. Schmitte, R.D. Dhingraf, R.P. Binzelg, A.M. Earleg, D.P. Cruikshanka,
S.A. Sternc, H.A. Weaverh, K. Ennicoa, C.B. Olkinc, the New Horizons Science TeamaNational Aeronautics and Space Administration (NASA), Ames Research Center, Space Science Division, Moﬀett Field, CA 94035, United States
Laboratoire de Métórologie Dynamique, IPSL, Sorbonne Universités, UPMC Univ Paris 06, CNRS, 4 place Jussieu, Paris 75005, FrancecSouthwest Research Institute, Boulder, CO 80302, United StatesdLowell Observatory, Flagstaﬀ, AZ, United Statese
Université Grenoble Alpes, CNRS, CNES, Institut de Planétologie et Astrophysique de Grenoble, Grenoble F-38000, FrancefDepartment of Physics, University of Idaho, 875 Perimeter Drive, Moscow, ID 83843, United Statesg
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA 02139, United StateshJohns Hopkins University Applied Physics Laboratory, Laurel, MD 20723, United Statesb

A R T I C LE I N FO

A B S T R A C T

Keywords:
Pluto
CH4
Paleoclimate
Modeling
GCM
Glacier
Volatile transport

Pluto's surface is covered in numerous CH4 ice deposits, that vary in texture and brightness, as revealed by the
New Horizons spacecraft as it ﬂew by Pluto in July 2015. These observations suggest that CH4 on Pluto has acomplex history, involving reservoirs of diﬀerent composition, thickness and stability controlled by volatile
processes occurring on diﬀerent timescales. In order to interpret these observations, we use a Pluto volatiletransport model able to simulate the cycles of N2 and CH4 ices over millions of years. By assuming ﬁxed solid
mixing ratios, we explore how changes in surface albedos, emissivities and thermal inertias impact volatiletransport. This work is therefore a direct and natural continuation of the work by Bertrand et al. (2018), which
only explored the N2 cycles. Results show that bright CH4 deposits can create cold traps for N2 ice outside
Sputnik Planitia, leading to a strong coupling between the N2 and CH4 cycles. Depending on the assumed albedo
for CH4 ice, the model predicts CH4 ice accumulation (1) at the same equatorial latitudes where the Bladed
Terrain Deposits are observed, supporting the idea that these CH4-rich deposits are massive and perennial, or (2)at mid-latitudes (25°− 70°), forming a thick mantle which is consistent with New Horizons observations. In our
simulations, both CH4 ice reservoirs are not in an equilibrium state and either one can dominate the other overlong timescales, depending on the assumptions made for the CH4 albedo. This suggests that long-term volatiletransport exists between the observed reservoirs. The model also reproduces the formation of N2 deposits at midlatitudes and in the equatorial depressions surrounding the Bladed Terrain Deposits, as observed by New
Horizons. At the poles, only seasonal CH4 and N2 deposits are obtained in Pluto's current orbital conﬁguration.
Finally, we show that Pluto's atmosphere always contained, over the last astronomical cycles, enough gaseous
CH4 to absorb most of the incoming Lyman-α ﬂux.

1. Introduction
1.1. Pluto's ices as observed by New Horizons in 2015
In July 2015, our vision of Pluto changed as the New Horizons
spacecraft revealed a frozen world with unprecedented landscapes in
the Solar System (Stern et al., 2015). The ﬁrst analysis of spectral datafrom the Linear Etalon Imaging Spectral Array (LEISA) instrument onboard New Horizons showed that Pluto's water ice bedrock is coveredby volatile ices such as N2, CH4 and CO, except in some parts of the*equatorial regions, covered only by dark tholins (Grundy et al., 2016).
Detailed spectroscopic analysis then revealed a more complex volatile
ice distribution with diﬀerent types of ice mixtures on Pluto's surface(Schmitt et al., 2017; Protopapa et al., 2017).
The exact nature of the observed deposits is not easy to derive fromthese spectroscopic analyses, because they involve many parameterssuch as the abundance, dilution state, texture, or grain size, which arepoorly constrained (Schmitt et al., 2017). A ﬁrst extraction of theseparameters at the global scale is solved through sophisticated inversion
of a Hapke's radiative transfer model of the LEISA data (Protopapa

Corresponding author.
E-mail address: tanguy.bertrand@nasa.gov (T. Bertrand).

https://doi.org/10.1016/j.icarus.2019.02.007
Received 29 August 2018; Received in revised form 19 December 2018; Accepted 6 February 2019
Available online 05 April 20190019-1035/ © 2019 Elsevier Inc. All rights reserved.

Icarus 329 (2019) 148–165

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1.2. Modeling of volatile transport on Pluto

et al., 2017). However, spectroscopic analyses of the surface do notprovide information about the thickness of these deposits. The thickness
can be inferred from geological insights using high resolution images
from the LOng-Range Reconnaissance Imager (LORRI) instrument andalbedo maps, that help distinguish a thin frost of ice from a massive
deposit. A simpliﬁed global picture of the volatile ice reservoirs on
Pluto is shown in Fig. 1.
The most prominent volatile ice deposit on Pluto's surface is akilometer-thick ice sheet made of N2 ice, mixed with CH4 and CO,
which is sequestered in Sputnik Planitia1, the vast topographic basin at
the anti-Charon longitude (Stern et al., 2015; Grundy et al., 2016). This
perennial glacier is the main reservoir of N2 ice.
Methane is detected almost everywhere in the northern hemisphere,with varying brightness, textures and mixtures (such as CH4-rich ice
and CH4 diluted in N2-rich ice), as highlighted in the available maps ofthe equivalent width of absorption in the Multi-spectral Visible Imaging
Camera (MVIC) CH4 ﬁlter (Grundy et al., 2016; Earle et al., 2018b) as
well as in LEISA maps (Protopapa et al., 2017; Schmitt et al., 2017).
The North Pole is covered by relatively pure and bright CH4-rich ice,with an estimated Bond albedo higher than 0.7 (Buratti et al., 2017).
The mid-latitudes plains (25°N–70° N) are covered in mixtures ofN2-rich and CH4-rich ices following a latitudinal trend (Schmitt et al.,2017; Protopapa et al., 2017; Earle et al., 2018b). The latitudes
55°N–70° N are enriched in CH4, with few N2-rich deposits mostly
conﬁned in the depressions. The latitudes 35°N–55° N are dominated by
N2-rich ices, while the latitudes 25°N–35° N are covered again mainly ofCH4-rich ices (Protopapa et al., 2017) . Interestingly, the CH4-rich deposits in these regions seem to form a relatively thick mantle, maybe
100–1000 m, given the fact that they cover some craters and give to thesurface a smooth aspect.
The equatorial regions (25°S-25°N) show a greater diversity of terrains in longitude, in terms of albedo (Buratti et al., 2017), color (Olkinet al., 2017) and composition (Schmitt et al., 2017). Outside Sputnik
Planitia, in the region of Tartarus Dorsa (East of Tombaugh Regio, 5°S28°N), relatively pure CH4-rich ice has been detected in the Bladed
Terrain Deposits (BTD, Moore et al., 2018; Schmitt et al., 2017;
Protopapa et al., 2017; Earle et al., 2018b). These terrains are characterized by parallel sets of steep ridges and sharp crests and are situated on high ground (above 2 km), which may indicate very massive
CH4-rich deposits, at least 300 m thick (Moore et al., 2018). They are
relatively dark, with an estimated Bond albedo between 0.5 and 0.6(Buratti et al., 2017). Their distinctive texture on Pluto's maps suggeststhat they extend further east, from longitudes 210°E to 40°E, and further south, down to 25°S (see Fig. 3 in Olkin et al., 2017; Moore et al.,2018). They also seem to be interspersed with N2-rich ﬂat-ﬂooredbright plains located in the depressions and valleys of these regions.
Finally, the eastern part of Tombaugh Regio (between Sputnik
Planitia and Tartarus Dorsa) is bright and also contains N2-rich andCH4-rich ices with N2 mostly detected in the depressions (Schmitt et al.,2017; Protopapa et al., 2017).
These observations raise the following questions: What drives theobserved ice distribution and the diversity of N2-rich and CH4-richterrains? Are these reservoirs perennial (lasting for many Pluto years,
e.g. glaciers) or seasonal (disappearing over one Pluto year, e.g. frosts)?
How do they evolve over astronomical and seasonal timescales? In thispaper, we aim to provide answers to these questions by simulating thelong-term evolution of N2 and CH4 ice, using the Pluto volatile transportmodel developed at the Laboratoire de Météorologie Dynamique (LMD,
Bertrand and Forget, 2016; Bertrand et al., 2018).

