Highly Depleted Alkali Metals in Jupiter
’
s Deep Atmosphere
Ananyo Bhattacharya
1
, Cheng Li
1
, Sushil K. Atreya
1
, Paul G. Steffes
2
, Steven M. Levin
3
, Scott J. Bolton
4
,
Tristan Guillot
5
, Pranika Gupta
1
, Andrew P. Ingersoll
6
, Jonathan I. Lunine
7
, Glenn S. Orton
3
, Fabiano A. Oyafuso
3
,
J. Hunter Waite
8
, Amadeo Bellotti, and Michael H. Wong
9
1
University of Michigan, Ann Arbor, USA;
ananyo@umich.edu
2
Georgia Institute of Technology, USA
3
NASA Jet Propulsion Laboratory, USA
4
Southwest Research Institute, USA
5
Université Côte d
’
Azur, France
6
California Institute of Technology, USA
7
Cornell University, USA
8
Waite Science LLC, USA
9
University of California, Berkeley, USA
Received 2023 April 12; revised 2023 June 6; accepted 2023 June 19; published 2023 July 27
Abstract
Water and ammonia vapors are known to be the major sources of spectral absorption at pressure levels observed by
the microwave radiometer
(
MWR
)
on Juno. However, the brightness temperatures and limb darkening observed by
the MWR at its longest-wavelength channel of 50 cm
(
600 MHz
)
in the
fi
rst nine perijove passes indicate the
existence of an additional source of opacity in the deep atmosphere of Jupiter
(
pressures beyond 100 bar
)
. The
absorption properties of ammonia and water vapor, and their relative abundances in Jupiter
’
s atmosphere, do not
provide suf
fi
cient opacity in the deep atmosphere to explain the 600 MHz channel observation. Here we show that
free electrons due to the ionization of alkali metals, i.e., sodium and potassium, with subsolar metallicity,
[
M
/
H
]
(
log-based 10 relative concentration to solar
)
in the range of
[
M
/
H
]
=
−
2to
[
M
/
H
]
=
−
5, can provide the missing
source of opacity in the deep atmosphere. If the alkali metals are not the source of additional opacity in the MWR
data, then their metallicity at 1000 bars can only be even lower. This upper bound of
−
2 on the metallicity of the
alkali metals contrasts with the other heavy elements
—
C, N, S, Ar, Kr, and Xe
—
that are all enriched relative to
their solar abundances, having a metallicity of approximately
+
0.5.
Uni
fi
ed Astronomy Thesaurus concepts:
Chemical abundances
(
224
)
;
Jupiter
(
873
)
;
Solar system
(
1528
)
;
Extrasolar gaseous giant planets
(
509
)
1. Introduction
The alkali metals sodium and potassium have been previously
detected in the atmospheres of hot Jupiters and a super-Neptune,
together with lithium
(
Chen et al.
2018
)
in the latter. The
detections show a large range of abundances from highly
substellar to superstellar values
(
Demory et al.
2011
;Welbanks
et al.
2019
)
. Alkali metal abundances are important in
understanding the formation of hot Jupiters and represent a
bridge between the refractory and volatile elements, which in
molecular form seed the growth of planets. Obtaining the
abundance of alkali metals in Jupiter can potentially serve as a
fi
rst constraint on the ratio of rocky to icy material in the interior
of the solar system
’
s largest planet, when combined with the
elemental and molecular abundances provided by the Galileo
Probe Mass Spectrometer
(
GPMS; Atreya et al.
1999
,
2019
;
Wong et al.
2004
)
and the Juno constraints on water
(
Li et al.
2020
)
. Here we derive observationally based abundances of
alkali metals in Jupiter
’
s atmosphere to determine whether they
are enriched relative to solar, like the other heavy elements, or
depleted.
To obtain these abundances requires knowing the deep
structure of Jupiter
’
s atmosphere. The shallower part of
Jupiter
’
s atmosphere has been previously investigated at
microwave frequencies by the Very Large Array
(
VLA
)
telescope
(
de Pater & Dunn
2003
; de Pater et al.
2019
)
. VLA
probes Jupiter at frequencies in the range of 74 MHz to 50 GHz
(
de Pater et al.
2019
)
. However, confusion from Jupiter
’
s
powerful synchrotron radiation does not allow VLA to observe
Jupiter
’
s atmosphere below 5 GHz
(
de Pater & Dunn
2003
)
,
limiting its reach to less than 5 bars, leaving the deep
atmosphere of Jupiter inaccessible from microwave and radio
frequency observatories from Earth. The orbit of Juno and the
spin of the spacecraft allow the spacecraft to make observations
at low frequencies, i.e., 0.6 and 1.2 GHz, by avoiding the
energetic electron belts around Jupiter from its
fi
eld of view.
Access to greater depths allows for the investigation of the bulk
elemental abundances of N and O in Jupiter
(
Bolton et al.
2017
;
Janssen et al.
2017
; Steffes et al.
2017
)
.
The Microwave Radiometer
(
MWR
)
instrument on board the
Juno orbiter is a passive radiometer that is designed to measure
the internal heat emitted by Jupiter
’
s atmosphere at six different
frequencies, ranging from 0.6 to 22 GHz
(
Janssen et al.
2017
)
.
The brightness temperature measured by MWR at these
frequencies sounds different levels of Jupiter
’
s atmosphere
corresponding to pressures from 0.3 to 250 bar
(
Janssen et al.
2017
)
. In addition, the highly inclined polar orbit and rotation
of the Juno spacecraft aided the high spatial resolution
necessary for probing Jupiter
’
s atmosphere at various latitudes
(
Bolton et al.
2017
)
.
Previous analysis of the MWR data at 0.6 GHz found an
unanticipated limb-darkening signal, which cannot be explained
The Astrophysical Journal Letters,
952:L27
(
13pp
)
, 2023 August 1
https:
//
doi.org
/
10.3847
/
2041-8213
/
ace115
© 2023. The Author
(
s
)
. Published by the American Astronomical Society.
Original content from this work may be used under the terms
of the
Creative Commons Attribution 4.0 licence
. Any further
distribution of this work must maintain attribution to the author
(
s
)
and the title
of the work, journal citation and DOI.
1
by nominal absorbers such as ammonia and water
(
Li et al.
