Science 28Feb2020

using procedures developed earlier in the
mission, accounting for the solid angle sub-
tended by Arrokoth within the antenna beam
( 15 , 17 , 36 , 37 ). Accounting for the 414.4-km^2
cross section of Arrokoth and noise from in-
strument and background, we obtain a mean
brightness temperatureTB, averaged across
the night-side visible face of Arrokoth, of
TB=29±5K,whichiswithintherangeof
brightness temperatures estimated from an
earlier analysis ( 1 ). To translate that bright-
ness temperature to a kinetic temperature
requires knowledge of the X-band emissivity
of Arrokoth’s surface, which is not known but
most likely lies in the range 0.7 to 0.9 ( 36 ).
Thermophysical models were used to assess
the implications of thisTBmeasurement ( 15 ). For
each surface element of the three-dimensional
(3D) shape model ( 3 ), we balanced radiative
losses and thermal conduction against inso-
lation (received sunlight) and also reradia-
tion from other parts of Arrokoth’s surface
visible from that location. Accounting for self-
shadowing and surface reradiation makes this
modeling inherently global in scope ( 38 ). Sub-
surface thermal evolution was simulated with
a 1D thermal diffusion prescription ( 15 ). For
simplicity, we assume that Arrokoth’s obliq-
uity does not precess and that its orbit is
circular, with a semimajor axis of 44.2 AU
and period of 298 years. At this distance, the
incident solar radiation fluxF⊙is 0.7 W m–^2.
Given Arrokoth’s 99.3° obliquity ( 2 ), seasonal
effects are strong. We determined the sub-
solar latitude along approximately 300 equally
spaced temporal nodes over one orbital period
( 15 ). During the New Horizons flyby, the sub-
solar latitude was approximately–62°. At each
orbital node, the daily averaged (15.9-hour pe-
riod) solar insolation was calculated, account-
ing for self-shadowing. With these diurnally
averaged insolation profiles, we determined
the surface temperature on every element over

the course of an orbit. We assumed that the

subsurface thermal response is in the time-

asymptotic limit, meaning there is no net gain

or loss of thermal energy into or out of the

interior over the course of one orbit ( 39 ). This

assumption requires heat from radioactive

decay inside Arrokoth to be negligible and re-

quires the interior to have reached thermal

equilibrium with the Sun over the course of

the lifetime of the Solar System (see below).

We assume that the low–bond albedo [AB=

0.06 ( 1 , 3 )] surface of Arrokoth is character-

ized by a very low thermal inertia (G= 2.5 J

m–^2 s–1/2K–^1 ) typical of loosely consolidated

granular material, as inferred from infrared

observations of KBOs ( 40 ). The thermal in-

ertia is given byG≡

ffiffiffiffiffiffiffiffiffiffi

krCp

p

,wherekis thermal

conductivity,ris density, andCpis specific

heat at constant pressure. Arrokoth’sbulkden-

sity must be at least 290 kg m–^3 ( 3 )andden-

sities of small KBOs and comet nuclei tend to

be higher than that, but generally less than

1000 kg m–^3 ( 41 , 42 ). The density near the

surface that matters for Arrokoth’sthermal

response is even more uncertain and could

differ substantially from the bulk density. We

assume a generic density ofr= 500 kg m–^3 ( 3 )

and thatCp=350Jkg–^1 K–^1 .Underthese

assumptions, the corresponding thermal

conductivity is 3.6 × 10−^5 Wm–^1 K–^1 ,verylow

relative to values determined for surfaces in

the inner Solar System. These values corre-

spond to a seasonal thermal skin depthl=

0.55 m, wherel≡

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

ktsðrCp 2 pÞ^1

p

andtsis the

298-year seasonal period ( 43 ). This value is

similar to the electrical skin depth ( 36 ). The

subsolar equilibrium temperatureT*=58K

was obtained fromesT*^4 =(1–AB)F⊙, where

eis emissivity [commonly assumed to be 0.9;

e.g., ( 40 , 43 )],sis the Stefan-Boltzmann con-

stant (5.67 × 10−^8 Wm–^2 K–^4 ), andF⊙is the

solar flux at 44.2 AU. The thermal parameter

Q≡Gw 0 1/2s–^1 T*–^3 characterizes the efficiency

of the energy transport rate (per K) of ther-

mal conduction across one seasonal skin depth

relative to radiative losses ( 43 ), which is about

Q≡0.02 for Arrokoth. Such a small value ofQ

indicates that the surface layers are highly

insulating, leading to extreme variations in

surface temperature over the course of a year.

Winter surface temperatures are much lower

than peak summer temperatures. The low con-

ductivity might only pertain to a surficial layer.

If deeper below the surface the texture is more

compacted with greater granular contact, the

conductivity would likely be higher. We can

estimate the body’s thermalization time scale

by calculating the thermal wave propagation

time (tthermalization≡ 2 prCpR^2 k–^1 )acrossa

length scaleRcorresponding to the charac-

teristic radius of the short axes of both lobes

(~3.5 km). For values ofkgreater than 10−^4 W

m–^1 K–^1 , this time scale is less than the age of

the Solar System, supporting our assumption

of a time-asymptotic state.

Figure 7A shows the insolation averaged

over an orbit from two viewing positions. The

flattenedshapeandhighobliquityleadtothe

equator receiving less energy on average

(~0.1 W m–^2 ) than the poles (~0.2 W m–^2 ).

Owing to self-shadowing, the neck region gen-

erally receives less energy than the equato-

rial zone (ranging from 0.06 to 0.08 W m–^2 ).

Figure 7B shows the additional radiation

received from thermal emission from other

parts of Arrokoth itself, again averaged over

an orbit. Our model indicates that the neck

region is warmed by this trapping process,

receiving about 0.025 to 0.04 W m–^2 from self-

reradiation, which partially offsets the effect of

shadowing. Figure 7C shows the orbital aver-

age of the warming due to self-reradiation. The

neck region experiences the greatest amount

of relative warming, in the range of ~1 to 3 K.

Maryland crater also receives enhanced ther-

mal reradiation, but the relative warming in

Grundyet al.,Science 367 , eaay3705 (2020) 28 February 2020 5of10

Fig. 5. Principal components analysis of the CA04 infrared spectral imaging data.(AtoE) Same as Fig. 2, but for the LEISA observation in Fig. 4. Edge pixels
have been removed; the white outlines show the full extent of Arrokoth.

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