Global volatile transport models of Pluto have been used to explain
how changes in insolation over the course of Pluto's orbit aﬀect thesurface and subsurface temperatures (which plays a key role in the
Pluto environment), resulting in latitudinal variations of distribution ofvolatile ices (Young, 1993; Hansen and Paige, 1996; Spencer et al.,
1997; Young, 2012, Young, 2013; Hansen et al., 2015; Toigo et al.,2015; Olkin et al., 2015; Bertrand and Forget, 2016; Bertrand et al.,2018).
In particular, Bertrand and Forget (2016) (hereinafter referred to as
BF2016) simulated the transport of N2, CH4 and CO ices over tens of
thousands Earth years and obtained a seasonal cycle that reproduces, toﬁrst order, the ices distribution observed by New Horizons in 2015.
They showed that N2 ice inevitably accumulates inside Sputnik Planitia
basin, because of an atmosphere-topography process: the N2 surfacepressure and condensing temperature are higher at the bottom of thebasin than outside, and therefore the N2 deposits in the basin arewarmer and loose more energy by thermal infrared cooling, which isbalanced by a stronger N2 condensation at that location (so that enoughlatent heat is released to ensure that the surface remains at the equilibrium temperature). In their simulations, the equatorial regions (apartfrom Sputnik Planitia) always remained warmer than at least one of thetwo poles (at any given time) and therefore no volatile condensed there,
which explained the dark equatorial band of Pluto. They also showedthat the lower volatility of CH4 ice at Pluto's surface temperatures allows it to exist elsewhere than in the Sputnik Planitia ice sheet, forming
frost even at locations where N2 ice would immediately sublime. In
their model, CH4 ice seasonally covered both hemispheres, and, if its
albedo was high enough, N2 was able to condense on it and form alatitudinal band around 45°N in 2015, in agreement with New Horizons
observations (Fig. 1). This impact of the ice albedo is also highlighted
by Earle et al. (2018a), who suggest that runaway albedo variations are
more eﬃcient in the equatorial regions than at the poles, forming stark
contrasts in albedo and volatile abundance.
However, the simulations performed in BF2016, and in most previous volatile transport modeling studies on Pluto, had two main limitations. First, they only considered small amounts of ice and were
therefore not able to reproduce the formation of perennial glaciers. For
instance, the globally averaged volatile ice reservoir used in BF2016 is
only of few millimeters, in order to reach a steady state over the annual
timescale. Secondly, they only focused on the 104 Earth years timescales, with the present orbital and obliquity parameters. Yet Pluto's
high obliquity (currently around 119.6°) varies by about 23° over a
period of 2.8 millions of Earth years (2.8 Myrs herein refers to the astronomical timescale) while Pluto's longitude of perihelion regresses by
360° over 3.7 Myrs (Dobrovolskis et al., 1997; Spencer et al., 1997).
Both parameters impact the duration and intensity of the seasons, andthe latitudes where volatile ices accumulate (Binzel et al., 2017; Earleet al., 2017).
Recently, Bertrand et al. (2018) (hereinafter referred to as B2018)
improved the Pluto volatile transport model described in BF2016 byimplementing the most recent topography data of Pluto, the variationsof obliquity, longitude of perihelion and eccentricity with time, and by
taking into account a realistic N2 reservoir as well as a N2 ice viscous
ﬂow model. Thanks to this modeling eﬀort, they explored the cycles ofN2 over several astronomical cycles (up to 30 Myrs). Their results explained many geological features of Sputnik Planitia, such as the evidence of recent and past glacial ﬂow and erosion, the presence of
sublimation pits in the southern portion of the ice sheet, as well as thebrightness and composition of the surface ice. They also showed thatlarge N2 ice deposits can remain relatively stable and persist over tensof millions of years in the equatorial regions or over mid-latitudinalbands, in particular at low elevations.

1
The place names mentioned in this paper include a mix of oﬃcially approved names and informal names.

149

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T. Bertrand, et al.

Fig. 1. The diﬀerent types of terrains observed on Pluto (left) and the associated N2-CH4 mixtures (right). The color scale is described in details in Schmitt et al.
(2017): A–B relatively pure CH4 ice, or N2-rich ice with grains < few cm and CH4 > 1%. D–E large N2-rich grains (> 10 cm) with small amount of CH4 (0.1–1%). C
N2-rich ice with both medium N2 grain size (< few cm) and CH4 < 1%. F very large N2 ice grains (> 20 cm) with CH4 > 1%.

1.3. Objectives of this paper

Table 1
Settings and surface conditions assumed in our simulations. In this work weassess the impact of subsurface thermal inertia and CH4 ice albedo.

In this paper, we want to carry this work forward and explore theCH4 cycles over astronomical and seasonal timescales with the latest
version of the Pluto volatile transport model. In particular, our objectives are:

Paleo-timestep
Reservoirs (global average)
AlbedoEmissivity
Thermal inertia
Atmospheric mixing timescale
CH4 ice mixing ratio in N2

1. To determine the latitudes where CH4 ice tends to accumulate overmillions of years.
2. To investigate how the CH4 albedo impacts the N2 condensationsublimation cycles and the latitudinal ices distribution.
3. To compare our results with New Horizons observations of Pluto's
surface (e.g. Stern et al., 2015; Grundy et al., 2016; Moore et al.,2016), explain the observed latitudinal distribution of volatile ices
(Schmitt et al., 2017; Protopapa et al., 2017), infer the nature(perennial or seasonal) of the observed deposits, and discuss thepossible scenarios for their formation.

Δt= 100,000 Earth years
R N2 =300 maRCH4 =4 mb
A N2 = 0.7 ACH4 = 0.5–0.8 Abedrock= 0.1
ε N2 = 0.8 εCH4 = 0.8 εbedrock= 1
TI=400–1500 SIc
τN2 = 1 s τCH4 = 107 s
0.5 %

a

Fills Sputnik Planitia up to 2500 m below the mean surface level.
In Section 4, an inﬁnite reservoir is used.
c
SI= J s−0.5 m−2 K−1.
b

We perform simulations over 30 Myrs using the paleoclimate mode,
the N2 ice viscous ﬂow scheme and the ice equilibration algorithm
described in details in B2018: the model is run over 5 Pluto years, thenthe annual mean ice rate of the last Pluto year is used to estimate the
new amounts of ice over a paleo-timestep Δt and ﬁnally the topography
is updated according to the new amounts of ice and the orbital parameters and the obliquity of Pluto are changed according to the new
epoch t+Δt. The maximal change of obliquity within Δt must remain
lower than the latitudinal resolution used. Here we use Δt = 100,000
Earth years, that is about 400 Pluto orbits, allowing fast computing
times and reasonable time resolution, with a maximal change of obliquity within that timeframe of about 3° (Binzel et al., 2017).
Most of the atmospheric eﬀects are neglected in the model (clouds,
radiative eﬀect of the atmsphere...). As in BF2016, volatile transport
occurs through the atmosphere via a parametrization of the atmospheric circulation, using a characteristic timescale τCH4 = 107 s (aboutfour terrestrial months) to globally mix gaseous CH4.

To fulﬁll these objectives, we adapt the Pluto volatile transportmodel described in B2018 so that it also takes into account the CH4
cycle. In Section 2, we detail the recent model improvements, the assumptions made and the simulation settings. The results are presented
in two independent sections. We ﬁrst perform simulations with a global
uniform CH4 ice albedo (Section 3). Then, we perform simulations with
two CH4 albedo values (Section 4) depending on the latitude of thedeposit, with a low value in the equatorial regions (old dark deposits)
and high values in the mid-to-polar regions (bright deposits, above 30°).
Our results are summarized in Table 2, and discussed in Section 5.
2. The Pluto volatile transport model
We use the latest version of the LMD Pluto volatile transport model,
as described in BF2016, B2018 and Forget et al. (2017). The model
settings are similar to those in B2018 except for the following changes,
summarized in Table 1.

2.2. Assumptions on the state of N2 and CH4 ice in the model
On Pluto, CH4 and N2 easily mix together and are not expected toexist in perfectly pure state (Trafton, 2015; Tan and Kargel, 2018).
Analysis of the New Horizons LEISA spectral observations of Pluto's
surface has been performed using sophisticated spectral models andreveal complex mixtures in diﬀerent amounts, also involving CO andcontamination by tholins (Grundy et al., 2016; Protopapa et al., 2017;
Schmitt et al., 2017). Most of the volatile ice covering Pluto's surface

2.1. General settings of the simulations
The simulations of this paper are performed on a horizontal grid of
32×24 points, which corresponds to a grid-point spacing of 7.5° inlatitude by 11.25° in longitude (about 150 km at the equator).
150

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T. Bertrand, et al.

Table 2
Settings and results of the simulations performed from 30 Myrs ago to present-day. From left to right, settings are: Run name (* indicates that the run is illustrated byﬁgures in this paper), thermal inertia of N2, CH4, H2O ice, equatorial and mid-to-polar CH4 albedo. Results are: Loss of equatorial CH4 ice after 30 Myrs, year of
maximum pressure in current epoch, latitudes between which perennial N2 ice deposits (pN2) are obtained in the northern hemisphere, maximal thickness of theseperennial deposits, same for seasonal deposits (sN2), and maximal thickness of the equatorial N2 ice deposits (formed on the modeled BTD).
Name

TI N2

TI CH4(J s−1/2 m−2 K−1)
#TI888_050_060#TI888_050_065*#TI888_050_068#TI888_050_072*#TI888_050_080*#TI888_050_065_phase#TI888_050_072_phase*#TI888_050_080_phase#TI888_030_065#TI888_030_072*#TI888_060_072*#TI888_060_080#TI888_065_072#TI888_065_080#TI884_050_065*#TI884_050_072*#TI8812_050_065*#TI8812_050_072*#TI848_050_065#TI848_050_072#TI8128_050_065#TI8128_050_072#TI488_050_065#TI488_050_072#TI1288_050_065#TI1288_050_072#TI444_050_072#TI444_050_080#TI844_050_060#TI844_050_065#TI844_050_072#TI8412_050_065#TI8412_050_072#TI8124_050_060#TI8124_050_065#TI8124_050_072#TI81212_050_065#TI81212_050_072

800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
400
400
1200
1200
400
400
800
800
800
800
800
800
800
800
800
800

800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
800
400
400
1200
1200
800
800
800
800
400
400
400
400
400
400
400
1200
1200
1200
1200
1200

TI H2 OA CH4 eq

A CH4 poles

L CH4

Yp

(m)
800
800
800
800
800
800
800
800
800
800
800
800
800
800
400
400
1200
1200
800
800
800
800
800
800
800
800
400
400
400
400
400
1200
1200
400
400
400
1200
1200

0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.3
0.3
0.6
0.6
0.65
0.65
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5
0.5

0.6
0.65
0.68
0.72
0.8
0.65
0.72
0.8
0.65
0.72
0.72
0.8
0.72
0.8
0.65
0.72
0.65
0.72
0.65
0.72
0.65
0.72
0.65
0.72
0.65
0.72
0.72
0.8
0.6
0.65
0.72
0.65
0.72
0.6
0.65
0.72
0.65
0.72

75
87
88
91
92
72
86
88
1794
1776
10
6
3
1
85
90
85
91
106
106
67
73
86
90
87
92
105
100
105
108
108
133
108
59
66
72
66
71

1998.6
1996.91995.1
2000.42017.92000.4
1998.62017.91996.92014.4
1996.92000.4
2002.1
1996.92014.42019.6
1995.1
2014.4
1996.92005.6
1996.91998.6
1995.1
2002.1
1995.1
2000.42010.92016.1
2010.92014.42014.4
1996.91995.1
2007.42012.62019.6
1995.1
1996.9Lat pN2

Max pN2

Lat sN2

Max sN2

Max eqN2

(°)

(m)

(°)

(m)

(m)

30
30
30–37.5
30–37.5

1.5
4.0
4.9
7.3

30–37.5
30–37.530
30–37.5

3.2
8.6
4.9
7.7

30–37.530
30–37.530
30–37.530
30–37.530
30
30
30–37.530
30–37.5
30–37.5
30–37.530
30
30–37.530
30–37.5