2020
)
. Based on investigations of thermodynamic models of
Jupiter
’
s deep atmosphere between 50 bar and 1 kbar
(
Weidenschilling & Lewis
1973
; Fegley & Lodders
1994
)
,we
conjecture that the free electrons from thermally ionized alkali
metals may provide the missing opacity. Alkali metals are
expected to undergo condensation to form clouds in the deep
atmosphere
(
Visscher et al.
2006
;Morleyetal.
2012
)
.Na
2
Sand
KCl are the
fi
rst chemical species to condense in the above
pressure range and thereby act as a sink for atomic sodium and
potassium
(
Fegley & Lodders
1994
)
. Furthermore, high-
temperature environments cause alkali metals to undergo
ionization due to their low ionization energies
(
Bagenal et al.
2007
)
. Density and temperature play a role in governing the
electron densities according to the Saha ionization equation
(
Equation
(
2
))
. Electrons generated from alkali metal ionization
act as a source of absorption at microwave frequencies that
could affect the brightness temperatures at the 0.6 GHz
frequency channel. Therefore, the objective of this study is to
determine the alkali metal abundance in the deep atmosphere of
Jupiter.
To facilitate comparison of our results on alkali metals with
those of the extrasolar planets, we express the abundances of
nonhydrogen and helium elements using astronomical
terminology, e.g., metallicity. The metallicity
(
[
M
/
H
]
)
of an
element is the logarithm of the ratio of the elemental abundance
in a system to the stellar
(
or solar, for the solar system
)
elemental abundance. Generally, the metallicity of a star is
de
fi
ned in terms of the ratio of the number of Fe atoms to the
number of hydrogen atoms. Here we de
fi
ne the metallicity in
terms of the alkali metal abundance in Jupiter to that of the Sun,
e.g., for potassium,
[
K
/
H
]
=
log
10
(
N
K
/
N
H
)
Jupiter
–
log10
(
N
K
/
N
H
)
Sun
. For the giant planets, iron and silicon are not
measurable, emphasizing the importance of proxy indicators
such as the alkali metals along with other elements measured
by GPMS.
2. Methods
Brightness temperatures from nine perijoves
—
i.e., PJ 1, 3
–
9,
and 12
—
have been taken into consideration for this article.
Variations in brightness temperatures have been observed
across the planetocentric latitudes from pole to pole in the 0.6
and 1.2 GHz channels. These variations can be attributed to
various sources of origin from the atmosphere and space
environment. The most important sources of the observed
variability are:
(
i
)
changes in atmospheric structure and
composition;
(
ii
)
Jupiter
’
s synchrotron radiation in the
microwave band; and
(
iii
)
the variation in acceleration due to
gravity due to the nonspherical shape of Jupiter. The latter
sources, i.e., synchrotron and gravity, need to be taken into
account for proper interpretations of MWR observations. They
will aid in investigating the true variability in Jupiter
’
s deep
atmosphere.
The contribution of Jupiter
’
s gravity can be corrected by
taking into account the nonspherical shape of Jupiter.
Brightness temperatures are corrected using a gravity
correction factor, de
fi
ned as the ratio of theoretical
T
b
at a
given latitude to that at the equator of Jupiter, taking into
consideration the acceleration due to gravity at the latitude.
Thereby, it transforms the Juno observations at each latitude for
equatorial gravity, which effectively removes the variation in
T
b
due to changes in Jupiter
’
s gravity from the equator to the
poles.
Energetic electrons in Jupiter
’
s space environment contribute
to the synchrotron radiation
(
Levin et al.
2001
; de Pater &
Dunn
2003
; Santos-Costa et al.
2017
)
. The signature of the
emission is observed in MWR data across all the perijoves,
which leads to anomalous changes in
T
b
. Data at extremely
high latitudes are polluted by synchrotron emission and thus
remain of no use for investigating Jupiter
’
s deep atmosphere.
Therefore, we only consider the MWR data between
−
60
°
and
60
°
latitude. The correction for synchrotron and other sources
of anomalous
T
b
is done by
fi
ltering the data at 0.6 and 1.2 GHz
for each perijove. The process is carried out by sorting the
deviations of
T
b
from the least value of T
b
in a group and
removing the values greater than a
fi
lter cutoff temperature of
the order of 2 K.
3. Results
3.1. Sources of Microwave Opacity
The weighting function of Jupiter
’
s atmospheric absorption
and emission at a given microwave frequency determines the
contribution of each region in the atmosphere to the observed
brightness temperature at the given frequency. The peak
structure of the weighting function gives the range of pressure
levels corresponding to the measurements. The weighting
function can be expressed as a function of the microwave
opacity of the atmosphere
(
Equation
(
1
))
. Here,
T
b
is the
brightness temperature,
W
(
p
)
is the weighting function as a
function of pressure, and
T
(
p
)
is the physical temperature
pro
fi
le of the atmosphere:
()()()
T
W pT pd P
ln .
1
b
ò
=
-¥
¥
Figure
1
shows the relative weighting functions, i.e., the
weighting function divided by the maximum value of the
function, at 0.6 GHz and 1.2 GHz, with and without alkali
metals. In the absence of alkali metals, the relative weighting
functions peak at 100 bar and 30 bar, respectively
(
Janssen
et al.
2017
)
. At 0.6 GHz, the relative weighting function
extends to the deeper atmosphere below the 100 bar level, and
therefore the
T
b
derived using this channel is sensitive to the
sources of microwave opacity present in the deep atmosphere at
p
greater than 100 bar. The relative weighting function at the
0.6 GHz channel shows a broad shape with a second maxima at
kilobar pressure levels, which is attributed to the increase in the
mass absorption coef
fi
cients of water vapor with pressure. The
mass absorption coef
fi
cient of ammonia decreases after a
maximum near 1000 bar, and eventually water vapor dominates
the opacity in the deep atmosphere. Moreover, the inclusion of
free electrons as sources of opacity due to alkali metal
ionization causes a decrease in the value of the relative
weighting function at 0.6 GHz around 100 bar, and a global
maximum in the relative weighting function emerges at
∼
1
kbar pressure
(
magenta line
)
. The shift of the global maximum
can be attributed to the increase in opacity from free electrons
with pressure as the ionization fraction of alkali metals
increases with temperature under thermal equilibrium condi-
tions
(
Saha
1920
; described later in this section
)
. The inclusion
of lower amounts of alkali metals
(
[
M
/
H
]
=
−
5
)
will lead to a
peak at deeper levels
(
Figure
1
)
. However, as the metallicity is
increased to solar, the maximum drifts toward lower pressures
around the 1 kbar level. This could be attributed to the fact that
2
The Astrophysical Journal Letters,
952:L27
(
13pp
)
, 2023 August 1
Bhattacharya et al.
a higher abundance of alkali metals can produce a higher
amount of electrons at relatively lower pressures
(
magenta
line
)
, whereas a low abundance of alkali metals in Jupiter
would need to reach higher pressure
(
>
1 kbar
)
to produce
equivalent opacity
(
blue line
)
. Therefore, the abundance of
alkali metals directly affects the shape of the weighting
function.