4.7
10.5
6.2
3.8
14.6
5.5
9.4
2.0
11.2
2.4
5.5
2.8
6.2
8.3
6.7
7.3
10.9
10.2
6.3
15.5

30
30–37.5
30
30

5.0
6.4
2.1
6.1

30–90
37.5–90
37.5–90
45–90
45–90
30–90
30–90
30–90
45–90
45–90
37.5–90
45–90
52.5–90
45–90
22.5–90
22.5–90
37.5–90
45–90
37.5–90
45–90
37.5–90
37.5–90
37.5–90
45–90
37.5–90
45–90
22.5–90
22.5–90
22.5–90
22.5–90
22.5–90
37.5–90
45–90
30–90
22.5–90
22.5–90
37.5–90
37.5–90

0.33
0.51
0.59
0.75
0.90
0.08
0.34
0.77
0.54
0.76
0.66
0.86
0.11
0.68
0.51
0.81
0.44
0.70
0.58
0.78
0.47
0.71
0.51
0.77
0.57
0.74
0.77
0.93
0.46
0.56
0.79
0.56
0.73
0.31
0.49
0.81
0.50
0.63

0
0
0
0
0
0
0
0
0
0
77
97
357
185
0
0
0
0
78
72
0
0
0
0
0
0
91
105
22
82
83
72
82
0
0
0
0
0

Pure CH4 ice is an approximation for unsaturated CH4-rich ice. We
make the approximation that such a CH4-rich ice behaves almost likepure CH4 ice, in terms of temperature and vapor pressure at saturationof CH4. It can form after sublimation of N2 ice (in which it was trapped
before) or directly on a volatile-free surface (its lower volatility than N2
allows it to condense where N2 would instantly sublime). For instance,
CH4-rich ice has been observed on top of mountains in the region of
Cthulhu, where N2 could not have condensed at ﬁrst (because of thesigniﬁcantly high altitude and low albedo of these terrains).
When both CH4 and N2 ices are present on the surface, we assume
that CH4 is diluted in a solid solution N2:CH4 with 0.5% of CH4, as
retrieved from telescopic observations (Merlin, 2015) and overall fromthe New Horizons LEISA spectroscopic data (see spectra g and j inTable 3 in Protopapa et al., 2017). This modeled N2-rich:CH4 ice sublimes by conserving the 0.5% of diluted CH4. In the next sections of thispaper, we refer to this phase as N2 ice.
The impact of N2-rich + CH4-rich mixtures is out of the scope of thispaper, and we neglect their eﬀect in the model. By doing so, we assume
that this state corresponds to a short transient phase. In the future, weplan to investigate further stratiﬁcation mechanisms and implement
them in the volatile transport model. To do this, experimental studies ofthese processes are also strongly needed.

seems to be dominated by N2-rich:CH4 (e.g. Sputnik Planitia) or CH4rich:N2 (e.g. the north pole). Observations also suggest mixtures of bothN2-rich + CH4-rich at some locations, but the exact nature of these
deposits is uncertain for now because they could fall into three distinct
possible categories: (1) intimate mixture or intermolecular mutual attraction, at the grain scale, (2) geographic mixtures (N2-rich + CH4rich could be observed at the pixel scale but not be mixed, strictly
speaking, as they could be spatially disconnected at smaller scales), (3)stratiﬁcation (a thin layer of CH4-rich ice could form at the top of a N2rich deposit).
The scenario of intimate mixtures suggests a perfect thermodynamic
equilibrium of two types of crystals at signiﬁcant depth, strictly following the binary phase diagram. This is typical of instantaneous
thermodynamic equilibrium but should not apply to Pluto, which we
believe is a non-equilibrium dynamical environment with continuous
exchange of materials. Instead, CH4-rich and N2-rich ices may co-exist
because of dynamical processes such as sublimation, which would leadto stratiﬁcation (N2 sublimation leaving CH4 behind and leading to a
CH4-rich ice layer on top of the N2 -rich ice).
However, the mechanisms controlling the formation and evolutionof such N2-rich + CH4-rich mixtures remain largely unknown. With
regards to this, the model presented in this paper is rather simple. As in
BF2016, it does not compute any evolution of ice mixing ratio. In thesimulations, the surface is either volatile-free, covered by pure CH4 ice
or by N2-rich:CH4 ice.
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2.3. Surface properties

2.5. Other settings related to the CH4 cycle

As in B2018, we use a reference N2 ice albedo and emissivity which
remain ﬁxed to 0.7 and 0.8 respectively. The surface N2 pressure simulated in the model is constrained by these values. The albedo andemissivity of the bare ground (volatile-free surface) are set to 0.1 and 1
respectively, which corresponds to a terrain covered by dark tholins
such as Cthulhu. CH4 ice emissivity is ﬁxed to 0.8 in all simulations, but
we explore diﬀerent values of CH4 ice albedo, ranging from 0.3 to 0.8
depending on the simulation (the reference albedo is 0.5). Note that CO
is also transported by the model, but plays no role, as we assume italways “follows” N2.
The reference seasonal thermal inertia (TI) of the subsurface isuniformly set to 800 SI, as in B2018. However we also performed simulations using a uniform soil TI set to 400 or 1200 SI (Section 3.3),
and simulations in which each type of terrain (water ice bedrock, N2 or
CH4 ice) has its own TI ranging from 400 to 1200 SI (see Table 2 andSection 4.6).
We also tested some scenarios in which the N2 ice surface emissivity
depends on its temperature and crystalline phase (e.g. simulation#TI888_050_065_phase). We assumed a minimal emissivity of εα=0.3
when the ice is in its α-phase, with a surface temperature Ts below thetransition temperature of Tα−β=35.6 K and a maximal emissivity of
εβ=0.8 in its β-phase, based on the results from Stansberry and Yelle(1999). We use a simple hyperbolic tangent function for the transition:

The model does not allow CH4 ice to ﬂow and the topography does
not change according to the accumulation or loss of CH4 ice (it onlychanges according to the variation of N2 ice thickness). These choices
are driven by the fact that (1) the CH4 reservoir involved in the model isrelatively low (see above) and (2) the CH4 ice may be too rigid to leadto a signiﬁcant glacial ﬂow activity (Eluszkiewicz and Stevenson, 1990;
Moore et al., 2017, 2018), as suggested by the steep slopes of the BTD's
ridges (20°), which is also why these terrains are described as massive
deposits instead of glaciers.
Finally, for the simulations performed with a uniform CH4 ice albedo (Section 3), we prohibit CH4 to condense in the Sputnik Planitia
N2 ice sheet (we do not allow any CH4 in SP). By doing this, we preventthe entire CH4 reservoir to be trapped in Sputnik Planitia after several
Myrs and we always conserve the same mass of CH4 ice outside thebasin. On Pluto, mechanisms or other sources must exist to maintain acertain amount of CH4 ice outside Sputnik Planitia (see Discussions in
Section 5). For instance, saturation of N2-rich ice with CH4, or formation of a CH4-rich layer on top of N2-rich ice are processes that could
limit further condensation of CH4 in SP, and maintain signiﬁcantamounts of CH4 ice outside SP.

ε N2 =

1[1 + tanh(3(Tα − β − Ts ))](εα − εβ ) + εα23. Simulations with a uniform CH4 ice albedo
In this section we investigate where CH4 ice tends to accumulate
over astronomical timescales.

(1)

As predicted by Stansberry and Yelle (1999), the N2 ice surface
temperature in these simulations remains at the transition temperatureof 35.6 K during most of Pluto's northern fall and winter, because theemissivity change leads to a negative feedback of surface temperatures.
The exchange of latent heat between both phases also leads to a negative feedback and plays a role in locking the temperature to thetransition, but here we neglect this eﬀect for the sake of simplicity. Notethat the α-phase of N2 ice has never been observed in the outer solar
system. Here we only test the case of an extremely low emissivity for N2
ice in α-phase, which enables us to assess the maximum possible eﬀectof this change on Pluto's climate.

3.1. Initial state of the simulation
The simulations are performed using the New Horizons topography
data, starting with all N2 ice ﬁlling a deep modeled Sputnik Planitia
basin up to 2.5 km below the mean surface level, and with a 4-meter
thick layer of CH4 ice covering the entire globe. The simulation is
performed with a unique albedo for CH4 ice, set to 0.5, and a uniform
thermal inertia of 800 SI. We then let the volatile ices evolve over
30 Myrs.
3.2. Results: formation of massive equatorial deposits and mid-to-polar
frosts of CH4

2.4. Reservoirs
Fig. 2 shows the evolution of the CH4 ice distribution obtained overthe last 30 Myrs. The ice quickly accumulates in the equatorial regions.
Typically, after 10 Myrs, 20–40 m thick CH4 deposits (1–2× 104 kgm−2) are formed between 12°S and 22.5° N (by accumulation of theCH4 ice which was initially placed at the poles). The maximal net rates
of sublimation are obtained at the poles. Above 30° latitude, 4 m of ice
can disappear within one astronomical cycle (2.8 Myrs). By extrapolation, if we had started with a global CH4 ice reservoir of 100 m, we
would have obtained ∼ 1 km thick deposits in the equatorial regions
after 50–100 Myrs.
Why is CH4 ice accumulating at the equator? Because of Pluto's highobliquity, ranging from 104° to 127° over 2.8 Myrs, the polar regions
receive more solar ﬂux than the equator on average. If one assumes
medium to large soil thermal inertia, this leads to colder equatorial
regions on average over several Myrs (see Fig. 4.B in B2018). In addition to the obliquity cycle, Pluto's solar longitude of perihelion (Lsperi)
oscillates over a period of 3.7 Myrs and leads to asymmetries in theseasons (Dobrovolskis et al., 1997; Binzel et al., 2017). For instance,
when Pluto's Lsperi is close to 90°, the northern polar latitudes undergo ashort and intense summer (close to the perihelion) and a long and intense winter (close to the aphelion) while the southern polar latitudes
undergo a long summer far from the sun and a short winter close to thesun, and vice versa when the orbital conditions are reversed (Lsperi close
to 270°). As a result, the northern hemisphere tends to be colder onannual average when Pluto's Lsperi is close to 90°, and warmer when