The main sources of microwave opacity at 0.6 and 1.2 GHz
are ammonia, water vapor, free electrons, and collision-induced
absorption by hydrogen and helium. Hydrogen
–
hydrogen and
hydrogen
–
helium collisions are the dominant sources of
collision-induced absorption processes in Jupiter. Their
magnitude is well constrained due to the invariance of the
hydrogen and helium abundances in Jupiter
’
s deep atmosphere.
The microwave absorption behavior of water and ammonia
vapor has been investigated by laboratory experiments that
show the pressure and temperature dependence of mass
absorption coef
fi
cients
(
Karpowicz & Steffes
2011
; Devaraj
et al.
2014
; Bellotti et al.
2016
)
. In addition, hydrogen,
methane, and water vapor contribute to line broadening in the
ammonia vapor absorption. The models based on laboratory
experiments show signi
fi
cant divergent behavior when
extrapolated to pressures greater than 50 bar and 550 K
(
Bellotti et al.
2016
)
. In order to obtain a robust estimate of the
range of absorption coef
fi
cients at higher temperatures, we test
a grid model describing a power scaling relationship with
temperature, based on the Hanley et al.
(
2009
)
model of
ammonia absorption. For water vapor absorption at microwave
frequencies, the laboratory models show divergence by orders
of magnitude. However, recent laboratory measurements
(
Steffes et al.
2023
)
at high pressure show that the water vapor
absorption can be explained by the Bellotti et al.
(
2016
)
model.
Therefore, the Bellotti et al.
(
2016
)
model is chosen to compute
the water vapor opacity, which incorporates water opacity
measurements at high temperatures above 500 K.
Free electrons in the atmosphere can act as a source of
opacity at microwave wavelengths through the process of free
–
free absorption, in which electrons absorb photons during
collisions with other ions and electrons. Electrons can be
generated by the ionization of various elemental and molecular
species in the atmosphere. Due to their low ionization energies,
alkali metals, i.e., Na and K, are expected to be the major
sources of free electrons in the atmosphere
(
Heays & Bosman
2017
)
. In Jupiter
’
s atmosphere, the pressure and temperatures
corresponding to the transition between the alkali metals and
their compounds are calculated using an equilibrium cloud
condensation model
(
ECCM; Weidenschilling & Lewis
1973
;
Atreya et al.
1999
)
for Jupiter
’
s adiabat, with saturation vapor
pressures of Na
2
S and KCl
(
Visscher et al.
2006
; Morley et al.
2012
)
. The condensation of alkali metals at solar abundance
(
Figure
2
)
takes place at 352 bar for KCl and 796 bar for Na
2
S,
with corresponding temperatures of 967 K and 1234 K,
respectively, assuming thermodynamic equilibrium. The
condensation of Na
2
S at deeper levels, and a higher solar
abundance of Na compared to K
(
Asplund et al.
2009
)
, will
cause Na
2
S clouds to be signi
fi
cantly more massive than KCl
clouds. Thermochemical equilibrium models indicate the
formation of metal hydrides and hydroxides in the gas phase,
but they are much lower in abundance
(
Fegley & Lodders
1994
)
as compared to the condensates, therefore they will not
act as the primary sink of alkali metals in Jupiter. Condensation
of the alkali metal compounds occurs when the partial pressure
of a compound exceeds its saturation vapor pressure. If
Figure 1.
Relative weighting functions at 0.6 GHz
(
black
)
and 1.2 GHz
(
gray
)
for a Jupiter adiabat considering the Hanley model
(
Hanley et al.
2009
)
for NH
3
absorption. The functions peak at 100 bar and 30 bar at 0.6 GHz and 1.2 GHz, respectively, without the inclusion of alkali metals. The inclusion of alkal
i metals
(
orange, magenta, and blue lines
)
decreases the relative weighting function at
∼
100 bar and produces a second peak that is observed at
∼
1 kbar pressure, due to the
opacity contributed by free electrons from alkali metal ionization. As the metallicity of the alkali metals increases, the global maximum of the weig
hting function shifts
toward a lower pressure.
3
The Astrophysical Journal Letters,
952:L27
(
13pp
)
, 2023 August 1
Bhattacharya et al.
condensation occurs, it causes depletion in the alkali metal
abundances at altitudes above the condensation level.
At high pressures 100 bar and beyond, alkali metals would
undergo ionization to form cold plasma, and the electrons
generated in the process would act as an additional source of
opacity at microwave frequencies. The number density of free
electrons due to the ionization of alkali metal atoms in the gas
phase is calculated using the Saha
(
1920
)
ionization
Equation
(
2
)
, assuming Jupiter
’
s atmosphere to be in a state
of thermal equilibrium. The ionization equation itself assumes a
single-component gas-phase system. Therefore, we add the
electron densities from the ionization of sodium and potassium
to determine the total number density of free electrons. Here,
N
e
is the electron density,
N
is the number density,
ò
is the
ionization energy,
λ
is the de Broglie wavelength,
g
0
and
g
1
are
statistical weights,
k
B
is the Boltzmann constant,
m
e
is the mass
of the electron, and
h
is Planck
’
s constant:
()
N
NN
g
g
e
2
,2
e
e
kT
2
3
1
0
B
l
-
=
-
()
h
mk T
2
.3
e
2
B
l
p
=
The brightness temperatures correspond to electromagnetic
radiation traveling from the interior of Jupiter radially outward
through the atmospheric layers. Thus, the transmission through
the deep atmosphere is similar to the transmission through a
cold plasma medium. The refractive index of microwaves
propagating through a cold plasma medium can be described
by the Appleton
–
Hartree equation
(
Helliwell
2014
)
. The
formulation is applicable to low-temperature plasma media,
both in the presence or absence of magnetic
fi
elds. At
100
–
1000 bar pressure levels, the contribution of the magnetic
fi
eld is insigni
fi
cant in the Appleton
–
Hartree formulation
(
Helliwell
2014
)
. Therefore, a simpli
fi
ed version of the
Appleton
–
Hartree equation
(
Equation
(
4
))
is used to calculate
the complex refractive index of the deep atmosphere, using the
electron number density calculated from the Saha ionization
equation. For an unmagnetized cold plasma medium, i.e.,
Jupiter
’
s deep atmosphere, the Appleton
–
Hartree equation is
simpli
fi
ed to:
()
n
X
iZ
1
1
,4
2
=-
-
()
Q
2
.5
ch
a
p
l
=
Here,
X
=
0
2
2
w
w
,
Z
=
n
w
,
ω
0
is the electron plasma frequency,
ω
is
the angular frequency of microwave radiation,
ω
h
is the
electron gyrofrequency,
ν
is the electron-neutral collision
frequency,
λ
ch
is the frequency of a given MWR channel,
n
is
the refractive index,
α
is the extinction coef
fi
cient, and
Q
is the
quality factor, i.e., the ratio of squares of real and imaginary
parts of the refractive index.
3.2. Radiative Transfer Modeling
In order to draw a comparison between the MWR
observations and theoretical knowledge of Jupiter
’
s atmos-
phere, a benchmark model for the ideal Jupiter atmosphere is
constructed using a moist hydrostatic adiabat following the
ideal gas law
(
Li et al.
2018b
,
2018a
)
. The speci
fi
c heat of
hydrogen is estimated from the mixing ratio of ortho- and para-
hydrogen, assuming thermal equilibrium between the ortho and
Figure 2.
Condensation curves of NH
3
,H
2
O, H
2
S, and the alkali metals Na
2
S and KCl at solar abundance. Our calculations are based on the ECCM
(
Atreya
et al.
1999
)
and saturation vapor pressure corresponding to Na
2
S and KCl
(
Visscher et al.
2006
; Morley et al.
2012
)
. The cloud bases are at the levels where the
condensation curves cross the adiabat considering
T
1bar
=
166.1 K
(
Seiff et al.
1998
)
.
4
The Astrophysical Journal Letters,
952:L27
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13pp
)
, 2023 August 1
Bhattacharya et al.
para states. Moreover, the temperature pro
fi
le of Jupiter
’
s
atmosphere is constructed for two cases of reference
temperatures:
(
i
)
T
=
166.1 K at the 1 bar pressure level from
the Galileo Probe
(
Seiff et al.
1998
)
; and
(
ii
)
T
=
168.8 K at the
1 bar pressure level based on the re-analysis of the Voyager
radio occultation experiment at Jupiter
(
Gupta et al.
2022
)
.
Ammonia and water vapor are considered vapors for the moist
adiabat and their partial pressure is controlled by the cloud
condensation process, by forcing the partial pressures to be
equal to their saturation vapor pressures. In the deep
atmosphere of Jupiter, water and ammonia are not expected
to form clouds; however, alkali metals are expected to undergo
condensation. Therefore, a similar approach is applied to alkali
metals to estimate the concentration of alkali metals present in
the gas phase available for the ionization process.
Spectral radiance is proportional to the physical temperature
of the atmosphere in the Rayleigh
–
Jeans limit. For microwave
frequencies, we compute the brightness temperature
(
T
b
)
from
the physical temperature using Equation
(
1
)
. The opacity of
Jupiter
’
s atmosphere is the sum of the opacities from the
individual sources discussed in the previous section, i.e.,
ammonia, water, free electrons, and collision-induced absorp-
tion. The abundances of ammonia and water vapor have been
assumed to be 2.7 and
fi
ve times the solar abundance
(
Li et al.
2020
,
2017
)
. Because there is no a priori information on the
alkali metal abundance in Jupiter, we therefore compare two
cases, one without alkali metals
(
baseline
)
and another with
alkali metals
(
treatment
)
, in order to provide a comparison
between our current knowledge of Jupiter and MWR data.
The spatial resolution of the MWR data also provides the
limb-darkening coef
fi
cient at six microwave frequencies. Limb
darkening
(
L
d
)
is de
fi
ned as the percent change in
T
b
at a given
viewing angle relative to
T
b
, at a position looking vertically
down to the planet center, i.e., the nadir. For our simulations,
we compute the limb darkening at a 45
°
angle from the nadir.
The MWR channels at 0.6 and 1.2 GHz are chosen to provide a
comparison between theory and observations at higher
pressures, using
T
b
and
L
d
as the observables for comparison.
The benchmark case of the ideal Jupiter atmosphere is
compared with MWR observations as a function of latitude
between
−
40
°
and 40
°
planetocentric latitude. Data from
higher latitudes are neglected, due to the presence of signatures
from synchrotron radiation that are inseparable from the
atmospheric contribution.
Latitudinal variations in brightness temperatures are
observed at both 0.6 and 1.2 GHz
(
Figure
3
, panels
(
a
)
and
(
c
))
. The small-scale variations in
T
b
and
L
d
in all the panels
can be attributed to variations in the atmospheric temperature
structure and composition. It is important to note that the
baseline case
(
without alkali metals
)
corresponds to two
Figure 3.
Limb-darkening and brightness temperature MWR observations compared with simulation results at 0.6 and 1.2 GHz, corresponding to Jovian adiabats a
t
(
i
)
T
1bar
=
166.1 K and
(
ii
)
T
1bar
=
168.8 K.
(
a
)
T
b
vs. latitude at 0.6 GHz.
(
b
)
L
d
vs. latitude at 0.6 GHz.
(
c
)
T
b
vs. latitude at 1.2 GHz.
(
d
)
L
d
vs. latitude at 1.2 GHz.