All simulations are run with N2 ice initially placed in Sputnik
Planitia in an 10 km deep elliptical basin, as described in B2018. N2 ice
ﬁlls this modeled basin up to 2.5 km below the mean surface level,
which corresponds to a global N2 reservoir of ∼300 m. N2 is allowed tocondense and sublime everywhere on Pluto's surface, depending on thecomputed local surface thermal balance.
The simulations performed with a uniform CH4 ice albedo(Section 3) use a global CH4 reservoir of 2000 kg m−2, which corresponds to 4 m, if we assume a CH4 ice density of 500 kg m−3 (Leyrat
et al., 2016). This amount is low compared to the total reservoir of CH4
ice expected on Pluto. Indeed, the BTD only could correspond to a reservoir of 22 m on global average if we assume that they cover an
equatorial surface equivalent to 10° in latitudes and 180° in longitudes
and that they are only 500 m thick. This is a lower limit for CH4 ice,
since the BTD may be thicker and since other km-thick reservoirs may
exist in the mid-latitudinal regions. However, running simulations withsuch a CH4 ice reservoir is challenging, because the CH4 condensationsublimation rates are very low. Typically, one meter of CH4 ice evolves
over one million years. Therefore the total amount of CH4 ice in our
simulations is a trade-oﬀ between having the largest possible reservoir
and reaching a steady state for ice distribution within tens of Myrs.
Alternatively, the simulations performed with a dual CH4 ice albedo(Section 4) are initialized with an inﬁnite source of CH4 ice at the location of the observed BTD in the equatorial regions.
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Section 5).
Note that our modeling does not reproduce the “bladed” aspect of
the BTD nor explain why they are mostly located in the eastern hemisphere, although it may be due to the fact that the dark tholin-covered
surface in the western hemisphere (Cthulhu) prevents condensation of
CH4 (assuming that the BTD formed after Cthulhu). It is likely that thislongitudinal asymmetry has dynamical origins and therefore it should
be investigated by using 3D global climate models (which include a full3D dynamical core).
Although thick deposits of CH4 ice are not stable at the poles, thin
CH4 frost (< 1 mm) always form there seasonally, as illustrated by
Fig. 2. They form during fall-winter, when the equatorial deposits andthe CH4 frosts at the opposite pole (spring-summer) feed the atmosphere with gaseous CH4. In BF2016, a similar result was obtained but
because the simulations were not performed with a large enough reservoir of CH4 ice, no thick deposit was obtained at the equator and thepolar frosts disappeared in the early spring.
Fig. 2. Evolution over 30 Myrs of the perennial and seasonal deposits of CH4 iceon Pluto in our simulation with a unique CH4 ice albedo of 0.5 (the values
shown correspond to the zonal annual mean amount of CH4 ice in kg m−2, forthe areas outside of Sputnik Planitia). CH4 ice quickly accumulates in theequatorial regions, where it forms massive deposits. At higher latitudes, only
thin seasonal CH4 deposits form. The black vertical lines indicate the periods
where Lsperi is close to 90° and 270° (when seasonal asymmetries are thestrongest).

3.3. Sensitivity to the reservoir, soil thermal inertia and CH4 ice albedo
Changing the initial spatial distribution of CH4 ice (e.g. only at thepoles, or over a speciﬁc longitudinal or latitudinal band) does not impact the results: CH4 ice would still accumulate at the equator, with aslight extent to northern latitudes, while mm-thin deposits would form
elsewhere during polar winter. If we increase the CH4 reservoir, thenthicker CH4 deposits are obtained at the equator. The CH4 mid-to-polar
frosts remain qualitatively and quantitatively the same year after year
because they are controlled by the location of the equatorial deposits.
Changing the albedo of CH4 ice leads to major changes in the results. If we lower the uniform CH4 ice albedo, the ice becomes warmer,
resulting in higher sublimation rates and larger amounts of CH4 to betransported to other sinks. In this case, we obtain more extended
equatorial deposits and episodic thicker perennial deposits at the poles(see middle panel in Fig. 3). If we increase the uniform CH4 ice albedo,
then CH4 ice may become cold enough to trigger N2 condensation on it,
which strongly impacts both volatile cycles. This eﬀect is explored in
Section 4.
Results are also sensitive to the soil thermal inertia, as shown in
Fig. 3. When a high thermal inertia is used (> 1500 SI), surface temperatures tend to be much warmer at the poles than at the equator on
average over several Myrs (see B2018) and thus CH4 ice accumulates
closer to the equator, while less frost forms at the poles. When a low
thermal inertia is used (< 400 SI), the surface temperatures reachhigher values in summer and lower values in winter and tend to bewarmer at the equator than at the poles on average over several Myrs.
In this case, large perennial reservoirs can form periodically in the midto-polar regions. However this case predicts, for the present time, large

Pluto's Lsperi is close to 270° (see Fig. 4.A in B2018).
However, our results show that when Lsperi is close to 90°, the intense northern summer (occurring close to the perihelion) removes asigniﬁcant amount of CH4 ice at the north pole and during this epoch
CH4 ice accumulates at the equator and in the southern hemisphere.
Conversely, when Lsperi is close to 270°, CH4 accumulates at the equatorand in the northern hemisphere. This is illustrated by Fig. 2 showingthat CH4 deposits extend to higher latitudes (20°S and 45°N) during theperiods of asymmetric seasons (Lsperi close to 90° or 270°).
On average over one astronomical cycle, the equatorial regions are a
net accumulation zone of CH4 ice, while the poles are a net sublimation
zone. This result is consistent with New Horizons observations of theCH4-rich BTD in the equatorial regions (Moore et al., 2018, 2016) andsupports the fact that they are thick and perennial CH4 deposits.
Fig. 2 also shows that the modeled CH4 deposits are not symmetricto the equator, as they tend to be more extended to the northern latitudes, in accordance with the observed latitudinal extent of the BTD(5°S-25°N). This is because during the last 70 Myrs, the Lsperi value athigh obliquity remained close to 90° and led to an asymmetry of insolation and surface temperatures which favors a slightly warmer south
hemisphere (see details and Fig. 5 in B2018, and Discussions in

Fig. 3. Same as Fig. 2 but assuming a thermal inertia TI=400 SI coupled with a CH4 ice albedo A CH4 =0.3 (left), TI=800 SI and A CH4 =0.3 (middle), TI=1500 SI and
A CH4 =0.5 (right). The low TI case was performed with a lower albedo for CH4 ice (0.3) in order to limit the eﬀect of N2 condensation on CH4 ice (this eﬀect is
explored in Section 4). The brown color represents the dark, tholin-covered bedrock.
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Fig. 4. Simulation #TI888_050_072. A. Evolution of the perennial CH4 ice deposits: minimum amount of surface CH4 ice (per Pluto year, over the last 12 millions ofEarth years, that is ∼4 obliquity cycles). Seasonal deposits (frosts) are not shown. The dark-red band at the equator indicates the latitudes of the modeled BTD, which
are an inﬁnite source of CH4 in the simulations. The dark-brown color represents the dark, tholin-covered bedrock. The blue markers (cross and star) indicate thepresence of N2 ice perennial deposits, which are obtained at low elevations only (patchy deposits: cross) or over all longitudes (latitudinal band: star). B. Variation of
the amount of surface CH4 ice as shown in the panel A, for diﬀerent latitudes and normalized at t=−12 Myrs. At the northern polar latitudes, perennial deposits formand disappear at each astronomical cycle.

particle settling/contamination (which serves as a darkening agent) andslight diﬀerences of composition (Buratti et al., 2017; Stern et al.,2015). As an example, CH4-rich ice is much brighter in the mid-to-polar
than in the BTD (Buratti et al., 2017).
In this section, we intend to explore this sensitivity and better represent the cycle of CH4 by considering two diﬀerent albedos for CH4
ice in the model, based on a criterion in latitude. In accordance with
New Horizons observations, we assume that the mid-to-polar deposits
are bright (albedo=0.65–0.8) and that the equatorial massive CH4 ice
deposits are dark (albedo=0.5–0.65). We also explore the impact of TI
on the results (TI=400–1200 SI). The albedos of the volatile-free surface and of N2 ice remain always ﬁxed to 0.1 and 0.7 respectively.
The results of this section are summarized in Section 4.7 by Fig. 15
and Table 2. Note that all results shown for the current Pluto year are
the outcome of 30 Myrs simulations.
4.1. Initial state of the simulations
Fig. 5. Reference simulation #TI888_050_072. Evolution of the latitudinal
distribution of the deposits over a current annual timescale (at longitude 0°).
The solid dark line shows the position of the subsolar point with time. Bluecolors indicate the presence of N2 ice and CH4 ice while red colors indicate thepresence of CH4 ice only. The lighter the color, the thinner is the deposit. The
dark-red band at the equator indicates the latitudes of the modeled BTD, which
are an inﬁnite source of CH4 in the simulations. The dark-brown color represents the dark, tholin-covered bedrock.

N2 ice is placed in Sputnik Planitia only. We place an unlimited CH4
ice reservoir in the equatorial regions roughly at the locations of theobserved BTD: 15°S-15°N, 140°W-15°E. The rest of the surface is initially volatile-free (assumed to be a tholin-covered water ice bedrockwith an albedo of 0.1). We then run the simulations and let the volatileices evolve over 30 Myrs.

reservoirs of CH4 ice in the south hemisphere only, which is not consistent with the observations.

Our reference simulation is named #TI888_050_072, which meansthat is the simulation performed with a thermal inertia (TI) of 800 SI for
N2, CH4 and water ices, an albedo for CH4 equatorial deposits of 0.5 andan albedo for CH4 mid-to-polar deposits of 0.72.

4.2. Reference simulation: accumulation of CH4 ice at mid-latitudes

4. Simulations with darker CH4 ice near the equator than at mid
and high latitudes

4.2.1. The astronomical cycles of CH4
Fig. 4 shows the evolution of the perennial CH4 (in red) and N2 (bluemarkers) ice deposits obtained over the last 12 Myrs. In this reference
simulation, mid-to-polar CH4 deposits form at higher latitudes than 30°.
Below, the equatorial regions remain volatile-free or covered by themodeled BTD, which is consistent with the observation of dark equatorial regions on Pluto (e.g. Cthulhu). These CH4 deposits are cold enough to trigger N2 condensation and allow the formation of perennial or

CH4 ice is known to play a complex role on Pluto's climate andvolatile ices cycles since it can cold trap N2 ice if its albedo is highenough (Bertrand and Forget, 2016; Earle et al., 2018a). In our model,
the albedo of CH4 ice is a key sensitivity parameter and we usually
represent it by one value only, constant with time. However, on Pluto,
the real value is not very well known and varies with time and space,because of diﬀerent processes involving metamorphism eﬀects, haze154

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Fig. 6. Simulation #TI888_030_072. Same as Figs. 4 and 5 (legends are the same), except for an equatorial CH4 ice albedo of 0.3 (very dark BTD).