5
The Astrophysical Journal Letters,
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)
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Bhattacharya et al.
different temperature pro
fi
les of Jupiter
’
s atmosphere for two
different T
1
bar
. There is an agreement between the baseline
case and observations at 1.2 GHz in the equatorial region
(
panel
(
c
))
. On the other hand, the brightness temperatures at
0.6 GHz are lower than the baseline case by 40
–
60 K at all
latitudes
(
panel
(
a
))
, indicating the possibility of an additional
source of opacity. Such a source is also supported by a
depressed
L
d
observed by MWR; it is 4% less than the
L
d
magnitude of the ideal Jupiter atmosphere across all latitudes
(
panel
(
b
))
. The mismatch between the baseline and
observations at 0.6 GHz is much greater than the uncertainty
in measurements and variations in
T
b
and
L
d
. Since the
brightness temperatures correspond to different pressure
regions in the atmosphere, the anomalous observations at
0.6 GHz must be attributed to the presence of an additional
opacity source in the deep atmosphere or to a different opacity
source that absorbs more effectively at 0.6 GHz than at
1.2 GHz. We test four confounding factors:
(
i
)
the distribution
of ammonia;
(
ii
)
the ammonia opacity at temperatures
exceeding the range of laboratory measurements;
(
iii
)
the
opacity of water at high temperatures; and
(
iv
)
the contribution
of alkali metals. The theoretical brightness temperature and
limb darkening at 0.6 GHz and 1.2 GHz are shown in Figure
3
.
The latitudinal distribution of brightness temperatures and
limb darkening from the forward model indicates the decrease
in limb darkening from the equator to the pole at 0.6 GHz. This
is opposite to the variation of limb darkening at 1.2 GHz across
the latitudes. This effect could be attributed to the free electrons
in the deep atmosphere, which could be inferred from the shift
in contribution functions toward higher pressures in the
presence of alkali metals
(
Figure
1
)
. Alkali metals greatly
affect the absorption behavior at 0.6 GHz, which dominates the
effect of gravitation on limb darkening.
3.3. Ammonia, Water, and Alkali Metals
Brightness temperature variations with latitude and the
spectral inversion of brightness temperatures show a nonuni-
form distribution of ammonia vapor in Jupiter
’
s atmosphere in
the deep atmosphere region
(
Ingersoll et al.
2017
; Li et al.
2017
)
. Therefore, the nonuniform distribution of ammonia
could contribute to variations in the microwave opacity of the
deep atmosphere. In order to estimate the effect of ammonia
concentration variations, we perturb the ammonia pro
fi
le in the
model and use a scaling factor to vary the magnitude of the
ammonia vapor concentration in the model, as described in
Equation
(
6
)
:
()()(()())()
qPqPqPq
Ps
.6
NH
NH ,0
NH ,0
NH ,MWR
3
333
=- -
Here,
q
NH
3
is the ammonia mass mixing ratio at a given
pressure
P
and
()
P
q
NH ,0
3
is the homogeneous ammonia mixing
ratio, which is set to 2.7 times solar abundance for
NH
3
∼
360 ppm
(
Li et al.
2017
)
from the deep atmosphere
until the NH
3
vapor saturation point. Above the saturation
point, the mixing ratio follows the NH
3
saturation vapor
pressure curve.
q
NH ,MWR
3
(
P
)
is the mixing ratio retrieved from
MWR inversion. We use a scaling factor to vary the ammonia
mixing ratio between the homogeneous case to the MWR-
derived pro
fi
les. The scaling factor, s, ranges from 0 to 1.5,
where 0 is the case for the homogeneous mixing ratio.
Increasing s to 1 will change the ammonia pro
fi
le to the MWR
inversion case for the equator and midlatitude regions. We also
extend the scaling factor to 1.5, in order to take into account the
low ammonia mixing ratio observed at the North Equatorial
Belt of Jupiter
(
Li et al.
2017
)
.
NH
3
opacity measurements are currently not available for
high temperatures
(
550
–
3000 K
)
corresponding to Jupiter
’
s
deep atmosphere, and there is a decrease in the magnitude of
the absorption of NH
3
at high pressures. Therefore, we invoke
a scaling factor for the NH
3
absorption coef
fi
cient to provide an
estimation of the opacity at high temperatures. The mass
absorption coef
fi
cient of ammonia is estimated by multiplying
the temperature scaling law to the absorption coef
fi
cient based
on Hanley et al.
(
2009
; Equation
(
7
))
. In this equation,
α
is the
absorption coef
fi
cient of NH
3
, h is the opacity factor,
T
is the
temperature, and
T
c
is the reference temperature equal to 750 K.
The NH
3
opacity models show that the absorption coef
fi
cient
peaks at 750 K and decreases at temperatures beyond 750 K. In
the simulations, the scaling factor is multiplied to the NH
3
opacity at temperatures higher than
T
c
. The power-law index
(
h
)
is varied from 1 to 5, keeping the ammonia concentration
constant, i.e., 2.7 times solar abundance. We also keep the
water vapor constant at
fi
ve times solar abundance, as the
laboratory measurements demonstrate that water vapor
absorption does not show a signi
fi
cant increase with pressure,
and it can be said to be relatively transparent when compared to
the previous model of microwave absorption
(
Steffes et al.
2023
)
:
()()
⎛
⎝
⎞
⎠
T
T
NH
.
7
c
h
3
a
~
Changing the ammonia pro
fi
le and introducing the additional
temperature-dependent scaling factor produce brightness
temperatures and limb darkening that are divergent from the
MWR data at 0.6 GHz, as shown in Figure
4
(
a
)
. The difference
between
T
b
from the model and observations is in the range of
50
–
200 K at 0.6 GHz. Reducing the ammonia concentration
causes a monotonic increase in
T
b
and a decrease in
L
d
. Further,
reducing the ammonia opacity shows a similar trend in
T
b
,
while a saturation in
L
d
is expected at a power-law factor of 5.