(1) Around the North Pole (above 75°N), CH4 condenses as a thin frost(< 1 mm) during fall and triggers the condensation of N2 ice on it
during winter. When spring begins (Earth year 1988), the thin N2
deposit (< 1 cm) starts to sublime. It disappears around year 2000,
revealing a bright thin CH4 frost that will last until 2017 before
disappearing and leaving the dark substrate volatile-free during theentire summer. This is consistent with Fig. 4.A, which predicts that
there is no perennial deposit at the North Pole for the current
epoch.
(2) At mid-latitudes (45°N–75° N), seasonal 1-m thick N2 ice deposits
cover CH4 ice during most of the year, except during late spring andsummer. During this period, N2 ice sublimes from the pole andreveals the CH4 ice mantle which starts to sublime as well.
However, over the entire Pluto year, there is a net accumulation of
CH4 ice at these latitudes, leading to the formation of a thick mantleof CH4 ice over Myrs, as shown in Fig. 4.A.
(3) Between 30°N and 45° N, a perennial latitudinal band of N2 ice isobtained.

seasonal N2 deposits. Those located around 30°N or 30°S remain perennial at all times, while those located at higher latitudes remain perennial only during 1–2 Myrs during each astronomical cycle, as shownin Fig. 4. Note that these perennial N2 ice deposits remain less than
15 m thick, as shown in Table 2. At the North Pole, thin perennial CH4
deposits (< 1 m) alternate with seasonal deposits over an astronomical
cycle. Between 60°N and 75° N, perennial CH4 ice deposits (< 1 m)
remain stable with time, while at northern mid-latitudes (25°N–60° N),
a net accumulation of CH4 ice is obtained (Fig. 4.B). The stability andaccumulation of CH4 ice at these latitudes are due to (1) the condensation of N2 ice on top of the bright CH4 ice, which is able to protect
CH4 from sublimation during most of the year and cold-trap even more
CH4, (2) the presence of inﬁnite amounts of CH4 ice at the equator(BTD), which continuously feed the atmosphere with gaseous CH4. Indeed, the BTD are found to be a net sublimation zone of CH4 ice overastronomical timescales, transporting CH4 ice to the mid-to-polar regions. As shown in Table 2 and Fig. 4, ∼90 m of CH4 ice are lost by the
BTD and 30 m of CH4 ice accumulated between 30°N and 60° after
30 Myrs.
We performed the same simulations but starting at t0 =-100, -200
and -300 Myrs, in order to verify if the transport of CH4 ice from the
BTD to the mid-latitudes also occurs in diﬀerent conﬁguration for
Pluto's orbit (the entire period of the cycle obliquity + solar longitudeof perihelion at maximum obliquity is 375 Myrs, as shown in Fig. 5 in
B2018). We obtained similar results. Consequently, assuming that the
Milankovitch cycles on Pluto remain stable with time, if we let thissimulation evolve over 1 billion years, 3 km of CH4 ice would have beentransferred from the BTD to the mid-latitudes, where CH4 ice would
form a 1 km thick mantle. These results are consistent with the observations of New Horizons showing that the mid-latitudes are coveredby a kilometer-thick mantle of volatile ice (Howard et al., 2017). Theysuggest that CH4 has been accumulated there since hundreds of Myrs by
the action of N2 condensation-sublimation, and that the BTD have been
losing signiﬁcant amounts of CH4 ice by sublimation. We further discuss
this point in Section 5.

The southern hemisphere is covered by up to 1 m thick N2 ice deposits during most of the year except during late summer, where it
sublimes from the pole and reveals the CH4 ice mantle. Around 1988,
when southern fall begins, N2 ice condenses and ﬁrst covers the South
Pole and then the mid-latitudes. A net accumulation of CH4 ice occurs
in the southern hemisphere over seasonal and astronomical timescales.
4.3. Sensitivity to the albedo of the equatorial CH4 deposits
Three diﬀerent scenarios are obtained in our simulations if we increase or decrease the albedo of the modeled BTD (A CH4 eq ):(1) If A CH4 eq ≪ 0.6, the BTD are dark and warm enough so that they
never trigger N2 condensation. Lower albedo values lead to enhanced sublimation rates of CH4 above these deposits and larger
amounts of CH4 ice transported to the mid-to-polar regions. For
instance, Fig. 6 shows the results obtained from simulation#TI888_030_072, performed with an equatorial CH4 albedo of 0.3.
In this simulation, up to 1 km of CH4 ice has been lost from the BTD
after 30 Myrs (Table 2), and transported to the mid-to-polar regions. In this case, CH4 is able to remain around the north pole andform perennial deposits at all times.
(2) If A CH4 eq ≈ 0.6, condensation of N2 occurs on the CH4 equatorial
deposits but only at low elevations (simulations #TI888_060_072,#TI888_060_080, #TI888_065_072, #TI888_065_080). The case of#TI888_065_072 is shown in Fig. 7. Up to 200–300 m thick N2 ice
deposits form in the low-elevated equatorial regions where CH4 ice

4.2.2. The current seasonal cycle of CH4
Fig. 4 shows that, at astronomical scale, present-time Pluto is in aperiod of its Milankovitch cycle where N2 and CH4 perennial deposits
are not favored at high latitudes, compared to other periods (such as
2 Myrs ago for instance). Fig. 5 shows the latitudinal distribution of N2(in blue, mixed with CH4) and CH4 (in red, no N2) ice obtained over acurrent Pluto year and after 30 Myrs of simulation.
In the northern hemisphere, we can distinguish three diﬀerent regions in latitudes.

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Fig. 7. Simulation #TI888_060_072. Same as Figs. 4 and 5, except for an equatorial CH4 ice albedo of 0.60 (relatively bright BTD).

pole during half of an obliquity cycle. During the current-year Pluto, N2
ice covers the bright CH4 ice up to the poles during most of the year,
except during a short period in summer. In this simulation, long-term
accumulation of CH4 ice is obtained everywhere outside the equatorial
regions.

is present (see blue-star markers in Fig. 7.A and Max eqN2 in Table 2).
The high altitude BTD remain N2-free and feed the atmosphere withgaseous CH4 as they sublime, allowing the formation of perennial
and seasonal CH4 deposits at the poles. These mid-to-polar deposits
are thinner than in the reference case because part of the equatorial
source of gaseous CH4 is trapped by N2 ice.
(3) If A CH4 eq ≫ 0.6, then the BTD are bright enough to trigger N2 condensation at most altitudes. They are covered and cold trapped by
200–300 m of N2 ice (see Table 2), mostly in the low-elevated regions since this is enough N2 to ﬂow downhill. These N2 deposits
remain relatively stable at such equatorial latitudes, as demonstrated by B2018 as well. In this case, the CH4 sublimation at theequator is limited and thus there is not enough gaseous CH4
available to form mid-to-polar deposits. As a result, Pluto's surface
outside the equatorial regions remains volatile-free, which is notrealistic (no simulation result is shown for this case).

4.5. Sensitivity to N2 ice phase emissivity
The emissivity of N2 ice in its α-phase is less than that in its β-phase(Stansberry and Yelle, 1999; Lellouch et al., 2011b). Here we tested thesensitivity of the results to the N2 ice emissivity by assuming that it
varies between εα=0.3 in α-phase and εβ=0.8 in β-phase, as describedin Section 2.3. This assumption has a strong impact on the N2 cycle
because the change of emissivity forces the ice surface temperature toremain at the transition temperature Tα−β=35.6 K during most of
Pluto's northern fall and winter. Consequently, higher annual mean N2
ice surface temperature and surface pressure are obtained.
Fig. 10 shows the results obtained for simulation#TI888_050_072_phase, which reproduces the reference simulation but
taking into account the change of N2 ice emissivity. The main diﬀerences with the results from the reference simulation (Figs. 4 and 5) are:(1) N2 ice does not form thick perennial deposits outside Sputnik Planitia. Over a current annual timescale, N2 ice deposits in the mid-topolar regions are only seasonal and disappear during summer. In thelast 12 Myrs, perennial deposits are obtained only at low elevations, (2)No N2 ice forms at the south pole during a current Pluto year, (3) CH4
ice does not accumulate above 50°N and below 70°S.
Consequently, the decrease of N2 ice emissivity with temperature isan example of negative feedback which would limit the formation of N2
deposits outside Sputnik Planitia.

To summarize, Table 2 shows that the amount of CH4 ice lost by themodeled BTD over 30 Myrs is about 1 m, 10 m, 100 m or 1000 m assuming a CH4 ice albedo of 0.65, 0.6, 0.5, or 0.3 respectively.

4.4. Sensitivity to the albedo of the mid-to-polar CH4 deposits
Our results are also very sensitive to the albedo of the mid-to-polar
CH4 ice deposits. When this albedo is higher than 0.6, N2 ice tends tocondense on the CH4 ice during fall-winter and form seasonal (few mm
thick) or perennial deposits (up to 20 m thick), as shown for the reference case by Figs. 4 and 5. If the mid-to-polar CH4 ice albedo is lower
than 0.6, then only thin seasonal frosts of CH4 are obtained at the poles
during fall-winter, as they do not trigger N2 condensation. This casecorresponds to the results obtained in Section 3 and in BF2016.
The higher the albedo of mid-to-polar CH4 ice, the more N2 condenses, at higher latitudes, and the longer it remains and traps CH4
during Pluto's year. For instance, in our simulation using a mid-to-polar
CH4 ice albedo of 0.65 (#TI888_050_065, Fig. 8), we obtain perennial
N2 deposits at 30°N and very thin seasonal N2 deposits at higher latitudes and in the southern hemisphere above 50°S. As a result, CH4 icedoes not form thick deposits outside 50°N-50°S, but only seasonal frosts(e.g. the northern polar frost quickly disappears after 2013).
This is to be compared with the reference simulation (Figs. 4 and 5),
where the brighter mid-to-polar CH4 ice albedo (0.72) triggers N2
condensation at higher latitudes and leads to thick CH4 ice deposits up
to 70°N and 90°S, while the northern polar frost quickly disappears
after 2017.
Finally, in the more extreme case of a mid-to-polar ice albedo of 0.8(#TI888_050_080, Fig. 9), perennial deposits of N2 ice extend up to the

4.6. Sensitivity to the thermal inertia of the diﬀerent ices
In the previous sections, simulations have been performed assuming
a global uniform thermal inertia. In reality, the ices have diﬀerent
thermal inertia as it depends on the porosity of the material, the size ofgrains (larger grains lead to higher thermal inertia)... In this section, weallow each ice to have its own TI in the model, ranging from 400 SI to1200 SI, and we explore the impact of these changes on the results(summarized in the second part of Table 2).
For instance, simulation #TI8412_050_065 has been performed witha thermal inertia of 800 SI for N2 ice (“8”), 400 SI for CH4 ice (“4”) and1200 SI (“12”) for the water ice bedrock. In the model, TI evolves withtime depending on the new thickness of the volatile ice on Pluto's
surface. If a 1 m thick layer of CH4 ice lies on water ice in the model,
then the TI is set to 400 SI over the ﬁrst meter of the subsurface and to156

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Fig. 8. Simulation #TI888_050_065. Same as Figs. 4 and 5, except for a mid-to-polar CH4 ice albedo of 0.65.