Changing the ammonia pro
fi
le and ammonia opacity has a
similar effect in
T
b
and
L
d
at 1.2 GHz, but, overall, the
variations in the MWR observations at 1.2 GHz can be
explained by these two factors and do not require the inclusion
of alkali metals. The 1.2 GHz observations correspond to
∼
20 bar
(
Figure
1
)
, much above the cloud base of alkali metals,
and at relatively lower pressure levels. Therefore, the
contribution of free electrons to opacity is expected to be less,
due to the lower temperatures, and the opacity contribution of
the ammonia vapor dominates at 1.2 GHz. However, a
comparison of MWR observations at both frequencies clearly
implies that variations in the ammonia vapor opacity cannot
solely explain the anomalous observations at the 0.6 GHz
channel.
Figures
4
(
c
)
and
(
d
)
examine the overall effect of alkali
metals and ammonia vapor on
T
b
and
L
d
at 0.6 GHz and
1.2 GHz. We vary the alkali metal metallicities in a range from
0to
−
7
(
the solar abundance of Na and K, according to
Asplund et al.
2009
)
for each condition of the NH
3
pro
fi
le
scaling and NH
3
opacity scaling. The volume mixing ratios of
Na and K corresponding to the abundance in the
solar photosphere
(
Asplund et al.
2009
)
are 3.46
×
10
−
6
(
[
Na
/
H
]
=
−
5.76
)
and 2.14
×
10
−
7
(
[
K
/
H
]
=
−
6.97
)
, respec-
tively. Therefore, we simulate a wide range of ammonia
6
The Astrophysical Journal Letters,
952:L27
(
13pp
)
, 2023 August 1
Bhattacharya et al.
opacity conditions for a given alkali metal abundance
(
colored
dots
)
. Both the NH
3
pro
fi
le and opacity scaling cause changes
in
T
b
and
L
d
, which are shown by the annotations in the
fi
gure.
The variation in
T
b
and
L
d
is similar to the pattern in Figure
4
(
a
)
. The NH
3
pro
fi
le scaling causes a decrease in L
d
, while the
scaling of the NH
3
vapor opacity causes
L
d
to increase at
0.6 GHz. For each case of metallicity, we then perform a
scaling in ammonia vapor and ammonia opacity, as described
previously in this section. This provides us with a matrix of
T
b
and
L
d
to take into account all possible sources of opacity, i.e.,
collision-induced absorption, ammonia, water vapor, and free
electrons from alkali metals. The free electron opacity is
calculated from the Hartree
–
Appleton equation explained in the
previous section.
When we compare the new model result with the MWR
observations
(
Figure
4
(
b
))
, we observe that the model matches
with the observations at 0.6 GHz for free electrons corresp-
onding to alkali metal metallicities in the range of
−
2to
−
5
(
chocolate-colored patches
)
, i.e., 10
−
2
to 10
−
5
times the solar
abundance. There is an agreement between the model and
Figure 4.
Comparisons are drawn between the Juno MWR observations and the results of the radiative transfer model for
T
b
and
L
d
at 0.6 GHz and 1.2 GHz, keeping
the water abundance constant at
∼
fi
ve times solar abundance.
(
a
)
and
(
b
)
Jupiter
’
s atmosphere in the absence of alkali metals with only variations in the NH
3
vapor
pro
fi
le and the NH
3
opacity.
(
c
)
and
(
d
)
Jupiter
’
s atmosphere in the presence of alkali metals with variations in the NH
3
vapor pro
fi
le and the NH
3
opacity. The NH
3
pro
fi
le of Jupiter
’
s atmosphere is varied using a scale from 0 to 1.5, to take into account the contribution of the nonuniform distribution of NH
3
vapor observed by
MWR
(
Li et al.
2017
)
. The NH
3
opacity at temperatures above 750 K undergoes power-law scaling as a function of atmospheric temperature
(
Equation
(
7
))
. In the
absence of alkali metals, the changes in the NH
3
vapor pro
fi
le and the scaling in the NH
3
vapor opacity deviate signi
fi
cantly from the Juno MWR observations at
0.6 GHz. However, in the presence of alkali metals of low metallicity, i.e., in the range of
−
2to
−
5, there is an agreement between the model results and MWR
observations. Observations at 1.2 GHz can be explained by variations in the NH
3
vapor pro
fi
le and the NH
3
opacity independent of the opacity contributions from
alkali metals.
7
The Astrophysical Journal Letters,
952:L27
(
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)
, 2023 August 1
Bhattacharya et al.
observations at 1.2 GHz for the same range of metallicities. The
addition of free electrons from alkali metals dominates the
effect of gravity
(
Figure
5
)
, and we expect the limb darkening
to decrease from the equator to the poles, assuming a uniform
mixing ratio of water and ammonia vapor. It serves as a
baseline to understand the sole effect of free electrons on the
latitudinal variation of microwave radiation from Jupiter
’
s deep
atmosphere.
4. Discussions
We infer the metallicity of the alkali metals in Jupiter to be
much lower than the solar value. A possible indication of the
low metallicity of the alkali metals in a hot Jupiter exoplanet
was
fi
rst proposed by Demory et al.
(
2011
)
, as one plausible
explanation for the high albedo of Kepler-7b. They derived an
alkali metal abundance 10
–
100 times lower than the solar
value. Since then, the abundances of alkali metals have been
derived for several other giant exoplanets, with abundances
ranging from
∼
100 times below solar to
∼
100 times above
solar, although the uncertainties are large. Recent observations
of two hot Jupiters or Saturns with clear or mostly clear
atmospheres have been made. The alkali metal abundance for
one such hot Jupiter
(
HAT-P-1b
)
was found to be subsolar
(
Chen et al.
2022
)
, while it was found to be solar to greatly
supersolar for the other
(
WASP-96b; Nikolov et al.
2022
)
.
Considering the relatively small sample size of hot Jupiters
with clear atmospheres, it is premature to make a meaningful
comparison between their alkali metal metallicities and the
metallicity in Jupiter presented in this paper. On the other hand,
it is instructive to compare the abundance of alkali metals in
Jupiter from this work with the abundances of the other heavy
elements. While the opacity contribution from alkali metals
suggests that Na and K are strongly depleted relative to solar at
Figure 5.
Latitudinal variation of the brightness temperature and limb darkening of Jupiter
’
s atmosphere at 0.6 GHz and 1.2 GHz at
[
M
/
H
]
=
−
3.