400–1200 SI) than albedos, although the TI of the water ice bedrock
signiﬁcantly impacts the distribution of the thin polar deposits (seeFig. 13 and Fig. 14).

1200 SI below (in practice in the model the conductivity is modiﬁed tocorrespond to the required thermal inertia).
Changing the TI of N2 ice (e.g. simulations #TI488 or #TI1288)
does not signiﬁcantly change the ice distribution. This is because to ﬁrst
order, the variation of the exchanged mass of N2 between the surface
and the atmosphere is independent of thermal inertia, as detailed in
Section 2.2 in B2018.
Changing the TI of CH4 ice has also little impact on the ices distribution. Lower values of TI allows for colder CH4 ice during winter,and eventually to slightly larger seasonal and perennial reservoirs of N2
ice at the poles (simulations #TI848,#TI8412). The impact is also
limited by the fact that the simulated CH4 ice deposits are thin (fewmeter thick), because the initial reservoir is low (see Section 2.4).
Changing the TI of water ice has a signiﬁcant impact on the thin
volatile ice deposits, and therefore mostly at the poles (Figs. 11–14).
Low TI allows colder poles in winter and the formation of thicker CH4
and N2 deposits there (simulations #TI884). For instance, in the case of
a mid-to-polar CH4 ice albedo of 0.65 (#TI884_05_065, Fig. 11), thenorthern polar N2 deposit remains until years 2015–2020, and the CH4
frost until 2025. This is to be compared with simulation #TI888_05_065(Fig. 8), where the northern frosts only last until 2000 and 2010 respectively, and where no N2 condenses at the south pole. The eﬀect iseven stronger if we compare #TI884_05_072 (Fig. 13) with the reference case TI888_05_072 (Fig. 5). The N2 polar deposit remains longer
in northern spring and disappears after 2038, while the polar frost of
CH4 remains during the entire Pluto year.
To summarize, our results are much less sensitive to TI (in the range

4.7. Summary of simulation results
Fig. 15 gives an overview of the diﬀerent simulations performed inthis Section 4 and the diﬀerent ices distributions obtained depending on
the assumed albedo for CH4 ice. Fig. 15.1 shows how the simulations
were initialized: N2 ice ﬁlls Sputnik Planitia while unlimited amounts of
CH4 ice are placed roughly at the location of the BTD. If the CH4 ice
albedo remains well below 0.6, only seasonal CH4 frosts form at thepoles, as shown in Fig. 15.2. If the modeled BTD have an albedo well
above 0.6 (Fig. 15.3), then they become cold enough to trigger N2
condensation. The N2 ice deposits thus formed trap the CH4 ice, whichcannot feed the atmosphere with gaseous CH4. As a result, there is no
gaseous CH4 left in the system and no frost can form at the poles, which
remain volatile-free at all times. Using an albedo for the BTD around
0.6 allows the formation of N2 ice deposits only in the depressions ofthese terrains, as shown in Fig. 15.4. The high-altitude BTD remains N2free and feed the system with CH4, allowing the formation of seasonal
frosts at the poles. Finally, if the albedo of the mid-to-polar CH4 deposits is set higher than 0.6 (Fig. 15.5), then N2 can condense and form
thin seasonal deposits at the poles and larger deposits at mid-latitudes,
which can be perennial or seasonal (up to few tens of meter thick, inparticular in depressions). These N2 deposits are able to trap large
amounts of CH4 ice, resulting in the formation of a thick mid-latitudinal

Fig. 9. Simulation #TI888_050_080. Same as Figs. 4 and 5, except for a mid-to-polar CH4 ice albedo of 0.8.
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Fig. 10. Simulation #TI888_050_072_phase. Same as Figs. 4 and 5, except that the N2 ice emissivity varies according to its phase (α or β) from εα=0.3 to εβ=0.8.

occurs in year 2000 when the northern polar deposit of N2 disappears.
Simulations with a peak surface pressure occurring after 2010 are(1) the ones with a very high mid-to-polar CH4 albedo, leading to bothhemispheres covered by N2 ice during northern spring (these cases are
not realistic because they do not correspond to the ice distribution
observed by New Horizons), (2) the ones with a thermal inertia forwater ice around 400 SI (#TI444, #TI884, #TI12124). In these cases,
the thin northern polar deposit of N2 lasts until 2010–2015, (3) the ones
without N2 ice outside SP (like in BF2016). This scenario is only obtained when using in the model a “dark” mid-to-polar CH4 albedo (lessthan 0.6).
These results suggest that the southern hemisphere of Pluto is notentirely covered by N2-rich ice, otherwise the peak surface pressure
would have occurred much earlier than 2015 (a similar result is foundin Young, 2013; Olkin et al., 2015). At most, a thin mid-latitude band of
N2-rich ice (similar to that observed in the northern hemisphere) could
be present in the southern hemisphere in 2015.

mantle of CH4 ice.

4.8. Surface pressure and CH4 atmospheric mixing ratio
4.8.1. The peak surface pressure during northern spring
Simulations from BF2016 predicted an evolution of surface pressurein accordance with the stellar occultation observations conducted from
Earth since 1988. The threefold increase of pressure observed would
result from N2 ice heating when (1) Sputnik Planitia is most exposed to
sunlight (shortly after the northern spring equinox in 1989) and (2)Pluto is close to the Sun. Their model also predicts that the atmosphericpressure should decrease in the following decades, after reaching its
maximum around 2015, because of the orbitally-driven decline of insolation above Sputnik Planitia.
Here, in this paper, although the general aspect of the annual evolution of surface pressure remains unchanged (see Fig. 2.a in BF2016),
the peak surface pressure occurs earlier than 2015 in many of our simulations. The main diﬀerences between the simulations of this paper
and those from BF2016 are the presence of N2 ice deposits outside
Sputnik Planitia that slightly aﬀect the evolution of pressure (by enhancing the global condensation or sublimation ﬂow) and the better
resolution of the Sputnik Planitia basin (BF2016 only assumed a circular crater).
Our simulations show that the annual pressure peak occurs when
the area of the sublimation source in the northern hemisphere becomesless than the area of the condensation sink in the southern hemisphere.
For instance, in the reference simulation (#TI888_050_072), the peak

4.8.2. Evolution of surface pressure over astronomical timescales
In all simulations of this paper, the surface pressure obtained remains within few mPa-Pa, with a maximal value of 4 Pa over 30 Myrs.
This is in the same range than the values obtained in B2018 (see Fig. 16of their paper, lines obtained with an albedo of 0.7 for N2 ice). We could
have expected higher values in the results of this paper because we
obtained N2 deposits at the poles. However, the increase of pressure dueto their sublimation in summer is always balanced by the strong condensation ﬂux at the opposite pole.

Fig. 11. Simulation #TI884_050_065. Same as Figs. 4 and 5, except for a mid-to-polar CH4 ice albedo of 0.65 and a TI for water ice of 400 SI.
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Fig. 12. Simulation #TI8812_050_065. Same as Figs. 4 and 5, except for a mid-to-polar CH4 ice albedo of 0.65 and a TI for water ice of 1200 SI.

mixing ratio of CH4 or the entire atmosphere collapsed in Pluto's past,then a direct photolysis of surface ices and tholins could have happened, which would help in understanding the high degree of processing of the dark material in Cthulhu (Grundy et al., 2018).
To do that, we ﬁrst estimate the total incident ﬂux of Lyman-α at
Pluto over one orbit (Ftot), considering the solar as well as the interplanetary medium (IPM) Lyman-α sources (Gladstone et al., 2015), as
given by Eqs. 2 and 5 in Bertrand and Forget (2017):

4.8.3. Evolution of CH4 atmospheric mixing ratio over astronomicaltimescales
The atmospheric mixing ratio of CH4 obtained is very sensitive tomodel parameters (Bertrand and Forget, 2016), in particular thosecontrolling the BTD (main source of gaseous CH4). Fig. 16 shows theannual maximum and minimum values obtained over astronomicaltimescales for diﬀerent simulations. We note that (1) The CH4 atmospheric mixing ratio remains within 0.001–1 % in most of the simulations, including the reference case, (2) Higher values can be obtained
for a lower equatorial CH4 albedo (0.01–10 % with an albedo of 0.3),(3) Lower values are obtained when N2 condenses on the equatorial
CH4 deposits (10−4–10−2%), (4) The lower the albedo of the mid-topolar CH4 deposits, the higher the concentration of CH4 in the atmosphere (because of the higher equilibrium temperature and pressure of
CH4 and because there is less N2 deposit forming and therefore more
CH4 ice available to feed the atmosphere with gaseous CH4).