8
The Astrophysical Journal Letters,
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)
, 2023 August 1
Bhattacharya et al.
the level probed by MWR at 0.6 GHz, all other heavy elements
are enriched by a factor of approximately 3 to 5, while nitrogen
is highly variable but enriched, and the water abundance
remains uncertain
(
Mahaffy et al.
2000
; Li et al.
2017
,
2020
;
Atreya et al.
2019
)
. The comparison to other heavy metal
measurements from Galileo Probe
corresponds to much lower
pressures, i.e.,
<
22 bars. The estimation of the alkali metal
metallicity from MWR implies lower metallicity at much
higher pressures. The results
(
Figure
4
(
b
))
provide an important
constraint on the alkali metal abundance at pressures sensitive
to the 0.6 GHz channel.
[
M
/
H
]
=
−
1 for alkali metals provides
too much opacity, while too little abundance or the absence of
alkali metals does not provide suf
fi
cient opacity to match the
MWR observations at 0.6 GHz.
The low abundance of alkali metals indicated by the MWR
observations could be attributed to any of the following
scenarios.
(
i
)
Initially enriched alkali metals, consistent with the
other heavy elements in the atmosphere, are depleted by
chemical reactions with other constituents deep in the
atmosphere, resulting in a low abundance of Na and K at the
∼
1 kbar level, suf
fi
cient to provide the free electrons to explain
the MWR data at 0.6 GHz. Fegley & Lodders
(
1994
)
predict,
for example, the formation of gas-phase species of Na and K in
the atmosphere, i.e., NaCl, NaOH, and KOH. Should there be
chemical mechanisms that could selectively deplete K in the
atmosphere, leaving Na to be the most signi
fi
cant contributor to
the free electrons in the deep atmosphere, the metallicity of Na
would be expected to be in the range of 0 to
−
2, i.e., a solar to
highly subsolar abundance
(
Appendix
B
)
.
(
ii
)
Unconventional
planet formation processes, whereby Jupiter did not accrete a
solar complement of alkali metals, or the alkali metals are not
well mixed at greater depths. If the depletion of alkali metals at
∼
1 kbar inferred in this paper is representative of their bulk
abundance, it could be indicative of the depletion of all rock-
forming elements, with signi
fi
cant implications for the
formation and evolution of Jupiter. Our conclusion of depletion
is based on the data of the 0.6 GHz channel, whose weighting
function peaks at the 1 kbar level with the inclusion of alkali
metals. Thus, we are con
fi
dent about the result only at this
level. Alkali metals could well be more abundant deeper in the
atmosphere, and they could have been depleted by some as yet
unknown mechanism before reaching the 1 kbar level, though
the degree of depletion would have to be huge. Barshay &
Lewis
(
1978
)
considered one such possibility, where silicates
were found to be a way of sequestrating gas-phase alkali
metals. However, a later study by Fegley & Lodders
(
1994
)
found it to be an ineffective mechanism. Further modeling and
laboratory studies are needed to cover the full parameter space
of the combined thermochemistry of alkali metal and rock
cloud-forming species corresponding to the very-high-temper-
ature and high-pressure conditions of the deep atmosphere of
Jupiter, together with any dynamical effects, before drawing
any
fi
rm conclusions about the depletion of alkali metals in
bulk Jupiter below the level to which the MWR data of this
paper are sensitive.
The new constraints on the abundances of alkalis are linked
to their low ionization potential, and the fact that the electrons
that they provide directly affect the opacities at 0.6 and
1.2 GHz
(
see Equation
(
4
))
. But, when present, they are strong
absorbers at visible wavelengths
(
e.g., Burrows et al.
2000
)
and
therefore directly affect the planetary radiative
fl
ux. The low
abundances that we derive imply that a radiative zone may be
present in Jupiter
(
Guillot et al.
1994
,
2004
)
. Interestingly, this
could at the same time explain the relatively low abundance of
CO observed in Jupiter
’
s atmosphere compared to expectations
for a fully convective deep atmosphere
(
Cavalié et al.
2023
)
.
Acknowledgments
This work was supported by the NASA Juno Program, under
NASA Contract NNM06AA75C from the Marshall Space
Flight Center supporting the Juno Mission Science team,
through subcontract 699056KC and Q99063JAR to the
University of Michigan from the Southwest Research Institute.
Part of this research was carried out at the Jet Propulsion
Laboratory, California Institute of Technology, under a
contract with the National Aeronautics and Space Administra-
tion
(
80NM0018D0004
)
.
Software and Third-party Data Repository Citations: the
software for the radiative transfer package will be available at
the Zenodo archive
(
Bhattacharya et al.
2023a
)
and the MWR
data used in this work, and the associated
fi
les for data
visualization, are available at the archive
(
Bhattacharya et al.
2023b
)
. They can be made available upon request.
Software:
High-performance Atmospheric Radiation Pack-
age
(
HARP; Li et al.
2018b
; Bhattacharya et al.
2023a
)
.
Appendix A
Electron Density and Conductivity
The electron density of Jupiter
’
s atmosphere is governed by
two fundamental processes:
(
i
)
the condensation of alkali metal
condensates, i.e., Na
2
S and KCl; and
(
ii
)
the ionization of alkali
metals in thermal equilibrium. Figure
2
shows the pressure
levels corresponding to the cloud base of Na
2
S and KCl, based
on their saturation vapor pressures. Cloud condensation
reduces the amount of alkali metals available in the gas phase
that act as a source of free electrons and restricts the abundance
of Na and K, corresponding to their respective saturation vapor
pressures. In the cloud region, the electron density is controlled
by the saturation vapor pressure of alkali metals, whereas
below the cloud base, electron densities are governed by the
metallicity of alkali metals. Therefore, it is evident that
condensation controls the electron density and, accordingly,
conductivity at low pressure levels. Condensation-limited
ionization is observed at low pressure
(
below 1 kbar
)
,
irrespective of the alkali metal abundance as the electron
density lines converge
(
Figure
A1
(
a
))
. Figures
A1
(
a
)
and
(
b
)
show the presence of a kink in the electron density and their
respective conductivity at the cloud base, corresponding to
different alkali metal abundances. However, condensation does
not play a signi
fi
cant role in governing the electron densities at
the
∼
1 kbar pressure level corresponding to the global maxima
in the weighting function at 0.6 GHz
(
Figure
1
)
.