Ftot (dp) =FEarth
*0.875 + FIPM
4dp2

(2)

We assume a constant solar Lyman-α ﬂux at Earth FEarth = 4 × 1015
ph m−2 s−1, a constant IPM ﬂux at Pluto FIPM = 7.25 × 1011 ph m−2
s−1 and a constant extinction factor of 0.875. The IPM ﬂux does notstrongly depend on the Sun-Pluto distance dp (Gladstone et al., 2015),
therefore we consider it constant over time. The integration of Ftot overone Pluto orbit gives an annual mean incident Lyman-α ﬂux of 1.3×
1012 ph m−2 s−1. We then use Eq. (1) in B2018 to estimate the fractionof this incident Lyman-α ﬂux reaching the surface (Beer's law), by
feeding this equation with the values of surface pressure and atmospheric CH4 mixing ratio obtained from our simulations over 30 Myrs.
Fig. 17 shows the results for the same simulations than those shownin Fig. 16. The atmosphere remains relatively opaque at Lyman-α wavelengths over astronomical timescales. For the most realistic simulations, the fraction of the annual mean incident ﬂux that reaches thesurface varies between 0.01 and 10% over time, with the lowest values
obtained during high-obliquity periods, when mid-to-polar N2 ice

4.8.4. Opacity of Pluto's atmosphere at Lyman-α wavelengths
On Pluto, solar ultraviolet light is dominated by Lyman-α photons,
which control much of the photodissociation of CH4 and of the subsequent hydrocarbon photochemistry (Gladstone et al., 2016; Grundy
et al., 2018). Bertrand and Forget (2017) showed that the photochemical reactions are photon-limited in present-day Pluto's atmosphere, i.e. that enough gaseous CH4 is present for all photons to beabsorbed by CH4 molecules.
Here we want to assess the opacity of Pluto's atmosphere at Lyman-α
wavelengths over astronomical timescales. Indeed, if the atmosphericFig. 13. Simulation #TI884_050_072. Same as Figs. 4 and 5, except for a TI for water ice of 400 SI.
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Fig. 14. Simulation #TI8812_050_072. Same as Figs. 4 and 5, except for a TI for water ice of 1200 SI.

ratio is less than 0.01% over an entire year, as it is the case for thesimulations where N2 covers the equatorial CH4 deposits(#TI888_065_072, orange line). In this case, the CH4 cycle is disrupted
because the sources of gaseous CH4 are trapped by N2 ice, and CH4 canno longer block the energetic radiation, which would act directly on
Pluto's surface ices.

deposits are less stable. Over a current-year Pluto, we estimate that thefraction of Lyman-α reaching Pluto's surface is less than 1% of the total
ﬂux received. These fractions of Lyman-α ﬂux may be suﬃcient to havea signiﬁcant eﬀect on the chemistry of the N2:CH4:CO ice mixtures(Materese et al., 2015; Grundy et al., 2018). Indeed, even if most of the
Lyman-α ﬂux is greatly attenuated most of the time, the photolysis of
the ices goes on, albeit more slowly.
The fraction becomes negligible when the atmosphere is enriched ingaseous CH4, as it is the case if a low albedo of the equatorial CH4
deposits is considered (#TI888_030_072, green line). However, most of
the incident ﬂux can reach the surface if the atmospheric CH4 mixing

5. Discussions
In this section, we ﬁrst compare our results with Pluto's observations
and further discuss the possible scenarios for the formation and

Fig. 15. Summary of the simulation obtained in Section 4.
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relatively old, as suggested by their dark albedo (∼ 0.5, Buratti et al.,2017). The lack of craters suggests an upper limit on their age of
300 Myrs (Moore et al., 2018), although ancient craters may have beenerased by intense sublimation of these terrains. We estimate that ∼1 km thick CH4-rich deposits could form in the equatorial regions (30°S30°N) over 50–100 Myrs, assuming an initial reservoir elsewhere (e.g.
at the poles as in Section 3). Once this reservoir is depleted, extra
hundreds of Myrs would be necessary to collect CH4 ice from the edgesof the equatorial regions toward more equatorial latitudes and to pileup km-thick amounts of ice. If the BTD are only few hundreds meter
thick, they could have formed over 50 Myrs or less.
In the model, the equatorial CH4 deposits form at all longitudes
outside Sputnik Planitia. In reality, on Pluto, the unusual color of theseterrains is only seen between longitudes 210°E and 40°E (Olkin et al.,2017; Moore et al., 2018; Earle et al., 2018b), and ground-based observations support the presence of more CH4-rich deposits at theselongitudes (Grundy and Buie, 2001; Grundy et al., 2013). This longitudinal asymmetry must be investigated with a full 3D Global Climate
Model since it may be due to a dynamical eﬀect of Pluto's atmosphere.
We also show in Section 4 that if the mid-to-polar CH4 deposits arebright enough (we evaluate the critical CH4 albedo around ACH4=0.6),
then mm-thick seasonal or meter-thick perennial N2 deposits can formin these regions, preferentially at low elevations. In this case, we ﬁndthat the BTD are not stable and correspond to a net sublimation zone at
the astronomical timescale, because CH4 ice is transferred from the BTD
toward the mid-latitudes regions where it remains trapped by the perennial or seasonal N2 deposits. Assuming a CH4 albedo of 0.5 for themodeled BTD, we obtain a loss L CH4∼100 m of ice over the 30 Myrs inmost of our simulations (see Table 2). The km-thick BTD could therefore disappear within 300 Myrs.
These results suggest that the BTD were thicker in the past, and are
now gradually disappearing. This is to be related to their “bladed”
morphology, thought to be controlled by sublimation process (Moores
et al., 2017; Moore et al., 2017, 2018).

Fig. 16. Evolution of the annual maximum (solid line) and minimum (dashedline) global mean atmospheric mixing ratio of CH4 for diﬀerent simulations of
this paper.

5.1.2. The perennial reservoirs of N2 ice
Our simulations show that, the closer to the equator, the moreperennial are the N2 reservoirs (outside of Sputnik Planitia). As a general trend, our model simulates two types of perennial N2 reservoirs(apart from Sputnik Planitia). First, up to 200–300 m thick N2 ice deposits can form at the equator, at low elevations where relatively brightCH4 ice remains (albedo ∼0.6). This result is consistent with the detection of N2 ice in East Tombaugh Regio, in the depressions surrounding the BTD and in some deep craters in Cthulhu (e.g. Elliot
crater, where evidences of polygonal cells may be supportive of a thickdeposit), and suggests that these deposits may be stable over several
Myrs. Second, a 10–20 m-thick mid-latitudinal band (30–45° N) of N2
ice forms in most of our simulations and remains over several Myrs,
which is consistent with observations (see Fig. 15 in Schmitt et al.,2017; Protopapa et al., 2017). The extent of such N2 ice deposits toward
lower latitudes is limited by the presence of tholin-covered regions,which tend to darken the surrounding areas thus preventing further
accumulation of volatile ice.
All N2 ice deposits are balanced by the main reservoir in Sputnik
Planitia: as they form, the reservoir and therefore the surface level of N2
ice within the basin decreases which reinforces the N2 condensation in
the basin (Bertrand and Forget, 2016), thus limiting the amount of N2
ice that can form elsewhere. We also note that CH4-rich ice on Pluto
may not be trapped and buried by very large N2-rich deposits, since N2
ice is twice as dense as that of CH4 and may sink through the CH4 ice.
For instance, on Triton, the Cantaloupe terrain may result from such a
process (Schenk and Jackson, 1993).

Fig. 17. Fraction of Lyman-α ﬂux reaching Pluto's surface (on annual average)
for the same simulations than on Fig. 16.

evolution of the N2 and CH4 reservoirs.
5.1. Comparison of our results with Pluto's observations
5.1.1. The massive equatorial CH4 deposits
In our model, CH4 ice spontaneously tends to accumulate in theequatorial regions over astronomical timescales (see Section 3),
forming thick perennial CH4 deposits. This explains the presence of themassive equatorial CH4-rich Bladed Terrain Deposits observed by New
Horizons (Moore et al., 2018, 2016,Earle et al., 2018b).
We obtain a slightly larger accumulation of CH4 ice north of theequator, which is consistent with the observed extension of the BTD,
ranging in latitude from about 5°S to 28°N (see Fig. 4 in Earle et al.,2018b; Moore et al., 2018). This location is reproduced by our simulations when assuming a medium-to-high soil thermal inertia (Fig. 2).
Similar results are obtained by starting the same simulation at anotherepoch. The equatorial deposits are also slightly more extended to thenorth if we start the simulation at t0 = −100 Myrs, but to the south if
we start at t0 = −200 or −300 Myrs, which are assumed to be diﬀerent
epochs with a perihelion occurring at northern fall or winter during
maximum obliquity periods (Fig. 5 in B2018).
Our results show that 30 Myrs is too short a period of time to form
km-thick equatorial CH4-rich deposits like the BTD. The BTD may be

5.1.3. The mid-to-polar N2 and CH4 deposits
At the north pole, New Horizons detected CH4-rich deposits (Grundy
et al., 2016; Schmitt et al., 2017; Protopapa et al., 2017). Most of our161

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Fig. 18. The perennial reservoirs of N2 and CH4 ice identiﬁed on Pluto. The black arrows represent the possible exchanges of volatile ice that may occur overtimescales of millions of years.

(also shown in Earle et al., 2018b). At these latitudes, which border thedark tholin-covered regions, N2 ice deposits are not stable due to thedarker albedo and the high rate of contamination and darkening bytholins. However, CH4-rich frosts may form and last until spring/summer or even last longer and form perennial deposits.
Note that the exact latitudes where the volatile ice deposits form in
the model are sensitive to the surface properties (albedo, emissivity,
thermal inertia). In addition, dilution and mixing processes of these ices
should impact their latitudinal distribution.