The electron density of the deep atmosphere is much lower
than in the case of alkali metals at solar abundance. It is the true
representation of the electron density of the deep atmosphere.
At greater pressures, hydrogen behaves as a semiconductor and
becomes the major contributor to the electron density
(
Liu et al.
2008
)
. The electrical conductivity of the atmosphere is
calculated using Drude
’
s equation. It provides an estimate of
the conductivity due to the free electrons provided by alkali
metal ionization.
9
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)
, 2023 August 1
Bhattacharya et al.
Appendix B
Selective Depletion of Alkali Metals
Even though Na
2
S has a deeper condensation level
compared to KCl, the cloud condensation is governed by
atmospheric temperature and does not re
fl
ect the chemical
reactivity of alkali metals. K is more electropositive than Na
and, therefore, is expected to be more reactive as compared to
Na. Therefore, it is possible that there could be a chemical
mechanism that could selectively deplete K into other
compounds, leaving Na as the only source of free electrons
in Jupiter. Under such conditions, we
fi
nd that the Na
Figure A1.
(
a
)
Electron density of Jupiter
’
s deep atmosphere at the solar abundance and
[
M
/
H
]
=
−
3 and
−
4.
(
b
)
Electrical conductivity of Jupiter
’
s deep atmosphere
at the solar abundance and
[
M
/
H
]
=
−
3 and
−
4.
10
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)
, 2023 August 1
Bhattacharya et al.
metallicity should be in the range of 0 to
–
3 to match the MWR
observations. The increase in alkali metal metallicities can be
attributed to two factors:
(
i
)
the low ionization energy of K; and
(
ii
)
Na
2
S condenses much below KCl
(
Figure
2
)
. Therefore, a
larger amount of Na is required to produce enough free
electrons to match the MWR brightness temperatures and limb
darkening.
The elimination of K from the atmosphere highlights the role
of the elemental abundance of Na that is required to match the
MWR observations. The results of the forward model in Figure
B1
indicate the possible solutions of Na metallicity under
different conditions of ammonia vapor concentration pro
fi
les
and microwave opacities. It is observed that the range of Na
metallicity is expected to be from 0 to
−
3, i.e., from solar
abundance to highly subsolar abundance. Thus, the metallicity
of Na required is expected to be higher than those considering
both Na and K to be sources of free electrons.
Appendix C
Jovian Adiabats and Comparison of MWR with High-
temperature Adiabat
Figure
2
shows that the brightness temperatures at 600 MHz
from two adiabats differ by approximately 15 K. The relative
weighting function for the adiabats is that of the ideal Jupiter
’
s
atmosphere without the inclusion of opacity due to free
electrons from alkali metals. It shows a peak at
∼
100 bar. From
the difference in physical temperature of the atmospheres of the
two adiabats, it is seen that the difference reaches
∼
10
–
15 K at
the 100 bar level
(
Figure
C1
)
. The weighting function at 600
MHz also extends below 100 bar, which could explain the
difference in brightness temperatures. An interesting observa-
tion is that the difference in adiabat temperatures increases with
the increase in atmospheric pressure. This increase can be
attributed to the temperature-dependent speci
fi
c heat of the
atmospheric constituents.
The interior models of Jupiter generally use a high
temperature in the range of 170
–
180 K at the outer boundary
(
1 bar pressure level; Gupta et al.
2022
; Miguel et al.
2022
)
.
These temperatures are about 10
–
15 K higher than the
measurements from the Galileo Probe
(
166.1 K; Seiff et al.
1998
)
and Voyager radio occultation re-analysis
(
168.8 K;
Gupta et al.
2022
)
. Simulations of brightness temperatures and
limb darkening at 0.6 and 1.2 GHz are carried out for all cases
of alkali metal metallicities, ammonia concentrations, and
opacity variations, assuming
T
1bar
=
175 K. It can be clearly
seen in Figure
C2
that the high temperature at 1 bar does not
match the entire range of MWR observations for both the
frequencies. Some alternate possibilities could be the presence
of a nonadiabatic gradient or a radiative layer in Jupiter
’
s deep
atmosphere that could possibly account for a higher
temperature at the 1 bar level. However, the mismatch with
MWR at 1.2 GHz poses a serious question about the
assumption. The current measurements of temperature at the
1 bar level are from limited radio occultation experiments.
There is a need for radio science experiments from the equator
to the poles, in order to estimate the true variability in
temperatures at 1 bar.
Figure B1.
Limb-darkening and brightness temperature comparison of MWR observations and forward model results at 600 MHz and 1.2 GHz for metallicities
ranging from 0 to
−
7 at different ammonia vapor concentration pro
fi
les and opacities. This showcases the sole effect of free electrons due to the ionization of Na,
without considering any contribution from K.
11
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)
, 2023 August 1
Bhattacharya et al.
ORCID iDs
Ananyo Bhattacharya
https:
/
/
orcid.org
/
0000-0003-
1898-8080
Sushil K. Atreya
https:
/
/
orcid.org
/
0000-0002-1972-1815
Steven M. Levin
https:
/
/
orcid.org
/
0000-0003-2242-5459
Tristan Guillot
https:
/
/
orcid.org
/
0000-0002-7188-8428
Pranika Gupta
https:
/
/
orcid.org
/
0000-0002-9566-0372
Jonathan I. Lunine
https:
/
/
orcid.org
/
0000-0003-2279-4131
Glenn S. Orton
https:
/
/
orcid.org
/
0000-0001-7871-2823
J. Hunter Waite
https:
/
/
orcid.org
/
0000-0002-1978-1025
Michael H. Wong
https:
/
/
orcid.org
/
0000-0003-2804-5086
Figure C1.
Pressure vs. temperature difference in the temperatures of Jovian adiabats constructed using
T
1bar
=
168.8 K and
T
1bar
=
166.1 K.
Figure C2.
Limb-darkening and brightness temperature comparison of MWR observations and forward model results at 600 MHz and 1.2 GHz for metallicities
ranging from 0 to
−
7 at different ammonia vapor concentration pro
fi
les and opacities considering
T
1bar
=
175 K.
12
The Astrophysical Journal Letters,
952:L27
(
13pp
)
, 2023 August 1
Bhattacharya et al.
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