simulations reproduce this trend by predicting a seasonal (mm-thick)CH4 ice deposit exposed on Pluto's surface at the north pole in 2015
(e.g. Figs. 5, 11), quickly disappearing and revealing the dark volatilefree surface during the following years. However, such a thin deposit
should have allowed the spectrometers on-board New Horizons for thedetection of the water ice bedrock below. The fact that water ice has notbeen detected anywhere in the polar region strongly suggests that atleast several centimeters or even meters of CH4-rich ice cover this region (or else the water ice is buried under photolytic byproducts).
Simulations #TI888_030_072 and #TI888_050_080 (Figs. 6 and 8
respectively) show that such perennial CH4-rich deposits can be obtained at the poles, by assuming a very dark albedo for the BTD or avery bright albedo for the polar CH4 deposits. These results may berelated to the yellow aspect of the polar region in false-color images(Olkin et al., 2017). For instance, the color may be due to the presenceof tholins mixed with (or seen through) the thin CH4-rich frost (Grundy
et al., 2018). Alternatively, the polar reservoir of CH4 may be perennial
and has accumulated tholins over the last Myrs. The higher concentration of tholins in these deposits may be responsible for their peculiar color.
At northern mid-latitudes, we obtain the formation of N2 ice deposits (on the bright CH4 deposits), which tend to be seasonal above
37°N as they sublime from the poles during end spring/summer. This
result explains the mid-latitudinal band of N2-rich ice observed in 2015
(Protopapa et al., 2017; Schmitt et al., 2017), and is consistent with thelatitudinal distribution of the diﬀerent ice mixtures observed at theselatitudes, indicative of N2:CO sublimation processes (Protopapa et al.,2017; Schmitt et al., 2017). Our results predict that N2 ice sublimation
will continue during northern spring/summer (with a sublimation front
advancing southward, as suggested in Protopapa et al., 2017) and reveal more CH4-rich terrains, while the redeposition of N2 ice will occur
in the southern winter hemisphere. Note that N2 ice is always morestable in the depressions than outside, which explains the patchy distribution of N2 found at northern mid-latitudes (see Fig. 15 in Schmitt
et al., 2017).
In the model, the seasonal mid-latitudinal N2 ice deposits are able totrap large amounts of CH4 ice, provided that a constant source is present elsewhere (in this case, the BTD). This also occurs in simulations
performed at other epochs (t0 = −100, −200, −300 Myrs) and explains the thick mantle of ice observed by New Horizons at these latitudes.
In the model, the N2 ice deposits forming between 30°N and 37° N
tend to be perennial, because they are located in colder regions on
average over several Myrs (this is an eﬀect of subsurface thermal inertia, as shown by Fig. 4.b in B2018). At lower latitudes, the dark albedo of the equatorial volatile-free surface prevent further N2 condensation. However, thin CH4 frosts may form on these dark terrains
during winter (see e.g. Fig. 11). This is consistent with the third latitudinal band observed on Pluto and mentioned in Protopapa et al.
(2017), where CH4-rich deposits are observed between 20°N and 30° N

5.1.4. Best case simulations
A simulation that best matches Pluto's observation would show (1)an ice distribution in 2015 as observed by New Horizons, that is with
CH4 ice exposed at the north pole and N2 ice subliming at mid-latitudes,(2) a peak surface pressure occurring after 2015, and (3) an atmospheric mixing ratio for CH4 around 0.5% in the period 2010–2015(Lellouch et al., 2015, 2011a). In this paper, although we exploredmany cases and obtained a plethora of results, it is diﬃcult to ﬁnd one
simulation that reconciles all these observations. Generally speaking,simulations performed with a thermal inertia for water ice of 400 SI
give the best results. This thermal inertia is low compared to the estimations (Leyrat et al., 2016) but allows for thicker deposits of CH4 atthe poles, which is consistent with the observations.
5.2. Scenario for the formation of observed CH4-rich and N2-rich reservoirs
We have identiﬁed two perennial reservoirs of volatile ice on Pluto
which add to Sputnik Planitia, as shown in Fig. 18: the mid-latitudinal
regions (mantle of CH4 ice and meter-thick N2 ice deposits) and theequatorial regions east of Sputnik Planitia (BTD of CH4 ice and lowaltitude N2 ice deposits).
Our model is able to reproduce the formation of the equatorial andmid-latitudinal perennial CH4 reservoirs, although not at the same time.
Indeed, both the BTD and the mid-latitudinal CH4 mantle need a sourceof available CH4 ice to form, and in our simulations one reservoir
dominates the other, depending on the assumed CH4 albedo. Thissuggests a complex history for the formation of these perennial reservoirs.
The reservoir in Sputnik Planitia must have been the ﬁrst to form,
since the basin is the oldest geologic feature identiﬁed on Pluto (Moore
et al., 2016, > 4 billion years) , and since its inﬁlling with all available
surface N2 ice has been modeled and estimated to be complete by tensof millions of years following its formation (Bertrand et al., 2018).
We could imagine that at a time in Pluto's history, large CH4-rich ice
deposits formed at the equator. At ﬁrst, they may have been covered by
N2-rich ice deposits, but as they thickened up and reached higher altitudes with time, N2-rich ice probably became less stable on these
deposits and remained in depressions only. The high-altitude CH4 ice
deposits may have then become older and darker with time, forming aplateau of darkened CH4-rich, precursor to the BTD. In our simulations,
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up to 10-m thick N2 deposits on the CH4 ice deposits, in particular at
low elevations. During northern spring and summer, these N2 deposits
sublime from the pole, explaining the latitudinal distribution of N2-richand CH4-rich ices observed by New Horizons in 2015 at the midnorthern latitudes (Protopapa et al., 2017; Schmitt et al., 2017).
At the north pole, the disappearance of CH4-rich frost during thenext decade predicted by most of our simulation may not happen because the observations suggest larger deposits than those simulated.
However, this is a testable prediction, as well as the removal of N2-rich
ice from the northern high latitudes, since it should result in changes in
Pluto's spectrum and maybe albedo and color, observable from Earth.
Our simulations also show that a large amount of CH4 ice can accumulate in the mid-latitudes due to the cold-trap eﬀect of N2 ice,forming a thick mantle consistent with the observations of Pluto's surface by New Horizons. In the model, CH4 ice is moved from the Bladed
Terrain Deposits, which tends to disappear as the mid-latitude mantle
forms.
These simulations indicate that there is always enough gaseous CH4
in Pluto's atmosphere for it to remain relatively opaque at Lyman-α
wavelengths over astronomical cycles, in particular during high-tomoderate obliquity periods. However, the small amounts of Lyman-α
ﬂux reaching the surface can be signiﬁcant to the surface chemistry.
Finally, our results highlight the strong coupling between the CH4
and the N2 cycle and the role of CH4 material as a controlling agent of
this coupling. They suggest a complex history for Pluto's perennial reservoirs as large amounts of CH4 ice may have been exchanged between
Sputnik Planitia, the Bladed Terrain, and the mid-latitudes, over timescales of hundreds of million years. The evolution of these reservoirs
may be driven by positive (“run-away”) or negative feedbacks involving
ice albedo, emissivity, dilution and mixing coeﬃcient, contaminationby haze particles, or ice irradiation. In order to improve our understanding of Pluto's surface, future versions of the Pluto volatile transport model should implement these processes and explore how they
impact Pluto's climate.

we show that there is a net transport of CH4 ice from the BTD to the
mid-latitudes, suggesting that the thick mantle of CH4 ice is subsequent
to the BTD, which could have formed by erosional sublimation.
Consequently, if the BTD formed very early in Pluto's history, why havethey not entirely disappeared by now? One solution is that the current
BTD formed only recently in Pluto's history, and may be currently
disappearing. One could imagine that the astronomical cycles of Pluto
may have changed over the last billion years and created the conditions
for the BTD only recently. However, Pluto is thought to be subject tovery little perturbations (Dobrovolskis et al., 1997) and the presence of
non-eroded ancient craters at the equator demonstrates a certain stability of the astronomical cycles (Binzel et al., 2017). Another solution
is that a long-term cycle exists between the perennial reservoirs, as illustrated by the black arrows in Fig. 18. In this case, processes not taken
into account in our model must exist and reﬁll Pluto's system with CH4
gas and ice.
For instance, large amounts of CH4 could be released at the northernand southern edges of the Sputnik Planitia ice sheet during the highobliquity periods, where intense N2 sublimation occurs (Bertrand et al.,2018). In fact, New Horizons observations of the northern edge of theice sheet revealed very dark plains of N2-rich ice enriched in CH4 ice(1–2 %, compared to 0.3% in the rest of the ice sheet), which supports
this scenario (Protopapa et al., 2017).
Albedo and topography run-away variations may also play a signiﬁcant role in redistributing N2 and CH4 ice to diﬀerent reservoirs(Earle et al., 2018a), as well as changes in ice composition, saturation,
contamination or irradiation (Schmitt et al., 2017; Protopapa et al.,2017; Grundy et al., 2018). Another possibility is the re-supply of large
amounts of CH4 from Pluto's interior, where sources of CH4 clathrate
could be stored and released over time via outgassing or cryovolcanism,
as proposed on Titan (Lunine and Atreya, 2008; Moore et al., 2016).
The lack of knowledge about these mechanisms makes it diﬃcult toinfer the total CH4 inventory in the system. A lower limit could be estimated by assuming that the high latitudes are only covered by thinlayers of CH4 ice and that most of the CH4 reservoir is contained in theBladed Terrain Deposits (the contribution of 0.3–0.5 % of CH4 in the N2
reservoir of Sputnik Planitia is negligible). Such a reservoir has been
estimated to be 22 m on global average in Section 2.4, for 500 m thick
BTD, but could be raised to 100 m if we assume 2–2.5 km thick BTD. An
upper limit of 1 km could be estimated by considering the BTD and a 1km thick CH4 mantle at latitudes higher than 15° (740 m on global
average). Note that the weak escape rate of CH4 observed by New
Horizons suggests that the reservoir of CH4 changed by only 28 m over
the age of the solar system (Gladstone et al., 2016).

Acknowledgments
This work was supported by the CNES. It is based on observations of
the New Horizons space mission. The authors thank the whole NASA
New Horizons instrument and scientiﬁc team for their excellent work on
a fantastic mission and their interest in this research. T. B. was supported for this research by an appointment to the National Aeronautics
and Space Administration (NASA) Post-doctoral Program at the Ames
Research Center administered by Universities Space Research
Association (USRA) through a contract with NASA.

6. Conclusions
References
The Pluto volatile transport model has been used to simulate theevolution of large N2 and CH4 ice reservoirs over seasonal and astronomical timescales, in response to the Milankovitch paleoclimate cycles. This complements the work done by B2018, which only exploredthe cycles of N2.
Our simulations reproduce the formation of massive perennial deposits of CH4-rich ice at the equator, explaining the observation of theBladed Terrain Deposits at these locations. The conﬁguration of Pluto's
orbit and obliquity is responsible for the small but detectable asymmetry of these terrains around the equator, which form further in thenorth than in the south, as seen in our model.
We demonstrate that high CH4 ice albedo values may suﬃciently
cool the surface and trigger N2 condensation which then cold traps
more CH4 ice. We obtained a plethora of results depending on the assumed albedo for CH4 ice, which controls the perennial or seasonal
nature of the deposits. Assuming relatively dark Bladed Terrain
Deposits allows the formation of perennial N2 ice in the depressions ofthese terrains only, which is consistent with the observations. Assuming
relatively bright mid-to-polar CH4 ice deposits leads to the formation of

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